Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
488 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D47 |
| commutator | C2×C4×C47 | C24 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#459 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #459 | D47 |
| hypocenter | C47 | #3109 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #459 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15689671 | C2 | semidirect |
| 2. C4×D4×D47 | C2 | semidirect |
| 3. #15689440 | C2 | semidirect |
| 4. #15689414 | C2 | semidirect |
| 5. #15689413 | C2 | semidirect |
| 6. #15689315 | C2 | semidirect |
| 7. #15689255 | C2 | semidirect |
| 8. #15689235 | C2 | semidirect |
| 9. #15689232 | C2 | semidirect |
| 10. #15689179 | C2 | semidirect |
| 11. C47×#459 | C2 | semidirect |
| 16. #13094024 | C22 | semidirect |
| 23. D4×Dic47 | C22 | semidirect |
| 30. #13093956 | C22 | semidirect |
| 31. #13093955 | C22 | semidirect |
| 32. C4⋊(C47⋊C8) | C22 | semidirect |
| 35. #13093945 | C22 | semidirect |
| 37. #13093934 | C22 | semidirect |
| 39. #127×C47 | C22 | semidirect |
| 41. C4⋊C8×C47 | C22 | semidirect |
| 42. #102×C47 | C22 | semidirect |
| 96. D4×C47 | #41 | semidirect |
| 112. D188 | #41 | semidirect |
| 161. #459 | D47 | semidirect |
| 166. C47 | #3109 | semidirect |
| 173. #127 | C2×D47 | semidirect |
| 191. C4⋊C8 | C2×D47 | semidirect |
| 195. #102 | C2×D47 | semidirect |
| 256. D4 | #10625352 | semidirect |