↑

Learn more

Refine search

Subgroup label Subgroup order Cyclic Abelian Solvable
Normal Characteristic Perfect Maximal Central
Ambient label Ambient order Direct product Semidirect product
Quotient label Subgroup index Cyclic quotient Abelian quotient Solvable quotient
Maximal quotient Non-trivial proper Hall subgroup Sylow subgroup
Sort order Select

Results (1-50 of 536 matches)

Next   displayed columns for results
Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1344.8572.1.a1.a1 $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_1$ $1$ ✓
1344.8572.2.a1.a1 $C_{56}:D_6$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8572.2.b1.a1 $C_{24}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8572.2.c1.a1 $C_8:D_{42}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8572.2.d1.a1 $D_{28}:D_6$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8572.2.e1.a1 $D_{28}.D_6$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8572.2.f1.a1 $D_{12}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8572.2.g1.a1 $D_{12}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8572.2.h1.a1 $D_{12}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8572.2.i1.a1 $D_{12}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8572.2.j1.a1 $D_{84}:C_2^2$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8572.2.k1.a1 $D_{28}.D_6$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8572.2.l1.a1 $C_{24}.D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8572.2.m1.a1 $C_{24}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8572.2.n1.a1 $C_{24}.D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8572.2.o1.a1 $C_{24}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
1344.8572.3.a1.a1 $D_8:D_{14}$ $2^{6} \cdot 7$ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $3$ $-$
1344.8572.4.a1.a1 $D_8\times C_{21}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.b1.a1 $C_{28}.D_6$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.c1.a1 $C_{21}:D_8$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.d1.a1 $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.e1.a1 $C_{21}:D_8$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.f1.a1 $D_4\times D_{21}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.g1.a1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.h1.a1 $C_{28}:D_6$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.i1.a1 $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.j1.a1 $C_{21}:D_8$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.k1.a1 $D_4:D_{21}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.l1.a1 $C_{21}:D_8$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.m1.a1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.n1.a1 $C_{12}.D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.o1.a1 $S_3\times D_{28}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.p1.a1 $D_{28}:S_3$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.q1.a1 $C_{168}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.r1.a1 $C_{12}.D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.s1.a1 $D_{12}:D_7$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.t1.a1 $C_{21}:D_8$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.u1.a1 $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.v1.a1 $C_7:D_{24}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.w1.a1 $C_{168}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.x1.a1 $D_{84}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.y1.a1 $D_7\times C_{24}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.z1.a1 $C_{21}:\OD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.ba1.a1 $C_3\times D_{56}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.bb1.a1 $D_{28}:S_3$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.bc1.a1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.bd1.a1 $C_3:D_{56}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.be1.a1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.bf1.a1 $C_{168}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
1344.8572.4.bg1.a1 $D_{21}:C_8$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $D_{56}:D_6$ $2^{6} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
Next   displayed columns for results