Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
2525 conjugacy classes of subgroups; only the 1003 normal subgroups are shown.
This group has 2525 conjugacy classes of subgroups — too many to draw. Only its 1003 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, cosocle | C23 | C25 |
| commutator | C22 | C24×C4 |
| prime radical | C22×2−1+4 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#519 | C2 | semidirect |
| 3. C22×C4×Q8 | C2 | semidirect |
| 4. #2341 | C2 | semidirect |
| 5. Q8×C22⋊C4 | C2 | semidirect |
| 6. #2311 | C2 | semidirect |
| 7. #2297 | C2 | semidirect |
| 10. C2×2−1+4 | C4 | semidirect |
| 36. C2×#41 | C2×C4 | semidirect |
| 40. C22×Q8 | C2×C4 | semidirect |
| 72. C2×Q8 | C22⋊C4 | semidirect |
| 137. C2×C4 | 2−1+4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×2−1+4 | 2 |
| C2×#519 | 2 |
| C22×C4×Q8 | 2 |
| #2341 | 2 |
| Q8×C22⋊C4 | 2 |
| #2311 | 2 |
| #2297 | 2 |