Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
491 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 491 conjugacy classes of subgroups — too many to draw. Only its 407 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×C8 | C22 |
| commutator | C2 | C22×C4×C8 |
| Frattini, cosocle | C42 | C24 |
| socle | C23 | C2×C42 |
| prime radical | C24 | C42 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C8 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #1450 | C2 | direct (N × H) |
| 4. C2×#322 | C2 | semidirect |
| 5. C2×C82 | C2 | semidirect |
| 18. #322 | C22 | semidirect |
| 19. C82 | C22 | semidirect |
| 22. C22×C8 | C8 | semidirect |
| 56. C2×C8 | C2×C8 | semidirect |
| 101. C2 | #1450 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#431 | 2 |
| C22×C4×C8 | 2 |
| #1450 | 2 |
| C2×#322 | 2 |
| C2×C82 | 2 |