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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 136 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
672.458.1.a1.a1 $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $C_1$ $1$ ✓
672.458.2.a1.a1 $C_2\times D_{84}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
672.458.2.b1.a1 $C_{42}:Q_8$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
672.458.2.c1.a1 $C_6:C_{56}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
672.458.2.d1.a1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
672.458.2.d1.b1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
672.458.2.d1.c1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
672.458.2.d1.d1 $C_{21}:\SD_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
672.458.3.a1.a1 $C_8:D_{14}$ $2^{5} \cdot 7$ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $3$ $-$
672.458.4.a1.a1 $C_2\times C_{84}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
672.458.4.b1.a1 $D_{84}$ $2^{3} \cdot 3 \cdot 7$ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
672.458.4.b1.b1 $D_{84}$ $2^{3} \cdot 3 \cdot 7$ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
672.458.4.c1.a1 $C_{21}:Q_8$ $2^{3} \cdot 3 \cdot 7$ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
672.458.4.c1.b1 $C_{21}:Q_8$ $2^{3} \cdot 3 \cdot 7$ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
672.458.4.d1.a1 $C_3:C_{56}$ $2^{3} \cdot 3 \cdot 7$ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
672.458.4.d1.b1 $C_3:C_{56}$ $2^{3} \cdot 3 \cdot 7$ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
672.458.4.e1.a1 $C_2\times D_{42}$ $2^{3} \cdot 3 \cdot 7$ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2^{2}$ $-$
672.458.4.f1.a1 $C_{14}:C_{12}$ $2^{3} \cdot 3 \cdot 7$ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2^{2}$ $-$
672.458.4.g1.a1 $D_{84}$ $2^{3} \cdot 3 \cdot 7$ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2^{2}$ $-$
672.458.4.h1.a1 $C_{21}:Q_8$ $2^{3} \cdot 3 \cdot 7$ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2^{2}$ $-$
672.458.6.a1.a1 $C_{14}:Q_8$ $2^{4} \cdot 7$ ✓ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $S_3$ $2 \cdot 3$
672.458.6.b1.a1 $C_2\times D_{28}$ $2^{4} \cdot 7$ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
672.458.6.c1.a1 $C_2\times C_{56}$ $2^{4} \cdot 7$ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
672.458.6.d1.a1 $C_{56}:C_2$ $2^{4} \cdot 7$ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
672.458.6.d1.b1 $C_{56}:C_2$ $2^{4} \cdot 7$ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
672.458.6.d1.c1 $C_{56}:C_2$ $2^{4} \cdot 7$ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
672.458.6.d1.d1 $C_{56}:C_2$ $2^{4} \cdot 7$ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
672.458.7.a1.a1 $Q_8:D_6$ $2^{5} \cdot 3$ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $7$ $-$
672.458.8.a1.a1 $C_2\times C_{42}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $D_4$ $2^{3}$
672.458.8.b1.a1 $C_{84}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
672.458.8.c1.a1 $C_{84}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $D_4$ $2^{3}$
672.458.8.d1.a1 $D_{42}$ $2^{2} \cdot 3 \cdot 7$ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2^{3}$ $-$
672.458.8.d1.b1 $D_{42}$ $2^{2} \cdot 3 \cdot 7$ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2^{3}$ $-$
672.458.8.e1.a1 $D_{42}$ $2^{2} \cdot 3 \cdot 7$ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2^{3}$ $-$
672.458.8.e1.b1 $D_{42}$ $2^{2} \cdot 3 \cdot 7$ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2^{3}$ $-$
672.458.8.f1.a1 $C_7:C_{12}$ $2^{2} \cdot 3 \cdot 7$ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2^{3}$ $-$
672.458.8.f1.b1 $C_7:C_{12}$ $2^{2} \cdot 3 \cdot 7$ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2^{3}$ $-$
672.458.12.a1.a1 $C_2\times C_{28}$ $2^{3} \cdot 7$ ✓ ✓ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $D_6$ $2^{2} \cdot 3$
672.458.12.b1.a1 $C_7:Q_8$ $2^{3} \cdot 7$ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $D_6$ $2^{2} \cdot 3$
672.458.12.b1.b1 $C_7:Q_8$ $2^{3} \cdot 7$ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $D_6$ $2^{2} \cdot 3$
672.458.12.c1.a1 $C_2\times D_{14}$ $2^{3} \cdot 7$ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
672.458.12.d1.a1 $C_{14}:C_4$ $2^{3} \cdot 7$ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
672.458.12.e1.a1 $D_{28}$ $2^{3} \cdot 7$ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
672.458.12.e1.b1 $D_{28}$ $2^{3} \cdot 7$ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
672.458.12.f1.a1 $D_{28}$ $2^{3} \cdot 7$ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
672.458.12.g1.a1 $C_{56}$ $2^{3} \cdot 7$ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
672.458.12.g1.b1 $C_{56}$ $2^{3} \cdot 7$ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
672.458.12.h1.a1 $C_7:Q_8$ $2^{3} \cdot 7$ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
672.458.14.a1.a1 $C_6:C_8$ $2^{4} \cdot 3$ ✓ ✓ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $D_7$ $2 \cdot 7$
672.458.14.b1.a1 $C_2\times D_{12}$ $2^{4} \cdot 3$ $C_{42}:\SD_{16}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 7$ $-$
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