Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1287 conjugacy classes of subgroups; only the 311 normal subgroups are shown.
This group has 1287 conjugacy classes of subgroups — too many to draw. Only its 311 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C23 |
| commutator | C23 | C23×C4 |
| Frattini, socle, cosocle | C24 | C24 |
| prime radical | C23×D4 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×C4⋊C4 | C2 | semidirect |
| 3. C2×C4×C22⋊C4 | C2 | semidirect |
| 4. C2×#376 | C2 | semidirect |
| 5. #1445 | C2 | semidirect |
| 6. #1439 | C2 | semidirect |
| 12. C2×C4×D4 | C4 | semidirect |
| 62. C2×C42 | D4 | semidirect |
| 119. C42 | C22⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D4 | 2 |
| C2×C4×C4⋊C4 | 2 |
| C2×C4×C22⋊C4 | 2 |
| C2×#376 | 2 |
| #1445 | 2 |
| #1439 | 2 |
| #1438 | 2 |