Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#461 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #461 | D47 |
| hypocenter | C47 | #3036 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #461 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13094051 | C2 | semidirect |
| 2. #15689674 | C2 | semidirect |
| 3. C4×D4×D47 | C2 | semidirect |
| 4. #15689341 | C2 | semidirect |
| 5. #15689340 | C2 | semidirect |
| 6. #15689325 | C2 | semidirect |
| 7. #15689319 | C2 | semidirect |
| 8. #15689318 | C2 | semidirect |
| 9. #15689145 | C2 | semidirect |
| 10. #15689123 | C2 | semidirect |
| 11. C47×#461 | C2 | semidirect |
| 20. #13094021 | C22 | semidirect |
| 21. #13094013 | C22 | semidirect |
| 34. C4⋊(C47⋊C8) | C22 | semidirect |
| 35. Dic47⋊C8 | C22 | semidirect |
| 36. #13093948 | C22 | semidirect |
| 37. #13093946 | C22 | semidirect |
| 38. #13093944 | C22 | semidirect |
| 40. C4⋊Q8×C47 | C22 | semidirect |
| 42. C4⋊C8×C47 | C22 | semidirect |
| 43. #103×C47 | C22 | semidirect |
| 53. D4×D47 | D4 | semidirect |
| 146. C4×C47 | AGL(1,ℤ/8) | semidirect |
| 167. #461 | D47 | semidirect |
| 172. C47 | #3036 | semidirect |
| 182. C4⋊Q8 | C2×D47 | semidirect |
| 200. C4⋊C8 | C2×D47 | semidirect |
| 202. #103 | C2×D47 | semidirect |
| 311. C4 | #13094051 | semidirect |