Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
159 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 159 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #327 |
| commutator | C2×C8 | C42 |
| Frattini, cosocle | C22×M16 | C22 |
| socle | C2 | #1294 |
| prime radical | C24 | SD16 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ C22×M16 ◁ G | |
| LECS | G ▷ C22×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C2×#108 | C4 | semidirect |
| 8. C2×#108 | C4 | semidirect |
| 11. #349 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#349 | 2 |
| #1811 | 2 |
| C2×H(3,ℤ/4) | 2 |