Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 175 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 | C4×C43 | C23×C4 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#442 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #442 | D43 |
| hypocenter | C43 | #2943 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #442 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#10621900 | C2 | semidirect |
| 3. #14583011 | C2 | semidirect |
| 4. #14583007 | C2 | semidirect |
| 5. #14583005 | C2 | semidirect |
| 6. #14582999 | C2 | semidirect |
| 7. #14582996 | C2 | semidirect |
| 8. #14582934 | C2 | semidirect |
| 9. #14582892 | C2 | semidirect |
| 10. #97×D43 | C2 | semidirect |
| 11. C43×#442 | C2 | semidirect |
| 13. #13063344 | C4 | semidirect |
| 46. #10621900 | C2×C4 | semidirect |
| 50. D8×C43 | C2×C4 | semidirect |
| 57. #10621883 | C2×C4 | semidirect |
| 69. Dic172 | C2×C4 | semidirect |
| 71. C8×D43 | C2×C4 | semidirect |
| 118. #442 | D43 | semidirect |
| 126. C43 | #2943 | semidirect |
| 167. D8 | C4×D43 | semidirect |