Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
5956 conjugacy classes of subgroups; only the 3203 normal subgroups are shown.
This group has 5956 conjugacy classes of subgroups — too many to draw. Only its 3203 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C24×D43 |
| commutator, socle | C2×C43 | C26 |
| Frattini | C2 | C25×D43 |
| Fitting | C43×#585 | C2 |
| hypercenter | #585 | D43 |
| hypocenter | C43 | C2×#585 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C4 ◁ #585 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583736 | C2 | semidirect |
| 2. #14583735 | C2 | semidirect |
| 3. #14583734 | C2 | semidirect |
| 4. 2−1+4×D43 | C2 | semidirect |
| 5. H(5,𝔽2)×D43 | C2 | semidirect |
| 6. C2×#41×D43 | C2 | semidirect |
| 7. C43×#585 | C2 | semidirect |
| 8. #13063373 | C22 | semidirect |
| 9. #13063372 | C22 | semidirect |
| 10. #13063371 | C22 | semidirect |
| 11. #13063370 | C22 | semidirect |
| 12. C2×#10621902 | C22 | semidirect |
| 13. C2×#10621898 | C22 | semidirect |
| 14. C2×#10621900 | C22 | semidirect |
| 15. #41×D43 | C22 | semidirect |
| 16. #41×D43 | C22 | semidirect |
| 17. #41×D43 | C22 | semidirect |
| 18. #41×D43 | C22 | semidirect |
| 19. C2×Q8×D43 | C22 | semidirect |
| 20. C2×D4×D43 | C22 | semidirect |
| 21. C22×C4×D43 | C22 | semidirect |
| 22. 2−1+4×C43 | C22 | semidirect |
| 23. H(5,𝔽2)×C43 | C22 | semidirect |
| 24. C2×#41×C43 | C22 | semidirect |
| 26. #41×C43 | C23 | semidirect |
| 27. #41×C43 | C23 | semidirect |
| 28. C2×Q8×C43 | C23 | semidirect |
| 29. C2×D4×C43 | C23 | semidirect |
| 30. C22×C4×C43 | C23 | semidirect |
| 31. C2×C22⋊D43 | C23 | semidirect |
| 32. C22×Dic43 | C23 | semidirect |
| 33. #10621902 | C23 | semidirect |
| 34. #10621902 | C23 | semidirect |
| 36. Q8×D43 | C23 | semidirect |
| 37. #10621900 | C23 | semidirect |
| 38. #10621900 | C23 | semidirect |
| 40. D4×D43 | C23 | semidirect |
| 41. #10621898 | C23 | semidirect |
| 42. #10621898 | C23 | semidirect |
| 43. C2×D172 | C23 | semidirect |
| 46. C2×C4×D43 | C23 | semidirect |
| 47. C2×C4×D43 | C23 | semidirect |
| 48. C2×Dic86 | C23 | semidirect |
| 81. D43 | #585 | direct (N × H) |
| 85. #585 | D43 | direct (N × H) |
| 89. C43 | C2×#585 | semidirect |
| 92. 2−1+4 | C2×D43 | semidirect |
| 95. H(5,𝔽2) | C2×D43 | semidirect |
| 103. C2×#41 | C2×D43 | semidirect |
| 114. #41 | C22×D43 | semidirect |
| 115. #41 | C22×D43 | semidirect |
| 119. C2×Q8 | C22×D43 | semidirect |
| 124. C2×D4 | C22×D43 | semidirect |
| 130. C22×C4 | C22×D43 | semidirect |