Finite Group DatabasebetaFinite Group DatabasebetaOrder 31424.
330 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 111 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×D491 |
| commutator, socle, cosocle | C22×C491 | C24 |
| Fitting | #120×C491 | C2 |
| hypercenter | #120 | D491 |
| hypocenter | C491 | #525 |
| LCS | G ▷ C22×C491 ▷ C491 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#21463327 | C2 | semidirect |
| 2. C23×Dic491 | C2 | semidirect |
| 3. #30628321 | C2 | semidirect |
| 4. #30628318 | C2 | semidirect |
| 5. #30628314 | C2 | semidirect |
| 6. #30628309 | C2 | semidirect |
| 7. #30628306 | C2 | semidirect |
| 8. D4×Dic491 | C2 | semidirect |
| 9. (C22⋊D491)⋊C4 | C2 | semidirect |
| 10. #30628293 | C2 | semidirect |
| 11. #120×C491 | C2 | semidirect |
| 13. C2×Dic982 | C22 | semidirect |
| 16. C2×C22⋊D491 | C22 | semidirect |
| 22. C22×Dic491 | C22 | semidirect |
| 23. C2×C4×D491 | C22 | semidirect |
| 24. C4⋊Dic491 | C22 | semidirect |
| 25. Dic491⋊C4 | C22 | semidirect |
| 26. Dic491⋊C4 | C22 | semidirect |
| 29. C22⋊Dic491 | C22 | semidirect |
| 30. (C2×D491)⋊C4 | C22 | semidirect |
| 31. C4×Dic491 | C22 | semidirect |
| 46. C2×Dic491 | D4 | semidirect |
| 69. C22×C491 | #41 | semidirect |
| 86. C491 | #525 | semidirect |
| 95. #120 | D491 | semidirect |
| 158. C22 | #21463327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21463327 | 2 |
| C23×Dic491 | 2 |
| #30628321 | 2 |
| #30628318 | 2 |
| #30628314 | 2 |
| #30628309 | 2 |
| #30628306 | 2 |
| D4×Dic491 | 2 |
| (C22⋊D491)⋊C4 | 2 |
| #30628293 | 2 |
| #120×C491 | 2 |
| #525 | 491 |