Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 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 | C2×#41×C431 | C2 |
| hypercenter | C2×#41 | D431 |
| hypocenter | C431 | #546 |
| LCS | G ▷ C22×C431 ▷ C431 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D4×D431 | C2 | semidirect |
| 2. #28352178 | C2 | semidirect |
| 3. #28352172 | C2 | semidirect |
| 4. #28352165 | C2 | semidirect |
| 5. #28352163 | C2 | semidirect |
| 6. #28352161 | C2 | semidirect |
| 7. #28352157 | C2 | semidirect |
| 8. D4×Dic431 | C2 | semidirect |
| 9. C4×C22⋊D431 | C2 | semidirect |
| 10. C2×(C2×D431)⋊C4 | C2 | semidirect |
| 11. C2×#41×C431 | C2 | semidirect |
| 16. C2×C22⋊D431 | C22 | semidirect |
| 18. C22×Dic431 | C22 | semidirect |
| 20. C4⋊Dic431 | C22 | semidirect |
| 21. Dic431⋊C4 | C22 | semidirect |
| 22. Dic431⋊C4 | C22 | semidirect |
| 23. C22⋊Dic431 | C22 | semidirect |
| 24. C22⋊Dic431 | C22 | semidirect |
| 27. (C2×D431)⋊C4 | C22 | semidirect |
| 28. (C2×D431)⋊C4 | C22 | semidirect |
| 29. (C2×D431)⋊C4 | C22 | semidirect |
| 30. C4×Dic431 | C22 | semidirect |
| 32. C2×Q8×C431 | C22 | semidirect |
| 34. C2×D4×C431 | C22 | semidirect |
| 35. C22×C4×C431 | C22 | semidirect |
| 36. C22×C4×C431 | C22 | semidirect |
| 56. D4×C431 | D4 | semidirect |
| 75. C2×D431 | #41 | semidirect |
| 90. C431 | #546 | semidirect |
| 92. C2×#41 | D431 | semidirect |
| 105. C2×Q8 | C2×D431 | semidirect |
| 112. C2×D4 | C2×D431 | semidirect |
| 115. C22×C4 | C2×D431 | semidirect |
| 116. C22×C4 | C2×D431 | semidirect |
| 141. D4 | C22⋊D431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D431 | 2 |
| #28352178 | 2 |
| #28352172 | 2 |
| #28352165 | 2 |
| #28352163 | 2 |
| #28352161 | 2 |
| #28352157 | 2 |
| D4×Dic431 | 2 |
| C4×C22⋊D431 | 2 |
| C2×(C2×D431)⋊C4 | 2 |
| C2×#41×C431 | 2 |
| #546 | 431 |