The database currently contains $275{,}339{,}797$ subgroups from among $544{,}831$ different groups. You can browse further statistics.

Browse

By ambient order: 1-64  65-127  128  129-255  256  257-383  384  385-511  513-1000  1001-1500  1501-2000  2001- 

By subgroup order: 1-16  17-32  33-64  65-128  129-256  257-512  513-1000  1001- 

By property: normal  non-normal  abelian  cyclic  maximal  central  perfect  characteristic 

A random subgroup

Search

Subgroup label e.g. 8.4 Subgroup order e.g. 4, or a range like 3..5
Ambient label e.g. 128.207 Ambient order e.g. 128
Quotient label e.g. 16.5 Subgroup index e.g. 16
Cyclic Abelian
Normal Solvable
Characteristic Perfect
Maximal Central
Direct product Semidirect product
Cyclic quotient Abelian quotient
Solvable quotient Maximal quotient
Non-trivial proper
Hall subgroup Sylow subgroup
Display:

Find

Group or subgroup label
e.g. 8.3 or 12.4.2.b1.a1