Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
252 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C61 | C2×D4 |
| commutator | C4 | C22×C16×C61 |
| Frattini, cosocle | C4×C8 | C23×C61 |
| socle | C22×C61 | C8×D4 |
| prime radical | C2×D8×C61 | C8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C61 ◁ C4×C16×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D4×C16×C61 | C2 | semidirect |
| 3. C61×#1367 | C2 | semidirect |
| 4. C61×D4⋊C16 | C2 | semidirect |
| 5. C61×#1312 | C2 | semidirect |
| 32. D8×C61 | C16 | semidirect |
| 49. D4×C61 | C2×C16 | semidirect |
| 60. C8×C61 | C2×C16 | semidirect |
| 62. #12062 | C61 | direct (N × H) |
| 73. D4×C16 | C2×C61 | semidirect |
| 75. #1367 | C2×C61 | semidirect |
| 76. D4⋊C16 | C2×C61 | semidirect |
| 77. #1312 | C2×C61 | semidirect |
| 92. C61 | #12062 | direct (N × H) |
| 109. D8 | C16×C61 | semidirect |
| 126. D4 | C2×C16×C61 | semidirect |
| 137. C8 | C2×C16×C61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×C16×C61 | 2 |
| C8×D8×C61 | 2 |
| C61×#1367 | 2 |
| C61×D4⋊C16 | 2 |
| C61×#1312 | 2 |
| #12062 | 61 |