Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
4449 conjugacy classes of subgroups.
The subgroup lattice has 511 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#106 |
| commutator | C2×C8 | C24×C4 |
| Frattini, cosocle | C22×C8 | C25 |
| socle | C22 | C23×#106 |
| prime radical | C25 | C2×SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C22×#117 ◁ C22×#405 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #494153 | C2 | semidirect |
| 6. #494152 | C2 | semidirect |
| 19. #33324 | C4 | semidirect |
| 21. C2×#2108 | C4 | semidirect |
| 31. #12904 | C22 | semidirect |
| 32. #12903 | C22 | semidirect |
| 84. #2108 | C2×C4 | semidirect |
| 85. C4×M32 | C2×C4 | semidirect |
| 87. C2×#346 | C2×C4 | semidirect |
| 88. C2×C4×C16 | C2×C4 | semidirect |
| 139. C2×M32 | C4⋊C4 | semidirect |
| 140. C2×M32 | C4⋊C4 | semidirect |
| 148. C22×C16 | C4⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#2155 | 2 |
| C2×#33324 | 2 |
| C2×#20807 | 2 |
| #6371130 | 2 |
| #494153 | 2 |
| #494152 | 2 |