Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
4632 conjugacy classes of subgroups; only the 1157 normal subgroups are shown.
This group has 4632 conjugacy classes of subgroups — too many to draw. Only its 1157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D43 |
| commutator | C2×C43 | C24×C4 |
| Frattini | C22 | C24×D43 |
| Fitting | C22×C22⋊C4×C43 | C2 |
| socle | C24×C43 | C23 |
| hypercenter | C22×C22⋊C4 | D43 |
| hypocenter | C43 | C23×C22⋊C4 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C24 ◁ C22×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×C4×D43 | C2 | semidirect |
| 3. C22×C22⋊Dic43 | C2 | semidirect |
| 4. C22×(C2×D43)⋊C4 | C2 | semidirect |
| 5. C2×C22⋊C4×D43 | C2 | direct (N × H) |
| 6. C22×C22⋊C4×C43 | C2 | semidirect |
| 8. C24×D43 | C4 | semidirect |
| 12. C23×Dic43 | C22 | semidirect |
| 14. C22×C4×D43 | C22 | semidirect |
| 15. C2×C22⋊Dic43 | C22 | semidirect |
| 16. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 17. C22⋊C4×D43 | C22 | direct (N × H) |
| 19. C23×C4×C43 | C22 | semidirect |
| 20. C2×C22⋊C4×C43 | C22 | semidirect |
| 22. C24×C43 | C2×C4 | semidirect |
| 29. C23×D43 | C2×C4 | semidirect |
| 30. C23×D43 | C2×C4 | semidirect |
| 36. C22×C4×C43 | C23 | semidirect |
| 38. C22×Dic43 | C23 | semidirect |
| 40. C2×C4×D43 | C23 | semidirect |
| 41. C22⋊C4×C43 | C23 | semidirect |
| 42. C22⋊Dic43 | C23 | semidirect |
| 43. (C2×D43)⋊C4 | C23 | semidirect |
| 47. C23×C43 | C22×C4 | semidirect |
| 55. C22×D43 | C22⋊C4 | direct (N × H) |
| 57. C22×D43 | C22×C4 | semidirect |
| 58. C22×D43 | C22×C4 | semidirect |
| 63. C2×C4×C43 | C24 | semidirect |
| 65. C2×Dic43 | C24 | semidirect |
| 69. C22×C43 | C2×C22⋊C4 | semidirect |
| 71. C22×C43 | C23×C4 | semidirect |
| 77. C2×D43 | C2×C22⋊C4 | direct (N × H) |
| 79. C2×D43 | C23×C4 | semidirect |
| 85. C2×C43 | C22×C22⋊C4 | semidirect |
| 89. D43 | C22×C22⋊C4 | direct (N × H) |
| 95. C22×C22⋊C4 | D43 | direct (N × H) |
| 96. C43 | C23×C22⋊C4 | semidirect |
| 106. C23×C4 | C2×D43 | semidirect |
| 110. C2×C22⋊C4 | C2×D43 | direct (N × H) |
| 122. C24 | C4×D43 | semidirect |
| 130. C22×C4 | C22×D43 | semidirect |
| 133. C22⋊C4 | C22×D43 | direct (N × H) |
| 148. C23 | C2×C4×D43 | semidirect |
| 156. C2×C4 | C23×D43 | semidirect |
| 166. C22 | C22⋊C4×D43 | direct (N × H) |
| 168. C22 | C22×C4×D43 | semidirect |
| 176. C2 | C2×C22⋊C4×D43 | direct (N × H) |