Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | D4×D127 |
| commutator | C4×C127 | C24 |
| Frattini | C4 | C23×D127 |
| Fitting | #135×C127 | C2 |
| socle | C2×C127 | C22×D4 |
| hypercenter | #135 | D127 |
| hypocenter | C127 | #575 |
| LCS | G ▷ C4×C127 ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #135 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #41×D127 | C2 | semidirect |
| 2. #16861241 | C2 | semidirect |
| 3. #16861238 | C2 | semidirect |
| 4. #16861236 | C2 | semidirect |
| 5. #16861233 | C2 | semidirect |
| 6. #16861231 | C2 | semidirect |
| 7. #16861229 | C2 | semidirect |
| 8. C2×#14523231 | C2 | semidirect |
| 9. #135×C127 | C2 | semidirect |
| 12. #14523248 | C22 | semidirect |
| 15. Q8×D127 | C22 | semidirect |
| 17. D4×D127 | C22 | semidirect |
| 20. Dic508 | C22 | semidirect |
| 21. #14523238 | C22 | semidirect |
| 22. #14523237 | C22 | semidirect |
| 23. #14523236 | C22 | semidirect |
| 24. #14523235 | C22 | semidirect |
| 25. D1016 | C22 | semidirect |
| 26. #14523233 | C22 | semidirect |
| 27. #14523231 | C22 | semidirect |
| 28. #14523231 | C22 | semidirect |
| 29. C2×C127⋊C8 | C22 | semidirect |
| 30. #41×C127 | C22 | semidirect |
| 31. Q16×C127 | C22 | semidirect |
| 32. SD16×C127 | C22 | semidirect |
| 33. D8×C127 | C22 | semidirect |
| 34. C2×C8×C127 | C22 | semidirect |
| 75. C127 | #575 | semidirect |
| 84. #135 | D127 | semidirect |
| 91. #41 | C2×D127 | semidirect |
| 99. Q16 | C2×D127 | semidirect |
| 103. SD16 | C2×D127 | semidirect |
| 106. D8 | C2×D127 | semidirect |
| 110. C2×C8 | C2×D127 | semidirect |