Finite Group DatabasebetaFinite Group DatabasebetaOrder 3904.
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×D61 |
| commutator, socle, cosocle | C22×C61 | C24 |
| Frattini | C22 | C23×D61 |
| Fitting | C4×D4×C61 | C2 |
| hypercenter | C4×D4 | D61 |
| hypocenter | C61 | #525 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11758222 | C2 | semidirect |
| 2. C22×C4×D61 | C2 | semidirect |
| 3. #14519762 | C2 | semidirect |
| 4. #14519759 | C2 | semidirect |
| 5. #14519755 | C2 | semidirect |
| 6. #14519754 | C2 | semidirect |
| 7. #14519750 | C2 | semidirect |
| 8. #14519749 | C2 | semidirect |
| 9. #14519747 | C2 | semidirect |
| 10. #14519745 | C2 | semidirect |
| 11. C4×D244 | C2 | semidirect |
| 12. C4×C22⋊D61 | C2 | semidirect |
| 13. C4×C22⋊D61 | C2 | semidirect |
| 14. #14519734 | C2 | semidirect |
| 15. C4×D4×C61 | C2 | semidirect |
| 19. C22×C4×C61 | C22 | semidirect |
| 23. C2×C22⋊D61 | C22 | semidirect |
| 33. C2×C4×D61 | C22 | semidirect |
| 34. C2×Dic122 | C22 | semidirect |
| 35. C4⋊C4×C61 | C22 | semidirect |
| 37. C22⋊C4×C61 | C22 | semidirect |
| 38. C42×C61 | C22 | semidirect |
| 40. C22⋊Dic61 | C22 | semidirect |
| 45. #11758198 | C22 | semidirect |
| 46. #11758198 | C22 | semidirect |
| 47. C4⋊Dic61 | C22 | semidirect |
| 48. #11758196 | C22 | semidirect |
| 49. #11758196 | C22 | semidirect |
| 50. #11758196 | C22 | semidirect |
| 51. #11758196 | C22 | semidirect |
| 52. C4×Dic61 | C22 | semidirect |
| 85. C4×D61 | D4 | semidirect |
| 92. C22×C61 | #41 | semidirect |
| 103. C2×D61 | #41 | semidirect |
| 123. C61 | #525 | semidirect |
| 137. C4×D4 | D61 | semidirect |
| 157. C22×C4 | C2×D61 | semidirect |
| 163. C4⋊C4 | C2×D61 | semidirect |
| 173. C22⋊C4 | C2×D61 | semidirect |
| 175. C42 | C2×D61 | semidirect |
| 225. C22 | #11758222 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758222 | 2 |
| C22×C4×D61 | 2 |
| #14519762 | 2 |
| #14519759 | 2 |
| #14519755 | 2 |
| #14519754 | 2 |
| #14519750 | 2 |
| #14519749 | 2 |
| #14519747 | 2 |
| #14519745 | 2 |
| C4×D244 | 2 |
| C4×C22⋊D61 | 2 |
| #14519734 | 2 |
| C4×D4×C61 | 2 |
| #525 | 61 |