Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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×D43 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#459 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #459 | D43 |
| hypocenter | C43 | #3294 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #459 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583554 | C2 | semidirect |
| 2. #14583534 | C2 | semidirect |
| 3. #14583245 | C2 | semidirect |
| 4. #14583211 | C2 | semidirect |
| 5. #14583180 | C2 | semidirect |
| 6. #14583132 | C2 | semidirect |
| 7. #14583031 | C2 | semidirect |
| 8. C4×#10621882 | C2 | semidirect |
| 9. #14582964 | C2 | semidirect |
| 10. #102×D43 | C2 | semidirect |
| 11. C43×#459 | C2 | semidirect |
| 16. C2×C8×D43 | C22 | semidirect |
| 17. #13063325 | C22 | semidirect |
| 22. #13063296 | C22 | semidirect |
| 26. C4⋊C4×D43 | C22 | semidirect |
| 27. #13063259 | C22 | semidirect |
| 28. #13063258 | C22 | semidirect |
| 30. #13063246 | C22 | semidirect |
| 31. #13063246 | C22 | semidirect |
| 32. #13063246 | C22 | semidirect |
| 34. (C2×D43)⋊C8 | C22 | semidirect |
| 35. C4×C43⋊C8 | C22 | semidirect |
| 36. C2×D8×C43 | C22 | semidirect |
| 38. C4×D4×C43 | C22 | semidirect |
| 39. C4⋊C8×C43 | C22 | semidirect |
| 40. #102×C43 | C22 | semidirect |
| 103. D172 | D8 | semidirect |
| 104. D172 | #41 | semidirect |
| 149. #459 | D43 | semidirect |
| 154. C43 | #3294 | semidirect |
| 159. C2×D8 | C2×D43 | semidirect |
| 171. C4×D4 | C2×D43 | semidirect |
| 175. C4⋊C8 | C2×D43 | semidirect |
| 181. #102 | C2×D43 | semidirect |