Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
3843 conjugacy classes of subgroups.
The subgroup lattice has 316 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×C42 |
| commutator | C4 | C23×C4×C8 |
| Frattini, cosocle | C4×C8 | C25 |
| socle | C22 | C23×#97 |
| prime radical | C22×#41 | C42 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C42 ◁ G | |
| LECS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #479910 | C2 | semidirect |
| 5. #479908 | C2 | semidirect |
| 6. C2×#11404 | C2 | semidirect |
| 24. #11406 | C22 | semidirect |
| 25. #11405 | C22 | semidirect |
| 28. #11404 | C22 | semidirect |
| 29. C2×#1313 | C22 | semidirect |
| 34. #3407 | C8 | semidirect |
| 98. #504 | C2×C8 | semidirect |
| 100. C2×M32 | C2×C8 | semidirect |
| 194. M32 | C22×C8 | semidirect |
| 196. C2×C16 | C22×C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3407 | 2 |
| C2×#17316 | 2 |
| #479910 | 2 |
| #479908 | 2 |
| C2×#11404 | 2 |