Finite Group DatabasebetaFinite Group DatabasebetaOrder 128.
246 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24 |
| prime radical | #535 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×#41 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×SD16 | C2 | semidirect |
| 2. C2×#131 | C2 | semidirect |
| 3. #536 | C2 | semidirect |
| 5. #468 | C2 | semidirect |
| 6. #465 | C2 | semidirect |
| 7. #427 | C2 | semidirect |
| 8. #419 | C2 | semidirect |
| 9. #418 | C2 | semidirect |
| 18. C2×M16 | C22 | semidirect |
| 20. C22×C8 | C22 | semidirect |
| 26. C22⋊Q8 | C22 | semidirect |
| 31. #107 | C22 | semidirect |
| 32. #106 | C22 | semidirect |
| 33. #103 | C22 | semidirect |
| 58. C2×C8 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×SD16 | 2 |
| C2×#131 | 2 |
| #536 | 2 |
| #535 | 2 |
| #468 | 2 |
| #465 | 2 |
| #427 | 2 |
| #419 | 2 |
| #418 | 2 |