Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
357 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 357 conjugacy classes of subgroups — too many to draw. Only its 215 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×C4 | C24 |
| commutator | C22 | C23×C8 |
| socle, prime radical | C23 | C23×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 32. C4⋊Q8 | C8 | semidirect |
| 52. C4×C8 | Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊Q8 | 2 |
| #1984 | 2 |
| #1939 | 2 |
| #1916 | 2 |
| #1831 | 2 |
| C8×C4⋊C4 | 2 |
| #1744 | 2 |