Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
689 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 689 conjugacy classes of subgroups — too many to draw. Only its 209 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×C22⋊C4 |
| commutator | C23 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | C22×D4 | C2×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ 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. C22×#101 | C2 | semidirect |
| 4. #1966 | C2 | semidirect |
| 5. #1901 | C2 | semidirect |
| 6. #1801 | C2 | semidirect |
| 7. #1784 | C2 | semidirect |
| 8. C4×#101 | C2 | semidirect |
| 85. #101 | D4 | direct (N × H) |
| 167. D4 | #101 | direct (N × H) |
| 206. C22 | C2×#101 | semidirect |
| 216. C4 | C2×#101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Q8 | 2 |
| D4×M16 | 2 |
| C22×#101 | 2 |
| #1966 | 2 |
| #1901 | 2 |
| #1801 | 2 |
| #1784 | 2 |
| C4×#101 | 2 |