Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
349 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 349 conjugacy classes of subgroups — too many to draw. Only its 123 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 | C2×C42 |
| Frattini, cosocle | C2×C42 | C23 |
| socle | C23 | C2×C22⋊C4 |
| prime radical | C22×D4 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C43 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #1767 | C2 | semidirect |
| 3. #1744 | C2 | semidirect |
| 5. #1279 | C2 | semidirect |
| 19. D4⋊C8 | C4 | semidirect |
| 43. C4⋊C8 | C2×C4 | semidirect |
| 46. C4×C8 | C2×C4 | semidirect |
| 98. D4 | #97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×D4 | 2 |
| #1767 | 2 |
| #1744 | 2 |
| C2×D4⋊C8 | 2 |
| #1279 | 2 |