Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 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×D431 |
| commutator, socle, cosocle | C22×C431 | C24 |
| Fitting | #121×C431 | C2 |
| hypercenter | #121 | D431 |
| hypocenter | C431 | #538 |
| LCS | G ▷ C22×C431 ▷ C431 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28352184 | C2 | semidirect |
| 2. #28352175 | C2 | semidirect |
| 3. #28352173 | C2 | semidirect |
| 4. #28352168 | C2 | semidirect |
| 5. #28352161 | C2 | semidirect |
| 6. #28352157 | C2 | semidirect |
| 7. D4×Dic431 | C2 | semidirect |
| 8. C2×(C2×D431)⋊C4 | C2 | semidirect |
| 9. #121×C431 | C2 | semidirect |
| 11. C2×Dic862 | C22 | semidirect |
| 15. C22×Dic431 | C22 | semidirect |
| 16. C4⋊Dic431 | C22 | semidirect |
| 17. C4⋊Dic431 | C22 | semidirect |
| 18. Dic431⋊C4 | C22 | semidirect |
| 20. C22⋊Dic431 | C22 | semidirect |
| 25. C4×Dic431 | C22 | semidirect |
| 27. C2×D4×C431 | C22 | semidirect |
| 29. C4⋊C4×C431 | C22 | semidirect |
| 30. C22⋊C4×C431 | C22 | semidirect |
| 74. C431 | #538 | semidirect |
| 81. #121 | D431 | semidirect |
| 90. C2×D4 | C2×D431 | semidirect |
| 97. C4⋊C4 | C2×D431 | semidirect |
| 104. C22⋊C4 | C2×D431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28352184 | 2 |
| #28352175 | 2 |
| #28352173 | 2 |
| #28352168 | 2 |
| #28352161 | 2 |
| #28352157 | 2 |
| D4×Dic431 | 2 |
| C2×(C2×D431)⋊C4 | 2 |
| #121×C431 | 2 |
| #538 | 431 |