Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
203 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 203 conjugacy classes of subgroups — too many to draw. Only its 89 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×C22⋊C4 |
| commutator | C2×C4 | C2×C42 |
| Frattini, cosocle | C2×C42 | C23 |
| socle | C22 | C4×C22⋊C4 |
| prime radical | C23 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C4×C8 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. #446 | C4 | semidirect |
| 12. C8×Q8 | C4 | semidirect |
| 23. #333 | C4 | semidirect |
| 24. #332 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2960 | 2 |
| C8×C4⋊C4 | 2 |
| #1542 | 2 |
| #1503 | 2 |
| #1452 | 2 |
| #1303 | 2 |
| #1301 | 2 |