Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
208 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 59 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 | C2×#102 |
| commutator | C2×C8 | C22×C4 |
| Frattini, cosocle | C22×C8 | C23 |
| prime radical | #3050 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2112 | C2 | semidirect |
| 3. #1808 | C2 | semidirect |
| 4. #1348 | C2 | semidirect |
| 5. #1347 | C2 | semidirect |
| 6. C2×#135 | C4 | semidirect |
| 10. #467 | C4 | semidirect |
| 12. #466 | C4 | semidirect |
| 16. #427 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3050 | 2 |
| #2112 | 2 |
| #1808 | 2 |
| #1348 | 2 |
| #1347 | 2 |