Finite Group DatabasebetaFinite Group DatabasebetaOrder 128.
204 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24 |
| socle | C22 | C22×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #532 | C2 | semidirect |
| 2. #529 | C2 | semidirect |
| 3. #501 | C2 | semidirect |
| 4. #496 | C2 | semidirect |
| 5. #490 | C2 | semidirect |
| 6. #489 | C2 | semidirect |
| 7. #469 | C2 | semidirect |
| 8. #468 | C2 | semidirect |
| 9. C4×SD16 | C2 | semidirect |
| 10. C4×D8 | C2 | semidirect |
| 11. C4×M16 | C2 | semidirect |
| 110. C8 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #532 | 2 |
| #529 | 2 |
| #501 | 2 |
| #496 | 2 |
| #490 | 2 |
| #489 | 2 |
| #469 | 2 |
| #468 | 2 |
| C4×SD16 | 2 |
| C4×D8 | 2 |
| C4×M16 | 2 |