Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
743 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 743 conjugacy classes of subgroups — too many to draw. Only its 191 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 | C2×#525 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#407 | C2 | semidirect |
| 3. #2280 | C2 | semidirect |
| 4. #1895 | C2 | semidirect |
| 5. #1894 | C2 | semidirect |
| 6. #1875 | C2 | semidirect |
| 7. #1873 | C2 | semidirect |
| 8. #1825 | C2 | semidirect |
| 9. #1788 | C2 | semidirect |
| 14. #525 | C4 | semidirect |
| 25. C2×#103 | C22 | semidirect |
| 26. C2×#102 | C22 | semidirect |
| 36. #340 | C22 | semidirect |
| 37. #340 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#525 | 2 |
| C2×#407 | 2 |
| #2280 | 2 |
| #1895 | 2 |
| #1894 | 2 |
| #1875 | 2 |
| #1873 | 2 |
| #1825 | 2 |
| #1788 | 2 |