Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
949 conjugacy classes of subgroups; only the 495 normal subgroups are shown.
This group has 949 conjugacy classes of subgroups — too many to draw. Only its 495 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25 |
| prime radical | C24 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #3249 | C2 | direct (N × H) |
| 3. C2×#477 | C2 | semidirect |
| 5. C2×#462 | C2 | semidirect |
| 20. #477 | C22 | semidirect |
| 22. #462 | C22 | semidirect |
| 76. C22×C4 | Q16 | semidirect |
| 121. C2×C4 | C2×Q16 | semidirect |
| 147. C2 | #3249 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#533 | 2 |
| #3249 | 2 |
| C2×#477 | 2 |
| C2×#467 | 2 |
| C2×#462 | 2 |
| C22×C4⋊C8 | 2 |