Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
3607 conjugacy classes of subgroups; only the 1119 normal subgroups are shown.
This group has 3607 conjugacy classes of subgroups — too many to draw. Only its 1119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C23 |
| commutator | C22 | C24×C4 |
| Frattini, cosocle | C2×C4 | C25 |
| socle | C24 | C22×C4 |
| prime radical | C26 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×M16 | C2 | semidirect |
| 3. C2×#407 | C2 | direct (N × H) |
| 4. C22×C22⋊C8 | C2 | semidirect |
| 14. C22×M16 | C22 | semidirect |
| 15. C23×C8 | C22 | semidirect |
| 16. #407 | C22 | direct (N × H) |
| 17. C2×C22⋊C8 | C22 | semidirect |
| 41. C2×M16 | C23 | semidirect |
| 43. C22×C8 | C23 | semidirect |
| 44. C22⋊C8 | C23 | semidirect |
| 52. C24 | M16 | semidirect |
| 80. C2×C8 | C24 | semidirect |
| 92. C23 | C2×M16 | semidirect |
| 117. C22 | #407 | direct (N × H) |
| 121. C22 | C22×M16 | semidirect |
| 129. C2 | C2×#407 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C4 | 2 |
| C23×M16 | 2 |
| C2×#407 | 2 |
| C22×C22⋊C8 | 2 |