Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
298 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 86 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 | C2×D4×C61 | D8 |
| 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×#2241 | C2 | semidirect |
| 3. C61×#2209 | C2 | semidirect |
| 5. C61×#1365 | C2 | semidirect |
| 6. C61×#1332 | C2 | semidirect |
| 92. D4×C61 | Q32 | semidirect |
| 109. #12346 | C61 | direct (N × H) |
| 125. #2241 | C2×C61 | semidirect |
| 126. #2209 | C2×C61 | semidirect |
| 128. #1365 | C2×C61 | semidirect |
| 129. #1332 | C2×C61 | semidirect |
| 152. C61 | #12346 | direct (N × H) |
| 220. D4 | Q32×C61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#3338 | 2 |
| C61×#2241 | 2 |
| C61×#2209 | 2 |
| C61×#1669 | 2 |
| C61×#1365 | 2 |
| C61×#1332 | 2 |
| C61×D4⋊C16 | 2 |
| #12346 | 61 |