<PAGE>   1
                                                                    EXHIBIT 21.1

                SUBSIDIARIES OF THERMADYNE HOLDINGS CORPORATION

<TABLE>
<CAPTION>
                                                         JURISDICTION
                                                              OF
NAME                                                     ORGANIZATION
----                                                     ------------
<S>                                                      <C>
Arcair Stoody Europe S.A. ...........................    Belgium
C&G Systems Holding, Inc. ...........................    Delaware
C&G Systems, Inc. ...................................    Illinois
Canadian Cylinder Company ...........................    Canada
Comet Property Holdings, Inc. .......................    Philippines
Comweld Group Pty. Ltd. .............................    Australia
Comweld Philippines Inc. ............................    Philippines
Coyne Natural Gas Systems, Inc. .....................    Missouri
Duxtech Pty. Ltd. ...................................    Australia
Genset SpA ..........................................    Italy
Greymo S.A. .........................................    Spain
Marison Cylinder Company ............................    Delaware
MECO Holding Company ................................    Delaware
Modern Engineering Company, Inc. ....................    Missouri
Philippine Welding Equipment Inc. ...................    Philippines
PT Catu Tehnik Arya Unggul ..........................    Indonesia
PT Comweld Indonesia ................................    Indonesia
Quetack Pty. Ltd. ...................................    Australia
Quetala Pty. Ltd. ...................................    Australia
Quetala Unit Trust ..................................    Australia
Stoody Company ......................................    Delaware
TAG Realty, Inc. ....................................    Texas
THC Italia Srl ......................................    Italy
Thermadyne Asia/Pacific Pty. Ltd. ...................    Singapore
Thermadyne Asia SDN BHD .............................    Malaysia
Thermadyne Australia Pty. Ltd. ......................    Australia
Thermadyne Cylinder Company .........................    California
Thermadyne de Brasil LTDA ...........................    Brazil
Thermadyne de Mexico S.A. de C.V. ...................    Mexico
Thermadyne Foreign Sales Corporation ................    Barbados
Thermadyne Industries, Inc. .........................    Delaware
Thermadyne Industries Ltd. ..........................    United Kingdom
Thermadyne International Corp. ......................    Delaware
Thermadyne Italia Srl ...............................    Italy
Thermadyne Japan, K.K. ..............................    Japan
Thermadyne Korea, Ltd. ..............................    Korea
Thermadyne Receivables, Inc. ........................    Delaware
Thermadyne Welding Products Canada, Ltd. ............    Canada
Thermal Arc, Inc. ...................................    Delaware
Thermadyne Mfg. LLC .................................    Delaware
Thermadyne Capital Corp. ............................    Delaware
Victor Equipment Company ............................    Delaware
Victor Coyne International, Inc. ....................    Delaware
Woodland Cryogenics Company .........................    Delaware
Tweco Products, Inc. ................................    Delaware
Wichita Warehouse Corp. .............................    Kansas
Thermal Dynamics Corp. ..............................    Delaware
Ocim Srl ............................................    Italy
Thermal Acc Philippines Inc. ........................    Philippines
Thermadyne Hong Kong Limited ........................    Hong Kong
</TABLE>