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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
672.941.1.a1.a1 $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ ✓ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $C_1$ $1$ ✓
672.941.2.a1.a1 $D_{42}:C_4$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
672.941.2.a1.b1 $D_{42}:C_4$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
672.941.2.a1.c1 $D_{42}:C_4$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
672.941.2.b1.a1 $C_{42}.D_4$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
672.941.2.b1.b1 $C_{42}.D_4$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
672.941.2.b1.c1 $C_{42}.D_4$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
672.941.2.c1.a1 $C_4\times C_{84}$ $2^{4} \cdot 3 \cdot 7$ ✓ ✓ ✓ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $C_2$ $2$ ✓
672.941.3.a1.a1 $C_4^2:D_7$ $2^{5} \cdot 7$ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $3$ $-$
672.941.4.a1.a1 $C_2\times D_{42}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
672.941.4.b1.a1 $C_2\times C_{84}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
672.941.4.b1.b1 $C_2\times C_{84}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
672.941.4.b1.c1 $C_2\times C_{84}$ $2^{3} \cdot 3 \cdot 7$ ✓ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
672.941.4.c1.a1 $C_{42}:C_4$ $2^{3} \cdot 3 \cdot 7$ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
672.941.4.c1.b1 $C_{42}:C_4$ $2^{3} \cdot 3 \cdot 7$ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
672.941.4.c1.c1 $C_{42}:C_4$ $2^{3} \cdot 3 \cdot 7$ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $C_2^2$ $2^{2}$ ✓
672.941.6.a1.a1 $C_4\times C_{28}$ $2^{4} \cdot 7$ ✓ ✓ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $S_3$ $2 \cdot 3$
672.941.6.b1.a1 $D_{14}:C_4$ $2^{4} \cdot 7$ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
672.941.6.b1.b1 $D_{14}:C_4$ $2^{4} \cdot 7$ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
672.941.6.b1.c1 $D_{14}:C_4$ $2^{4} \cdot 7$ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
672.941.6.c1.a1 $C_{14}.D_4$ $2^{4} \cdot 7$ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
672.941.6.c1.b1 $C_{14}.D_4$ $2^{4} \cdot 7$ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
672.941.6.c1.c1 $C_{14}.D_4$ $2^{4} \cdot 7$ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 3$ $-$
672.941.7.a1.a1 $C_4^2:S_3$ $2^{5} \cdot 3$ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $7$ $-$
672.941.8.a1.a1 $C_2\times C_{42}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $C_2^3$ $2^{3}$ ✓
672.941.8.b1.a1 $D_{42}$ $2^{2} \cdot 3 \cdot 7$ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2^{3}$ $-$
672.941.8.b1.b1 $D_{42}$ $2^{2} \cdot 3 \cdot 7$ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2^{3}$ $-$
672.941.8.b1.c1 $D_{42}$ $2^{2} \cdot 3 \cdot 7$ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2^{3}$ $-$
672.941.8.c1.a1 $C_{84}$ $2^{2} \cdot 3 \cdot 7$ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2^{3}$ $-$
672.941.8.c1.b1 $C_{84}$ $2^{2} \cdot 3 \cdot 7$ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2^{3}$ $-$
672.941.8.c1.c1 $C_{84}$ $2^{2} \cdot 3 \cdot 7$ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2^{3}$ $-$
672.941.8.d1.a1 $C_{21}:C_4$ $2^{2} \cdot 3 \cdot 7$ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2^{3}$ $-$
672.941.8.d1.b1 $C_{21}:C_4$ $2^{2} \cdot 3 \cdot 7$ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2^{3}$ $-$
672.941.8.d1.c1 $C_{21}:C_4$ $2^{2} \cdot 3 \cdot 7$ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2^{3}$ $-$
672.941.12.a1.a1 $C_2\times C_{28}$ $2^{3} \cdot 7$ ✓ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $D_6$ $2^{2} \cdot 3$
672.941.12.a1.b1 $C_2\times C_{28}$ $2^{3} \cdot 7$ ✓ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $D_6$ $2^{2} \cdot 3$
672.941.12.a1.c1 $C_2\times C_{28}$ $2^{3} \cdot 7$ ✓ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $D_6$ $2^{2} \cdot 3$
672.941.12.b1.a1 $C_2\times D_{14}$ $2^{3} \cdot 7$ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
672.941.12.c1.a1 $C_{14}:C_4$ $2^{3} \cdot 7$ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
672.941.12.c1.b1 $C_{14}:C_4$ $2^{3} \cdot 7$ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
672.941.12.c1.c1 $C_{14}:C_4$ $2^{3} \cdot 7$ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2^{2} \cdot 3$ $-$
672.941.14.a1.a1 $C_4\times C_{12}$ $2^{4} \cdot 3$ ✓ ✓ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $D_7$ $2 \cdot 7$
672.941.14.b1.a1 $D_6:C_4$ $2^{4} \cdot 3$ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 7$ $-$
672.941.14.b1.b1 $D_6:C_4$ $2^{4} \cdot 3$ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 7$ $-$
672.941.14.b1.c1 $D_6:C_4$ $2^{4} \cdot 3$ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 7$ $-$
672.941.14.c1.a1 $C_6.D_4$ $2^{4} \cdot 3$ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 7$ $-$
672.941.14.c1.b1 $C_6.D_4$ $2^{4} \cdot 3$ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 7$ $-$
672.941.14.c1.c1 $C_6.D_4$ $2^{4} \cdot 3$ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $2 \cdot 7$ $-$
672.941.16.a1.a1 $C_{42}$ $2 \cdot 3 \cdot 7$ ✓ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $D_4:C_2$ $2^{4}$
672.941.16.a1.b1 $C_{42}$ $2 \cdot 3 \cdot 7$ ✓ ✓ $C_4^2:D_{21}$ $2^{5} \cdot 3 \cdot 7$ $D_4:C_2$ $2^{4}$
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