Finite Group DatabasebetaFinite Group DatabasebetaOrder 128.
135 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 135 conjugacy classes of subgroups — too many to draw. Only its 56 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 | C2×C4 | C22×C4 |
| Frattini, cosocle | C22×C4 | C23 |
| socle | C22 | C4×D4 |
| prime radical | C2×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C8 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#108 | C2 | semidirect |
| 3. #424 | C2 | semidirect |
| 6. #339 | C2 | semidirect |
| 7. #336 | C2 | semidirect |
| 23. #103 | C4 | semidirect |
| 24. #103 | C4 | semidirect |
| 25. #102 | C4 | semidirect |
| 26. #102 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#131 | 2 |
| C2×#108 | 2 |
| #424 | 2 |
| C2×#104 | 2 |
| #416 | 2 |
| #339 | 2 |
| #336 | 2 |