Finite Group DatabasebetaFinite Group DatabasebetaOrder 31936.
240 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 240 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×D4×C499 | C2 |
| hypercenter | C4×D4 | D499 |
| hypocenter | C499 | #540 |
| LCS | G ▷ C22×C499 ▷ C499 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #30630347 | C2 | semidirect |
| 2. #30630342 | C2 | semidirect |
| 3. #30630334 | C2 | semidirect |
| 4. #30630333 | C2 | semidirect |
| 5. #30630326 | C2 | semidirect |
| 6. #30630325 | C2 | semidirect |
| 7. #30630324 | C2 | semidirect |
| 8. #30630322 | C2 | semidirect |
| 9. C4×D1996 | C2 | semidirect |
| 10. #30630308 | C2 | semidirect |
| 11. C4×D4×C499 | C2 | semidirect |
| 79. C499 | #540 | semidirect |
| 90. C4×D4 | D499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30630347 | 2 |
| #30630342 | 2 |
| #30630334 | 2 |
| #30630333 | 2 |
| #30630326 | 2 |
| #30630325 | 2 |
| #30630324 | 2 |
| #30630322 | 2 |
| C4×D1996 | 2 |
| #30630308 | 2 |
| C4×D4×C499 | 2 |
| #540 | 499 |