Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
367 conjugacy classes of subgroups; only the 265 normal subgroups are shown.
This group has 367 conjugacy classes of subgroups — too many to draw. Only its 265 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 | C4 | C23×C8 |
| Frattini, cosocle | C42 | C24 |
| socle | C22 | C22×C4⋊C4 |
| prime radical | C2×#41 | C2×C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C4×#41 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #1565 | C2 | semidirect |
| 4. #1564 | C2 | semidirect |
| 5. C2×#335 | C2 | semidirect |
| 23. #131 | C8 | semidirect |
| 53. M16 | C2×C8 | semidirect |
| 58. C2×C8 | C2×C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2988 | 2 |
| C4×#131 | 2 |
| #1565 | 2 |
| #1564 | 2 |
| C2×#335 | 2 |