Finite Group DatabasebetaFinite Group DatabasebetaOrder 32192.
162 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C503 | C2×D4 |
| commutator | C4 | C22×C4×C503 |
| Frattini, cosocle | C2×C4 | C23×C503 |
| prime radical | C2×#41×C503 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C503 ◁ C22×C4×C503 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×M16×C503 | C2 | semidirect |
| 3. C2×C4⋊C4×C503 | C2 | semidirect |
| 4. #103×C503 | C2 | semidirect |
| 5. #102×C503 | C2 | semidirect |
| 7. #41×C503 | C4 | semidirect |
| 21. Q8×C503 | C2×C4 | semidirect |
| 24. D4×C503 | C2×C4 | semidirect |
| 51. C503 | #417 | direct (N × H) |
| 52. #417 | C503 | direct (N × H) |
| 54. C2×M16 | C2×C503 | semidirect |
| 55. C2×C4⋊C4 | C2×C503 | semidirect |
| 56. #103 | C2×C503 | semidirect |
| 57. #102 | C2×C503 | semidirect |
| 59. #41 | C4×C503 | semidirect |
| 73. Q8 | C2×C4×C503 | semidirect |
| 76. D4 | C2×C4×C503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×C503 | 2 |
| C2×M16×C503 | 2 |
| C2×C4⋊C4×C503 | 2 |
| #103×C503 | 2 |
| #102×C503 | 2 |
| #417 | 503 |