Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
713 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 713 conjugacy classes of subgroups — too many to draw. Only its 187 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 | C2×D4 |
| commutator | C2×C4 | C2×C42 |
| Frattini, cosocle | C23×C4 | C23 |
| socle | C23 | C2×C22⋊C4 |
| prime radical | C22×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#339 | C2 | semidirect |
| 4. #1728 | C2 | semidirect |
| 5. C4×#95 | C2 | semidirect |
| 10. C2×C4×Q8 | C4 | semidirect |
| 12. C2×C4×D4 | C4 | semidirect |
| 20. C2×#104 | C4 | semidirect |
| 46. C2×M16 | C2×C4 | semidirect |
| 71. C2×C42 | C2×C4 | semidirect |
| 168. Q8 | #95 | semidirect |
| 174. D4 | #95 | semidirect |
| 195. C2×C4 | #104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#41 | 2 |
| C22×#104 | 2 |
| C2×#339 | 2 |
| #1728 | 2 |
| C4×#95 | 2 |