Finite Group DatabasebetaFinite Group DatabasebetaOrder 1984.
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×C31 | C2×D4 |
| commutator | C4 | C22×C4×C31 |
| Frattini, cosocle | C2×C4 | C23×C31 |
| prime radical | C2×#41×C31 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C22×C4×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×M16×C31 | C2 | semidirect |
| 3. C2×C4⋊C4×C31 | C2 | semidirect |
| 4. C31×#103 | C2 | semidirect |
| 5. C31×#102 | C2 | semidirect |
| 7. #41×C31 | C4 | semidirect |
| 21. Q8×C31 | C2×C4 | semidirect |
| 24. D4×C31 | C2×C4 | semidirect |
| 46. #417 | C31 | direct (N × H) |
| 53. C2×M16 | C2×C31 | semidirect |
| 54. C2×C4⋊C4 | C2×C31 | semidirect |
| 55. #103 | C2×C31 | semidirect |
| 56. #102 | C2×C31 | semidirect |
| 57. C31 | #417 | direct (N × H) |
| 59. #41 | C4×C31 | semidirect |
| 73. Q8 | C2×C4×C31 | semidirect |
| 76. D4 | C2×C4×C31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×C31 | 2 |
| C2×M16×C31 | 2 |
| C2×C4⋊C4×C31 | 2 |
| C31×#103 | 2 |
| C31×#102 | 2 |
| #417 | 31 |