Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
994 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 382 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | #127 |
| commutator, Frattini, cosocle | C42 | C24×C41 |
| prime radical | C2×#127×C41 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C2×C42×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C41×#498 | C2 | semidirect |
| 3. C41×#1705 | C2 | direct (N × H) |
| 4. C2×C82×C41 | C2 | semidirect |
| 9. C41×#498 | C22 | semidirect |
| 14. C82×C41 | C22 | semidirect |
| 40. C2×C8×C41 | SD16 | semidirect |
| 58. C8×C41 | C2×SD16 | semidirect |
| 59. C2×#1705 | C41 | direct (N × H) |
| 67. C2×#498 | C2×C41 | semidirect |
| 69. #1705 | C2×C41 | direct (N × H) |
| 70. C2×C82 | C2×C41 | semidirect |
| 72. C2×C41 | #1705 | direct (N × H) |
| 78. #498 | C22×C41 | semidirect |
| 83. C82 | C22×C41 | semidirect |
| 84. C41 | C2×#1705 | direct (N × H) |
| 110. C2×C8 | SD16×C41 | semidirect |
| 128. C8 | C2×SD16×C41 | semidirect |
| 137. C2 | C41×#1705 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C41×#498 | 2 |
| C2×C41×#492 | 2 |
| C41×#1705 | 2 |
| C2×C82×C41 | 2 |
| C2×#1705 | 41 |