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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 248 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1008.598.1.a1.a1 $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_1$ $1$ ✓
1008.598.2.a1.a1 $C_{42}.D_6$ $2^{3} \cdot 3^{2} \cdot 7$ ✓ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_2$ $2$ ✓
1008.598.2.b1.a1 $C_{21}:D_{12}$ $2^{3} \cdot 3^{2} \cdot 7$ ✓ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_2$ $2$ ✓
1008.598.2.c1.a1 $S_3\times D_{42}$ $2^{3} \cdot 3^{2} \cdot 7$ ✓ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_2$ $2$ ✓
1008.598.2.d1.a1 $C_{42}:D_6$ $2^{3} \cdot 3^{2} \cdot 7$ ✓ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_2$ $2$ ✓
1008.598.2.e1.a1 $D_{42}:C_6$ $2^{3} \cdot 3^{2} \cdot 7$ ✓ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_2$ $2$ ✓
1008.598.2.f1.a1 $C_{21}:D_{12}$ $2^{3} \cdot 3^{2} \cdot 7$ ✓ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_2$ $2$ ✓
1008.598.2.g1.a1 $C_6.D_{42}$ $2^{3} \cdot 3^{2} \cdot 7$ ✓ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_2$ $2$ ✓
1008.598.3.a1.a1 $D_6:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $3$ $-$
1008.598.3.b1.a1 $C_{12}:D_{14}$ $2^{4} \cdot 3 \cdot 7$ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $3$ $-$
1008.598.4.a1.a1 $S_3\times C_{42}$ $2^{2} \cdot 3^{2} \cdot 7$ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_2^2$ $2^{2}$ ✓
1008.598.4.b1.a1 $C_3^2\times D_{14}$ $2^{2} \cdot 3^{2} \cdot 7$ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_2^2$ $2^{2}$ ✓
1008.598.4.c1.a1 $C_{42}:S_3$ $2^{2} \cdot 3^{2} \cdot 7$ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_2^2$ $2^{2}$ ✓
1008.598.4.d1.a1 $C_3\times D_{42}$ $2^{2} \cdot 3^{2} \cdot 7$ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_2^2$ $2^{2}$ ✓
1008.598.4.e1.a1 $C_3:D_{42}$ $2^{2} \cdot 3^{2} \cdot 7$ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_2^2$ $2^{2}$ ✓
1008.598.4.f1.a1 $C_3:C_{84}$ $2^{2} \cdot 3^{2} \cdot 7$ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_2^2$ $2^{2}$ ✓
1008.598.4.g1.a1 $C_{21}:C_{12}$ $2^{2} \cdot 3^{2} \cdot 7$ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_2^2$ $2^{2}$ ✓
1008.598.4.h1.a1 $S_3\times D_{21}$ $2^{2} \cdot 3^{2} \cdot 7$ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2^{2}$ $-$
1008.598.4.h1.b1 $S_3\times D_{21}$ $2^{2} \cdot 3^{2} \cdot 7$ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2^{2}$ $-$
1008.598.4.i1.a1 $C_{21}:D_6$ $2^{2} \cdot 3^{2} \cdot 7$ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2^{2}$ $-$
1008.598.4.i1.b1 $C_{21}:D_6$ $2^{2} \cdot 3^{2} \cdot 7$ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2^{2}$ $-$
1008.598.6.a1.a1 $C_{21}:D_4$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $S_3$ $2 \cdot 3$
1008.598.6.b1.a1 $C_3:D_{28}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $S_3$ $2 \cdot 3$
1008.598.6.c1.a1 $C_{21}:D_4$ $2^{3} \cdot 3 \cdot 7$ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3$ $-$
1008.598.6.d1.a1 $D_6:C_{14}$ $2^{3} \cdot 3 \cdot 7$ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3$ $-$
1008.598.6.e1.a1 $C_2\times D_{42}$ $2^{3} \cdot 3 \cdot 7$ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3$ $-$
1008.598.6.f1.a1 $C_7\times D_{12}$ $2^{3} \cdot 3 \cdot 7$ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3$ $-$
1008.598.6.g1.a1 $S_3\times D_{14}$ $2^{3} \cdot 3 \cdot 7$ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3$ $-$
1008.598.6.h1.a1 $S_3\times D_{14}$ $2^{3} \cdot 3 \cdot 7$ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3$ $-$
1008.598.6.i1.a1 $S_3\times D_{14}$ $2^{3} \cdot 3 \cdot 7$ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3$ $-$
1008.598.6.j1.a1 $S_3\times D_{14}$ $2^{3} \cdot 3 \cdot 7$ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3$ $-$
1008.598.6.k1.a1 $C_3\times D_{28}$ $2^{3} \cdot 3 \cdot 7$ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3$ $-$
1008.598.6.l1.a1 $C_{21}:D_4$ $2^{3} \cdot 3 \cdot 7$ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3$ $-$
1008.598.6.m1.a1 $C_7:D_{12}$ $2^{3} \cdot 3 \cdot 7$ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3$ $-$
1008.598.6.n1.a1 $D_{21}:C_4$ $2^{3} \cdot 3 \cdot 7$ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3$ $-$
1008.598.6.o1.a1 $C_4\times D_{21}$ $2^{3} \cdot 3 \cdot 7$ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3$ $-$
1008.598.7.a1.a1 $D_6:D_6$ $2^{4} \cdot 3^{2}$ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $7$ $-$
1008.598.8.a1.a1 $C_3\times C_{42}$ $2 \cdot 3^{2} \cdot 7$ ✓ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $C_2^3$ $2^{3}$ ✓
1008.598.8.b1.a1 $C_3:D_{21}$ $2 \cdot 3^{2} \cdot 7$ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $D_4$ $2^{3}$
1008.598.8.b1.b1 $C_3:D_{21}$ $2 \cdot 3^{2} \cdot 7$ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $D_4$ $2^{3}$
1008.598.8.c1.a1 $S_3\times C_{21}$ $2 \cdot 3^{2} \cdot 7$ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2^{3}$ $-$
1008.598.8.d1.a1 $C_3^2\times D_7$ $2 \cdot 3^{2} \cdot 7$ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2^{3}$ $-$
1008.598.8.e1.a1 $C_{21}:S_3$ $2 \cdot 3^{2} \cdot 7$ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2^{3}$ $-$
1008.598.8.f1.a1 $C_3\times D_{21}$ $2 \cdot 3^{2} \cdot 7$ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2^{3}$ $-$
1008.598.9.a1.a1 $D_4\times D_7$ $2^{4} \cdot 7$ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $3^{2}$ $-$
1008.598.12.a1.a1 $S_3\times C_{14}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $D_6$ $2^{2} \cdot 3$
1008.598.12.b1.a1 $C_3\times D_{14}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $D_6$ $2^{2} \cdot 3$
1008.598.12.c1.a1 $C_3\times D_{14}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $D_6$ $2^{2} \cdot 3$
1008.598.12.d1.a1 $D_{42}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $D_6$ $2^{2} \cdot 3$
1008.598.12.e1.a1 $C_3:C_{28}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ $D_{42}:D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $D_6$ $2^{2} \cdot 3$
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