Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
1138677 conjugacy classes of subgroups; only the 469973 normal subgroups are shown.
This group has 1138677 conjugacy classes of subgroups — too many to draw. Only its 469973 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C27 | C23 |
| commutator, Frattini, cosocle | C22 | C28 |
| prime radical | C26×D4 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C27 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C27×C4 | C2 | semidirect |
| 3. C24×#123 | C2 | direct (N × H) |
| 4. C25×C4⋊C4 | C2 | semidirect |
| 5. C25×C22⋊C4 | C2 | semidirect |
| 6. C25×C22⋊C4 | C2 | semidirect |
| 15. C26×C4 | C22 | semidirect |
| 16. C23×#123 | C22 | direct (N × H) |
| 17. C24×C4⋊C4 | C22 | semidirect |
| 18. C24×C22⋊C4 | C22 | semidirect |
| 19. C24×C22⋊C4 | C22 | semidirect |
| 36. C25×C4 | C23 | semidirect |
| 37. C22×#123 | C23 | direct (N × H) |
| 38. C23×C4⋊C4 | C23 | semidirect |
| 39. C23×C22⋊C4 | C23 | semidirect |
| 40. C23×C22⋊C4 | C23 | semidirect |
| 61. C24×C4 | C24 | semidirect |
| 62. C2×#123 | C24 | direct (N × H) |
| 63. C22×C4⋊C4 | C24 | semidirect |
| 64. C22×C22⋊C4 | C24 | semidirect |
| 65. C22×C22⋊C4 | C24 | semidirect |
| 71. C25 | #123 | direct (N × H) |
| 87. C23×C4 | C25 | semidirect |
| 88. #123 | C25 | direct (N × H) |
| 89. C2×C4⋊C4 | C25 | semidirect |
| 90. C2×C22⋊C4 | C25 | semidirect |
| 91. C2×C22⋊C4 | C25 | semidirect |
| 97. C24 | C2×#123 | direct (N × H) |
| 113. C22×C4 | C26 | semidirect |
| 114. C4⋊C4 | C26 | semidirect |
| 115. C22⋊C4 | C26 | semidirect |
| 116. C22⋊C4 | C26 | semidirect |
| 122. C23 | C22×#123 | direct (N × H) |
| 142. C22 | C23×#123 | direct (N × H) |
| 152. C2 | C24×#123 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C26×D4 | 2 |
| C27×C4 | 2 |
| C24×#123 | 2 |
| C25×C4⋊C4 | 2 |
| C25×C22⋊C4 | 2 |