Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
2528 conjugacy classes of subgroups; only the 1197 normal subgroups are shown.
This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 1197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D61 |
| commutator | C2×C61 | C24×C4 |
| Frattini | C22 | C24×D61 |
| Fitting | C23×D4×C61 | C2 |
| socle | C24×C61 | C23 |
| hypercenter | C23×D4 | D61 |
| hypocenter | C61 | C22×C4×D4 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×Dic61 | C2 | semidirect |
| 2. C2×D4×Dic61 | C2 | direct (N × H) |
| 3. C22×C4⋊Dic61 | C2 | semidirect |
| 4. C22×C22⋊Dic61 | C2 | semidirect |
| 5. C22×C4×Dic61 | C2 | semidirect |
| 11. C23×Dic61 | C22 | semidirect |
| 12. D4×Dic61 | C22 | direct (N × H) |
| 13. C2×C4⋊Dic61 | C22 | semidirect |
| 14. C2×C22⋊Dic61 | C22 | semidirect |
| 15. C2×C4×Dic61 | C22 | semidirect |
| 17. C22×D4×C61 | C4 | semidirect |
| 22. C24×C61 | C2×C4 | semidirect |
| 25. C2×D4×C61 | C2×C4 | semidirect |
| 27. C22×C4×C61 | C2×C4 | semidirect |
| 32. C22×Dic61 | D4 | direct (N × H) |
| 36. C22×Dic61 | C23 | semidirect |
| 37. C22⋊Dic61 | C23 | semidirect |
| 38. C4⋊Dic61 | C23 | semidirect |
| 39. C4×Dic61 | C23 | semidirect |
| 44. C23×C61 | C22×C4 | semidirect |
| 49. D4×C61 | C22×C4 | semidirect |
| 50. C2×C4×C61 | C22×C4 | semidirect |
| 55. C2×Dic61 | C2×D4 | direct (N × H) |
| 62. C22×C61 | C4×D4 | semidirect |
| 64. C22×C61 | C23×C4 | semidirect |
| 68. C4×C61 | C23×C4 | semidirect |
| 71. Dic61 | C22×D4 | direct (N × H) |
| 74. C2×C61 | C2×C4×D4 | semidirect |
| 84. C61 | C22×C4×D4 | semidirect |
| 86. C22×D4 | Dic61 | direct (N × H) |
| 100. C24 | C2×Dic61 | semidirect |
| 103. C2×D4 | C2×Dic61 | direct (N × H) |
| 113. C22×C4 | C2×Dic61 | semidirect |
| 124. C23 | C22×Dic61 | semidirect |
| 127. D4 | C22×Dic61 | direct (N × H) |
| 135. C2×C4 | C22×Dic61 | semidirect |
| 140. C22 | D4×Dic61 | direct (N × H) |
| 142. C22 | C23×Dic61 | semidirect |
| 149. C4 | C23×Dic61 | semidirect |
| 151. C2 | C2×D4×Dic61 | direct (N × H) |