Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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 | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#474 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #474 | D43 |
| hypocenter | C43 | Q8×D8 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #474 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D4×Dic86 | C2 | semidirect |
| 2. #14583564 | C2 | semidirect |
| 3. #14583303 | C2 | semidirect |
| 4. #14583302 | C2 | semidirect |
| 5. #14583180 | C2 | semidirect |
| 6. #14583178 | C2 | semidirect |
| 7. #14583177 | C2 | semidirect |
| 8. #14583023 | C2 | semidirect |
| 11. C43×#474 | C2 | semidirect |
| 61. #10621882 | Q8 | semidirect |
| 78. D4×C43 | C2×Q8 | semidirect |
| 91. D172 | C2×Q8 | semidirect |
| 97. Dic86 | D8 | semidirect |
| 100. C43⋊C8 | C2×Q8 | semidirect |
| 131. #474 | D43 | semidirect |
| 135. C43 | Q8×D8 | semidirect |
| 208. D4 | Q8×D43 | semidirect |