Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
384 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 384 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 | 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 | C2×#501 |
| 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 |
| 79. C8×D43 | Q8 | semidirect |
| 102. C8×C43 | C2×Q8 | semidirect |
| 103. C43⋊C8 | C2×Q8 | semidirect |
| 124. D43 | #501 | direct (N × H) |
| 132. #501 | D43 | direct (N × H) |
| 136. C43 | C2×#501 | semidirect |
| 228. C8 | Q8×D43 | semidirect |