Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
330 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 157 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 | C22×D4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C42 | C24 |
| socle | C22 | C2×C4×D4 |
| prime radical | C2×#135 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ #431 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2990 | C2 | semidirect |
| 3. #1591 | C2 | semidirect |
| 4. #1585 | C2 | semidirect |
| 5. C8×D8 | C2 | semidirect |
| 6. #1567 | C2 | semidirect |
| 7. #1489 | C2 | semidirect |
| 8. C8×M16 | C2 | semidirect |
| 89. D8 | M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2990 | 2 |
| C4×#135 | 2 |
| #1591 | 2 |
| #1585 | 2 |
| C8×D8 | 2 |
| #1567 | 2 |
| #1489 | 2 |
| C8×M16 | 2 |