Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
428 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4 |
| Frattini, cosocle | C23×C4 | C23 |
| prime radical | #2856 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #1797 | C2 | semidirect |
| 3. C2×#327 | C2 | semidirect |
| 4. C4×#95 | C2 | semidirect |
| 5. C2×#127 | C4 | semidirect |
| 15. #390 | C4 | semidirect |
| 16. #384 | C4 | semidirect |
| 54. #95 | D4 | semidirect |
| 198. C4 | #327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2856 | 2 |
| #1797 | 2 |
| C2×#327 | 2 |
| C4×#95 | 2 |