Finite Group DatabasebetaFinite Group DatabasebetaOrder 31936.
192 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 95 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×D499 |
| commutator, socle, cosocle | C22×C499 | C24 |
| Fitting | C4×Q8×C499 | C2 |
| prime radical | C22×D499 | C23 |
| hypercenter | C4×Q8 | D499 |
| hypocenter | C499 | #541 |
| LCS | G ▷ C22×C499 ▷ C499 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #30630349 | C2 | semidirect |
| 4. #30630343 | C2 | semidirect |
| 5. #30630342 | C2 | semidirect |
| 6. #30630341 | C2 | semidirect |
| 9. C4×Dic998 | C2 | semidirect |
| 11. C4×Q8×C499 | C2 | semidirect |
| 67. C499 | #541 | semidirect |
| 78. C4×Q8 | D499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30630349 | 2 |
| #30630346 | 2 |
| #30630345 | 2 |
| #30630343 | 2 |
| #30630342 | 2 |
| #30630341 | 2 |
| #30630331 | 2 |
| #30630327 | 2 |
| C4×Dic998 | 2 |
| #30630308 | 2 |
| C4×Q8×C499 | 2 |
| #541 | 499 |