Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
6560 conjugacy classes of subgroups; only the 3213 normal subgroups are shown.
This group has 6560 conjugacy classes of subgroups — too many to draw. Only its 3213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C24×D43 |
| commutator | C2×C43 | C26 |
| Frattini | C2 | C25×D43 |
| Fitting | C2×H(5,𝔽2)×C43 | C2 |
| socle | C22×C43 | C25 |
| hypercenter | C2×H(5,𝔽2) | D43 |
| hypocenter | C43 | C22×H(5,𝔽2) |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C2×H(5,𝔽2) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063371 | C2 | semidirect |
| 2. C2×#13063370 | C2 | semidirect |
| 3. H(5,𝔽2)×D43 | C2 | direct (N × H) |
| 4. C2×#41×D43 | C2 | semidirect |
| 5. C22×D4×D43 | C2 | semidirect |
| 6. C2×H(5,𝔽2)×C43 | C2 | semidirect |
| 7. C24×D43 | C22 | semidirect |
| 8. #13063371 | C22 | semidirect |
| 9. #13063370 | C22 | semidirect |
| 10. C2×#10621902 | C22 | semidirect |
| 11. C2×#10621898 | C22 | semidirect |
| 12. C2×#10621900 | C22 | semidirect |
| 13. #41×D43 | C22 | semidirect |
| 14. C2×Q8×D43 | C22 | semidirect |
| 15. C22×D172 | C22 | semidirect |
| 16. C22×C22⋊D43 | C22 | semidirect |
| 17. C2×D4×D43 | C22 | semidirect |
| 18. C2×D4×D43 | C22 | semidirect |
| 19. C2×D4×D43 | C22 | semidirect |
| 20. C22×C4×D43 | C22 | semidirect |
| 21. H(5,𝔽2)×C43 | C22 | semidirect |
| 22. C2×#41×C43 | C22 | semidirect |
| 23. C22×D4×C43 | C22 | semidirect |
| 24. C24×C43 | C23 | semidirect |
| 27. C23×D43 | C23 | semidirect |
| 28. C23×D43 | C23 | semidirect |
| 29. #41×C43 | C23 | semidirect |
| 30. C2×Q8×C43 | C23 | semidirect |
| 31. C2×D4×C43 | C23 | semidirect |
| 32. C2×D4×C43 | C23 | semidirect |
| 33. C22×C4×C43 | C23 | semidirect |
| 34. C2×C22⋊D43 | C23 | semidirect |
| 35. C2×C22⋊D43 | C23 | semidirect |
| 36. C22×Dic43 | C23 | semidirect |
| 37. #10621902 | C23 | semidirect |
| 38. Q8×D43 | C23 | semidirect |
| 39. #10621900 | C23 | semidirect |
| 40. D4×D43 | C23 | semidirect |
| 41. D4×D43 | C23 | semidirect |
| 42. #10621898 | C23 | semidirect |
| 43. C2×D172 | C23 | semidirect |
| 44. C2×D172 | C23 | semidirect |
| 46. C2×C4×D43 | C23 | semidirect |
| 47. C2×C4×D43 | C23 | semidirect |
| 48. C2×Dic86 | C23 | semidirect |
| 51. C23×C43 | C24 | semidirect |
| 58. C22×D43 | C24 | semidirect |
| 59. Q8×C43 | C24 | semidirect |
| 60. D4×C43 | C24 | semidirect |
| 62. C2×C4×C43 | C24 | semidirect |
| 63. C22⋊D43 | C24 | semidirect |
| 65. C2×Dic43 | C24 | semidirect |
| 66. D172 | C24 | semidirect |
| 68. C4×D43 | C24 | semidirect |
| 69. Dic86 | C24 | semidirect |
| 77. C2×D43 | H(5,𝔽2) | direct (N × H) |
| 84. C2×C43 | C2×H(5,𝔽2) | semidirect |
| 87. D43 | C2×H(5,𝔽2) | direct (N × H) |
| 91. C2×H(5,𝔽2) | D43 | direct (N × H) |
| 94. C43 | C22×H(5,𝔽2) | semidirect |
| 98. H(5,𝔽2) | C2×D43 | direct (N × H) |
| 103. C2×#41 | C2×D43 | semidirect |
| 110. C22×D4 | C2×D43 | semidirect |
| 116. C24 | C22×D43 | semidirect |
| 120. #41 | C22×D43 | semidirect |
| 123. C2×Q8 | C22×D43 | semidirect |
| 130. C2×D4 | C22×D43 | semidirect |
| 131. C2×D4 | C22×D43 | semidirect |
| 136. C22×C4 | C22×D43 | semidirect |
| 146. C23 | C23×D43 | semidirect |
| 148. Q8 | C23×D43 | semidirect |
| 151. D4 | C23×D43 | semidirect |
| 157. C2×C4 | C23×D43 | semidirect |
| 173. C2 | H(5,𝔽2)×D43 | direct (N × H) |