Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
527 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 527 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24 |
| prime radical | C24 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #2061 | C2 | semidirect |
| 5. #2060 | C2 | semidirect |
| 35. C2×M16 | Q8 | semidirect |
| 57. #117 | Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3458 | 2 |
| C2×#428 | 2 |
| #2317 | 2 |
| #2061 | 2 |
| #2060 | 2 |
| #1742 | 2 |
| #1733 | 2 |