Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
Only the 14008 normal subgroups are shown; non-normal subgroups are omitted.
The subgroup lattice has 248 nodes (normal subgroups only) — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C22×#120 |
| commutator | C23×C4 | C24×C4 |
| Frattini, cosocle | C24×C4 | C25 |
| prime radical | C25×2−1+4 | C2 |
| LCS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C26×C4 ◁ G | |
| LECS | G ▷ C24×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72267485 | C2 | semidirect |
| 2. #72267484 | C2 | semidirect |
| 3. C2×#392114 | C2 | semidirect |
| 5. C2×#392129 | C2 | semidirect |
| 6. C2×#392123 | C2 | semidirect |
| 7. C24×2−1+4 | C4 | semidirect |
| 11. C22×#1793 | C22 | semidirect |
| 12. C22×#1789 | C22 | semidirect |
| 13. C2×#20601 | C22 | semidirect |
| 14. C22×#1784 | C22 | semidirect |
| 17. C2×#13922 | C22 | semidirect |
| 34. C23×#104 | C23 | semidirect |
| 35. C22×#417 | C23 | semidirect |
| 36. C23×#101 | C23 | semidirect |
| 38. C22×#391 | C23 | semidirect |
| 42. C22×2−1+4 | C22⋊C4 | semidirect |
| 129. 2−1+4 | #379 | semidirect |
| 167. C24 | #1793 | semidirect |
| 230. C22 | #392129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72267485 | 2 |
| #72267484 | 2 |
| C2×#392114 | 2 |
| C25×2−1+4 | 2 |
| C2×#392129 | 2 |
| C2×#392123 | 2 |