Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
505877 conjugacy classes of subgroups; only the 108373 normal subgroups are shown.
This group has 505877 conjugacy classes of subgroups — too many to draw. Only its 108373 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 | D4 |
| commutator | C4 | C26×C4 |
| Frattini, cosocle | C2×C4 | C27 |
| prime radical | C26×D4 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C27 ◁ C26×C4 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C26×C8 | C2 | semidirect |
| 3. C25×C4⋊C4 | C2 | semidirect |
| 4. C24×#102 | C2 | direct (N × H) |
| 8. C25×D4 | C4 | semidirect |
| 13. C25×C8 | C22 | semidirect |
| 15. C24×C4⋊C4 | C22 | semidirect |
| 16. C23×#102 | C22 | direct (N × H) |
| 25. C24×D4 | C2×C4 | semidirect |
| 34. C24×C8 | C23 | semidirect |
| 36. C23×C4⋊C4 | C23 | semidirect |
| 37. C22×#102 | C23 | direct (N × H) |
| 50. C23×D4 | C22×C4 | semidirect |
| 60. C23×C8 | C24 | semidirect |
| 62. C22×C4⋊C4 | C24 | semidirect |
| 63. C2×#102 | C24 | direct (N × H) |
| 69. C25 | #102 | direct (N × H) |
| 77. C22×D4 | C23×C4 | semidirect |
| 87. C22×C8 | C25 | semidirect |
| 89. C2×C4⋊C4 | C25 | semidirect |
| 90. #102 | C25 | direct (N × H) |
| 96. C24 | C2×#102 | direct (N × H) |
| 104. C2×D4 | C24×C4 | semidirect |
| 114. C2×C8 | C26 | semidirect |
| 116. C4⋊C4 | C26 | semidirect |
| 122. C23 | C22×#102 | direct (N × H) |
| 129. D4 | C25×C4 | semidirect |
| 142. C22 | C23×#102 | direct (N × H) |
| 152. C2 | C24×#102 | 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 |
| C26×C8 | 2 |
| C25×C4⋊C4 | 2 |
| C24×#102 | 2 |