Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
310 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 105 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 | #2420 |
| commutator, Frattini, cosocle | C22×C4 | C24 |
| prime radical | C2×#41 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2950 | C2 | semidirect |
| 3. #2082 | C2 | semidirect |
| 5. #1979 | C2 | semidirect |
| 6. #1953 | C2 | semidirect |
| 8. #1833 | C2 | semidirect |
| 9. #1830 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#473 | 2 |
| #2950 | 2 |
| #2082 | 2 |
| #2049 | 2 |
| #1979 | 2 |
| #1953 | 2 |
| #1905 | 2 |
| #1833 | 2 |
| #1830 | 2 |
| #1814 | 2 |
| #1757 | 2 |