Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
238 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 99 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 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24 |
| prime radical | #3339 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #3336 | C2 | semidirect |
| 3. #2253 | C2 | semidirect |
| 4. #2237 | C2 | semidirect |
| 5. #2235 | C2 | semidirect |
| 6. #2234 | C2 | semidirect |
| 7. #2233 | C2 | semidirect |
| 8. #2229 | C2 | semidirect |
| 9. #2228 | C2 | semidirect |
| 10. #2220 | C2 | semidirect |
| 11. #2220 | C2 | semidirect |
| 12. C4×SD32 | C2 | semidirect |
| 13. #2169 | C2 | semidirect |
| 14. #2159 | C2 | semidirect |
| 15. #2159 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3339 | 2 |
| #3336 | 2 |
| #2253 | 2 |
| #2237 | 2 |
| #2235 | 2 |
| #2234 | 2 |
| #2233 | 2 |
| #2229 | 2 |
| #2228 | 2 |
| #2220 | 2 |
| C4×SD32 | 2 |
| #2169 | 2 |
| #2159 | 2 |