Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
528 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 145 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×#486 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #486 | D43 |
| hypocenter | C43 | C2×#486 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #486 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4⋊Q8×D43 | C2 | semidirect |
| 3. #14583247 | C2 | semidirect |
| 4. #14583246 | C2 | semidirect |
| 5. #14583245 | C2 | semidirect |
| 6. #14583244 | C2 | semidirect |
| 7. #102×D43 | C2 | semidirect |
| 8. C4×C8×D43 | C2 | semidirect |
| 9. C43×#486 | C2 | semidirect |
| 15. #13063325 | C22 | semidirect |
| 17. #13063324 | C22 | semidirect |
| 26. #13063247 | C22 | semidirect |
| 27. #13063246 | C22 | semidirect |
| 28. #13063245 | C22 | semidirect |
| 29. C4×C43⋊C8 | C22 | semidirect |
| 30. C8×Dic43 | C22 | semidirect |
| 31. C4⋊Q8×C43 | C22 | semidirect |
| 33. #102×C43 | C22 | semidirect |
| 34. C4×C8×C43 | C22 | semidirect |
| 126. D43 | #486 | direct (N × H) |
| 133. #486 | D43 | direct (N × H) |
| 136. C43 | C2×#486 | semidirect |
| 146. C4⋊Q8 | C2×D43 | semidirect |
| 158. #102 | C2×D43 | semidirect |
| 161. C4×C8 | C2×D43 | semidirect |