Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
246 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D127 |
| commutator | C22×C127 | C24 |
| Frattini | C22 | C23×D127 |
| Fitting | C2×C4⋊C4×C127 | C2 |
| socle | C23×C127 | C23 |
| hypercenter | C2×C4⋊C4 | D127 |
| hypocenter | C127 | C2×#126 |
| LCS | G ▷ C22×C127 ▷ C127 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16861204 | C2 | direct (N × H) |
| 2. C2×C4⋊Dic127 | C2 | semidirect |
| 3. C2×Dic127⋊C4 | C2 | semidirect |
| 7. C2×C4×Dic127 | C2 | semidirect |
| 8. C2×C4⋊C4×C127 | C2 | semidirect |
| 13. C4⋊Dic127 | C22 | semidirect |
| 14. Dic127⋊C4 | C22 | semidirect |
| 18. C4×Dic127 | C22 | semidirect |
| 22. C4⋊C4×C127 | C22 | semidirect |
| 54. C2×C127 | #126 | semidirect |
| 59. C127 | C2×#126 | semidirect |
| 64. C2×C4⋊C4 | D127 | semidirect |
| 78. C4⋊C4 | C2×D127 | semidirect |
| 115. C2 | #16861204 | direct (N × H) |