Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
203 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 203 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #476 |
| commutator | C2×C8 | C22×C4 |
| Frattini, cosocle | C22×C8 | C23 |
| socle | C2 | #1864 |
| prime radical | C2×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ C2×C4×C8 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2155 | C2 | semidirect |
| 5. #1945 | C2 | semidirect |
| 6. #1384 | C2 | semidirect |
| 7. #1376 | C2 | semidirect |
| 24. #360 | C4 | semidirect |
| 48. M32 | C2×C4 | semidirect |
| 55. #106 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#135 | 2 |
| #2155 | 2 |
| #2148 | 2 |
| #2145 | 2 |
| #1945 | 2 |
| #1384 | 2 |
| #1376 | 2 |