Finite Group DatabasebetaFinite Group DatabasebetaOrder 128.
220 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 102 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 | C22×D4 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ 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. #533 | C2 | semidirect |
| 3. #478 | C2 | semidirect |
| 4. #476 | C2 | semidirect |
| 5. #474 | C2 | semidirect |
| 6. #428 | C2 | semidirect |
| 7. #423 | C2 | semidirect |
| 12. C4⋊Q8 | C22 | semidirect |
| 13. C4⋊Q8 | C22 | semidirect |
| 14. #125 | C22 | semidirect |
| 27. #107 | C22 | semidirect |
| 28. #106 | C22 | semidirect |
| 29. C4⋊C8 | C22 | semidirect |
| 30. C4⋊C8 | C22 | semidirect |
| 38. C2×D4 | Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #533 | 2 |
| C2×C4×D4 | 2 |
| #478 | 2 |
| #476 | 2 |
| #474 | 2 |
| #428 | 2 |
| #423 | 2 |
| #418 | 2 |