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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 944 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
28449792.b.1.a1 $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ ✓ ✓ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $C_1$ $1$ ✓
28449792.b.2.a1 $C_2^9:(C_7^3:C_3\wr C_3)$ $2^{9} \cdot 3^{4} \cdot 7^{3}$ ✓ ✓ ✓ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $C_2$ $2$ ✓
28449792.b.3.A $C_2^9.C_7^3:C_3^2:S_3$ $2^{10} \cdot 3^{3} \cdot 7^{3}$ ✓ ✓ ✓ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $C_3$ $3$ ✓
28449792.b.3.B $C_2^6.C_7^2.F_8.C_3^3.C_2$ $2^{10} \cdot 3^{3} \cdot 7^{3}$ ✓ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $3$ $-$
28449792.b.6.A $C_2^9.C_7^3.C_3^3$ $2^{9} \cdot 3^{3} \cdot 7^{3}$ ✓ ✓ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $S_3$ $2 \cdot 3$
28449792.b.6.B $C_2^9:(C_7^3:\He_3)$ $2^{9} \cdot 3^{3} \cdot 7^{3}$ ✓ ✓ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $C_6$ $2 \cdot 3$ ✓
28449792.b.6.C $C_2^9:(C_7^3:C_9:C_3)$ $2^{9} \cdot 3^{3} \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $2 \cdot 3$ $-$
28449792.b.9.A $C_2^9.C_7^3.C_3.C_6$ $2^{10} \cdot 3^{2} \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $3^{2}$ $-$
28449792.b.9.B $C_2^6.C_7^2.F_8.C_3.C_6$ $2^{10} \cdot 3^{2} \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $3^{2}$ $-$
28449792.b.9.C $C_2^6.C_7^2.C_3.C_6\times F_8$ $2^{10} \cdot 3^{2} \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $3^{2}$ $-$
28449792.b.9.D $C_2^6.C_7^2.F_8.C_3.C_6$ $2^{10} \cdot 3^{2} \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $3^{2}$ $-$
28449792.b.9.E $C_2^6.C_7^2.F_8.C_3.C_6$ $2^{10} \cdot 3^{2} \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $3^{2}$ $-$
28449792.b.9.F $C_2^9.C_7^3:(C_3\times S_3)$ $2^{10} \cdot 3^{2} \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $3^{2}$ $-$
28449792.b.18.A $C_2^9.C_7^3.C_3^2$ $2^{9} \cdot 3^{2} \cdot 7^{3}$ ✓ ✓ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $C_3\times S_3$ $2 \cdot 3^{2}$
28449792.b.18.B $C_2^9.C_7^3.C_3^2$ $2^{9} \cdot 3^{2} \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $2 \cdot 3^{2}$ $-$
28449792.b.18.C $C_2^9.C_7^3.C_3^2$ $2^{9} \cdot 3^{2} \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $2 \cdot 3^{2}$ $-$
28449792.b.18.D $C_2^6.C_7^2.F_8.C_3^2$ $2^{9} \cdot 3^{2} \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $2 \cdot 3^{2}$ $-$
28449792.b.18.E $C_2^9.C_7^3.C_3^2$ $2^{9} \cdot 3^{2} \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $2 \cdot 3^{2}$ $-$
28449792.b.18.F $C_2^9.C_7^3:C_3^2$ $2^{9} \cdot 3^{2} \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $2 \cdot 3^{2}$ $-$
28449792.b.18.G $C_2^9:(C_7^3:C_9)$ $2^{9} \cdot 3^{2} \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $2 \cdot 3^{2}$ $-$
28449792.b.21.a1 $C_2^6.C_7^2.(C_6\times S_3\times A_4)$ $2^{10} \cdot 3^{3} \cdot 7^{2}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $3 \cdot 7$ $-$
28449792.b.24.a1 $C_2^6.C_7^3.C_3^3.C_2$ $2^{7} \cdot 3^{3} \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $2^{3} \cdot 3$ $-$
28449792.b.27.A $C_2^9.C_7^3.C_6$ $2^{10} \cdot 3 \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $3^{3}$ $-$
28449792.b.27.B $C_2^6:C_7.F_7\times F_8$ $2^{10} \cdot 3 \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $3^{3}$ $-$
28449792.b.27.C $C_2^9.C_7^3.C_6$ $2^{10} \cdot 3 \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $3^{3}$ $-$
28449792.b.27.D $C_2^9.C_7^3.C_6$ $2^{10} \cdot 3 \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $3^{3}$ $-$
28449792.b.27.E $C_2^6.C_7^2.S_3\times F_8$ $2^{10} \cdot 3 \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $3^{3}$ $-$
28449792.b.27.F $C_2^9.C_7\wr S_3$ $2^{10} \cdot 3 \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $3^{3}$ $-$
28449792.b.42.A $C_2^6.C_7^2.C_3.A_4.C_6$ $2^{9} \cdot 3^{3} \cdot 7^{2}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $2 \cdot 3 \cdot 7$ $-$
28449792.b.42.B $C_2^6.C_7^2.C_3.A_4.C_6$ $2^{9} \cdot 3^{3} \cdot 7^{2}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $2 \cdot 3 \cdot 7$ $-$
28449792.b.42.C $C_2^6.C_{14}^2.C_3^3.C_2$ $2^{9} \cdot 3^{3} \cdot 7^{2}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $2 \cdot 3 \cdot 7$ $-$
28449792.b.48.a1 $C_2^6.C_7^3.C_3^3$ $2^{6} \cdot 3^{3} \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $2^{4} \cdot 3$ $-$
28449792.b.54.A $C_2^9.C_7^3.C_3$ $2^{9} \cdot 3 \cdot 7^{3}$ ✓ ✓ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $C_3^2:C_6$ $2 \cdot 3^{3}$
28449792.b.54.B $F_8.C_2^6.C_7.C_{21}$ $2^{9} \cdot 3 \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $2 \cdot 3^{3}$ $-$
28449792.b.54.C $C_2^6.C_7^2.F_8.C_3$ $2^{9} \cdot 3 \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $2 \cdot 3^{3}$ $-$
28449792.b.54.D $C_2^6.C_7^2.F_8.C_3$ $2^{9} \cdot 3 \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $2 \cdot 3^{3}$ $-$
28449792.b.54.E $C_2^9.C_7\wr C_3$ $2^{9} \cdot 3 \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $2 \cdot 3^{3}$ $-$
28449792.b.54.F $C_2^9.C_7^3.C_3$ $2^{9} \cdot 3 \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $2 \cdot 3^{3}$ $-$
28449792.b.63.A $C_2^9.C_7.C_{21}.C_6$ $2^{10} \cdot 3^{2} \cdot 7^{2}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $3^{2} \cdot 7$ $-$
28449792.b.63.B $C_2^6.C_{14}^2.C_6^2$ $2^{10} \cdot 3^{2} \cdot 7^{2}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $3^{2} \cdot 7$ $-$
28449792.b.63.C $C_2^9.C_7^2.C_3.C_6$ $2^{10} \cdot 3^{2} \cdot 7^{2}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $3^{2} \cdot 7$ $-$
28449792.b.63.D $C_2^6.C_7^2.(C_6\times A_4).C_2$ $2^{10} \cdot 3^{2} \cdot 7^{2}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $3^{2} \cdot 7$ $-$
28449792.b.63.E $C_2^6.C_7^2.C_6^2.C_2^2$ $2^{10} \cdot 3^{2} \cdot 7^{2}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $3^{2} \cdot 7$ $-$
28449792.b.63.F $C_2^6.C_7^2.(C_6\times A_4).C_2$ $2^{10} \cdot 3^{2} \cdot 7^{2}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $3^{2} \cdot 7$ $-$
28449792.b.63.G $C_2^6.C_7^2.(C_6\times A_4).C_2$ $2^{10} \cdot 3^{2} \cdot 7^{2}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $3^{2} \cdot 7$ $-$
28449792.b.63.H $C_2^9.C_7^2:(C_3\times S_3)$ $2^{10} \cdot 3^{2} \cdot 7^{2}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $3^{2} \cdot 7$ $-$
28449792.b.72.A $C_2^6.C_7^3.C_3.C_6$ $2^{7} \cdot 3^{2} \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $2^{3} \cdot 3^{2}$ $-$
28449792.b.72.B $C_2^6.C_7^3.C_3.C_6$ $2^{7} \cdot 3^{2} \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $2^{3} \cdot 3^{2}$ $-$
28449792.b.72.C $C_7\times C_2^6.C_7^2.C_3.C_6$ $2^{7} \cdot 3^{2} \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $2^{3} \cdot 3^{2}$ $-$
28449792.b.72.D $C_2^6.C_7^3.C_3.C_6$ $2^{7} \cdot 3^{2} \cdot 7^{3}$ $C_2^9.C_7^3:C_3\wr S_3$ $2^{10} \cdot 3^{4} \cdot 7^{3}$ $2^{3} \cdot 3^{2}$ $-$
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