Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
5872 conjugacy classes of subgroups; only the 3213 normal subgroups are shown.
This group has 5872 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 | C2×2−1+4×C43 | C2 |
| socle | C22×C43 | C25 |
| hypercenter | C2×2−1+4 | D43 |
| hypocenter | C43 | C22×2−1+4 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C2×2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063373 | C2 | semidirect |
| 2. C2×#13063372 | C2 | semidirect |
| 3. 2−1+4×D43 | C2 | direct (N × H) |
| 4. C2×#41×D43 | C2 | semidirect |
| 5. C22×Q8×D43 | C2 | semidirect |
| 6. C2×2−1+4×C43 | C2 | semidirect |
| 7. #13063373 | C22 | semidirect |
| 8. #13063372 | C22 | semidirect |
| 9. C2×#10621902 | C22 | semidirect |
| 10. C2×#10621898 | C22 | semidirect |
| 11. C2×#10621900 | C22 | semidirect |
| 12. #41×D43 | C22 | semidirect |
| 13. C22×Dic86 | C22 | semidirect |
| 15. C2×Q8×D43 | C22 | semidirect |
| 16. C2×Q8×D43 | C22 | semidirect |
| 19. 2−1+4×C43 | C22 | semidirect |
| 20. C2×#41×C43 | C22 | semidirect |
| 21. C22×Q8×C43 | C22 | semidirect |
| 23. #41×C43 | C23 | semidirect |
| 25. C2×Q8×C43 | C23 | semidirect |
| 30. #10621902 | C23 | semidirect |
| 32. Q8×D43 | C23 | semidirect |
| 33. #10621900 | C23 | semidirect |
| 35. #10621898 | C23 | semidirect |
| 41. C2×Dic86 | C23 | semidirect |
| 63. C2×D43 | 2−1+4 | direct (N × H) |
| 70. C2×C43 | C2×2−1+4 | semidirect |
| 73. D43 | C2×2−1+4 | direct (N × H) |
| 77. C2×2−1+4 | D43 | direct (N × H) |
| 80. C43 | C22×2−1+4 | semidirect |
| 83. 2−1+4 | C2×D43 | direct (N × H) |
| 88. C2×#41 | C2×D43 | semidirect |
| 93. C22×Q8 | C2×D43 | semidirect |
| 100. #41 | C22×D43 | semidirect |
| 106. C2×Q8 | C22×D43 | semidirect |
| 145. C2 | 2−1+4×D43 | direct (N × H) |