Finite Group DatabasebetaFinite Group DatabasebetaOrder 31424.
252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 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 | #123×C491 | C2 |
| hypercenter | #123 | D491 |
| hypocenter | C491 | #560 |
| LCS | G ▷ C22×C491 ▷ C491 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #30628333 | C2 | semidirect |
| 2. #30628332 | C2 | semidirect |
| 3. #30628319 | C2 | semidirect |
| 4. #30628312 | C2 | semidirect |
| 5. #30628311 | C2 | semidirect |
| 6. #30628310 | C2 | semidirect |
| 7. #30628307 | C2 | semidirect |
| 8. #30628305 | C2 | semidirect |
| 9. #123×C491 | C2 | semidirect |
| 13. C2×D1964 | C22 | semidirect |
| 16. C2×C22⋊D491 | C22 | semidirect |
| 17. C2×C4×D491 | C22 | semidirect |
| 18. C4⋊Dic491 | C22 | semidirect |
| 19. Dic491⋊C4 | C22 | semidirect |
| 24. (C2×D491)⋊C4 | C22 | semidirect |
| 25. C4×Dic491 | C22 | semidirect |
| 27. C22×C4×C491 | C22 | semidirect |
| 28. C4⋊C4×C491 | C22 | semidirect |
| 30. C22⋊C4×C491 | C22 | semidirect |
| 74. C491 | #560 | semidirect |
| 79. #123 | D491 | semidirect |
| 94. C22×C4 | C2×D491 | semidirect |
| 97. C4⋊C4 | C2×D491 | semidirect |
| 104. C22⋊C4 | C2×D491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30628333 | 2 |
| #30628332 | 2 |
| #30628319 | 2 |
| #30628312 | 2 |
| #30628311 | 2 |
| #30628310 | 2 |
| #30628307 | 2 |
| #30628305 | 2 |
| #123×C491 | 2 |
| #560 | 491 |