Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
823 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 823 conjugacy classes of subgroups — too many to draw. Only its 211 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 | C23 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| socle | C22 | C22×C22⋊C4 |
| prime radical | C23×D4 | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2920 | C2 | semidirect |
| 3. #1466 | C2 | semidirect |
| 4. #1462 | C2 | semidirect |
| 5. #1460 | C2 | semidirect |
| 20. #432 | C22 | semidirect |
| 22. #431 | C22 | semidirect |
| 26. #323 | C22 | semidirect |
| 88. C2×D4 | M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D4 | 2 |
| #2920 | 2 |
| #1466 | 2 |
| #1462 | 2 |
| #1460 | 2 |