Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
7033 conjugacy classes of subgroups.
The subgroup lattice has 785 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 | C23×#41 | C2×C4 |
| 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 |
|---|---|---|
| 3. C22×#2110 | C2 | semidirect |
| 5. #492980 | C2 | semidirect |
| 6. #492979 | C2 | semidirect |
| 7. C2×#12547 | C2 | semidirect |
| 10. C2×#3407 | C4 | semidirect |
| 12. C22×#504 | C4 | semidirect |
| 13. C22×#504 | C4 | semidirect |
| 21. #33333 | C4 | semidirect |
| 22. #33333 | C4 | semidirect |
| 24. C2×#2113 | C4 | semidirect |
| 28. C2×#2110 | C22 | semidirect |
| 29. C22×#347 | C22 | semidirect |
| 35. #12616 | C22 | semidirect |
| 37. #12547 | C22 | semidirect |
| 38. C2×#1375 | C22 | semidirect |
| 61. C2×#504 | C2×C4 | semidirect |
| 62. C2×#504 | C2×C4 | semidirect |
| 74. C22×M32 | C2×C4 | semidirect |
| 75. C22×M32 | C2×C4 | semidirect |
| 88. C23×C16 | C2×C4 | semidirect |
| 108. #2113 | C2×C4 | semidirect |
| 109. #2113 | C2×C4 | semidirect |
| 110. #2112 | C2×C4 | semidirect |
| 112. C2×C22⋊C16 | C2×C4 | semidirect |
| 231. C2×M32 | C22⋊C4 | semidirect |
| 232. C2×M32 | C22⋊C4 | semidirect |
| 250. C22×C16 | C22⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3407 | 2 |
| C2×#33333 | 2 |
| C22×#2110 | 2 |
| #6369808 | 2 |
| #492980 | 2 |
| #492979 | 2 |
| C2×#12547 | 2 |