Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
229 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 229 conjugacy classes of subgroups — too many to draw. Only its 55 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 | #481 |
| commutator, Frattini, cosocle | C22×C8 | C23 |
| prime radical | C2×#469 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#365 | C2 | semidirect |
| 3. C2×#361 | C2 | semidirect |
| 4. C2×#361 | C2 | semidirect |
| 5. C2×#349 | C2 | semidirect |
| 6. #1811 | C2 | semidirect |
| 7. #1383 | C2 | semidirect |
| 51. M32 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#469 | 2 |
| C2×#365 | 2 |
| C2×#361 | 2 |
| C2×#349 | 2 |
| #1811 | 2 |
| #1383 | 2 |