Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
599 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 599 conjugacy classes of subgroups — too many to draw. Only its 183 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 | C2×#99 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C2×Q8 | C24 |
| prime radical | C22×#41 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C23×Q8 ◁ G | |
| LECS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#101 | C2 | semidirect |
| 3. #2133 | C2 | direct (N × H) |
| 4. C2×#356 | C2 | semidirect |
| 5. C2×#355 | C2 | semidirect |
| 22. C2×#101 | C22 | semidirect |
| 23. #356 | C22 | semidirect |
| 24. #355 | C22 | semidirect |
| 218. C2 | #2133 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#536 | 2 |
| C22×#101 | 2 |
| #2133 | 2 |
| C2×#356 | 2 |
| C2×#355 | 2 |