Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
446 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 70 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 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×C22⋊C4 | C23×C61 |
| prime radical | C61×#1595 | C2 |
| LCS | G ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C23×C61 ◁ C2×C22⋊C4×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C61×#2826 | C2 | semidirect |
| 2. C61×#2044 | C2 | semidirect |
| 3. C61×#1613 | C2 | semidirect |
| 5. C61×#1352 | C2 | semidirect |
| 6. C61×#1343 | C2 | semidirect |
| 7. C61×#1326 | C2 | semidirect |
| 172. #12137 | C61 | direct (N × H) |
| 206. #2826 | C2×C61 | semidirect |
| 207. #2044 | C2×C61 | semidirect |
| 208. #1613 | C2×C61 | semidirect |
| 210. #1352 | C2×C61 | semidirect |
| 211. #1343 | C2×C61 | semidirect |
| 212. #1326 | C2×C61 | semidirect |
| 241. C61 | #12137 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#2826 | 2 |
| C61×#2044 | 2 |
| C61×#1613 | 2 |
| C61×#1595 | 2 |
| C61×#1352 | 2 |
| C61×#1343 | 2 |
| C61×#1326 | 2 |
| #12137 | 61 |