Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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 | #3038 |
| 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. C2×#13063322 | C2 | semidirect |
| 3. C4×#10621898 | C2 | semidirect |
| 4. #14583100 | C2 | semidirect |
| 5. #14583095 | C2 | semidirect |
| 6. #14582905 | C2 | semidirect |
| 7. C43×#423 | C2 | semidirect |
| 12. C2×#10621873 | C22 | semidirect |
| 13. C2×D344 | C22 | semidirect |
| 17. C4×Dic86 | C22 | semidirect |
| 18. C4×D172 | C22 | semidirect |
| 23. #13063247 | C22 | semidirect |
| 26. C4⋊C8×C43 | C22 | semidirect |
| 32. #10621898 | D4 | semidirect |
| 78. D172 | C2×D4 | semidirect |
| 82. Dic86 | C2×D4 | semidirect |
| 94. C4×C43 | AGL(1,ℤ/8) | semidirect |
| 110. #423 | D43 | semidirect |
| 112. C43 | #3038 | semidirect |
| 130. C4⋊C8 | C2×D43 | semidirect |
| 201. C4 | #13063353 | semidirect |