Finite Group DatabasebetaFinite Group DatabasebetaOrder 31424.
330 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D491 |
| commutator, socle, cosocle | C22×C491 | C24 |
| Frattini | C22 | C23×D491 |
| Fitting | C23×C4×C491 | C2 |
| hypercenter | C23×C4 | D491 |
| hypocenter | C491 | #525 |
| LCS | G ▷ C22×C491 ▷ C491 | |
| UCS | C1 ◁ C2×C4 ◁ C23×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#21463328 | C2 | semidirect |
| 2. #30628320 | C2 | semidirect |
| 3. #30628316 | C2 | semidirect |
| 4. #30628311 | C2 | semidirect |
| 5. #30628306 | C2 | semidirect |
| 6. C4×C22⋊D491 | C2 | semidirect |
| 7. #30628296 | C2 | semidirect |
| 8. C23×C4×C491 | C2 | semidirect |
| 10. C2×Dic982 | C22 | semidirect |
| 11. C2×D1964 | C22 | semidirect |
| 14. C2×C4×D491 | C22 | semidirect |
| 15. C4⋊Dic491 | C22 | semidirect |
| 16. Dic491⋊C4 | C22 | semidirect |
| 19. (C2×D491)⋊C4 | C22 | semidirect |
| 20. C4×Dic491 | C22 | semidirect |
| 42. C2×C4×C491 | D4 | semidirect |
| 51. C22×C491 | #41 | semidirect |
| 65. C491 | #525 | semidirect |
| 68. C23×C4 | D491 | semidirect |
| 108. C2×C4 | C22⋊D491 | semidirect |
| 119. C22 | #21463328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21463328 | 2 |
| #30628320 | 2 |
| #30628316 | 2 |
| #30628311 | 2 |
| #30628306 | 2 |
| C4×C22⋊D491 | 2 |
| #30628296 | 2 |
| C23×C4×C491 | 2 |
| #525 | 491 |