Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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×#474 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #474 | D47 |
| hypocenter | C47 | #3294 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #474 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15689776 | C2 | semidirect |
| 2. D4×D188 | C2 | semidirect |
| 3. #15689471 | C2 | semidirect |
| 4. #15689438 | C2 | semidirect |
| 5. #15689360 | C2 | semidirect |
| 6. #15689319 | C2 | semidirect |
| 7. #15689258 | C2 | semidirect |
| 8. C4×#10625334 | C2 | semidirect |
| 9. #15689188 | C2 | semidirect |
| 10. #102×D47 | C2 | semidirect |
| 11. C47×#474 | C2 | semidirect |
| 15. C2×D376 | C22 | semidirect |
| 17. C2×C8×D47 | C22 | semidirect |
| 22. #13093999 | C22 | semidirect |
| 26. C4×D188 | C22 | semidirect |
| 27. C4⋊C4×D47 | C22 | semidirect |
| 28. #13093957 | C22 | semidirect |
| 29. #13093946 | C22 | semidirect |
| 31. #13093944 | C22 | semidirect |
| 32. #13093944 | C22 | semidirect |
| 33. #13093944 | C22 | semidirect |
| 34. (C2×D47)⋊C8 | C22 | semidirect |
| 35. C4×C47⋊C8 | C22 | semidirect |
| 36. C4⋊Q8×C47 | C22 | semidirect |
| 38. #107×C47 | C22 | semidirect |
| 39. C4⋊C8×C47 | C22 | semidirect |
| 87. D4×C47 | #41 | semidirect |
| 105. D188 | D8 | semidirect |
| 147. #474 | D47 | semidirect |
| 154. C47 | #3294 | semidirect |
| 161. C4⋊Q8 | C2×D47 | semidirect |
| 174. #107 | C2×D47 | semidirect |
| 175. C4⋊C8 | C2×D47 | semidirect |
| 240. D4 | #10625354 | semidirect |