Finite Group DatabasebetaFinite Group DatabasebetaOrder 25664.
250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 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×D401 |
| commutator, socle, cosocle | C22×C401 | C24 |
| Fitting | #121×C401 | C2 |
| hypercenter | #121 | D401 |
| hypocenter | C401 | #538 |
| LCS | G ▷ C22×C401 ▷ C401 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27165732 | C2 | semidirect |
| 2. #27165730 | C2 | semidirect |
| 3. #27165724 | C2 | semidirect |
| 4. #27165723 | C2 | semidirect |
| 5. #27165720 | C2 | semidirect |
| 6. #27165718 | C2 | semidirect |
| 7. #27165715 | C2 | semidirect |
| 8. #27165709 | C2 | semidirect |
| 9. #27165708 | C2 | semidirect |
| 10. #27165705 | C2 | semidirect |
| 11. #27165705 | C2 | semidirect |
| 12. C4×C22⋊D401 | C2 | semidirect |
| 13. #27165697 | C2 | semidirect |
| 14. C22⋊C4×D401 | C2 | semidirect |
| 15. #121×C401 | C2 | semidirect |
| 17. C2×Dic802 | C22 | semidirect |
| 22. C22×Dic401 | C22 | semidirect |
| 25. C4⋊Dic401 | C22 | semidirect |
| 26. #20264345 | C22 | semidirect |
| 27. #20264345 | C22 | semidirect |
| 28. #20264345 | C22 | semidirect |
| 29. #20264345 | C22 | semidirect |
| 33. C22⋊Dic401 | C22 | semidirect |
| 34. C22⋊Dic401 | C22 | semidirect |
| 35. C22⋊Dic401 | C22 | semidirect |
| 42. C4×Dic401 | C22 | semidirect |
| 43. C4×Dic401 | C22 | semidirect |
| 46. C2×D4×C401 | C22 | semidirect |
| 47. C22×C4×C401 | C22 | semidirect |
| 48. C4⋊C4×C401 | C22 | semidirect |
| 50. C22⋊C4×C401 | C22 | semidirect |
| 116. C401 | #538 | semidirect |
| 127. #121 | D401 | semidirect |
| 141. C2×D4 | C2×D401 | semidirect |
| 145. C22×C4 | C2×D401 | semidirect |
| 151. C4⋊C4 | C2×D401 | semidirect |
| 165. C22⋊C4 | C2×D401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27165732 | 2 |
| #27165730 | 2 |
| #27165724 | 2 |
| #27165723 | 2 |
| #27165720 | 2 |
| #27165718 | 2 |
| #27165715 | 2 |
| #27165709 | 2 |
| #27165708 | 2 |
| #27165705 | 2 |
| C4×C22⋊D401 | 2 |
| #27165697 | 2 |
| C22⋊C4×D401 | 2 |
| #121×C401 | 2 |
| #538 | 401 |