Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
442 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 442 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 |
| prime radical | D4×D8×C61 | C2 |
| 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 |
|---|---|---|
| 2. C61×#2248 | C2 | semidirect |
| 3. C61×#2208 | C2 | semidirect |
| 4. C61×#1669 | C2 | semidirect |
| 5. C61×#1361 | C2 | semidirect |
| 6. C61×#1331 | C2 | semidirect |
| 7. C61×D4⋊C16 | C2 | semidirect |
| 12. C61×#494 | C22 | semidirect |
| 20. C61×C4⋊C16 | C22 | semidirect |
| 22. C4×C16×C61 | C22 | semidirect |
| 23. C61×#335 | C22 | semidirect |
| 114. D4×C61 | SD32 | semidirect |
| 130. #12320 | C61 | direct (N × H) |
| 151. #2248 | C2×C61 | semidirect |
| 152. #2208 | C2×C61 | semidirect |
| 153. #1669 | C2×C61 | semidirect |
| 154. #1361 | C2×C61 | semidirect |
| 155. #1331 | C2×C61 | semidirect |
| 156. D4⋊C16 | C2×C61 | semidirect |
| 167. #494 | C22×C61 | semidirect |
| 175. C4⋊C16 | C22×C61 | semidirect |
| 177. C4×C16 | C22×C61 | semidirect |
| 178. #335 | C22×C61 | semidirect |
| 180. C61 | #12320 | direct (N × H) |
| 270. D4 | SD32×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×#2248 | 2 |
| C61×#2208 | 2 |
| C61×#1669 | 2 |
| C61×#1361 | 2 |
| C61×#1331 | 2 |
| C61×D4⋊C16 | 2 |
| #12320 | 61 |