Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
704005 conjugacy classes of subgroups; only the 419957 normal subgroups are shown.
This group has 704005 conjugacy classes of subgroups — too many to draw. Only its 419957 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 |
| 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×H(3,𝔽4) | C2 | direct (N × H) |
| 2. C24×#124 | C2 | semidirect |
| 3. C24×#120 | C2 | semidirect |
| 4. C28 | C22 | semidirect |
| 5. C25×Q8 | C22 | semidirect |
| 7. C22×H(3,𝔽4) | C22 | direct (N × H) |
| 8. C23×#124 | C22 | semidirect |
| 9. C23×#120 | C22 | semidirect |
| 10. C24×C22⋊C4 | C22 | semidirect |
| 11. C24×C42 | C22 | semidirect |
| 14. C27 | C23 | semidirect |
| 16. C24×Q8 | C23 | semidirect |
| 20. C2×H(3,𝔽4) | C23 | direct (N × H) |
| 21. C22×#124 | C23 | semidirect |
| 22. C22×#120 | C23 | semidirect |
| 23. C23×C22⋊C4 | C23 | semidirect |
| 24. C23×C42 | C23 | semidirect |
| 30. C26 | C24 | semidirect |
| 32. C23×Q8 | C24 | semidirect |
| 37. H(3,𝔽4) | C24 | direct (N × H) |
| 38. C2×#124 | C24 | semidirect |
| 39. C2×#120 | C24 | semidirect |
| 40. C22×C22⋊C4 | C24 | semidirect |
| 41. C22×C42 | C24 | semidirect |
| 49. C25 | C25 | semidirect |
| 51. C22×Q8 | C25 | semidirect |
| 56. #124 | C25 | semidirect |
| 57. #120 | C25 | semidirect |
| 58. C2×C22⋊C4 | C25 | semidirect |
| 59. C2×C42 | C25 | semidirect |
| 64. C24 | H(3,𝔽4) | direct (N × H) |
| 68. C24 | C26 | semidirect |
| 70. C2×Q8 | C26 | semidirect |
| 75. C22⋊C4 | C26 | semidirect |
| 76. C42 | C26 | semidirect |
| 81. C23 | C2×H(3,𝔽4) | direct (N × H) |
| 92. C22 | C22×H(3,𝔽4) | direct (N × H) |
| 97. C2 | C23×H(3,𝔽4) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×H(3,𝔽4) | 2 |
| C24×#124 | 2 |
| C24×#120 | 2 |