Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 153 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 | #3006 |
| 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. C22×#10621898 | C2 | semidirect |
| 2. C2×#13063353 | C2 | semidirect |
| 3. C2×#13063299 | C2 | semidirect |
| 4. #14583046 | C2 | semidirect |
| 5. #14583040 | C2 | semidirect |
| 6. #14583035 | C2 | semidirect |
| 7. #14582901 | C2 | semidirect |
| 8. C43×#407 | C2 | semidirect |
| 13. C2×#10621898 | C22 | semidirect |
| 14. C22×Dic86 | C22 | semidirect |
| 15. C22×D172 | C22 | semidirect |
| 16. C22×D172 | C22 | semidirect |
| 21. C2×#10621873 | C22 | semidirect |
| 22. C2×D344 | C22 | semidirect |
| 26. #13063299 | C22 | semidirect |
| 27. C2×C4⋊Dic43 | C22 | semidirect |
| 29. #13063250 | C22 | semidirect |
| 30. #13063247 | C22 | semidirect |
| 32. C2×M16×C43 | C22 | semidirect |
| 33. C22⋊C8×C43 | C22 | semidirect |
| 34. C22⋊C8×C43 | C22 | semidirect |
| 58. #10621898 | D4 | semidirect |
| 115. D172 | C2×D4 | semidirect |
| 120. Dic86 | C2×D4 | semidirect |
| 131. C22×C43 | AGL(1,ℤ/8) | semidirect |
| 163. #407 | D43 | semidirect |
| 164. C43 | #3006 | semidirect |
| 180. C2×M16 | C2×D43 | semidirect |
| 189. C22⋊C8 | C2×D43 | semidirect |
| 190. C22⋊C8 | C2×D43 | semidirect |
| 295. C22 | #13063353 | semidirect |