Finite Group DatabasebetaFinite Group DatabasebetaOrder 28096.
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×D439 |
| commutator, socle, cosocle | C22×C439 | C24 |
| Fitting | #120×C439 | C2 |
| hypercenter | #120 | D439 |
| hypocenter | C439 | #538 |
| LCS | G ▷ C22×C439 ▷ C439 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28380736 | C2 | semidirect |
| 2. #28380736 | C2 | semidirect |
| 3. #28380730 | C2 | semidirect |
| 4. #28380729 | C2 | semidirect |
| 5. #28380725 | C2 | semidirect |
| 6. #28380724 | C2 | semidirect |
| 7. #28380720 | C2 | semidirect |
| 8. #28380715 | C2 | semidirect |
| 9. #28380715 | C2 | semidirect |
| 10. #28380714 | C2 | semidirect |
| 11. #28380712 | C2 | semidirect |
| 12. D4×Dic439 | C2 | semidirect |
| 13. (C22⋊D439)⋊C4 | C2 | semidirect |
| 14. C2×C22⋊Dic439 | C2 | semidirect |
| 15. #120×C439 | C2 | semidirect |
| 16. C2×Dic878 | C22 | semidirect |
| 20. C2×C22⋊D439 | C22 | semidirect |
| 23. C22×Dic439 | C22 | semidirect |
| 24. C2×C4×D439 | C22 | semidirect |
| 25. C4⋊Dic439 | C22 | semidirect |
| 26. C4⋊Dic439 | C22 | semidirect |
| 27. Dic439⋊C4 | C22 | semidirect |
| 28. Dic439⋊C4 | C22 | semidirect |
| 29. Dic439⋊C4 | C22 | semidirect |
| 30. Dic439⋊C4 | C22 | semidirect |
| 38. C22⋊Dic439 | C22 | semidirect |
| 39. C22⋊Dic439 | C22 | semidirect |
| 40. (C2×D439)⋊C4 | C22 | semidirect |
| 41. (C2×D439)⋊C4 | C22 | semidirect |
| 42. C4×Dic439 | C22 | semidirect |
| 43. C4×Dic439 | C22 | semidirect |
| 116. C439 | #538 | semidirect |
| 129. #120 | D439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28380736 | 2 |
| #28380730 | 2 |
| #28380729 | 2 |
| #28380725 | 2 |
| #28380724 | 2 |
| #28380720 | 2 |
| #28380715 | 2 |
| #28380714 | 2 |
| #28380712 | 2 |
| D4×Dic439 | 2 |
| (C22⋊D439)⋊C4 | 2 |
| C2×C22⋊Dic439 | 2 |
| #120×C439 | 2 |
| #538 | 439 |