Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
142 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 103 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 | C4×C8 | C23 |
| commutator, socle | C22 | C2×C4×C8 |
| prime radical | C23 | C4×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C4×C8 ◁ G | |
| LECS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #1312 | C2 | semidirect |
| 5. #1312 | C2 | semidirect |
| 6. #1311 | C2 | semidirect |
| 7. C8×C16 | C2 | semidirect |
| 64. C16 | M16 | semidirect |
| 81. C8 | M32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2162 | 2 |
| C4×M32 | 2 |
| C8×M16 | 2 |
| #1312 | 2 |
| #1311 | 2 |
| C8×C16 | 2 |