Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
6560 conjugacy classes of subgroups; only the 3221 normal subgroups are shown.
This group has 6560 conjugacy classes of subgroups — too many to draw. Only its 3221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D43 |
| commutator | C2×C43 | C26 |
| Frattini | C2 | C25×D43 |
| Fitting | C23×D4×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C23×D4 | D43 |
| hypocenter | C43 | C22×H(5,𝔽2) |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063370 | C2 | direct (N × H) |
| 2. C22×#10621898 | C2 | semidirect |
| 3. C22×#10621900 | C2 | semidirect |
| 4. C23×C22⋊D43 | C2 | semidirect |
| 5. C22×D4×D43 | C2 | semidirect |
| 6. C23×D4×C43 | C2 | semidirect |
| 7. C24×D43 | C22 | semidirect |
| 8. #13063370 | C22 | direct (N × H) |
| 9. C2×#10621898 | C22 | semidirect |
| 10. C2×#10621900 | C22 | semidirect |
| 11. C22×Dic86 | C22 | semidirect |
| 12. C22×D172 | C22 | semidirect |
| 13. C22×C22⋊D43 | C22 | semidirect |
| 14. C22×C22⋊D43 | C22 | semidirect |
| 15. C22×C22⋊D43 | C22 | semidirect |
| 16. C2×D4×D43 | C22 | semidirect |
| 17. C23×Dic43 | C22 | semidirect |
| 18. C22×C4×D43 | C22 | semidirect |
| 19. C25×C43 | C22 | semidirect |
| 20. C22×D4×C43 | C22 | semidirect |
| 21. C22×D4×C43 | C22 | semidirect |
| 22. C23×C4×C43 | C22 | semidirect |
| 26. C24×C43 | C23 | semidirect |
| 29. C23×D43 | C23 | semidirect |
| 30. C2×D4×C43 | C23 | semidirect |
| 31. C2×D4×C43 | C23 | semidirect |
| 33. C22×C4×C43 | C23 | semidirect |
| 34. C2×C22⋊D43 | C23 | semidirect |
| 35. C2×C22⋊D43 | C23 | semidirect |
| 36. C2×C22⋊D43 | C23 | semidirect |
| 38. C22×Dic43 | C23 | semidirect |
| 39. #10621900 | C23 | semidirect |
| 40. D4×D43 | C23 | semidirect |
| 41. #10621898 | C23 | semidirect |
| 42. C2×D172 | C23 | semidirect |
| 43. C2×C4×D43 | C23 | semidirect |
| 44. C2×Dic86 | C23 | semidirect |
| 51. C23×C43 | C24 | semidirect |
| 55. C22×D43 | C24 | semidirect |
| 56. D4×C43 | C24 | semidirect |
| 58. C2×C4×C43 | C24 | semidirect |
| 59. C22⋊D43 | C24 | semidirect |
| 60. C22⋊D43 | C24 | semidirect |
| 62. C2×Dic43 | C24 | semidirect |
| 63. D172 | C24 | semidirect |
| 64. C4×D43 | C24 | semidirect |
| 65. Dic86 | C24 | semidirect |
| 69. C22×C43 | H(5,𝔽2) | semidirect |
| 81. C2×C43 | C2×H(5,𝔽2) | semidirect |
| 89. C23×D4 | D43 | semidirect |
| 90. C43 | C22×H(5,𝔽2) | semidirect |
| 92. C25 | C2×D43 | semidirect |
| 102. C22×D4 | C2×D43 | semidirect |
| 103. C22×D4 | C2×D43 | semidirect |
| 106. C23×C4 | C2×D43 | semidirect |
| 113. C24 | C22×D43 | semidirect |
| 122. C2×D4 | C22×D43 | semidirect |
| 123. C2×D4 | C22×D43 | semidirect |
| 128. C22×C4 | C22×D43 | semidirect |
| 139. C23 | C23×D43 | semidirect |
| 144. D4 | C23×D43 | semidirect |
| 149. C2×C4 | C23×D43 | semidirect |
| 156. C22 | #13063370 | direct (N × H) |
| 165. C2 | C2×#13063370 | direct (N × H) |