Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
348 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | #418 |
| commutator | C2×C8 | C22×C4×C61 |
| Frattini, cosocle | C4×C8 | C23×C61 |
| socle | C2×C61 | #1490 |
| prime radical | C61×#575 | C4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ C2×C8×C61 ◁ C4×M16×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C61×#2165 | C2 | semidirect |
| 3. C61×#1453 | C2 | semidirect |
| 4. C61×#1336 | C2 | semidirect |
| 5. C61×#1335 | C2 | semidirect |
| 16. C61×#364 | C22 | semidirect |
| 20. C61×#322 | C22 | semidirect |
| 21. C82×C61 | C22 | semidirect |
| 108. #11670 | C61 | direct (N × H) |
| 121. #2165 | C2×C61 | semidirect |
| 122. #1453 | C2×C61 | semidirect |
| 123. #1336 | C2×C61 | semidirect |
| 124. #1335 | C2×C61 | semidirect |
| 139. #364 | C22×C61 | semidirect |
| 143. #322 | C22×C61 | semidirect |
| 144. C82 | C22×C61 | semidirect |
| 145. C61 | #11670 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#2956 | 2 |
| C61×#2165 | 2 |
| C61×#1453 | 2 |
| C61×#1336 | 2 |
| C61×#1335 | 2 |
| #11670 | 61 |