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Note: Search results may be incomplete due to uncomputed quantities: Subgroup label (103813812 objects)

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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 53 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1568.218.2.a1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{28}.D_{28}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.223.2.a1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{28}.D_{28}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.224.2.a1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.253.2.b1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{28}.D_{28}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.264.2.a1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.267.2.a1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{28}.D_{28}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.416.2.b1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.C_2^3$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.417.2.a1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.C_2^3$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.431.2.c1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.C_2^3$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.432.2.d1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{28}.D_{28}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.433.2.c1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.C_2^3$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.439.2.d1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{28}.D_{28}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.442.2.b1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{28}.D_{28}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.443.2.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ $C_{14}^2.C_2^3$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.458.2.b1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $D_{28}.D_{14}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.459.2.b1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $D_{28}.D_{14}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.464.2.b1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{28}.D_{28}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.465.2.b1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{28}.D_{28}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.466.2.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.467.2.a1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{28}.D_{28}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.477.2.d1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.C_2^3$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.488.2.d1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.C_2^3$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.503.2.f1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.C_2^3$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.519.2.b1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.C_2^3$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.588.2.c1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{28}^2.C_2$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.589.2.c1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ $C_{28}.D_{28}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.595.2.d1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{28}^2:C_2$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.598.2.f1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2:Q_8$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.599.2.g1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.C_2^3$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.607.2.c1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.C_2^3$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.608.2.g1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.C_2^3$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.609.2.d1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ $C_{14}^2.C_2^3$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.609.2.d1.b1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ $C_{14}^2.C_2^3$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.617.2.d1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{28}.D_{28}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.622.2.b1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{56}:D_{14}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.625.2.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ $C_{28}.D_{28}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.629.2.b1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{28}.D_{28}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.644.2.d1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2:Q_8$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.655.2.d1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.C_2^3$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.658.2.b1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.662.2.c1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.C_2^3$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.665.2.b1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.671.2.b1.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.D_4$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.842.2.c1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_2.D_{14}^2$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.844.2.e1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $D_{28}:D_{14}$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.845.2.d1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_2.D_{14}^2$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.847.2.c1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ $C_2.D_{14}^2$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.849.2.e1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_2.D_{14}^2$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.879.2.a1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ $C_{14}^2:Q_8$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
1568.882.2.e1 $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ ✓ ✓ ✓ $C_{14}^2.C_2^3$ $2^{5} \cdot 7^{2}$ $C_2$ $2$ ✓
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