Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
725 conjugacy classes of subgroups; only the 399 normal subgroups are shown.
This group has 725 conjugacy classes of subgroups — too many to draw. Only its 399 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 | C2 | C22×C4×C8 |
| socle | C23 | C23×C4 |
| prime radical | C25 | C2×C4 |
| LCS | G ▷ C2 ▷ 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. C8×C22⋊C4 | C2 | semidirect |
| 4. C4×C22⋊C8 | C2 | semidirect |
| 9. C2×C22⋊C8 | C4 | semidirect |
| 12. C2×C4×C8 | C22 | semidirect |
| 16. #336 | C22 | semidirect |
| 26. C22×C8 | C2×C4 | semidirect |
| 28. C2×C22⋊C4 | C8 | semidirect |
| 34. C22⋊C8 | C2×C4 | semidirect |
| 52. C22×C4 | C2×C8 | semidirect |
| 63. C22⋊C4 | C2×C8 | semidirect |
| 73. C23 | C4×C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊C8 | 2 |
| C2×C4×C22⋊C4 | 2 |
| C8×C22⋊C4 | 2 |
| C4×C22⋊C8 | 2 |