Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 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×#441 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #441 | D43 |
| hypocenter | C43 | #2952 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #441 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14583381 | C2 | semidirect |
| 3. #14583012 | C2 | semidirect |
| 4. #14583010 | C2 | semidirect |
| 5. #14583006 | C2 | semidirect |
| 6. C4×#10621884 | C2 | semidirect |
| 7. #14582984 | C2 | semidirect |
| 8. #106×D43 | C2 | semidirect |
| 9. #14582899 | C2 | semidirect |
| 10. #14582856 | C2 | semidirect |
| 11. C43×#441 | C2 | semidirect |
| 13. #13063348 | C4 | semidirect |
| 42. #10621902 | C2×C4 | semidirect |
| 50. Q16×C43 | C2×C4 | semidirect |
| 57. #10621884 | C2×C4 | semidirect |
| 69. D344 | C2×C4 | semidirect |
| 71. C8×D43 | C2×C4 | semidirect |
| 120. #441 | D43 | semidirect |
| 126. C43 | #2952 | semidirect |
| 165. Q16 | C4×D43 | semidirect |