Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
247 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 247 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×C22⋊C4 |
| commutator | C23 | C2×C42 |
| Frattini, cosocle | C2×C42 | C23 |
| socle | C22 | C4×C22⋊C4 |
| prime radical | C22×D4 | C2×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C4×C8 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #1451 | C2 | semidirect |
| 5. C8×M16 | C2 | semidirect |
| 6. #1283 | C2 | semidirect |
| 7. #1283 | C2 | semidirect |
| 82. M16 | M16 | semidirect |
| 135. C8 | #100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#436 | 2 |
| C4×#100 | 2 |
| #1460 | 2 |
| #1451 | 2 |
| C8×M16 | 2 |
| #1283 | 2 |