Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
789 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 789 conjugacy classes of subgroups — too many to draw. Only its 155 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 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#532 | C2 | semidirect |
| 2. C2×#493 | C2 | semidirect |
| 3. C2×#486 | C2 | semidirect |
| 4. #2856 | C2 | semidirect |
| 5. #1999 | C2 | semidirect |
| 6. #1990 | C2 | semidirect |
| 7. #1957 | C2 | semidirect |
| 8. #1879 | C2 | semidirect |
| 9. C4×C22⋊C8 | C2 | semidirect |
| 61. C4⋊Q8 | D4 | semidirect |
| 65. #127 | D4 | semidirect |
| 144. C22×C4 | D8 | semidirect |
| 157. C2×C8 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#532 | 2 |
| C2×#493 | 2 |
| C2×#486 | 2 |
| #2856 | 2 |
| #1999 | 2 |
| #1990 | 2 |
| #1957 | 2 |
| #1879 | 2 |
| C4×C22⋊C8 | 2 |