Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
458 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 90 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×C61 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C61 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C42×C61 ◁ C8×D4×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D4×D8×C61 | C2 | semidirect |
| 2. C61×#2246 | C2 | semidirect |
| 3. C61×#2206 | C2 | semidirect |
| 4. C61×#1667 | C2 | semidirect |
| 5. C61×#1361 | C2 | semidirect |
| 6. C61×#1331 | C2 | semidirect |
| 7. C61×D4⋊C16 | C2 | semidirect |
| 13. C61×#493 | C22 | semidirect |
| 20. C61×C4⋊C16 | C22 | semidirect |
| 22. C4×C16×C61 | C22 | semidirect |
| 23. C61×#335 | C22 | semidirect |
| 82. D8×C61 | D8 | semidirect |
| 119. D4×C61 | D16 | semidirect |
| 134. #12316 | C61 | direct (N × H) |
| 156. D4×D8 | C2×C61 | semidirect |
| 157. #2246 | C2×C61 | semidirect |
| 158. #2206 | C2×C61 | semidirect |
| 159. #1667 | C2×C61 | semidirect |
| 160. #1361 | C2×C61 | semidirect |
| 161. #1331 | C2×C61 | semidirect |
| 162. D4⋊C16 | C2×C61 | semidirect |
| 175. #493 | C22×C61 | semidirect |
| 182. C4⋊C16 | C22×C61 | semidirect |
| 184. C4×C16 | C22×C61 | semidirect |
| 185. #335 | C22×C61 | semidirect |
| 187. C61 | #12316 | direct (N × H) |
| 245. D8 | D8×C61 | semidirect |
| 282. D4 | D16×C61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D8×C61 | 2 |
| C61×#2246 | 2 |
| C61×#2206 | 2 |
| C61×#1667 | 2 |
| C61×#1361 | 2 |
| C61×#1331 | 2 |
| C61×D4⋊C16 | 2 |
| #12316 | 61 |