Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
310 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 159 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42 | C2×D127 |
| commutator | C2×C127 | C23×C4 |
| Frattini | C22 | C23×D127 |
| Fitting | C2×C42×C127 | C2 |
| socle | C22×C127 | C24 |
| hypercenter | C2×C42 | D127 |
| hypocenter | C127 | C4×#41 |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C42 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×Dic254 | C2 | semidirect |
| 3. C4×D508 | C2 | semidirect |
| 4. C4×C22⋊D127 | C2 | semidirect |
| 5. #16861168 | C2 | semidirect |
| 6. #16861166 | C2 | semidirect |
| 7. C42×D127 | C2 | semidirect |
| 8. C2×C42×C127 | C2 | semidirect |
| 9. #14523248 | C4 | direct (N × H) |
| 27. Dic254 | C2×C4 | semidirect |
| 28. D508 | C2×C4 | semidirect |
| 29. C22⋊D127 | C2×C4 | semidirect |
| 33. C4×D127 | C2×C4 | semidirect |
| 36. C2×C4×C127 | C2×C4 | semidirect |
| 49. C4×C127 | #41 | semidirect |
| 56. C127 | C4×#41 | semidirect |
| 65. C2×C42 | D127 | semidirect |
| 93. C2×C4 | C4×D127 | semidirect |
| 108. C4 | #14523248 | direct (N × H) |