Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
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×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 | #3109 |
| 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. #14583447 | C2 | semidirect |
| 2. C4×D4×D43 | C2 | semidirect |
| 3. #14583216 | C2 | semidirect |
| 4. #14583190 | C2 | semidirect |
| 5. #14583189 | C2 | semidirect |
| 6. #14583091 | C2 | semidirect |
| 7. #14583031 | C2 | semidirect |
| 8. #14583011 | C2 | semidirect |
| 9. #14583008 | C2 | semidirect |
| 10. #14582955 | C2 | semidirect |
| 11. C43×#459 | C2 | semidirect |
| 16. #13063325 | C22 | semidirect |
| 23. D4×Dic43 | C22 | semidirect |
| 30. #13063257 | C22 | semidirect |
| 31. #13063256 | C22 | semidirect |
| 32. C4⋊(C43⋊C8) | C22 | semidirect |
| 35. #13063246 | C22 | semidirect |
| 37. #13063235 | C22 | semidirect |
| 39. #127×C43 | C22 | semidirect |
| 41. C4⋊C8×C43 | C22 | semidirect |
| 42. #102×C43 | C22 | semidirect |
| 96. D4×C43 | #41 | semidirect |
| 112. D172 | #41 | semidirect |
| 161. #459 | D43 | semidirect |
| 166. C43 | #3109 | semidirect |
| 173. #127 | C2×D43 | semidirect |
| 191. C4⋊C8 | C2×D43 | semidirect |
| 195. #102 | C2×D43 | semidirect |
| 256. D4 | #10621900 | semidirect |