Finite Group DatabasebetaFinite Group DatabasebetaOrder 31936.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 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 | #125×C499 | C2 |
| prime radical | #30630326 | C2 |
| hypercenter | #125 | D499 |
| hypocenter | C499 | #529 |
| LCS | G ▷ C22×C499 ▷ C499 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #30630346 | C2 | semidirect |
| 2. #30630339 | C2 | semidirect |
| 3. #30630336 | C2 | semidirect |
| 4. #30630331 | C2 | semidirect |
| 6. #30630316 | C2 | semidirect |
| 7. #30630313 | C2 | semidirect |
| 8. #30630313 | C2 | semidirect |
| 9. #30630309 | C2 | semidirect |
| 10. C42×D499 | C2 | semidirect |
| 11. #125×C499 | C2 | semidirect |
| 74. C499 | #529 | semidirect |
| 77. #125 | D499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30630346 | 2 |
| #30630339 | 2 |
| #30630336 | 2 |
| #30630331 | 2 |
| #30630326 | 2 |
| #30630316 | 2 |
| #30630313 | 2 |
| #30630309 | 2 |
| C42×D499 | 2 |
| #125×C499 | 2 |
| #529 | 499 |