Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
8414 conjugacy classes of subgroups; only the 6878 normal subgroups are shown.
This group has 8414 conjugacy classes of subgroups — too many to draw. Only its 6878 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C25×C11 | C23 |
| commutator, Frattini, cosocle | C22 | C26×C11 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C25×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C11×#125 | C2 | direct (N × H) |
| 8. C2×C11×#125 | C22 | direct (N × H) |
| 19. C11×#125 | C23 | direct (N × H) |
| 23. C23×#125 | C11 | direct (N × H) |
| 36. C22×#125 | C2×C11 | direct (N × H) |
| 40. C23×C11 | #125 | direct (N × H) |
| 53. C2×#125 | C22×C11 | direct (N × H) |
| 57. C22×C11 | C2×#125 | direct (N × H) |
| 71. #125 | C23×C11 | direct (N × H) |
| 75. C2×C11 | C22×#125 | direct (N × H) |
| 90. C11 | C23×#125 | direct (N × H) |
| 91. C23 | C11×#125 | direct (N × H) |
| 101. C22 | C2×C11×#125 | direct (N × H) |
| 108. C2 | C22×C11×#125 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C11×#125 | 2 |
| C23×C11×C4⋊C4 | 2 |
| C23×C42×C11 | 2 |
| C23×#125 | 11 |