Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
453 conjugacy classes of subgroups; only the 279 normal subgroups are shown.
This group has 453 conjugacy classes of subgroups — too many to draw. Only its 279 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 | C22×C42 |
| socle | C23 | C23×C4 |
| prime radical | C24 | C22×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 |
|---|---|---|
| 3. #1771 | C2 | semidirect |
| 4. C8×C4⋊C4 | C2 | semidirect |
| 10. #433 | C4 | semidirect |
| 40. C4⋊C8 | C2×C4 | semidirect |
| 43. #97 | C2×C4 | semidirect |
| 46. C4×C8 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#433 | 2 |
| #2296 | 2 |
| #1771 | 2 |
| C8×C4⋊C4 | 2 |
| #1750 | 2 |
| C4×C22⋊C8 | 2 |