Finite Group DatabasebetaFinite Group DatabasebetaOrder 25664.
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D401 |
| commutator, socle, cosocle | C22×C401 | C24 |
| Frattini | C22 | C23×D401 |
| Fitting | C4×D4×C401 | C2 |
| hypercenter | C4×D4 | D401 |
| hypocenter | C401 | #525 |
| LCS | G ▷ C22×C401 ▷ C401 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#20264366 | C2 | semidirect |
| 2. C22×C4×D401 | C2 | semidirect |
| 3. #27165722 | C2 | semidirect |
| 4. #27165719 | C2 | semidirect |
| 5. #27165715 | C2 | semidirect |
| 6. #27165714 | C2 | semidirect |
| 7. #27165710 | C2 | semidirect |
| 8. #27165709 | C2 | semidirect |
| 9. #27165707 | C2 | semidirect |
| 10. #27165705 | C2 | semidirect |
| 11. C4×D1604 | C2 | semidirect |
| 12. C4×C22⋊D401 | C2 | semidirect |
| 13. C4×C22⋊D401 | C2 | semidirect |
| 14. #27165694 | C2 | semidirect |
| 15. C4×D4×C401 | C2 | semidirect |
| 18. C2×Dic802 | C22 | semidirect |
| 24. C2×C22⋊D401 | C22 | semidirect |
| 31. C2×C4×D401 | C22 | semidirect |
| 32. C4⋊Dic401 | C22 | semidirect |
| 33. #20264345 | C22 | semidirect |
| 34. #20264345 | C22 | semidirect |
| 35. #20264345 | C22 | semidirect |
| 36. #20264345 | C22 | semidirect |
| 38. C22⋊Dic401 | C22 | semidirect |
| 43. #20264343 | C22 | semidirect |
| 44. #20264343 | C22 | semidirect |
| 45. C4×Dic401 | C22 | semidirect |
| 48. C22×C4×C401 | C22 | semidirect |
| 49. C4⋊C4×C401 | C22 | semidirect |
| 51. C22⋊C4×C401 | C22 | semidirect |
| 52. C42×C401 | C22 | semidirect |
| 76. C4×D401 | D4 | semidirect |
| 92. C22×C401 | #41 | semidirect |
| 103. C2×D401 | #41 | semidirect |
| 122. C401 | #525 | semidirect |
| 137. C4×D4 | D401 | semidirect |
| 157. C22×C4 | C2×D401 | semidirect |
| 163. C4⋊C4 | C2×D401 | semidirect |
| 173. C22⋊C4 | C2×D401 | semidirect |
| 175. C42 | C2×D401 | semidirect |
| 225. C22 | #20264366 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20264366 | 2 |
| C22×C4×D401 | 2 |
| #27165722 | 2 |
| #27165719 | 2 |
| #27165715 | 2 |
| #27165714 | 2 |
| #27165710 | 2 |
| #27165709 | 2 |
| #27165707 | 2 |
| #27165705 | 2 |
| C4×D1604 | 2 |
| C4×C22⋊D401 | 2 |
| #27165694 | 2 |
| C4×D4×C401 | 2 |
| #525 | 401 |