Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
613 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 613 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22⋊C4 |
| commutator | C2×C4 | C2×C42 |
| Frattini, cosocle | C23×C4 | C23 |
| socle | C23 | #95 |
| prime radical | C25 | D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #1297 | C2 | direct (N × H) |
| 5. C22×M16 | C4 | semidirect |
| 9. #407 | C4 | semidirect |
| 14. C4×C22⋊C4 | C4 | semidirect |
| 16. C2×#95 | C4 | semidirect |
| 32. C2×M16 | C2×C4 | semidirect |
| 43. #95 | C2×C4 | semidirect |
| 167. C2 | #1297 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#407 | 2 |
| C2×C4×C22⋊C4 | 2 |
| #1297 | 2 |