Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
6049 conjugacy classes of subgroups.
The subgroup lattice has 586 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×C42 |
| commutator | C4 | C22×C43 |
| Frattini, cosocle | C22×C8 | C25 |
| socle | C23 | C22×#97 |
| prime radical | C25 | C2×M16 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #492832 | C2 | direct (N × H) |
| 6. C2×#12541 | C2 | semidirect |
| 7. C2×C4×#347 | C2 | semidirect |
| 16. C2×#2110 | C4 | semidirect |
| 18. C22×#347 | C4 | semidirect |
| 23. #33324 | C4 | semidirect |
| 25. C2×#2108 | C4 | semidirect |
| 33. #12541 | C22 | semidirect |
| 34. C4×#347 | C22 | semidirect |
| 86. #2110 | C2×C4 | semidirect |
| 89. C2×#347 | C2×C4 | semidirect |
| 90. C2×#347 | C2×C4 | semidirect |
| 94. #2108 | C2×C4 | semidirect |
| 95. C4×M32 | C2×C4 | semidirect |
| 97. C2×#346 | C2×C4 | semidirect |
| 98. C2×C4×C16 | C2×C4 | semidirect |
| 158. C2×M32 | C42 | semidirect |
| 159. C2×M32 | C42 | semidirect |
| 167. C22×C16 | C42 | semidirect |
| 224. #347 | C22×C4 | semidirect |
| 225. #346 | C22×C4 | semidirect |
| 226. C4×C16 | C22×C4 | semidirect |
| 345. M32 | C2×C42 | semidirect |
| 349. C2×C16 | C2×C42 | semidirect |
| 582. C2 | #492832 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#2110 | 2 |
| C23×#347 | 2 |
| C2×#33324 | 2 |
| C2×#20331 | 2 |
| #492832 | 2 |
| C2×#12541 | 2 |
| C2×C4×#347 | 2 |