Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
577 conjugacy classes of subgroups; only the 263 normal subgroups are shown.
This group has 577 conjugacy classes of subgroups — too many to draw. Only its 263 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22⋊C4 |
| commutator | C22 | C23×C8 |
| Frattini, cosocle | C2×C8 | C24 |
| socle | C22 | C2×C22⋊C8 |
| prime radical | C22×#41 | C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8 ◁ C23×C8 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×M32 | C2 | semidirect |
| 3. #2115 | C2 | direct (N × H) |
| 4. C2×#349 | C2 | semidirect |
| 18. C2×M32 | C22 | semidirect |
| 20. #349 | C22 | semidirect |
| 170. C2 | #2115 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#131 | 2 |
| C22×M32 | 2 |
| #2115 | 2 |
| C2×#349 | 2 |