Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
994 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D172 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#407 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #407 | D43 |
| hypocenter | C43 | #3003 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ #407 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D172 | C2 | semidirect |
| 2. C2×#13063353 | C2 | semidirect |
| 3. #14583410 | C2 | semidirect |
| 4. #14583052 | C2 | semidirect |
| 5. #14583035 | C2 | semidirect |
| 6. #14582905 | C2 | semidirect |
| 7. C43×#407 | C2 | semidirect |
| 9. C2×#10621898 | C22 | semidirect |
| 16. C2×#10621873 | C22 | semidirect |
| 17. C2×D344 | C22 | semidirect |
| 19. #13063304 | C22 | semidirect |
| 20. #13063299 | C22 | semidirect |
| 23. #13063284 | C22 | semidirect |
| 24. #13063247 | C22 | semidirect |
| 26. C2×M16×C43 | C22 | semidirect |
| 27. C22⋊C8×C43 | C22 | semidirect |
| 47. C2×D172 | D4 | semidirect |
| 49. C2×D172 | C23 | semidirect |
| 51. C2×Dic86 | C23 | semidirect |
| 53. C2×C8×C43 | C23 | semidirect |
| 57. C4⋊Dic43 | C23 | semidirect |
| 98. C22×C43 | AGL(1,ℤ/8) | semidirect |
| 124. #407 | D43 | semidirect |
| 125. C43 | #3003 | semidirect |
| 137. C2×M16 | C2×D43 | semidirect |
| 145. C22⋊C8 | C2×D43 | semidirect |
| 173. C2×C8 | C22×D43 | semidirect |
| 222. C22 | #13063353 | semidirect |