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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 120 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
672.974.1.a1.a1 $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $C_1$ $1$ ✓
672.974.2.a1.a1 $D_{84}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
672.974.2.b1.a1 $C_{42}:Q_8$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
672.974.2.c1.a1 $\OD_{16}\times C_{21}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
672.974.2.d1.a1 $C_{168}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
672.974.2.d1.b1 $C_{168}:C_2$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
672.974.2.e1.a1 $C_{21}:Q_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
672.974.2.e1.b1 $C_{21}:Q_{16}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
672.974.3.a1.a1 $C_4.D_{28}$ $2^{5} \cdot 7$ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $3$ $-$
672.974.4.a1.a1 $C_2\times C_{84}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
672.974.4.b1.a1 $D_{84}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
672.974.4.c1.a1 $C_{21}:Q_8$ $2^{3} \cdot 3 \cdot 7$ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
672.974.4.c1.b1 $C_{21}:Q_8$ $2^{3} \cdot 3 \cdot 7$ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
672.974.4.d1.a1 $C_{21}:Q_8$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
672.974.4.e1.a1 $C_{168}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
672.974.4.e1.b1 $C_{168}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
672.974.4.f1.a1 $C_{21}:D_4$ $2^{3} \cdot 3 \cdot 7$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2^{2}$ $-$
672.974.4.g1.a1 $C_{42}:C_4$ $2^{3} \cdot 3 \cdot 7$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2^{2}$ $-$
672.974.4.h1.a1 $C_4\times D_{21}$ $2^{3} \cdot 3 \cdot 7$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2^{2}$ $-$
672.974.4.i1.a1 $C_{21}:Q_8$ $2^{3} \cdot 3 \cdot 7$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2^{2}$ $-$
672.974.6.a1.a1 $C_7\times \OD_{16}$ $2^{4} \cdot 7$ ✓ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $S_3$ $2 \cdot 3$
672.974.6.b1.a1 $D_{28}:C_2$ $2^{4} \cdot 7$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
672.974.6.c1.a1 $C_{14}:Q_8$ $2^{4} \cdot 7$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
672.974.6.d1.a1 $C_{56}:C_2$ $2^{4} \cdot 7$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
672.974.6.d1.b1 $C_{56}:C_2$ $2^{4} \cdot 7$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
672.974.6.e1.a1 $C_7:Q_{16}$ $2^{4} \cdot 7$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
672.974.6.e1.b1 $C_7:Q_{16}$ $2^{4} \cdot 7$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
672.974.7.a1.a1 $C_4.D_{12}$ $2^{5} \cdot 3$ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $7$ $-$
672.974.8.a1.a1 $C_2\times C_{42}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $D_4$ $2^{3}$
672.974.8.b1.a1 $C_{84}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $D_4$ $2^{3}$
672.974.8.c1.a1 $C_{84}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
672.974.8.d1.a1 $D_{42}$ $2^{2} \cdot 3 \cdot 7$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2^{3}$ $-$
672.974.8.e1.a1 $C_{21}:C_4$ $2^{2} \cdot 3 \cdot 7$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2^{3}$ $-$
672.974.8.e1.b1 $C_{21}:C_4$ $2^{2} \cdot 3 \cdot 7$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2^{3}$ $-$
672.974.8.f1.a1 $C_{21}:C_4$ $2^{2} \cdot 3 \cdot 7$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2^{3}$ $-$
672.974.12.a1.a1 $C_2\times C_{28}$ $2^{3} \cdot 7$ ✓ ✓ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $D_6$ $2^{2} \cdot 3$
672.974.12.b1.a1 $C_{56}$ $2^{3} \cdot 7$ ✓ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $D_6$ $2^{2} \cdot 3$
672.974.12.b1.b1 $C_{56}$ $2^{3} \cdot 7$ ✓ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $D_6$ $2^{2} \cdot 3$
672.974.12.c1.a1 $C_7:D_4$ $2^{3} \cdot 7$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
672.974.12.d1.a1 $C_{14}:C_4$ $2^{3} \cdot 7$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
672.974.12.e1.a1 $C_4\times D_7$ $2^{3} \cdot 7$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
672.974.12.f1.a1 $D_{28}$ $2^{3} \cdot 7$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
672.974.12.g1.a1 $C_7:Q_8$ $2^{3} \cdot 7$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
672.974.12.h1.a1 $C_7:Q_8$ $2^{3} \cdot 7$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
672.974.12.h1.b1 $C_7:Q_8$ $2^{3} \cdot 7$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
672.974.12.i1.a1 $C_7:Q_8$ $2^{3} \cdot 7$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
672.974.14.a1.a1 $C_3\times \OD_{16}$ $2^{4} \cdot 3$ ✓ ✓ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $D_7$ $2 \cdot 7$
672.974.14.b1.a1 $D_{12}:C_2$ $2^{4} \cdot 3$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 7$ $-$
672.974.14.c1.a1 $C_6:Q_8$ $2^{4} \cdot 3$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 7$ $-$
672.974.14.d1.a1 $C_{24}:C_2$ $2^{4} \cdot 3$ $C_4.D_{84}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 7$ $-$
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