Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
196 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 55 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 | #1519 |
| commutator | C2×C8 | C22×C4 |
| Frattini, cosocle | C2×M16 | C23 |
| prime radical | #3058 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×#131 ◁ G | |
| LECS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2115 | C2 | semidirect |
| 3. #1813 | C2 | semidirect |
| 4. #1341 | C2 | semidirect |
| 18. #349 | C22 | semidirect |
| 19. #338 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3058 | 2 |
| #2115 | 2 |
| #1813 | 2 |
| #1341 | 2 |