Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
816 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 238 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C61 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| prime radical | C22×D4×C61 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C43×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C61×#2868 | C2 | semidirect |
| 3. C61×#2043 | C2 | semidirect |
| 5. C61×#1839 | C2 | semidirect |
| 53. C42×C61 | SD16 | semidirect |
| 73. #32800 | C61 | direct (N × H) |
| 85. #2868 | C2×C61 | semidirect |
| 87. #2043 | C2×C61 | semidirect |
| 89. #1839 | C2×C61 | semidirect |
| 105. C61 | #32800 | direct (N × H) |
| 142. C42 | SD16×C61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#2868 | 2 |
| C61×#2860 | 2 |
| C61×#2043 | 2 |
| C61×#2013 | 2 |
| C61×#1839 | 2 |
| #32800 | 61 |