Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
395 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 395 conjugacy classes of subgroups — too many to draw. Only its 189 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 | C22×D4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| socle | C22 | C22×C4⋊C4 |
| prime radical | C22×D4 | Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C4×D4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #1950 | C2 | semidirect |
| 4. #1855 | C2 | semidirect |
| 5. #1837 | C2 | semidirect |
| 6. #1811 | C2 | semidirect |
| 7. C4×#108 | C2 | semidirect |
| 8. #1738 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×M16 | 2 |
| C2×#436 | 2 |
| #1950 | 2 |
| #1855 | 2 |
| #1837 | 2 |
| #1811 | 2 |
| C4×#108 | 2 |
| #1738 | 2 |