Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
155 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 155 conjugacy classes of subgroups — too many to draw. Only its 59 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 | #2058 |
| commutator, Frattini, cosocle | C22×C8 | C23 |
| prime radical | C23 | C2×SD16 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #405 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 40. M32 | Q8 | semidirect |
| 42. C2×C16 | Q8 | semidirect |
| 47. #108 | Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3163 | 2 |
| #2155 | 2 |
| C2×#365 | 2 |
| #1953 | 2 |
| #1389 | 2 |
| #1383 | 2 |
| #1378 | 2 |