Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
417 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 417 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24 |
| socle | C22 | C22×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#508 | C2 | semidirect |
| 2. #3147 | C2 | semidirect |
| 3. #2249 | C2 | semidirect |
| 4. #2248 | C2 | semidirect |
| 5. #2247 | C2 | semidirect |
| 6. #2246 | C2 | semidirect |
| 7. C2×C4×C16 | C2 | semidirect |
| 45. C2×C16 | D4 | semidirect |
| 109. C4 | #508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#508 | 2 |
| #3147 | 2 |
| #2249 | 2 |
| #2248 | 2 |
| #2247 | 2 |
| #2246 | 2 |
| C2×C4×C16 | 2 |