Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
588 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | C22×#99 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C2×Q8 | C24 |
| prime radical | #3499 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×D4 ◁ C2×2−1+4 ◁ G | |
| LECS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2889 | C2 | semidirect |
| 3. #2135 | C2 | semidirect |
| 4. #2133 | C2 | semidirect |
| 5. #2132 | C2 | semidirect |
| 6. C2×#356 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3499 | 2 |
| #2889 | 2 |
| #2135 | 2 |
| #2133 | 2 |
| #2132 | 2 |
| C2×#356 | 2 |