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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 123 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1568.224.1.a1.a1 $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ ✓ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $C_1$ $1$ ✓
1568.224.2.a1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.224.2.b1.a1 $C_{14}.D_{28}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.224.2.c1.a1 $C_{14}:C_{56}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.224.4.a1.a1 $C_{14}\times C_{28}$ $2^{3} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $C_2^2$ $2^{2}$ ✓
1568.224.4.b1.a1 $C_7^2:Q_8$ $2^{3} \cdot 7^{2}$ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $C_4$ $2^{2}$ ✓
1568.224.4.b1.b1 $C_7^2:Q_8$ $2^{3} \cdot 7^{2}$ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $C_4$ $2^{2}$ ✓
1568.224.4.c1.a1 $C_{14}:C_{28}$ $2^{3} \cdot 7^{2}$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2^{2}$ $-$
1568.224.4.d1.a1 $C_{14}.D_{14}$ $2^{3} \cdot 7^{2}$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2^{2}$ $-$
1568.224.4.e1.a1 $C_7^2:Q_8$ $2^{3} \cdot 7^{2}$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2^{2}$ $-$
1568.224.4.f1.a1 $C_7:C_{56}$ $2^{3} \cdot 7^{2}$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2^{2}$ $-$
1568.224.7.a1.a1 $C_{14}.Q_{16}$ $2^{5} \cdot 7$ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $7$ $-$
1568.224.7.b1.a1 $C_{14}.Q_{16}$ $2^{5} \cdot 7$ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $7$ $-$
1568.224.8.a1.a1 $C_{14}^2$ $2^{2} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $D_4$ $2^{3}$
1568.224.8.b1.a1 $C_7\times C_{28}$ $2^{2} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $C_2\times C_4$ $2^{3}$ ✓
1568.224.8.c1.a1 $C_7\times C_{28}$ $2^{2} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $D_4$ $2^{3}$
1568.224.8.d1.a1 $C_7^2:C_4$ $2^{2} \cdot 7^{2}$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2^{3}$ $-$
1568.224.8.e1.a1 $C_7:C_{28}$ $2^{2} \cdot 7^{2}$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2^{3}$ $-$
1568.224.8.e1.b1 $C_7:C_{28}$ $2^{2} \cdot 7^{2}$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2^{3}$ $-$
1568.224.14.a1.a1 $C_{14}:Q_8$ $2^{4} \cdot 7$ ✓ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $D_7$ $2 \cdot 7$
1568.224.14.b1.a1 $C_{14}:C_8$ $2^{4} \cdot 7$ ✓ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $D_7$ $2 \cdot 7$
1568.224.14.c1.a1 $Q_8\times C_{14}$ $2^{4} \cdot 7$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2 \cdot 7$ $-$
1568.224.14.d1.a1 $C_{28}:C_4$ $2^{4} \cdot 7$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2 \cdot 7$ $-$
1568.224.14.e1.a1 $C_{28}:C_4$ $2^{4} \cdot 7$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2 \cdot 7$ $-$
1568.224.14.f1.a1 $C_{28}:C_4$ $2^{4} \cdot 7$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2 \cdot 7$ $-$
1568.224.14.f1.b1 $C_{28}:C_4$ $2^{4} \cdot 7$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2 \cdot 7$ $-$
1568.224.14.f1.c1 $C_{28}:C_4$ $2^{4} \cdot 7$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2 \cdot 7$ $-$
1568.224.14.g1.a1 $C_2\times C_{56}$ $2^{4} \cdot 7$ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2 \cdot 7$ $-$
1568.224.16.a1.a1 $C_7\times C_{14}$ $2 \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $Q_{16}$ $2^{4}$
1568.224.16.b1.a1 $C_7\times C_{14}$ $2 \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $\SD_{16}$ $2^{4}$
1568.224.16.c1.a1 $C_7\times C_{14}$ $2 \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $C_2^2:C_4$ $2^{4}$
1568.224.28.a1.a1 $C_2\times C_{28}$ $2^{3} \cdot 7$ ✓ ✓ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $D_{14}$ $2^{2} \cdot 7$
1568.224.28.b1.a1 $C_2\times C_{28}$ $2^{3} \cdot 7$ ✓ ✓ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $D_{14}$ $2^{2} \cdot 7$
1568.224.28.c1.a1 $C_7:Q_8$ $2^{3} \cdot 7$ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $C_7:C_4$ $2^{2} \cdot 7$
1568.224.28.c1.b1 $C_7:Q_8$ $2^{3} \cdot 7$ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $C_7:C_4$ $2^{2} \cdot 7$
1568.224.28.d1.a1 $C_2\times C_{28}$ $2^{3} \cdot 7$ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2^{2} \cdot 7$ $-$
1568.224.28.d1.b1 $C_2\times C_{28}$ $2^{3} \cdot 7$ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2^{2} \cdot 7$ $-$
1568.224.28.d1.c1 $C_2\times C_{28}$ $2^{3} \cdot 7$ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2^{2} \cdot 7$ $-$
1568.224.28.e1.a1 $C_2\times C_{28}$ $2^{3} \cdot 7$ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2^{2} \cdot 7$ $-$
1568.224.28.f1.a1 $C_{14}:C_4$ $2^{3} \cdot 7$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2^{2} \cdot 7$ $-$
1568.224.28.g1.a1 $C_{14}:C_4$ $2^{3} \cdot 7$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2^{2} \cdot 7$ $-$
1568.224.28.h1.a1 $C_{14}:C_4$ $2^{3} \cdot 7$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2^{2} \cdot 7$ $-$
1568.224.28.i1.a1 $C_{14}:C_4$ $2^{3} \cdot 7$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2^{2} \cdot 7$ $-$
1568.224.28.i1.a2 $C_{14}:C_4$ $2^{3} \cdot 7$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2^{2} \cdot 7$ $-$
1568.224.28.i1.b1 $C_{14}:C_4$ $2^{3} \cdot 7$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2^{2} \cdot 7$ $-$
1568.224.28.i1.b2 $C_{14}:C_4$ $2^{3} \cdot 7$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2^{2} \cdot 7$ $-$
1568.224.28.i1.c1 $C_{14}:C_4$ $2^{3} \cdot 7$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2^{2} \cdot 7$ $-$
1568.224.28.i1.c2 $C_{14}:C_4$ $2^{3} \cdot 7$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2^{2} \cdot 7$ $-$
1568.224.28.j1.a1 $C_7\times Q_8$ $2^{3} \cdot 7$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2^{2} \cdot 7$ $-$
1568.224.28.j1.b1 $C_7\times Q_8$ $2^{3} \cdot 7$ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $2^{2} \cdot 7$ $-$
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