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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 (44 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
672.399.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{24}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.400.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{24}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.401.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{24}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.402.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{24}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.408.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{21}:Q_{16}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.420.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{24}.D_{14}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.421.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{56}:S_3$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.422.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{24}.D_{14}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.423.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{24}:D_7$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.424.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{24}.D_{14}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.500.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{42}.D_4$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.552.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_6\times D_{28}):C_2$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.574.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_3\times D_{14}):Q_8$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.578.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{84}:(C_2\times C_4)$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.579.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{84}:(C_2\times C_4)$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.580.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(S_3\times C_{14}):Q_8$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.581.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{42}.D_4$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.582.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{42}.D_4$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.586.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{21}:(C_4\times D_4)$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.597.336.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_{14}\times D_{12}):C_2$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.605.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{42}:D_4$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.607.336.a1 $C_2$ $2$ ✓ ✓ ✓ $C_{84}:D_4$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.608.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_2\times C_{12}).D_{14}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.609.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{12}:D_{28}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.610.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{28}:D_{12}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.614.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{84}:Q_8$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.617.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{42}.D_4$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.618.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_6:D_{28}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.619.336.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{14}:D_{12}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.1142.336.a1 $C_2$ $2$ ✓ ✓ ✓ $D_{12}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
1008.159.336.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_{28}:D_{18}$ $2^{4} \cdot 3^{2} \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
1008.596.336.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
1008.598.336.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
1008.712.336.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_{84}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
1008.739.336.a1 $C_3$ $3$ ✓ ✓ $C_{84}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
1008.784.336.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_{12}:D_{42}$ $2^{4} \cdot 3^{2} \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
1008.805.336.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_{84}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
1344.11329.336.b1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $D_{28}:S_4$ $2^{6} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
1680.512.336.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $D_{30}:D_{14}$ $2^{4} \cdot 3 \cdot 5 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
1680.517.336.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $D_{105}:D_4$ $2^{4} \cdot 3 \cdot 5 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
1680.691.336.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ ✓ $C_{140}:D_6$ $2^{4} \cdot 3 \cdot 5 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
1680.718.336.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{28}:D_{30}$ $2^{4} \cdot 3 \cdot 5 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
1680.799.336.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{12}:D_{70}$ $2^{4} \cdot 3 \cdot 5 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
1680.826.336.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{140}:D_6$ $2^{4} \cdot 3 \cdot 5 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
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