Finite Group DatabasebetaFinite Group DatabasebetaOrder 128.
171 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 171 conjugacy classes of subgroups — too many to draw. Only its 88 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 | C2×D4 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #499 | C2 | semidirect |
| 3. #485 | C2 | semidirect |
| 4. #483 | C2 | semidirect |
| 5. #479 | C2 | semidirect |
| 6. #467 | C2 | semidirect |
| 7. #467 | C2 | semidirect |
| 8. C4×Q16 | C2 | semidirect |
| 10. #427 | C2 | semidirect |
| 11. C2×#107 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #552 | 2 |
| #499 | 2 |
| #485 | 2 |
| #483 | 2 |
| #479 | 2 |
| #467 | 2 |
| C4×Q16 | 2 |
| C8×D4 | 2 |
| #427 | 2 |
| C2×#107 | 2 |