Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
338 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 151 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 | C23×D127 |
| commutator | C2×C127 | C23×C4 |
| Fitting | C4×D4×C127 | C2 |
| socle | C22×C127 | C24 |
| hypercenter | C4×D4 | D127 |
| hypocenter | C127 | #518 |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×D508 | C2 | semidirect |
| 3. D4×Dic127 | C2 | semidirect |
| 4. #16861171 | C2 | semidirect |
| 5. C4×C22⋊D127 | C2 | semidirect |
| 6. (C22⋊D127)⋊C4 | C2 | semidirect |
| 7. #16861167 | C2 | semidirect |
| 8. #16861166 | C2 | semidirect |
| 9. C2×(C2×D127)⋊C4 | C2 | semidirect |
| 10. C22⋊C4×D127 | C2 | semidirect |
| 11. C4×D4×C127 | C2 | semidirect |
| 15. D4×D127 | C4 | semidirect |
| 16. C22×Dic127 | C22 | semidirect |
| 18. C2×C4×D127 | C22 | semidirect |
| 19. C2×C4×D127 | C22 | semidirect |
| 20. C4⋊Dic127 | C22 | semidirect |
| 21. Dic127⋊C4 | C22 | semidirect |
| 22. Dic127⋊C4 | C22 | semidirect |
| 23. C22⋊Dic127 | C22 | semidirect |
| 27. (C2×D127)⋊C4 | C22 | semidirect |
| 28. (C2×D127)⋊C4 | C22 | semidirect |
| 29. C4×Dic127 | C22 | semidirect |
| 30. C4×Dic127 | C22 | semidirect |
| 32. C22×C4×C127 | C22 | semidirect |
| 33. C4⋊C4×C127 | C22 | semidirect |
| 34. C22⋊C4×C127 | C22 | semidirect |
| 35. C42×C127 | C22 | semidirect |
| 38. C22×D127 | C2×C4 | semidirect |
| 41. D508 | C2×C4 | semidirect |
| 42. C22⋊D127 | C2×C4 | semidirect |
| 50. C4×D127 | C2×C4 | semidirect |
| 52. D4×C127 | C2×C4 | semidirect |
| 83. C127 | #518 | semidirect |
| 91. C4×D4 | D127 | semidirect |
| 105. C22×C4 | C2×D127 | semidirect |
| 109. C4⋊C4 | C2×D127 | semidirect |
| 116. C22⋊C4 | C2×D127 | semidirect |
| 119. C42 | C2×D127 | semidirect |
| 128. D4 | C4×D127 | semidirect |