Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
278 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #481 |
| commutator, Frattini, cosocle | C2×C8 | C24 |
| socle | C2 | C2×#481 |
| prime radical | #3054 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ C22×M16 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#430 | C2 | semidirect |
| 3. #2239 | C2 | semidirect |
| 4. #2238 | C2 | semidirect |
| 5. #2155 | C2 | semidirect |
| 6. #2148 | C2 | semidirect |
| 7. C2×#349 | C2 | semidirect |
| 22. #365 | C22 | semidirect |
| 23. #362 | C22 | semidirect |
| 24. #361 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3054 | 2 |
| C2×#430 | 2 |
| #2239 | 2 |
| #2238 | 2 |
| #2155 | 2 |
| #2148 | 2 |
| C2×#349 | 2 |