Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1557 conjugacy classes of subgroups; only the 563 normal subgroups are shown.
This group has 1557 conjugacy classes of subgroups — too many to draw. Only its 563 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C4×#41 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#578 | C2 | semidirect |
| 2. #3499 | C2 | semidirect |
| 3. #3156 | C2 | semidirect |
| 4. #3152 | C2 | semidirect |
| 5. #3147 | C2 | semidirect |
| 6. C2×#494 | C2 | semidirect |
| 7. C4×#131 | C2 | semidirect |
| 43. #131 | D4 | semidirect |
| 124. C4 | #578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#578 | 2 |
| #3499 | 2 |
| #3156 | 2 |
| #3152 | 2 |
| #3147 | 2 |
| C2×#494 | 2 |
| C4×#131 | 2 |