Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
329 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 329 conjugacy classes of subgroups — too many to draw. Only its 117 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×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24 |
| prime radical | C23 | C2×#41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ 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 |
|---|---|
| #3078 | 2 |
| #2960 | 2 |
| C2×C4×Q16 | 2 |
| #2089 | 2 |
| #2047 | 2 |
| #1930 | 2 |
| #1837 | 2 |
| #1801 | 2 |