Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
5077 conjugacy classes of subgroups.
The subgroup lattice has 390 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C2×#106 |
| commutator | C2×C8 | C24×C4 |
| Frattini, cosocle | C22×C8 | C25 |
| prime radical | C25 | C2×SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C23×C42 ◁ C23×C4×C8 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C2×#12903 | C2 | direct (N × H) |
| 16. C2×C4×M32 | C4 | semidirect |
| 18. C22×#346 | C4 | semidirect |
| 19. C22×C4×C16 | C4 | semidirect |
| 24. #12903 | C22 | direct (N × H) |
| 61. C4×M32 | C2×C4 | semidirect |
| 63. C2×#346 | C2×C4 | semidirect |
| 64. C2×C4×C16 | C2×C4 | semidirect |
| 104. C2×M32 | C4⋊C4 | semidirect |
| 109. C22×C16 | C4⋊C4 | semidirect |
| 142. #346 | C22×C4 | semidirect |
| 143. C4×C16 | C22×C4 | semidirect |
| 214. M32 | C2×C4⋊C4 | semidirect |
| 217. C2×C16 | C2×C4⋊C4 | semidirect |
| 247. C22×C4 | #365 | semidirect |
| 312. C16 | C22×C4⋊C4 | semidirect |
| 334. C2×C4 | C2×#365 | semidirect |
| 367. C22 | #12903 | direct (N × H) |
| 378. C4 | C22×#365 | semidirect |
| 386. C2 | C2×#12903 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#365 | 2 |
| C22×C4×M32 | 2 |
| C22×#1848 | 2 |
| C22×#1844 | 2 |
| C2×#12903 | 2 |