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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 52 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
336.45.1.a1.a1 $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $C_1$ $1$ ✓
336.45.2.a1.a1 $C_6:C_{28}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
336.45.2.b1.a1 $C_{14}:C_{12}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
336.45.2.c1.a1 $C_{42}:C_4$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
336.45.3.a1.a1 $C_{14}.D_4$ $2^{4} \cdot 7$ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $3$ $-$
336.45.4.a1.a1 $C_2\times C_{42}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
336.45.4.b1.a1 $C_7:C_{12}$ $2^{2} \cdot 3 \cdot 7$ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $C_4$ $2^{2}$ ✓
336.45.4.b1.b1 $C_7:C_{12}$ $2^{2} \cdot 3 \cdot 7$ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $C_4$ $2^{2}$ ✓
336.45.4.c1.a1 $C_3:C_{28}$ $2^{2} \cdot 3 \cdot 7$ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $2^{2}$ $-$
336.45.4.d1.a1 $C_{21}:C_4$ $2^{2} \cdot 3 \cdot 7$ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $2^{2}$ $-$
336.45.6.a1.a1 $C_{14}:C_4$ $2^{3} \cdot 7$ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $S_3$ $2 \cdot 3$
336.45.6.b1.a1 $C_2\times C_{28}$ $2^{3} \cdot 7$ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
336.45.6.c1.a1 $C_{14}:C_4$ $2^{3} \cdot 7$ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
336.45.7.a1.a1 $C_{12}:C_4$ $2^{4} \cdot 3$ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $7$ $-$
336.45.8.a1.a1 $C_{42}$ $2 \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $C_2\times C_4$ $2^{3}$ ✓
336.45.8.b1.a1 $C_{42}$ $2 \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $D_4$ $2^{3}$
336.45.8.c1.a1 $C_{42}$ $2 \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $Q_8$ $2^{3}$
336.45.12.a1.a1 $C_2\times C_{14}$ $2^{2} \cdot 7$ ✓ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $D_6$ $2^{2} \cdot 3$
336.45.12.b1.a1 $C_7:C_4$ $2^{2} \cdot 7$ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $C_3:C_4$ $2^{2} \cdot 3$
336.45.12.b1.b1 $C_7:C_4$ $2^{2} \cdot 7$ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $C_3:C_4$ $2^{2} \cdot 3$
336.45.12.c1.a1 $C_{28}$ $2^{2} \cdot 7$ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
336.45.12.d1.a1 $C_7:C_4$ $2^{2} \cdot 7$ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
336.45.14.a1.a1 $C_6:C_4$ $2^{3} \cdot 3$ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $D_7$ $2 \cdot 7$
336.45.14.b1.a1 $C_2\times C_{12}$ $2^{3} \cdot 3$ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $2 \cdot 7$ $-$
336.45.14.c1.a1 $C_6:C_4$ $2^{3} \cdot 3$ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $2 \cdot 7$ $-$
336.45.16.a1.a1 $C_{21}$ $3 \cdot 7$ ✓ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $C_4:C_4$ $2^{4}$
336.45.21.a1.a1 $C_4:C_4$ $2^{4}$ $2$ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $3 \cdot 7$ $-$
336.45.24.a1.a1 $C_{14}$ $2 \cdot 7$ ✓ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $C_6:C_4$ $2^{3} \cdot 3$
336.45.24.b1.a1 $C_{14}$ $2 \cdot 7$ ✓ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $D_{12}$ $2^{3} \cdot 3$
336.45.24.c1.a1 $C_{14}$ $2 \cdot 7$ ✓ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $C_3:Q_8$ $2^{3} \cdot 3$
336.45.28.a1.a1 $C_2\times C_6$ $2^{2} \cdot 3$ ✓ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $D_{14}$ $2^{2} \cdot 7$
336.45.28.b1.a1 $C_{12}$ $2^{2} \cdot 3$ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $2^{2} \cdot 7$ $-$
336.45.28.b1.b1 $C_{12}$ $2^{2} \cdot 3$ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $2^{2} \cdot 7$ $-$
336.45.28.c1.a1 $C_3:C_4$ $2^{2} \cdot 3$ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $2^{2} \cdot 7$ $-$
336.45.28.d1.a1 $C_3:C_4$ $2^{2} \cdot 3$ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $2^{2} \cdot 7$ $-$
336.45.42.a1.a1 $C_2\times C_4$ $2^{3}$ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $2 \cdot 3 \cdot 7$ $-$
336.45.42.b1.a1 $C_2\times C_4$ $2^{3}$ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $2 \cdot 3 \cdot 7$ $-$
336.45.42.c1.a1 $C_2\times C_4$ $2^{3}$ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $2 \cdot 3 \cdot 7$ $-$
336.45.48.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $C_{12}:C_4$ $2^{4} \cdot 3$ ✓
336.45.56.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $C_4\times D_7$ $2^{3} \cdot 7$
336.45.56.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $C_7:D_4$ $2^{3} \cdot 7$
336.45.56.c1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $C_7:Q_8$ $2^{3} \cdot 7$
336.45.84.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $S_3\times D_7$ $2^{2} \cdot 3 \cdot 7$
336.45.84.b1.a1 $C_4$ $2^{2}$ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $2^{2} \cdot 3 \cdot 7$ $-$
336.45.84.b1.b1 $C_4$ $2^{2}$ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $2^{2} \cdot 3 \cdot 7$ $-$
336.45.84.c1.a1 $C_4$ $2^{2}$ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $2^{2} \cdot 3 \cdot 7$ $-$
336.45.84.d1.a1 $C_4$ $2^{2}$ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $2^{2} \cdot 3 \cdot 7$ $-$
336.45.112.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $C_{14}.D_4$ $2^{4} \cdot 7$ ✓
336.45.168.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $C_6.D_{14}$ $2^{3} \cdot 3 \cdot 7$ ✓
336.45.168.b1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{14}.D_{12}$ $2^{4} \cdot 3 \cdot 7$ $C_7:D_{12}$ $2^{3} \cdot 3 \cdot 7$ ✓
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