Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
145 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 145 conjugacy classes of subgroups — too many to draw. Only its 43 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 | #459 |
| commutator, Frattini, cosocle | C4×C8 | C23 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ C82 ◁ G | |
| LECS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2206 | C2 | semidirect |
| 2. #1712 | C2 | semidirect |
| 3. C8×D8 | C2 | semidirect |
| 4. #1370 | C2 | semidirect |
| 5. #1361 | C2 | semidirect |
| 47. D8 | D8 | semidirect |
| 78. C8 | D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2206 | 2 |
| #1712 | 2 |
| C8×D8 | 2 |
| #1370 | 2 |
| #1361 | 2 |