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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
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Results (1-50 of 150 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1568.405.1.a1.a1 $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $C_1$ $1$ ✓
1568.405.2.a1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.405.2.b1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.405.2.c1.a1 $C_{56}:C_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.405.2.d1.a1 $C_{14}.D_{28}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.405.2.e1.a1 $C_{56}:D_7$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.405.2.f1.a1 $C_7^2:Q_{16}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.405.2.g1.a1 $C_7^2:Q_{16}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.405.4.a1.a1 $D_7\times C_{28}$ $2^{3} \cdot 7^{2}$ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $C_2^2$ $2^{2}$ ✓
1568.405.4.b1.a1 $C_7:D_{28}$ $2^{3} \cdot 7^{2}$ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $C_2^2$ $2^{2}$ ✓
1568.405.4.c1.a1 $C_7^2:Q_8$ $2^{3} \cdot 7^{2}$ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $C_2^2$ $2^{2}$ ✓
1568.405.4.d1.a1 $C_7^2:Q_8$ $2^{3} \cdot 7^{2}$ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $C_2^2$ $2^{2}$ ✓
1568.405.4.e1.a1 $C_7^2:Q_8$ $2^{3} \cdot 7^{2}$ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $C_2^2$ $2^{2}$ ✓
1568.405.4.f1.a1 $C_7\times C_{56}$ $2^{3} \cdot 7^{2}$ ✓ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $C_2^2$ $2^{2}$ ✓
1568.405.4.g1.a1 $C_7:C_{56}$ $2^{3} \cdot 7^{2}$ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $C_2^2$ $2^{2}$ ✓
1568.405.4.h1.a1 $C_7:D_{28}$ $2^{3} \cdot 7^{2}$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2^{2}$ $-$
1568.405.4.i1.a1 $C_{14}.D_{14}$ $2^{3} \cdot 7^{2}$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2^{2}$ $-$
1568.405.4.j1.a1 $C_{14}.D_{14}$ $2^{3} \cdot 7^{2}$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2^{2}$ $-$
1568.405.4.k1.a1 $C_7^2:Q_8$ $2^{3} \cdot 7^{2}$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2^{2}$ $-$
1568.405.7.a1.a1 $C_4.D_{28}$ $2^{5} \cdot 7$ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $7$ $-$
1568.405.7.b1.a1 $Q_{16}:D_7$ $2^{5} \cdot 7$ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $7$ $-$
1568.405.8.a1.a1 $C_7\times D_{14}$ $2^{2} \cdot 7^{2}$ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $D_4$ $2^{3}$
1568.405.8.b1.a1 $C_7\times C_{28}$ $2^{2} \cdot 7^{2}$ ✓ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $C_2^3$ $2^{3}$ ✓
1568.405.8.c1.a1 $C_7:C_{28}$ $2^{2} \cdot 7^{2}$ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $D_4$ $2^{3}$
1568.405.8.d1.a1 $C_7:D_{14}$ $2^{2} \cdot 7^{2}$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2^{3}$ $-$
1568.405.8.e1.a1 $C_7:C_{28}$ $2^{2} \cdot 7^{2}$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2^{3}$ $-$
1568.405.8.f1.a1 $C_7:C_{28}$ $2^{2} \cdot 7^{2}$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2^{3}$ $-$
1568.405.8.g1.a1 $C_7^2:C_4$ $2^{2} \cdot 7^{2}$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2^{3}$ $-$
1568.405.14.a1.a1 $C_{56}:C_2$ $2^{4} \cdot 7$ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $D_7$ $2 \cdot 7$
1568.405.14.b1.a1 $C_7:Q_{16}$ $2^{4} \cdot 7$ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $D_7$ $2 \cdot 7$
1568.405.14.c1.a1 $D_{28}:C_2$ $2^{4} \cdot 7$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2 \cdot 7$ $-$
1568.405.14.d1.a1 $C_{14}:Q_8$ $2^{4} \cdot 7$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2 \cdot 7$ $-$
1568.405.14.e1.a1 $C_7\times \OD_{16}$ $2^{4} \cdot 7$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2 \cdot 7$ $-$
1568.405.14.f1.a1 $D_{28}:C_2$ $2^{4} \cdot 7$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2 \cdot 7$ $-$
1568.405.14.g1.a1 $Q_8\times D_7$ $2^{4} \cdot 7$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2 \cdot 7$ $-$
1568.405.14.h1.a1 $Q_8:D_7$ $2^{4} \cdot 7$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2 \cdot 7$ $-$
1568.405.14.i1.a1 $C_{56}:C_2$ $2^{4} \cdot 7$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2 \cdot 7$ $-$
1568.405.14.j1.a1 $C_{56}:C_2$ $2^{4} \cdot 7$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2 \cdot 7$ $-$
1568.405.14.k1.a1 $C_{56}:C_2$ $2^{4} \cdot 7$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2 \cdot 7$ $-$
1568.405.14.l1.a1 $C_{56}:C_2$ $2^{4} \cdot 7$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2 \cdot 7$ $-$
1568.405.14.l1.b1 $C_{56}:C_2$ $2^{4} \cdot 7$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2 \cdot 7$ $-$
1568.405.14.l1.c1 $C_{56}:C_2$ $2^{4} \cdot 7$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2 \cdot 7$ $-$
1568.405.14.m1.a1 $C_7\times Q_{16}$ $2^{4} \cdot 7$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2 \cdot 7$ $-$
1568.405.14.n1.a1 $C_7:Q_{16}$ $2^{4} \cdot 7$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2 \cdot 7$ $-$
1568.405.14.o1.a1 $C_7:Q_{16}$ $2^{4} \cdot 7$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2 \cdot 7$ $-$
1568.405.16.a1.a1 $C_7\times C_{14}$ $2 \cdot 7^{2}$ ✓ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $C_2\times D_4$ $2^{4}$
1568.405.16.b1.a1 $C_7\times D_7$ $2 \cdot 7^{2}$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2^{4}$ $-$
1568.405.16.c1.a1 $C_7:D_7$ $2 \cdot 7^{2}$ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $2^{4}$ $-$
1568.405.28.a1.a1 $C_4\times D_7$ $2^{3} \cdot 7$ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $D_{14}$ $2^{2} \cdot 7$
1568.405.28.b1.a1 $C_7:Q_8$ $2^{3} \cdot 7$ ✓ ✓ $C_{56}.D_{14}$ $2^{5} \cdot 7^{2}$ $D_{14}$ $2^{2} \cdot 7$
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