Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
4632 conjugacy classes of subgroups; only the 1413 normal subgroups are shown.
This group has 4632 conjugacy classes of subgroups — too many to draw. Only its 1413 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C25 | C2×D43 |
| commutator | C2×C43 | C24×C4 |
| Frattini | C22 | C24×D43 |
| Fitting | C24×C4×C43 | C2 |
| socle | C25×C43 | C22 |
| hypercenter | C24×C4 | D43 |
| hypocenter | C43 | C23×C22⋊C4 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C25 ◁ C24×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C24×Dic43 | C2 | semidirect |
| 3. C22×(C2×D43)⋊C4 | C2 | direct (N × H) |
| 4. C24×C4×C43 | C2 | semidirect |
| 7. C24×D43 | C4 | semidirect |
| 10. C23×Dic43 | C22 | semidirect |
| 11. C2×(C2×D43)⋊C4 | C22 | direct (N × H) |
| 14. C23×C4×C43 | C22 | semidirect |
| 22. C23×D43 | C2×C4 | semidirect |
| 25. C22×C4×C43 | C23 | semidirect |
| 27. C22×Dic43 | C23 | semidirect |
| 28. (C2×D43)⋊C4 | C23 | direct (N × H) |
| 29. C23×C43 | C22⋊C4 | semidirect |
| 37. C22×D43 | C22×C4 | semidirect |
| 40. C2×C4×C43 | C24 | semidirect |
| 42. C2×Dic43 | C24 | semidirect |
| 43. C22×C43 | C2×C22⋊C4 | semidirect |
| 51. C2×D43 | C23×C4 | semidirect |
| 55. C2×C43 | C22×C22⋊C4 | semidirect |
| 62. C24×C4 | D43 | semidirect |
| 64. C43 | C23×C22⋊C4 | semidirect |
| 73. C23×C4 | C2×D43 | semidirect |
| 87. C22×C4 | C22×D43 | semidirect |
| 94. C23 | (C2×D43)⋊C4 | direct (N × H) |
| 102. C2×C4 | C23×D43 | semidirect |
| 107. C22 | C2×(C2×D43)⋊C4 | direct (N × H) |
| 115. C2 | C22×(C2×D43)⋊C4 | direct (N × H) |