Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
2528 conjugacy classes of subgroups; only the 981 normal subgroups are shown.
This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 981 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C2×D43 |
| commutator | C2×C43 | C24×C4 |
| Frattini | C22 | C24×D43 |
| Fitting | C22×C42×C43 | C2 |
| socle | C24×C43 | C23 |
| hypercenter | C22×C42 | D43 |
| hypocenter | C43 | C22×C4×D4 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C23×C4 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×C4×D43 | C2 | semidirect |
| 3. C2×C4×D172 | C2 | direct (N × H) |
| 4. C22×C4⋊Dic43 | C2 | semidirect |
| 5. C22×(C2×D43)⋊C4 | C2 | semidirect |
| 6. C22×C42×C43 | C2 | semidirect |
| 8. C22×D172 | C4 | direct (N × H) |
| 12. C22×C4×D43 | C22 | semidirect |
| 13. C4×D172 | C22 | direct (N × H) |
| 14. C2×C4⋊Dic43 | C22 | semidirect |
| 15. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 19. C2×C42×C43 | C22 | semidirect |
| 23. C23×D43 | C2×C4 | semidirect |
| 26. C22×C4×C43 | C2×C4 | semidirect |
| 27. C22×C4×C43 | D4 | semidirect |
| 33. C2×D172 | C2×C4 | direct (N × H) |
| 36. C2×C4×D43 | C23 | semidirect |
| 37. C42×C43 | C23 | semidirect |
| 38. (C2×D43)⋊C4 | C23 | semidirect |
| 39. C4⋊Dic43 | C23 | semidirect |
| 47. C22×D43 | C22×C4 | semidirect |
| 50. C2×C4×C43 | C22×C4 | semidirect |
| 51. C2×C4×C43 | C2×D4 | semidirect |
| 57. D172 | C22×C4 | direct (N × H) |
| 59. C22×C43 | C4×D4 | semidirect |
| 67. C2×D43 | C23×C4 | semidirect |
| 69. C4×C43 | C23×C4 | semidirect |
| 70. C4×C43 | C22×D4 | semidirect |
| 73. C2×C43 | C2×C4×D4 | semidirect |
| 83. C22×C42 | D43 | semidirect |
| 84. C43 | C22×C4×D4 | semidirect |
| 97. C2×C42 | C2×D43 | semidirect |
| 110. C22×C4 | C4×D43 | semidirect |
| 111. C22×C4 | D172 | direct (N × H) |
| 117. C42 | C22×D43 | semidirect |
| 132. C2×C4 | C2×C4×D43 | semidirect |
| 133. C2×C4 | C2×D172 | direct (N × H) |
| 141. C22 | C4×D172 | direct (N × H) |
| 148. C4 | C22×C4×D43 | semidirect |
| 149. C4 | C22×D172 | direct (N × H) |
| 151. C2 | C2×C4×D172 | direct (N × H) |