Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
7846 conjugacy classes of subgroups; only the 6958 normal subgroups are shown.
This group has 7846 conjugacy classes of subgroups — too many to draw. Only its 6958 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 | C24×C11 | C24 |
| commutator, Frattini, cosocle | C22 | C26×C11 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q82×C11 | C2 | direct (N × H) |
| 6. Q82×C11 | C22 | direct (N × H) |
| 12. C22×Q8×C11 | Q8 | direct (N × H) |
| 21. C22×Q82 | C11 | direct (N × H) |
| 24. C2×Q8×C11 | C2×Q8 | direct (N × H) |
| 33. C2×Q82 | C2×C11 | direct (N × H) |
| 40. Q8×C11 | C22×Q8 | direct (N × H) |
| 47. Q82 | C22×C11 | direct (N × H) |
| 52. C22×C11 | Q82 | direct (N × H) |
| 59. C22×Q8 | Q8×C11 | direct (N × H) |
| 68. C2×C11 | C2×Q82 | direct (N × H) |
| 73. C2×Q8 | C2×Q8×C11 | direct (N × H) |
| 82. C11 | C22×Q82 | direct (N × H) |
| 87. Q8 | C22×Q8×C11 | direct (N × H) |
| 92. C22 | Q82×C11 | direct (N × H) |
| 98. C2 | C2×Q82×C11 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q82×C11 | 2 |
| C22×C11×C4⋊Q8 | 2 |
| C22×C4×Q8×C11 | 2 |
| C22×Q82 | 11 |