Finite Group DatabasebetaFinite Group DatabasebetaOrder 1984.
192 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D31 |
| commutator, socle, cosocle | C22×C31 | C24 |
| Fitting | C31×#125 | C2 |
| prime radical | C22×D31 | C23 |
| hypercenter | #125 | D31 |
| hypocenter | C31 | #541 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C31×#125 | C2 | semidirect |
| 8. #11758467 | C2 | semidirect |
| 9. #11758466 | C2 | semidirect |
| 10. #11758466 | C2 | semidirect |
| 11. #11758466 | C2 | semidirect |
| 12. #11758465 | C2 | semidirect |
| 13. #11758464 | C2 | semidirect |
| 15. C4×Dic62 | C2 | semidirect |
| 101. #125 | D31 | semidirect |
| 107. C31 | #541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#125 | 2 |
| #11758475 | 2 |
| #11758473 | 2 |
| #11758469 | 2 |
| #11758467 | 2 |
| #11758466 | 2 |
| #11758465 | 2 |
| #11758464 | 2 |
| #11758453 | 2 |
| C4×Dic62 | 2 |
| #541 | 31 |