Finite Group DatabasebetaFinite Group DatabasebetaOrder 128.
195 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 195 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 |
| prime radical | #121 | C22 |
| 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 |
|---|---|---|
| 2. C2×C4×Q8 | C2 | semidirect |
| 3. #483 | C2 | semidirect |
| 5. #479 | C2 | semidirect |
| 6. #464 | C2 | semidirect |
| 7. #451 | C2 | semidirect |
| 9. C4×Q16 | C2 | semidirect |
| 10. C4×SD16 | C2 | semidirect |
| 11. #431 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #529 | 2 |
| C2×C4×Q8 | 2 |
| #483 | 2 |
| #480 | 2 |
| #479 | 2 |
| #464 | 2 |
| #451 | 2 |
| #448 | 2 |
| C4×Q16 | 2 |
| C4×SD16 | 2 |
| #431 | 2 |