Finite Group DatabasebetaFinite Group DatabasebetaOrder 128.
217 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 217 conjugacy classes of subgroups — too many to draw. Only its 92 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. C4×#41 | C2 | semidirect |
| 3. #482 | C2 | semidirect |
| 4. #477 | C2 | semidirect |
| 5. #476 | C2 | semidirect |
| 6. #460 | C2 | semidirect |
| 7. #459 | C2 | semidirect |
| 8. #449 | C2 | semidirect |
| 9. C4×SD16 | C2 | semidirect |
| 10. C4×D8 | C2 | semidirect |
| 11. #431 | C2 | semidirect |
| 88. Q8 | #41 | semidirect |
| 96. D4 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #532 | 2 |
| C4×#41 | 2 |
| #482 | 2 |
| #477 | 2 |
| #476 | 2 |
| #460 | 2 |
| #459 | 2 |
| #449 | 2 |
| C4×SD16 | 2 |
| C4×D8 | 2 |
| #431 | 2 |