Question: Where is the 181st Infantry Brigade's headquarters in Rock Island Arsenal located in the U.S?

Context paragraphs:
191st Infantry Brigade (United States): The 191st Infantry Brigade was constituted on 24 June 1921 in the Organized Reserves as Headquarters and Headquarters Company, 191st Infantry Brigade, and assigned to the 96th Division.  It was organized in December 1921 at Portland, Oregon, and redesignated on 23 March 1925 as Headquarters and Headquarters Company, 191st Brigade, then redesignated on 24 August 1936 as Headquarters and Headquarters Company, 191st Infantry Brigade.  It was converted and redesignated on 6 April 1942 as the 96th Reconnaissance Troop (less 3d Platoon), 96th Division (Headquarters and Headquarters Company, 192d Infantry Brigade, concurrently converted and redesignated as the 3d Platoon, 96th Reconnaissance Troop, 96th Division).  The Troop was ordered into active military service on 15 August 1942 and reorganized at Camp Adair, Oregon, as the 96th Cavalry Reconnaissance Troop, an element of the 96th Infantry Division.  It was reorganized and redesignated on 16 August 1943 as the 96th Reconnaissance Troop, Mechanized, and then again reorganized and redesignated on 20 November 1945 as the 96th Mechanized Cavalry Reconnaissance Troop.  Following World War II service with the 96th Infantry Division in the Pacific, it was inactivated on 3 February 1946 at Camp Anza, California.

181st Infantry Brigade (United States): The 181st Infantry Brigade is an infantry brigade of the United States Army based at Fort McCoy, Wisconsin.  As an Active Component/Reserve Component (AC/RC) brigade, the unit serves primarily in a training role for other units of the US armed forces.  The brigade is subordinate to the First United States Army, headquartered at Rock Island Arsenal, Illinois.  It has six prime components.

Company C 1-181 Infantry: Company C, 1st Battalion, 181st Infantry Regiment is a rifle company in the 181st Infantry Regiment.  In the National Guard, companies often have two histories.  They share the history of the regiment to which they are assigned, but also may have a unique company history and lineage.  Therefore, Company C 1-181 IN shares the long history of the 181st Infantry Regiment (United States).  This site concentrates on the unique history of Company C as a militia / National Guard company in Cambridge, MA.  The company traces its history to 1831, when it was first mustered as the Cambridge Light Infantry.  It later served with Union forces in the American Civil War, and as a federalized Massachusetts National Guard regiment with the U.S. Army during the Spanish–American War, Mexican Border Campaign, World War I and World War II.  Most recently Company C has served in Bosnia, at Guantanamo Bay, Cuba, New Orleans following Hurricane Katrina, Iraq and Afghanistan.

Rock Island Arsenal: The Rock Island Arsenal comprises 946 acres , located on Arsenal Island, originally known as Rock Island, on the Mississippi River between the cities of Davenport, Iowa, and Rock Island, Illinois.  It lies within the state of Illinois.  It is home of First Army headquarters.  The island was originally established as a government site in 1816, with the building of Fort Armstrong.  It is now the largest government-owned weapons manufacturing arsenal in the United States.  It has manufactured military equipment and ordnance since the 1880s.  In 1919–1920 one hundred of the Anglo-American or Liberty Mark VIII tanks were manufactured, although too late for World War I.  It is designated as a National Historic Landmark.

Company B 1-181 Infantry: Company B 1st Battalion 181st Infantry Regiment is a rifle company in the 1st Battalion 181st Infantry Regiment.  In the National Guard, companies sometimes have two histories.  They share the history of the regiment to which they are assigned, but also may have a unique company history and lineage.  Therefore, Company B 1-181 IN shares the long history of the 181st Infantry Regiment (United States).  This site concentrates on the unique history of Company B as a militia / National Guard company in Gardner and Greenfield (Detachment 1), MA.  Company B served in the Continental Army during the American Revolution, with Union forces in the American Civil War, and as a federalized Massachusetts National Guard regiment with the U.S. Army during the Spanish–American War, Mexican Border Campaign, World War I and World War II.  Most recently the Company B has served in Guantanamo Bay Cuba, in New Orleans following Hurricane Katrina, and in Afghanistan.  (See below for the separate history of Detachment I in Greenfield.

181st Infantry Regiment (United States): The 181st Infantry Regiment shares the distinction of being the oldest combat regiment in the United States Army.  The regiment traces its history to 13 December 1636, when it was one of four colonial regiments of foot of the British Crown in Massachusetts.  It later served in the Continental Army during the American Revolution, with Union forces in the American Civil War, and as a federalized Massachusetts National Guard regiment with the U.S. Army during War with Spain, Mexican Border Campaign, World War I and World War II.  Most recently the 1st Battalion, 181st Infantry has served in Iraq, in New Orleans following Hurricane Katrina, and in Afghanistan.  The only active element of the regiment is the 1st Battalion, 181st Infantry Regiment, which returned from a year of service in Afghanistan in July 2011.  The 1st Battalion was mobilized in March 2017 for one year of service with the Multinational Force & Observers in the Sinai Peninsula of Egypt.

1181st Forward Support Company: The 1181st Forward Support Company is the forward support company (FSC) for the 1st Battalion, 181st Infantry Regiment.  It provides transportation, maintenance and logistical support to the battalion operations.  In the National Guard, companies sometimes have two histories.  They share the history of the regiment to which they are assigned, but also have a unique company history and lineage.  The 1181st FSC, for example, shares the history of the 181st Infantry Regiment.  The company traces its history to the end of the Revolutionary War when it was first mustered as the 5th company of the 8th Regiment of Massachusetts Militia.  It saw action in the Civil War as part of the 15th Massachusetts Infantry.  It later served during the Spanish–American War, Mexican Border Campaign, World War I and World War II.

Company D 1-181 Infantry: Company D 1st Battalion 181st Infantry Regiment is a heavy weapons company in the 181st Infantry Regiment.  It provides anti-armor and heavy machine gun support to the battalion operations.  In the National Guard, companies sometimes have two histories.  They share the history of the regiment to which they are assigned, but also may have a unique company history and lineage.  Therefore, Company D 1-181 IN shares the long history of the 181st Infantry Regiment (United States).  This site concentrates on the unique history of Company D as a militia / National Guard company in Whitinsville, MA.  The company traces its history to 1864 during the Civil War, when it was first mustered as the Company I, 5th Massachusetts Militia.  It later served as a federalized Massachusetts National Guard regiment with the U.S. Army during the Spanish–American War, Mexican Border Campaign, World War I and World War II.  Most recently the Company D has served in New Orleans following Hurricane Katrina, in Iraq and in Afghanistan.

Headquarters Company 1-181 Infantry: Headquarters Company 1-181 Infantry, Worcester, MA, is the command element for the 1st Battalion 181st Infantry Regiment of the Massachusetts Army National Guard.  In the National Guard, companies sometimes have two histories.  They share the history of the regiment to which they are assaigned, but also may have a unique company history and lineage.  Therefore, HHC 1-181 IN shares the long history of the 181st Infantry Regiment (United States).  While the 181st Infantry Regiment shares the distinction of being the oldest combat regiment in the United States Army, Headquarters Company was formed more recently during the Volunteer Militia craze of the 1890s.  During this time young men began to flock to the independent militia companies forming in each town and city.  These companies were both military units and social clubs.  This site concentrates on the unique history of HHC as a militia / National Guard company in Worcester., MA.  Headquarters Company (Wellington Rifles) has gone on to serve in the following conflicts: Spanish–American War, Mexican Border Campaign, World War I and World War II.  Most recently the company served in Iraq, in New Orleans following Hurricane Katrina, and in Afghanistan.

Company A 1-181 Infantry: Company A 1st Battalion 181st Infantry Regiment is the oldest active company in the 181st Infantry Regiment.  In the National Guard, companies can share the history of the regiment to which they are assigned, but also may have additional unique company history and lineage.  Company A traces its history to 1639, but also shares the history of the 104th Infantry Regiment and the 181st Infantry Regiment (United States).

Supporting paragraphs: 181st Infantry Brigade (United States) Rock Island Arsenal
Answer: Illinois