Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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×#501 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #501 | D43 |
| hypocenter | C43 | #3162 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #501 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #14583309 | C2 | semidirect |
| 4. #14583308 | C2 | semidirect |
| 5. #14583307 | C2 | semidirect |
| 6. #14583306 | C2 | semidirect |
| 7. #14583305 | C2 | semidirect |
| 11. C43×#501 | C2 | semidirect |
| 78. C8×D43 | Q8 | semidirect |
| 129. #501 | D43 | semidirect |
| 133. C43 | #3162 | semidirect |