Finite Group DatabasebetaFinite Group DatabasebetaOrder 128.
246 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C2×C4 | C24 |
| commutator, socle | C22 | C23×C4 |
| prime radical | #532 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#131 | C2 | semidirect |
| 3. #436 | C2 | semidirect |
| 4. #435 | C2 | semidirect |
| 5. C8×D4 | C2 | semidirect |
| 6. C2×C4⋊C8 | C2 | semidirect |
| 7. #408 | C2 | semidirect |
| 8. C4×M16 | C2 | semidirect |
| 44. M16 | D4 | semidirect |
| 95. C4 | #131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#131 | 2 |
| #532 | 2 |
| #436 | 2 |
| #435 | 2 |
| C8×D4 | 2 |
| C2×C4⋊C8 | 2 |
| #408 | 2 |
| C4×M16 | 2 |