Finite Group DatabasebetaFinite Group DatabasebetaOrder 128.
193 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 193 conjugacy classes of subgroups — too many to draw. Only its 90 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 | #121 | 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 |
|---|---|---|
| 2. C2×C4×Q8 | C2 | semidirect |
| 3. #484 | C2 | semidirect |
| 5. #479 | C2 | semidirect |
| 6. #464 | C2 | semidirect |
| 7. #451 | C2 | semidirect |
| 9. #441 | C2 | semidirect |
| 10. #440 | C2 | semidirect |
| 11. #432 | 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 |
| #484 | 2 |
| #481 | 2 |
| #479 | 2 |
| #464 | 2 |
| #451 | 2 |
| #448 | 2 |
| #441 | 2 |
| #440 | 2 |
| #432 | 2 |