Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1408 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 459 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D43 |
| commutator, socle | C22×C43 | C25 |
| Fitting | C43×H(3,𝔽4) | C2 |
| hypercenter | H(3,𝔽4) | D43 |
| hypocenter | C43 | C2×H(3,𝔽4) |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583642 | C2 | semidirect |
| 2. #14583641 | C2 | semidirect |
| 3. #124×D43 | C2 | semidirect |
| 4. #120×D43 | C2 | semidirect |
| 5. C43×H(3,𝔽4) | C2 | semidirect |
| 6. C24×D43 | C22 | semidirect |
| 7. C2×Q8×D43 | C22 | semidirect |
| 9. #13063314 | C22 | semidirect |
| 10. #13063313 | C22 | semidirect |
| 11. #13063312 | C22 | semidirect |
| 12. #13063311 | C22 | semidirect |
| 13. #13063295 | C22 | semidirect |
| 14. #13063294 | C22 | semidirect |
| 15. #13063293 | C22 | semidirect |
| 16. C22⋊C4×D43 | C22 | semidirect |
| 17. C42×D43 | C22 | semidirect |
| 18. #124×C43 | C22 | semidirect |
| 19. #120×C43 | C22 | semidirect |
| 20. C24×C43 | C23 | semidirect |
| 23. C23×D43 | C23 | semidirect |
| 24. C2×Q8×C43 | C23 | semidirect |
| 31. C2×Dic86 | C23 | semidirect |
| 32. C22⋊C4×C43 | C23 | semidirect |
| 33. C42×C43 | C23 | semidirect |
| 34. C22⋊Dic43 | C23 | semidirect |
| 35. (C2×D43)⋊C4 | C23 | semidirect |
| 36. C4×Dic43 | C23 | semidirect |
| 65. D43 | H(3,𝔽4) | direct (N × H) |
| 68. H(3,𝔽4) | D43 | direct (N × H) |
| 71. C43 | C2×H(3,𝔽4) | semidirect |
| 79. #124 | C2×D43 | semidirect |
| 83. #120 | C2×D43 | semidirect |
| 89. C24 | C22×D43 | semidirect |
| 92. C2×Q8 | C22×D43 | semidirect |
| 100. C22⋊C4 | C22×D43 | semidirect |
| 102. C42 | C22×D43 | semidirect |