Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
413 conjugacy classes of subgroups; only the 311 normal subgroups are shown.
This group has 413 conjugacy classes of subgroups — too many to draw. Only its 311 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 | C42 | C24 |
| commutator, socle | C22 | C22×C42 |
| prime radical | C2×#41 | C2×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C42 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #1452 | C2 | semidirect |
| 5. #1451 | C2 | semidirect |
| 6. #1451 | C2 | semidirect |
| 7. C2×#322 | C2 | semidirect |
| 92. C8 | #131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#41 | 2 |
| C4×#131 | 2 |
| #1452 | 2 |
| #1451 | 2 |
| C2×#322 | 2 |