Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×C22⋊D127 |
| commutator | C4×C127 | C24 |
| Frattini | C4 | C23×D127 |
| Fitting | 2−1+4×C127 | C2 |
| socle | C2×C127 | C22×D4 |
| hypercenter | 2−1+4 | D127 |
| hypocenter | C127 | #577 |
| LCS | G ▷ C4×C127 ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ 2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16861255 | C2 | semidirect |
| 2. #16861240 | C2 | semidirect |
| 3. #16861234 | C2 | semidirect |
| 4. #16861229 | C2 | semidirect |
| 5. C2×#14523235 | C2 | semidirect |
| 6. #16861216 | C2 | semidirect |
| 7. 2−1+4×C127 | C2 | semidirect |
| 12. #14523238 | C22 | semidirect |
| 13. #14523236 | C22 | semidirect |
| 14. #14523235 | C22 | semidirect |
| 15. #14523235 | C22 | semidirect |
| 16. #14523233 | C22 | semidirect |
| 17. #14523232 | C22 | semidirect |
| 18. C2×C127⋊C8 | C22 | semidirect |
| 21. #41×C127 | C22 | semidirect |
| 23. C2×Q8×C127 | C22 | semidirect |
| 53. C127 | #577 | semidirect |
| 55. 2−1+4 | D127 | semidirect |
| 66. #41 | C2×D127 | semidirect |
| 68. C2×Q8 | C2×D127 | semidirect |