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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 112 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
226464.a.1.a1.a1 $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_1$ $1$ ✓
226464.a.2.a1.a1 $D_{337}:C_{168}$ $2^{4} \cdot 3 \cdot 7 \cdot 337$ ✓ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_2$ $2$ ✓
226464.a.2.b1.a1 $C_{337}:C_{336}$ $2^{4} \cdot 3 \cdot 7 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_2$ $2$ ✓
226464.a.2.b1.b1 $C_{337}:C_{336}$ $2^{4} \cdot 3 \cdot 7 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_2$ $2$ ✓
226464.a.3.a1.a1 $D_{337}:C_{112}$ $2^{5} \cdot 7 \cdot 337$ ✓ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_3$ $3$ ✓
226464.a.4.a1.a1 $C_{1348}:C_{42}$ $2^{3} \cdot 3 \cdot 7 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_4$ $2^{2}$ ✓
226464.a.4.b1.a1 $C_{337}:C_{168}$ $2^{3} \cdot 3 \cdot 7 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_4$ $2^{2}$ ✓
226464.a.4.c1.a1 $C_{337}:C_{168}$ $2^{3} \cdot 3 \cdot 7 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_2^2$ $2^{2}$ ✓
226464.a.6.a1.a1 $D_{337}:C_{56}$ $2^{4} \cdot 7 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_6$ $2 \cdot 3$ ✓
226464.a.6.b1.a1 $C_{337}:C_{112}$ $2^{4} \cdot 7 \cdot 337$ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_6$ $2 \cdot 3$ ✓
226464.a.6.b1.b1 $C_{337}:C_{112}$ $2^{4} \cdot 7 \cdot 337$ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_6$ $2 \cdot 3$ ✓
226464.a.7.a1.a1 $D_{337}:C_{48}$ $2^{5} \cdot 3 \cdot 337$ ✓ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_7$ $7$ ✓
226464.a.8.a1.a1 $C_{674}:C_{42}$ $2^{2} \cdot 3 \cdot 7 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_8$ $2^{3}$ ✓
226464.a.8.b1.a1 $C_{1348}:C_{21}$ $2^{2} \cdot 3 \cdot 7 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_8$ $2^{3}$ ✓
226464.a.8.c1.a1 $C_{337}:C_{84}$ $2^{2} \cdot 3 \cdot 7 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_2\times C_4$ $2^{3}$ ✓
226464.a.12.a1.a1 $C_{1348}:C_{14}$ $2^{3} \cdot 7 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{12}$ $2^{2} \cdot 3$ ✓
226464.a.12.b1.a1 $C_{337}:C_{56}$ $2^{3} \cdot 7 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{12}$ $2^{2} \cdot 3$ ✓
226464.a.12.c1.a1 $C_{337}:C_{56}$ $2^{3} \cdot 7 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
226464.a.14.a1.a1 $D_{337}:C_{24}$ $2^{4} \cdot 3 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{14}$ $2 \cdot 7$ ✓
226464.a.14.b1.a1 $C_{337}:C_{48}$ $2^{4} \cdot 3 \cdot 337$ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{14}$ $2 \cdot 7$ ✓
226464.a.14.b1.b1 $C_{337}:C_{48}$ $2^{4} \cdot 3 \cdot 337$ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{14}$ $2 \cdot 7$ ✓
226464.a.16.a1.a1 $C_{337}:C_{42}$ $2 \cdot 3 \cdot 7 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_2\times C_8$ $2^{4}$ ✓
226464.a.16.b1.a1 $C_{337}:C_{42}$ $2 \cdot 3 \cdot 7 \cdot 337$ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{16}$ $2^{4}$ ✓
226464.a.16.b1.b1 $C_{337}:C_{42}$ $2 \cdot 3 \cdot 7 \cdot 337$ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{16}$ $2^{4}$ ✓
226464.a.21.a1.a1 $D_{337}:C_{16}$ $2^{5} \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{21}$ $3 \cdot 7$ ✓
226464.a.24.a1.a1 $C_{674}:C_{14}$ $2^{2} \cdot 7 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{24}$ $2^{3} \cdot 3$ ✓
226464.a.24.b1.a1 $C_{1348}:C_7$ $2^{2} \cdot 7 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{24}$ $2^{3} \cdot 3$ ✓
226464.a.24.c1.a1 $C_{337}:C_{28}$ $2^{2} \cdot 7 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_2\times C_{12}$ $2^{3} \cdot 3$ ✓
226464.a.28.a1.a1 $C_{1348}:C_6$ $2^{3} \cdot 3 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{28}$ $2^{2} \cdot 7$ ✓
226464.a.28.b1.a1 $C_{337}:C_{24}$ $2^{3} \cdot 3 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{28}$ $2^{2} \cdot 7$ ✓
226464.a.28.c1.a1 $C_{337}:C_{24}$ $2^{3} \cdot 3 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_2\times C_{14}$ $2^{2} \cdot 7$ ✓
226464.a.32.a1.a1 $C_{337}:C_{21}$ $3 \cdot 7 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_2\times C_{16}$ $2^{5}$ ✓
226464.a.42.a1.a1 $D_{337}:C_8$ $2^{4} \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{42}$ $2 \cdot 3 \cdot 7$ ✓
226464.a.42.b1.a1 $C_{337}:C_{16}$ $2^{4} \cdot 337$ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{42}$ $2 \cdot 3 \cdot 7$ ✓
226464.a.42.b1.b1 $C_{337}:C_{16}$ $2^{4} \cdot 337$ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{42}$ $2 \cdot 3 \cdot 7$ ✓
226464.a.48.a1.a1 $C_{337}:C_{14}$ $2 \cdot 7 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_2\times C_{24}$ $2^{4} \cdot 3$ ✓
226464.a.48.b1.a1 $C_{337}:C_{14}$ $2 \cdot 7 \cdot 337$ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{48}$ $2^{4} \cdot 3$ ✓
226464.a.48.b1.b1 $C_{337}:C_{14}$ $2 \cdot 7 \cdot 337$ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{48}$ $2^{4} \cdot 3$ ✓
226464.a.56.a1.a1 $C_{674}:C_6$ $2^{2} \cdot 3 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{56}$ $2^{3} \cdot 7$ ✓
226464.a.56.b1.a1 $C_{1348}:C_3$ $2^{2} \cdot 3 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{56}$ $2^{3} \cdot 7$ ✓
226464.a.56.c1.a1 $C_{337}:C_{12}$ $2^{2} \cdot 3 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_2\times C_{28}$ $2^{3} \cdot 7$ ✓
226464.a.84.a1.a1 $C_4\times D_{337}$ $2^{3} \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{84}$ $2^{2} \cdot 3 \cdot 7$ ✓
226464.a.84.b1.a1 $C_{337}:C_8$ $2^{3} \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{84}$ $2^{2} \cdot 3 \cdot 7$ ✓
226464.a.84.c1.a1 $C_{337}:C_8$ $2^{3} \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_2\times C_{42}$ $2^{2} \cdot 3 \cdot 7$ ✓
226464.a.96.a1.a1 $C_{337}:C_7$ $7 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_2\times C_{48}$ $2^{5} \cdot 3$ ✓
226464.a.112.a1.a1 $C_{337}:C_6$ $2 \cdot 3 \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_2\times C_{56}$ $2^{4} \cdot 7$ ✓
226464.a.112.b1.a1 $C_{337}:C_6$ $2 \cdot 3 \cdot 337$ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{112}$ $2^{4} \cdot 7$ ✓
226464.a.112.b1.b1 $C_{337}:C_6$ $2 \cdot 3 \cdot 337$ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{112}$ $2^{4} \cdot 7$ ✓
226464.a.168.a1.a1 $D_{674}$ $2^{2} \cdot 337$ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{168}$ $2^{3} \cdot 3 \cdot 7$ ✓
226464.a.168.b1.a1 $C_{1348}$ $2^{2} \cdot 337$ ✓ ✓ ✓ $D_{337}:C_{336}$ $2^{5} \cdot 3 \cdot 7 \cdot 337$ $C_{168}$ $2^{3} \cdot 3 \cdot 7$ ✓
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