Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
427 conjugacy classes of subgroups; only the 263 normal subgroups are shown.
This group has 427 conjugacy classes of subgroups — too many to draw. Only its 263 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C42 | C24 |
| socle | C23 | C2×C4⋊C4 |
| prime radical | C24 | C4⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #1566 | C2 | direct (N × H) |
| 4. C2×#334 | C2 | semidirect |
| 17. #334 | C22 | semidirect |
| 64. C2×C8 | M16 | semidirect |
| 105. C8 | C2×M16 | semidirect |
| 124. C2 | #1566 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#423 | 2 |
| C22×C4×C8 | 2 |
| #1566 | 2 |
| C2×#334 | 2 |