Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
253 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 253 conjugacy classes of subgroups — too many to draw. Only its 123 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 | C2×C4×C8 |
| Frattini, cosocle | C2×C42 | C23 |
| socle | C22 | C4×C22⋊C4 |
| prime radical | C24 | C42 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8 ◁ C2×C4×C8 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #1450 | C2 | semidirect |
| 4. #1281 | C2 | semidirect |
| 22. C2×M16 | C8 | semidirect |
| 26. C22×C8 | C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#405 | 2 |
| #1458 | 2 |
| #1450 | 2 |
| #1281 | 2 |