Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
286 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 112 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 | #120 |
| commutator | C2×C4 | C22×C4×C61 |
| Frattini, cosocle | C22×C4 | C23×C61 |
| prime radical | C2×#41×C61 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C22×C4×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C61×#428 | C2 | semidirect |
| 5. C61×#382 | C2 | semidirect |
| 6. C61×#343 | C2 | semidirect |
| 7. C61×#339 | C2 | semidirect |
| 22. #104×C61 | C4 | semidirect |
| 42. M16×C61 | C2×C4 | semidirect |
| 57. C42×C61 | C2×C4 | semidirect |
| 105. #1860 | C61 | direct (N × H) |
| 113. #428 | C2×C61 | semidirect |
| 116. #382 | C2×C61 | semidirect |
| 117. #343 | C2×C61 | semidirect |
| 118. #339 | C2×C61 | semidirect |
| 119. C61 | #1860 | direct (N × H) |
| 134. #104 | C4×C61 | semidirect |
| 154. M16 | C2×C4×C61 | semidirect |
| 169. C42 | C2×C4×C61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#520 | 2 |
| C61×#428 | 2 |
| C2×#104×C61 | 2 |
| C61×#417 | 2 |
| C61×#382 | 2 |
| C61×#343 | 2 |
| C61×#339 | 2 |
| #1860 | 61 |