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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 (44 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1944.3566.1944.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
5832.ik.1944.a1 $C_3$ $3$ ✓ ✓ $C_3^3.S_3^3$ $2^{3} \cdot 3^{6}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ ✓
5832.iu.1944.a1 $C_3$ $3$ ✓ ✓ ✓ $C_3^3.S_3^3$ $2^{3} \cdot 3^{6}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ ✓
5832.lu.1944.b1.a1 $C_3$ $3$ ✓ ✓ $C_3^3.S_3^3$ $2^{3} \cdot 3^{6}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ ✓
5832.lu.1944.b1.b1 $C_3$ $3$ ✓ ✓ $C_3^3.S_3^3$ $2^{3} \cdot 3^{6}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$ ✓
17496.hz.1944.D $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3^4.S_3^3$ $2^{3} \cdot 3^{7}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
17496.is.1944.c1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3^4.S_3^3$ $2^{3} \cdot 3^{7}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
17496.iv.1944.a1 $C_3^2$ $3^{2}$ ✓ ✓ $C_3^4.S_3^3$ $2^{3} \cdot 3^{7}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
17496.iv.1944.c1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3^4.S_3^3$ $2^{3} \cdot 3^{7}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
17496.nt.1944.a1 $C_3^2$ $3^{2}$ ✓ ✓ $C_3^4.S_3^3$ $2^{3} \cdot 3^{7}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
17496.nt.1944.c1 $C_9$ $3^{2}$ ✓ ✓ $C_3^4.S_3^3$ $2^{3} \cdot 3^{7}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
17496.ql.1944.b1 $C_3^2$ $3^{2}$ ✓ ✓ $D_9^3:C_3$ $2^{3} \cdot 3^{7}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
52488.fy.1944.G $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^5.S_3^3$ $2^{3} \cdot 3^{8}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
52488.fy.1944.H $C_3^3$ $3^{3}$ ✓ ✓ $C_3^5.S_3^3$ $2^{3} \cdot 3^{8}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
52488.gb.1944.F $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^5.S_3^3$ $2^{3} \cdot 3^{8}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
52488.go.1944.F $C_3^3$ $3^{3}$ ✓ ✓ $C_3^5.S_3^3$ $2^{3} \cdot 3^{8}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
52488.go.1944.H $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^5.S_3^3$ $2^{3} \cdot 3^{8}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
52488.nc.1944.B $C_3^3$ $3^{3}$ ✓ ✓ $C_3^5.S_3^3$ $2^{3} \cdot 3^{8}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
52488.qg.1944.B $C_3^3$ $3^{3}$ ✓ ✓ $C_3^5.S_3^3$ $2^{3} \cdot 3^{8}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
52488.qg.1944.C $C_3\times C_9$ $3^{3}$ ✓ ✓ $C_3^5.S_3^3$ $2^{3} \cdot 3^{8}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
157464.en.1944.F $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^6.S_3^3$ $2^{3} \cdot 3^{9}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
157464.er.1944.F $C_3^4$ $3^{4}$ ✓ ✓ $C_3^6.S_3^3$ $2^{3} \cdot 3^{9}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
157464.eu.1944.B $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^6.S_3^3$ $2^{3} \cdot 3^{9}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
157464.eu.1944.J $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^6.S_3^3$ $2^{3} \cdot 3^{9}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
157464.eu.1944.K $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^6.S_3^3$ $2^{3} \cdot 3^{9}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
157464.lx.1944.B $C_3^4$ $3^{4}$ ✓ ✓ $C_3^6.S_3^3$ $2^{3} \cdot 3^{9}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
157464.lx.1944.C $C_3^2\times C_9$ $3^{4}$ ✓ ✓ $C_3^6.S_3^3$ $2^{3} \cdot 3^{9}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
157464.qz.1944.C $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^6.S_3^3$ $2^{3} \cdot 3^{9}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
157464.qz.1944.D $C_3^2\times C_9$ $3^{4}$ ✓ ✓ $C_3^6.S_3^3$ $2^{3} \cdot 3^{9}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
157464.sp.1944.B $C_3^2\times C_9$ $3^{4}$ ✓ ✓ $C_9^4.(C_2^2\times C_6)$ $2^{3} \cdot 3^{9}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
472392.dm.1944.L $C_3^5$ $3^{5}$ ✓ ✓ $C_3^7.S_3^3$ $2^{3} \cdot 3^{10}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
472392.dm.1944.N $C_3^5$ $3^{5}$ ✓ ✓ ✓ $C_3^7.S_3^3$ $2^{3} \cdot 3^{10}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
472392.du.1944._.O $C_3^5$ $3^{5}$ ✓ ✓ ✓ $C_3^7.S_3^3$ $2^{3} \cdot 3^{10}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
472392.du.1944._.P $C_3^5$ $3^{5}$ ✓ ✓ $C_3^7.S_3^3$ $2^{3} \cdot 3^{10}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
472392.du.1944._.R $C_3^5$ $3^{5}$ ✓ ✓ $C_3^7.S_3^3$ $2^{3} \cdot 3^{10}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
472392.lf.1944.A $C_3^5$ $3^{5}$ ✓ ✓ $C_3^7.S_3^3$ $2^{3} \cdot 3^{10}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
1417176.dm.1944._.S $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^8.S_3^3$ $2^{3} \cdot 3^{11}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
1417176.dm.1944._.T $C_3^6$ $3^{6}$ ✓ ✓ $C_3^8.S_3^3$ $2^{3} \cdot 3^{11}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
1417176.dm.1944._.W $C_3^6$ $3^{6}$ ✓ ✓ $C_3^8.S_3^3$ $2^{3} \cdot 3^{11}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
1417176.hm.1944.A $C_3^6$ $3^{6}$ ✓ ✓ $C_3^8.S_3^3$ $2^{3} \cdot 3^{11}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
1417176.hm.1944.B $C_3^4:C_9$ $3^{6}$ ✓ $C_3^8.S_3^3$ $2^{3} \cdot 3^{11}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
4251528.bw.1944._.C $C_3^7$ $3^{7}$ ✓ ✓ $C_3^8.(C_3\times S_3^3)$ $2^{3} \cdot 3^{12}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
4251528.bw.1944._.L $C_3^7$ $3^{7}$ ✓ ✓ $C_3^8.(C_3\times S_3^3)$ $2^{3} \cdot 3^{12}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
4251528.bw.1944._.R $C_3^7$ $3^{7}$ ✓ ✓ $C_3^8.(C_3\times S_3^3)$ $2^{3} \cdot 3^{12}$ $C_3^2.S_3^3$ $2^{3} \cdot 3^{5}$
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