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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 678 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
336.178.336.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$
672.771.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_2\times C_{42}):Q_8$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.773.336.a1 $C_2$ $2$ ✓ ✓ ✓ $C_2^2:C_{12}\times D_7$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.774.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_7:(D_4\times C_{12})$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.775.336.b1 $C_2$ $2$ ✓ ✓ ✓ $C_3\times C_2^2:D_{28}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.776.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_4\times D_{14}):C_6$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.777.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3\times D_{14}:D_4$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.777.336.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3\times D_{14}:D_4$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.778.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3\times C_2^3.D_{14}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.781.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{84}:Q_8$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.784.336.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_4:C_{12}\times D_7$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.786.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{28}:C_{12}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.787.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_4\times D_{14}):C_6$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.788.336.c1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{12}:D_{28}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.789.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3\times D_{14}:Q_8$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.803.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{24}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.804.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{24}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.805.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{24}.D_{14}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.806.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{24}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.807.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{24}:D_{14}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.808.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{24}.D_{14}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.809.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{24}.D_{14}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.810.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{24}.D_{14}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.811.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{24}.D_{14}$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.812.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $D_{56}:C_6$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.827.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_7:C_{12}\times D_4$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.830.336.a1 $C_2$ $2$ ✓ ✓ ✓ $C_3\times D_{14}:D_4$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.831.336.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{84}:D_4$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.832.336.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_2\times C_{42}):D_4$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.833.336.a1 $C_2$ $2$ ✓ ✓ ✓ $C_{84}:D_4$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
672.1207.336.b1 $C_2$ $2$ ✓ ✓ ✓ $C_{84}:C_2^3$ $2^{5} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
1008.187.336.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_{36}:D_{14}$ $2^{4} \cdot 3^{2} \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
1008.710.336.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_{84}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
1008.712.336.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_{84}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
1008.723.336.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_6^2:D_{14}$ $2^{4} \cdot 3^{2} \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
1008.725.336.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_6^2:D_{14}$ $2^{4} \cdot 3^{2} \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
1008.830.336.a1 $C_3$ $3$ ✓ ✓ ✓ $C_{28}:C_6^2$ $2^{4} \cdot 3^{2} \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
1008.850.336.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_{12}:D_{42}$ $2^{4} \cdot 3^{2} \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓
1344.4368.336.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_3\times D_{14}:C_4^2$ $2^{6} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$
1344.4369.336.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_4\times D_{14}):C_{12}$ $2^{6} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$
1344.4369.336.d1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $(C_4\times D_{14}):C_{12}$ $2^{6} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$
1344.4370.336.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $(C_2\times C_{84}):Q_8$ $2^{6} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$
1344.4370.336.b1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $(C_2\times C_{84}):Q_8$ $2^{6} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$
1344.4372.336.b1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{14}.(D_4\times C_{12})$ $2^{6} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$
1344.4373.336.b1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_2^2.(C_{12}\times D_{14})$ $2^{6} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$
1344.4375.336.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{14}.(D_4\times C_{12})$ $2^{6} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$
1344.4376.336.b1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_6\times D_{14}):Q_8$ $2^{6} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$
1344.4376.336.b1.b1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_6\times D_{14}):Q_8$ $2^{6} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$
1344.4377.336.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $(C_2^2\times C_{12}).D_{14}$ $2^{6} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$
1344.4378.336.b1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $(C_6\times D_{14}).Q_8$ $2^{6} \cdot 3 \cdot 7$ $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$
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