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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 286 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1296.2922.1.a1.a1 $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_1$ $1$ ✓
1296.2922.2.a1.a1 $S_3\times C_3^2.A_4$ $2^{3} \cdot 3^{4}$ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_2$ $2$ ✓
1296.2922.2.b1.a1 $C_3^3.S_4$ $2^{3} \cdot 3^{4}$ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_2$ $2$ ✓
1296.2922.2.c1.a1 $C_3^3.S_4$ $2^{3} \cdot 3^{4}$ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_2$ $2$ ✓
1296.2922.3.a1.a1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_3$ $3$ ✓
1296.2922.3.b1.a1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $3$ $-$
1296.2922.3.c1.a1 $C_6^2:D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $3$ $-$
1296.2922.4.a1.a1 $C_3^3.A_4$ $2^{2} \cdot 3^{4}$ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1296.2922.4.b1.a1 $C_3^2.S_3^2$ $2^{2} \cdot 3^{4}$ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2^{2}$ $-$
1296.2922.6.a1.a1 $S_3\times C_6^2$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
1296.2922.6.b1.a1 $C_6^2.C_6$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_6$ $2 \cdot 3$ ✓
1296.2922.6.c1.a1 $C_3^2.S_4$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_6$ $2 \cdot 3$ ✓
1296.2922.6.d1.a1 $C_3^2.S_4$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
1296.2922.6.e1.a1 $C_3^2.S_4$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_6$ $2 \cdot 3$ ✓
1296.2922.6.f1.a1 $C_6\times S_3^2$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.2922.6.g1.a1 $C_6.S_3^2$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.2922.6.h1.a1 $C_3^3:D_4$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.2922.6.i1.a1 $C_3^2:D_{12}$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.2922.6.j1.a1 $C_6^2.C_6$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.2922.6.k1.a1 $C_6^2.C_6$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.2922.6.l1.a1 $C_6^2:C_6$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.2922.6.m1.a1 $C_3^2.S_4$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.2922.6.n1.a1 $C_6^2:C_6$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.2922.6.o1.a1 $C_3^2.S_4$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.2922.6.p1.a1 $C_3^2.S_4$ $2^{3} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.2922.8.a1.a1 $C_3^3.C_6$ $2 \cdot 3^{4}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2^{3}$ $-$
1296.2922.8.b1.a1 $D_9:C_3^2$ $2 \cdot 3^{4}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2^{3}$ $-$
1296.2922.8.c1.a1 $C_3^3.S_3$ $2 \cdot 3^{4}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2^{3}$ $-$
1296.2922.9.a1.a1 $C_6^2:C_2^2$ $2^{4} \cdot 3^{2}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $3^{2}$ $-$
1296.2922.9.b1.a1 $C_2^2:D_{18}$ $2^{4} \cdot 3^{2}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $3^{2}$ $-$
1296.2922.9.c1.a1 $C_{12}:D_6$ $2^{4} \cdot 3^{2}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $3^{2}$ $-$
1296.2922.9.d1.a1 $D_6:D_6$ $2^{4} \cdot 3^{2}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $3^{2}$ $-$
1296.2922.12.a1.a1 $C_3\times C_6^2$ $2^{2} \cdot 3^{3}$ ✓ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
1296.2922.12.b1.a1 $C_3^2.A_4$ $2^{2} \cdot 3^{3}$ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
1296.2922.12.c1.a1 $C_3^2.A_4$ $2^{2} \cdot 3^{3}$ ✓ ✓ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
1296.2922.12.d1.a1 $C_3^2\times D_6$ $2^{2} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
1296.2922.12.e1.a1 $C_3^2\times D_6$ $2^{2} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
1296.2922.12.f1.a1 $C_3^2\times D_6$ $2^{2} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
1296.2922.12.g1.a1 $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
1296.2922.12.h1.a1 $C_3^2:C_{12}$ $2^{2} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
1296.2922.12.i1.a1 $C_3^2:C_{12}$ $2^{2} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
1296.2922.12.j1.a1 $C_3^2.A_4$ $2^{2} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
1296.2922.12.k1.a1 $C_3^2.A_4$ $2^{2} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
1296.2922.12.l1.a1 $C_3^2.A_4$ $2^{2} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
1296.2922.12.m1.a1 $C_3^2.A_4$ $2^{2} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
1296.2922.12.n1.a1 $C_{18}:C_6$ $2^{2} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
1296.2922.12.o1.a1 $C_3\times S_3^2$ $2^{2} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
1296.2922.12.p1.a1 $S_3\times D_9$ $2^{2} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
1296.2922.12.q1.a1 $C_3\times S_3^2$ $2^{2} \cdot 3^{3}$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
1296.2922.16.a1.a1 $C_9:C_3^2$ $3^{4}$ $3$ $C_6^2.S_3^2$ $2^{4} \cdot 3^{4}$ $2^{4}$ $-$
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