Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
503 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 503 conjugacy classes of subgroups — too many to draw. Only its 187 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 | C22×D4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| socle | C22 | C2×C4×D4 |
| prime radical | #3150 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C4×C8 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#444 | C2 | semidirect |
| 3. #2931 | C2 | semidirect |
| 4. #1974 | C2 | semidirect |
| 5. #1963 | C2 | semidirect |
| 6. #1849 | C2 | semidirect |
| 7. #1726 | C2 | semidirect |
| 11. #497 | C4 | semidirect |
| 12. #496 | C4 | semidirect |
| 50. #97 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3150 | 2 |
| C2×#444 | 2 |
| #2931 | 2 |
| #1974 | 2 |
| #1963 | 2 |
| #1849 | 2 |
| #1726 | 2 |