Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 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 | C22×D172 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#423 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #423 | D43 |
| hypocenter | C43 | #3036 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #423 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063353 | C2 | semidirect |
| 2. #14583449 | C2 | semidirect |
| 3. C2×C4×D172 | C2 | semidirect |
| 4. #14583115 | C2 | semidirect |
| 5. #14583105 | C2 | semidirect |
| 6. #14583095 | C2 | semidirect |
| 7. #14582901 | C2 | semidirect |
| 8. C43×#423 | C2 | semidirect |
| 15. #13063325 | C22 | semidirect |
| 16. #13063322 | C22 | semidirect |
| 17. #13063313 | C22 | semidirect |
| 28. #13063250 | C22 | semidirect |
| 29. #13063247 | C22 | semidirect |
| 32. C4⋊C8×C43 | C22 | semidirect |
| 33. C4⋊C8×C43 | C22 | semidirect |
| 46. C2×D172 | D4 | semidirect |
| 118. C4×C43 | AGL(1,ℤ/8) | semidirect |
| 136. #423 | D43 | semidirect |
| 138. C43 | #3036 | semidirect |
| 160. C4⋊C8 | C2×D43 | semidirect |
| 161. C4⋊C8 | C2×D43 | semidirect |
| 250. C4 | #13063353 | semidirect |