Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
283 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 283 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C22×C8 | C23 |
| commutator | C22 | C22×C16 |
| socle | C23 | C22×C8 |
| prime radical | C24 | C2×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C8 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4⋊C16 | C2 | semidirect |
| 4. #1374 | C2 | semidirect |
| 53. C22×C4 | C16 | semidirect |
| 131. C22 | C4⋊C16 | semidirect |
| 143. C4 | C22⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C8 | 2 |
| C2×C4⋊C16 | 2 |
| C2×C22⋊C16 | 2 |
| #1374 | 2 |