Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
227 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 227 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | #120 |
| commutator | C42 | C22×C4 |
| Frattini, cosocle | C2×C42 | C23 |
| socle | C22 | #385 |
| prime radical | C22×D4 | Q8 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #1950 | C2 | semidirect |
| 3. #1567 | C2 | semidirect |
| 6. #1301 | C2 | semidirect |
| 7. #1278 | C2 | semidirect |
| 130. D4 | #108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×M16 | 2 |
| #1950 | 2 |
| #1567 | 2 |
| #1486 | 2 |
| C2×D4⋊C8 | 2 |
| #1301 | 2 |
| #1278 | 2 |