Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
622357 conjugacy classes of subgroups; only the 446037 normal subgroups are shown.
This group has 622357 conjugacy classes of subgroups — too many to draw. Only its 446037 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C26 | C24 |
| commutator, Frattini, cosocle | C22 | C28 |
| prime radical | C28 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C26 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#543 | C2 | direct (N × H) |
| 2. C24×C22⋊Q8 | C2 | semidirect |
| 5. C25×Q8 | C22 | semidirect |
| 7. C22×#543 | C22 | direct (N × H) |
| 8. C23×C22⋊Q8 | C22 | semidirect |
| 9. C24×C4⋊C4 | C22 | semidirect |
| 13. C27 | Q8 | semidirect |
| 17. C24×Q8 | C23 | semidirect |
| 21. C2×#543 | C23 | direct (N × H) |
| 22. C22×C22⋊Q8 | C23 | semidirect |
| 23. C23×C4⋊C4 | C23 | semidirect |
| 30. C26 | C2×Q8 | semidirect |
| 35. C23×Q8 | C24 | semidirect |
| 40. #543 | C24 | direct (N × H) |
| 41. C2×C22⋊Q8 | C24 | semidirect |
| 42. C22×C4⋊C4 | C24 | semidirect |
| 51. C25 | C22×Q8 | semidirect |
| 57. C22×Q8 | C25 | semidirect |
| 62. C22⋊Q8 | C25 | semidirect |
| 63. C2×C4⋊C4 | C25 | semidirect |
| 70. C24 | #543 | direct (N × H) |
| 73. C24 | C23×Q8 | semidirect |
| 79. C2×Q8 | C26 | semidirect |
| 84. C4⋊C4 | C26 | semidirect |
| 90. C23 | C2×#543 | direct (N × H) |
| 93. C23 | C24×Q8 | semidirect |
| 104. C22 | C22×#543 | direct (N × H) |
| 111. C2 | C23×#543 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#543 | 2 |
| C24×C22⋊Q8 | 2 |
| C25×C22⋊C4 | 2 |