Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
453 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 453 conjugacy classes of subgroups — too many to draw. Only its 195 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 | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | C22×D4 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ 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. #1949 | C2 | semidirect |
| 4. #1854 | C2 | semidirect |
| 5. #1853 | C2 | semidirect |
| 6. #1835 | C2 | semidirect |
| 7. #1809 | C2 | semidirect |
| 8. C4×#106 | C2 | semidirect |
| 9. #1736 | C2 | semidirect |
| 14. #436 | C4 | semidirect |
| 41. C2×M16 | C2×C4 | semidirect |
| 67. C4⋊C8 | C2×C4 | semidirect |
| 68. C22⋊C8 | C2×C4 | semidirect |
| 69. C4×C8 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#436 | 2 |
| #2352 | 2 |
| #1949 | 2 |
| #1854 | 2 |
| #1853 | 2 |
| #1835 | 2 |
| #1809 | 2 |
| C4×#106 | 2 |
| #1736 | 2 |