Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
4273 conjugacy classes of subgroups.
The subgroup lattice has 658 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22×C42 |
| commutator | C2×C4 | C23×C42 |
| Frattini, cosocle | C22×C8 | C25 |
| socle | C22 | C23×#97 |
| prime radical | C25 | C2×M16 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×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. #493130 | C2 | semidirect |
| 6. #493129 | C2 | semidirect |
| 15. #33397 | C4 | semidirect |
| 16. #33397 | C4 | semidirect |
| 18. C2×#2151 | C4 | semidirect |
| 24. #33324 | C4 | semidirect |
| 26. C2×#2108 | C4 | semidirect |
| 27. C2×#2108 | C4 | semidirect |
| 34. #12666 | C22 | semidirect |
| 94. #2151 | C2×C4 | semidirect |
| 95. #2151 | C2×C4 | semidirect |
| 96. #2150 | C2×C4 | semidirect |
| 98. C2×C4⋊C16 | C2×C4 | semidirect |
| 103. #2108 | C2×C4 | semidirect |
| 104. #2108 | C2×C4 | semidirect |
| 105. C4×M32 | C2×C4 | semidirect |
| 107. C2×#346 | C2×C4 | semidirect |
| 108. C2×C4×C16 | C2×C4 | semidirect |
| 182. C2×M32 | C4⋊C4 | semidirect |
| 183. C2×M32 | C4⋊C4 | semidirect |
| 200. C22×C16 | C4⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#33397 | 2 |
| C22×#2110 | 2 |
| C2×#33324 | 2 |
| #6369898 | 2 |
| #493130 | 2 |
| #493129 | 2 |
| C2×#12547 | 2 |