Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
383 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 383 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C43 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#475 | 2 |
| C2×#462 | 2 |
| #2862 | 2 |
| #2295 | 2 |
| #2066 | 2 |
| #2056 | 2 |
| #1988 | 2 |
| #1981 | 2 |
| #1842 | 2 |