Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
532 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 532 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×D43 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#493 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #493 | D43 |
| hypocenter | C43 | #3205 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #493 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583447 | C2 | semidirect |
| 2. #127×D43 | C2 | semidirect |
| 3. #14583275 | C2 | semidirect |
| 4. #14583246 | C2 | semidirect |
| 5. #14583245 | C2 | semidirect |
| 6. #14583092 | C2 | semidirect |
| 7. #14583031 | C2 | semidirect |
| 8. #14582950 | C2 | semidirect |
| 9. C43×#493 | C2 | semidirect |
| 14. C2×#10621882 | C22 | semidirect |
| 15. #13063325 | C22 | semidirect |
| 24. D4×Dic43 | C22 | semidirect |
| 26. Dic43⋊C8 | C22 | semidirect |
| 27. #13063247 | C22 | semidirect |
| 28. #13063246 | C22 | semidirect |
| 30. C4×C43⋊C8 | C22 | semidirect |
| 31. C2×D8×C43 | C22 | semidirect |
| 33. #127×C43 | C22 | semidirect |
| 34. C4×C8×C43 | C22 | semidirect |
| 100. C4×D43 | D8 | semidirect |
| 136. #493 | D43 | semidirect |
| 142. C43 | #3205 | semidirect |
| 148. C2×D8 | C2×D43 | semidirect |
| 155. #127 | C2×D43 | semidirect |
| 167. C4×C8 | C2×D43 | semidirect |