Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1976 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1976 conjugacy classes of subgroups — too many to draw. Only its 565 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D43 |
| commutator | C4×C43 | C25 |
| Frattini | C4 | C24×D43 |
| Fitting | C22×D8×C43 | C2 |
| socle | C23×C43 | C2×D4 |
| hypercenter | C22×D8 | D43 |
| hypocenter | C43 | C23×D8 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D4×D43 | C2 | semidirect |
| 2. C22×D344 | C2 | semidirect |
| 3. C22×#10621882 | C2 | semidirect |
| 4. C2×D8×D43 | C2 | direct (N × H) |
| 5. C22×C8×D43 | C2 | semidirect |
| 6. C22×D8×C43 | C2 | semidirect |
| 8. C22×D172 | C22 | semidirect |
| 11. C2×D4×D43 | C22 | semidirect |
| 13. C2×D344 | C22 | semidirect |
| 14. C2×#10621882 | C22 | semidirect |
| 15. D8×D43 | C22 | direct (N × H) |
| 16. C22×C43⋊C8 | C22 | semidirect |
| 17. C2×C8×D43 | C22 | semidirect |
| 18. C22×D4×C43 | C22 | semidirect |
| 19. C2×D8×C43 | C22 | semidirect |
| 20. C22×C8×C43 | C22 | semidirect |
| 27. C2×D4×C43 | C23 | semidirect |
| 32. D4×D43 | C23 | semidirect |
| 34. C2×D172 | C23 | semidirect |
| 37. D8×C43 | C23 | semidirect |
| 38. C2×C8×C43 | C23 | semidirect |
| 39. #10621882 | C23 | semidirect |
| 40. C2×C43⋊C8 | C23 | semidirect |
| 41. D344 | C23 | semidirect |
| 42. C8×D43 | C23 | semidirect |
| 50. C22×D43 | D8 | direct (N × H) |
| 53. D4×C43 | C24 | semidirect |
| 59. D172 | C24 | semidirect |
| 62. C8×C43 | C24 | semidirect |
| 63. C43⋊C8 | C24 | semidirect |
| 66. C22×C43 | C2×D8 | semidirect |
| 71. C2×D43 | C2×D8 | direct (N × H) |
| 78. C2×C43 | C22×D8 | semidirect |
| 81. D43 | C22×D8 | direct (N × H) |
| 86. C22×D8 | D43 | direct (N × H) |
| 88. C43 | C23×D8 | semidirect |
| 94. C22×D4 | C2×D43 | semidirect |
| 99. C2×D8 | C2×D43 | direct (N × H) |
| 102. C22×C8 | C2×D43 | semidirect |
| 114. C2×D4 | C22×D43 | semidirect |
| 121. D8 | C22×D43 | direct (N × H) |
| 124. C2×C8 | C22×D43 | semidirect |
| 138. D4 | C23×D43 | semidirect |
| 145. C8 | C23×D43 | semidirect |
| 153. C22 | D8×D43 | direct (N × H) |
| 161. C2 | C2×D8×D43 | direct (N × H) |