Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
2488 conjugacy classes of subgroups; only the 1157 normal subgroups are shown.
This group has 2488 conjugacy classes of subgroups — too many to draw. Only its 1157 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 | C22×C4⋊C4×C61 | C2 |
| socle | C24×C61 | C23 |
| hypercenter | C22×C4⋊C4 | D61 |
| hypocenter | C61 | C23×C4⋊C4 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C22×C4⋊Dic61 | C2 | semidirect |
| 4. C22×#11758196 | C2 | semidirect |
| 5. C2×C4⋊C4×D61 | C2 | direct (N × H) |
| 6. C22×C4⋊C4×C61 | C2 | semidirect |
| 11. C22×C4×D61 | C4 | semidirect |
| 14. C2×C4⋊Dic61 | C22 | semidirect |
| 15. C2×#11758196 | C22 | semidirect |
| 16. C4⋊C4×D61 | C22 | direct (N × H) |
| 19. C2×C4⋊C4×C61 | C22 | semidirect |
| 26. C22×C4×C61 | C2×C4 | semidirect |
| 30. C22×Dic61 | C2×C4 | semidirect |
| 34. C2×C4×D61 | C2×C4 | semidirect |
| 37. C4⋊C4×C61 | C23 | semidirect |
| 38. C4⋊Dic61 | C23 | semidirect |
| 39. #11758196 | C23 | semidirect |
| 44. C22×D61 | C4⋊C4 | direct (N × H) |
| 50. C2×C4×C61 | C22×C4 | semidirect |
| 54. C2×Dic61 | C22×C4 | semidirect |
| 58. C4×D61 | C22×C4 | semidirect |
| 59. C22×C61 | C2×C4⋊C4 | semidirect |
| 64. C2×D61 | C2×C4⋊C4 | direct (N × H) |
| 69. C4×C61 | C23×C4 | semidirect |
| 71. Dic61 | C23×C4 | semidirect |
| 73. C2×C61 | C22×C4⋊C4 | semidirect |
| 77. D61 | C22×C4⋊C4 | direct (N × H) |
| 83. C22×C4⋊C4 | D61 | direct (N × H) |
| 84. C61 | C23×C4⋊C4 | semidirect |
| 97. C2×C4⋊C4 | C2×D61 | direct (N × H) |
| 112. C22×C4 | C4×D61 | semidirect |
| 117. C4⋊C4 | C22×D61 | direct (N × H) |
| 134. C2×C4 | C2×C4×D61 | semidirect |
| 141. C22 | C4⋊C4×D61 | direct (N × H) |
| 149. C4 | C22×C4×D61 | semidirect |
| 151. C2 | C2×C4⋊C4×D61 | direct (N × H) |