Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
998 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 998 conjugacy classes of subgroups — too many to draw. Only its 557 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×C22⋊C4 |
| commutator | C22 | C22×C42 |
| Frattini, cosocle | C22×C4 | C24 |
| socle | C2 | C22×#95 |
| prime radical | C22×#41 | C22 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C22×#41 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×#344 | C2 | semidirect |
| 9. #568 | C4 | semidirect |
| 11. C2×#131 | C4 | semidirect |
| 35. C2×M16 | C2×C4 | semidirect |
| 36. C2×M16 | C2×C4 | semidirect |
| 40. C22×C8 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#568 | 2 |
| #3428 | 2 |
| C2×#344 | 2 |