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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 84 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
84.1.42.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_7:C_{12}$ $2^{2} \cdot 3 \cdot 7$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
84.7.42.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2\times F_7$ $2^{2} \cdot 3 \cdot 7$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
126.1.42.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_7:C_{18}$ $2 \cdot 3^{2} \cdot 7$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
126.7.42.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_3\times F_7$ $2 \cdot 3^{2} \cdot 7$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
126.9.42.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_{21}:C_6$ $2 \cdot 3^{2} \cdot 7$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
168.49.42.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $D_7:A_4$ $2^{3} \cdot 3 \cdot 7$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
210.1.42.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ ✓ $C_5\times F_7$ $2 \cdot 3 \cdot 5 \cdot 7$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
210.3.42.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $C_{35}:C_6$ $2 \cdot 3 \cdot 5 \cdot 7$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
294.1.42.a1.a1 $C_7$ $7$ ✓ ✓ ✓ $C_{49}:C_6$ $2 \cdot 3 \cdot 7^{2}$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
294.8.42.a1.a1 $C_7$ $7$ ✓ ✓ ✓ ✓ $C_7\times F_7$ $2 \cdot 3 \cdot 7^{2}$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
294.10.42.a1.a1 $C_7$ $7$ ✓ ✓ ✓ $C_7:F_7$ $2 \cdot 3 \cdot 7^{2}$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
294.11.42.a1.a1 $C_7$ $7$ ✓ ✓ ✓ $C_7:F_7$ $2 \cdot 3 \cdot 7^{2}$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
294.12.42.a1.a1 $C_7$ $7$ ✓ ✓ ✓ $C_7:F_7$ $2 \cdot 3 \cdot 7^{2}$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
294.13.42.a1.a1 $C_7$ $7$ ✓ ✓ $C_7:F_7$ $2 \cdot 3 \cdot 7^{2}$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
294.13.42.a1.b1 $C_7$ $7$ ✓ ✓ $C_7:F_7$ $2 \cdot 3 \cdot 7^{2}$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
294.13.42.a1.c1 $C_7$ $7$ ✓ ✓ $C_7:F_7$ $2 \cdot 3 \cdot 7^{2}$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
294.13.42.a1.d1 $C_7$ $7$ ✓ ✓ $C_7:F_7$ $2 \cdot 3 \cdot 7^{2}$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
294.13.42.a1.e1 $C_7$ $7$ ✓ ✓ $C_7:F_7$ $2 \cdot 3 \cdot 7^{2}$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
294.13.42.a1.f1 $C_7$ $7$ ✓ ✓ $C_7:F_7$ $2 \cdot 3 \cdot 7^{2}$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
294.13.42.a1.g1 $C_7$ $7$ ✓ ✓ $C_7:F_7$ $2 \cdot 3 \cdot 7^{2}$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
294.13.42.a1.h1 $C_7$ $7$ ✓ ✓ $C_7:F_7$ $2 \cdot 3 \cdot 7^{2}$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
294.14.42.a1.a1 $C_7$ $7$ ✓ ✓ $C_7:F_7$ $2 \cdot 3 \cdot 7^{2}$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
294.14.42.a1.b1 $C_7$ $7$ ✓ ✓ $C_7:F_7$ $2 \cdot 3 \cdot 7^{2}$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
462.2.42.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ ✓ $C_{11}\times F_7$ $2 \cdot 3 \cdot 7 \cdot 11$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
462.3.42.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $C_{77}:C_6$ $2 \cdot 3 \cdot 7 \cdot 11$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
546.7.42.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ ✓ $C_{13}\times F_7$ $2 \cdot 3 \cdot 7 \cdot 13$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
546.8.42.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_{91}:C_6$ $2 \cdot 3 \cdot 7 \cdot 13$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
546.9.42.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_{91}:C_6$ $2 \cdot 3 \cdot 7 \cdot 13$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
546.10.42.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_{91}:C_6$ $2 \cdot 3 \cdot 7 \cdot 13$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
546.11.42.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_{91}:C_6$ $2 \cdot 3 \cdot 7 \cdot 13$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
546.12.42.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_{91}:C_6$ $2 \cdot 3 \cdot 7 \cdot 13$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
714.2.42.a1.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ ✓ $C_{17}\times F_7$ $2 \cdot 3 \cdot 7 \cdot 17$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
714.3.42.a1.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ $C_{119}:C_6$ $2 \cdot 3 \cdot 7 \cdot 17$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
798.7.42.a1.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ ✓ $C_{19}\times F_7$ $2 \cdot 3 \cdot 7 \cdot 19$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
798.8.42.a1.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ $C_{133}:C_6$ $2 \cdot 3 \cdot 7 \cdot 19$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
798.9.42.a1.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ $C_{133}:C_6$ $2 \cdot 3 \cdot 7 \cdot 19$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
798.10.42.a1.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ $C_{133}:C_6$ $2 \cdot 3 \cdot 7 \cdot 19$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
798.11.42.a1.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ $C_{133}:C_6$ $2 \cdot 3 \cdot 7 \cdot 19$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
798.12.42.a1.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ $C_{133}:C_6$ $2 \cdot 3 \cdot 7 \cdot 19$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
966.2.42.a1.a1 $C_{23}$ $23$ $23$ ✓ ✓ ✓ ✓ $C_{23}\times F_7$ $2 \cdot 3 \cdot 7 \cdot 23$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
966.3.42.a1.a1 $C_{23}$ $23$ $23$ ✓ ✓ ✓ $C_{161}:C_6$ $2 \cdot 3 \cdot 7 \cdot 23$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
1050.21.42.a1.a1 $C_5^2$ $5^{2}$ $5$ ✓ ✓ ✓ $C_5^2:F_7$ $2 \cdot 3 \cdot 5^{2} \cdot 7$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
1050.25.42.a1.a1 $C_5^2$ $5^{2}$ $5$ ✓ ✓ ✓ $C_5^2:F_7$ $2 \cdot 3 \cdot 5^{2} \cdot 7$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
1218.6.42.a1.a1 $C_{29}$ $29$ $29$ ✓ ✓ ✓ ✓ $C_{29}\times F_7$ $2 \cdot 3 \cdot 7 \cdot 29$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
1218.7.42.a1.a1 $C_{29}$ $29$ $29$ ✓ ✓ ✓ $C_{203}:C_6$ $2 \cdot 3 \cdot 7 \cdot 29$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
1302.7.42.a1.a1 $C_{31}$ $31$ $31$ ✓ ✓ ✓ ✓ $C_{31}\times F_7$ $2 \cdot 3 \cdot 7 \cdot 31$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
1302.8.42.a1.a1 $C_{31}$ $31$ $31$ ✓ ✓ ✓ $C_{217}:C_6$ $2 \cdot 3 \cdot 7 \cdot 31$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
1302.9.42.a1.a1 $C_{31}$ $31$ $31$ ✓ ✓ ✓ $C_{217}:C_6$ $2 \cdot 3 \cdot 7 \cdot 31$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
1302.10.42.a1.a1 $C_{31}$ $31$ $31$ ✓ ✓ ✓ $C_{217}:C_6$ $2 \cdot 3 \cdot 7 \cdot 31$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
1302.11.42.a1.a1 $C_{31}$ $31$ $31$ ✓ ✓ ✓ $C_{217}:C_6$ $2 \cdot 3 \cdot 7 \cdot 31$ $F_7$ $2 \cdot 3 \cdot 7$ ✓
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