Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
309 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 309 conjugacy classes of subgroups — too many to draw. Only its 187 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C2×C8 | C24 |
| commutator, socle | C22 | C23×C8 |
| prime radical | C22×D4 | C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2168 | C2 | semidirect |
| 3. #2163 | C2 | semidirect |
| 4. #2112 | C2 | semidirect |
| 5. C2×C22⋊C16 | C2 | semidirect |
| 9. C2×M32 | C22 | semidirect |
| 10. C22×C16 | C22 | semidirect |
| 17. C4⋊C16 | C22 | semidirect |
| 19. C22⋊C16 | C22 | semidirect |
| 20. C22⋊C16 | C22 | semidirect |
| 21. #346 | C22 | semidirect |
| 90. C23 | M32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D4 | 2 |
| #2168 | 2 |
| #2163 | 2 |
| #2112 | 2 |
| C2×C22⋊C16 | 2 |