Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
308 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3058 | C2 | semidirect |
| 2. #2234 | C2 | semidirect |
| 3. #2218 | C2 | semidirect |
| 4. #2215 | C2 | semidirect |
| 5. #2184 | C2 | semidirect |
| 6. #2113 | C2 | semidirect |
| 7. C22×D8 | C22 | semidirect |
| 12. C2×M32 | C22 | semidirect |
| 13. C22×C16 | C22 | semidirect |
| 17. #466 | C22 | semidirect |
| 18. #427 | C22 | semidirect |
| 20. #367 | C22 | semidirect |
| 21. #366 | C22 | semidirect |
| 22. #357 | C22 | semidirect |
| 23. #357 | C22 | semidirect |
| 24. C22⋊C16 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3058 | 2 |
| #2234 | 2 |
| #2218 | 2 |
| #2215 | 2 |
| #2184 | 2 |
| #2113 | 2 |