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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 479 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
196.9.196.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $D_7^2$ $2^{2} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
392.18.196.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{14}.D_{14}$ $2^{3} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$ ✓
392.19.196.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{14}.D_{14}$ $2^{3} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$ ✓
392.20.196.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{14}:D_7$ $2^{3} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$ ✓
392.21.196.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_7:D_{28}$ $2^{3} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$ ✓
392.22.196.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_7^2:Q_8$ $2^{3} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$ ✓
392.41.196.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_7\times D_{14}$ $2^{3} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$ ✓
588.49.196.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ ✓ $C_3\times D_7^2$ $2^{2} \cdot 3 \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$ ✓
588.52.196.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $D_7\times D_{21}$ $2^{2} \cdot 3 \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$ ✓
588.53.196.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $C_{21}:D_{14}$ $2^{2} \cdot 3 \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$ ✓
784.48.196.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.49.196.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.50.196.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.51.196.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.52.196.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $D_{28}:D_7$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.53.196.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_7:D_{56}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.54.196.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.55.196.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{14}.D_{28}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.56.196.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{14}.D_{28}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.57.196.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_7^2:Q_{16}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.58.196.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_7^2:Q_{16}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.59.196.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_7^2:C_4^2$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.60.196.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{14}.D_{28}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.61.196.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{14}.D_{28}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.62.196.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{14}.D_{28}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.63.196.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{14}^2.C_2^2$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.118.196.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.119.196.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $D_{28}:D_7$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.120.196.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $D_{28}:D_7$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.121.196.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.122.196.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.123.196.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{28}.D_{14}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.124.196.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_4\times D_7^2$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.125.196.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $D_7\times D_{28}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.126.196.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_{28}:D_{14}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.127.196.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $D_{14}.D_{14}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.128.196.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $D_{14}.D_{14}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.129.196.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $D_{14}.D_{14}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.130.196.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{14}^2.C_2^2$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.131.196.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $D_{14}:D_{14}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.132.196.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{14}:D_{28}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.133.196.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{14}^2.C_2^2$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.134.196.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $D_{14}:D_{14}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.135.196.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $D_{14}:D_{14}$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
784.169.196.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $D_{14}^2$ $2^{4} \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
980.24.196.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ ✓ $C_5\times D_7^2$ $2^{2} \cdot 5 \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$ ✓
980.27.196.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $D_7\times D_{35}$ $2^{2} \cdot 5 \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$ ✓
980.28.196.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{35}:D_{14}$ $2^{2} \cdot 5 \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$ ✓
1176.140.196.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_{42}.D_{14}$ $2^{3} \cdot 3 \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
1176.141.196.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_{42}.D_{14}$ $2^{3} \cdot 3 \cdot 7^{2}$ $D_7^2$ $2^{2} \cdot 7^{2}$
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