هوهنشتاوفن
By 1271/74, Konrad married his second wife, Sophie (b. ca. 1259 - d. 24 August 1318), daughter of Dietrich the Wise, Margrave of Landsberg (second son of Henry III, Margrave of Meissen) and – according to some sources – widow of the last legitimate male member of the House of Hohenstaufen, Conradin, King of Sicily and Jerusalem. They had no children.