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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 377 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1296.879.1.a1.a1 $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ ✓ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_1$ $1$ ✓
1296.879.2.a1.a1 $C_6^2:D_9$ $2^{3} \cdot 3^{4}$ ✓ ✓ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_2$ $2$ ✓
1296.879.2.b1.a1 $C_6^2.C_{18}$ $2^{3} \cdot 3^{4}$ ✓ ✓ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_2$ $2$ ✓
1296.879.2.c1.a1 $C_6^2.D_9$ $2^{3} \cdot 3^{4}$ ✓ ✓ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_2$ $2$ ✓
1296.879.2.d1.a1 $C_3^2:(C_4\times D_9)$ $2^{3} \cdot 3^{4}$ ✓ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_2$ $2$ ✓
1296.879.2.d1.b1 $C_3^2:(C_4\times D_9)$ $2^{3} \cdot 3^{4}$ ✓ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_2$ $2$ ✓
1296.879.2.d1.c1 $C_3^2:(C_4\times D_9)$ $2^{3} \cdot 3^{4}$ ✓ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_2$ $2$ ✓
1296.879.2.d1.d1 $C_3^2:(C_4\times D_9)$ $2^{3} \cdot 3^{4}$ ✓ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_2$ $2$ ✓
1296.879.3.a1.a1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $3$ $-$
1296.879.3.b1.a1 $D_{18}.D_6$ $2^{4} \cdot 3^{3}$ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $3$ $-$
1296.879.4.a1.a1 $C_6^2:C_9$ $2^{2} \cdot 3^{4}$ ✓ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1296.879.4.b1.a1 $C_3^2:D_{18}$ $2^{2} \cdot 3^{4}$ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1296.879.4.b1.b1 $C_3^2:D_{18}$ $2^{2} \cdot 3^{4}$ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1296.879.4.c1.a1 $C_3^2:C_{36}$ $2^{2} \cdot 3^{4}$ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1296.879.4.c1.b1 $C_3^2:C_{36}$ $2^{2} \cdot 3^{4}$ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1296.879.4.d1.a1 $(C_3\times C_9):C_{12}$ $2^{2} \cdot 3^{4}$ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1296.879.4.d1.b1 $(C_3\times C_9):C_{12}$ $2^{2} \cdot 3^{4}$ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1296.879.4.e1.a1 $C_3^2:D_{18}$ $2^{2} \cdot 3^{4}$ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_4$ $2^{2}$ ✓
1296.879.4.e1.b1 $C_3^2:D_{18}$ $2^{2} \cdot 3^{4}$ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_4$ $2^{2}$ ✓
1296.879.4.e1.c1 $C_3^2:D_{18}$ $2^{2} \cdot 3^{4}$ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_4$ $2^{2}$ ✓
1296.879.4.e1.d1 $C_3^2:D_{18}$ $2^{2} \cdot 3^{4}$ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_4$ $2^{2}$ ✓
1296.879.6.a1.a1 $C_6^2.C_6$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
1296.879.6.b1.a1 $C_6.D_{18}$ $2^{3} \cdot 3^{3}$ ✓ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
1296.879.6.c1.a1 $C_6^2:C_6$ $2^{3} \cdot 3^{3}$ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.879.6.d1.a1 $C_6\times D_{18}$ $2^{3} \cdot 3^{3}$ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.879.6.e1.a1 $C_6\times D_{18}$ $2^{3} \cdot 3^{3}$ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.879.6.f1.a1 $C_6^2.C_6$ $2^{3} \cdot 3^{3}$ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.879.6.g1.a1 $C_6:C_{36}$ $2^{3} \cdot 3^{3}$ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.879.6.h1.a1 $C_6.S_3^2$ $2^{3} \cdot 3^{3}$ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.879.6.h1.b1 $C_6.S_3^2$ $2^{3} \cdot 3^{3}$ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.879.6.h1.c1 $C_6.S_3^2$ $2^{3} \cdot 3^{3}$ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.879.6.h1.d1 $C_6.S_3^2$ $2^{3} \cdot 3^{3}$ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.879.6.i1.a1 $C_6.D_{18}$ $2^{3} \cdot 3^{3}$ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.879.6.i1.b1 $C_6.D_{18}$ $2^{3} \cdot 3^{3}$ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.879.6.i1.c1 $C_6.D_{18}$ $2^{3} \cdot 3^{3}$ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.879.6.i1.d1 $C_6.D_{18}$ $2^{3} \cdot 3^{3}$ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $2 \cdot 3$ $-$
1296.879.8.a1.a1 $C_3^2:C_{18}$ $2 \cdot 3^{4}$ ✓ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_2^3$ $2^{3}$ ✓
1296.879.8.b1.a1 $C_3^2:C_{18}$ $2 \cdot 3^{4}$ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_2\times C_4$ $2^{3}$ ✓
1296.879.8.b1.b1 $C_3^2:C_{18}$ $2 \cdot 3^{4}$ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_2\times C_4$ $2^{3}$ ✓
1296.879.8.c1.a1 $C_3^2:D_9$ $2 \cdot 3^{4}$ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_2\times C_4$ $2^{3}$ ✓
1296.879.8.c1.b1 $C_3^2:D_9$ $2 \cdot 3^{4}$ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_2\times C_4$ $2^{3}$ ✓
1296.879.8.c1.c1 $C_3^2:D_9$ $2 \cdot 3^{4}$ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_2\times C_4$ $2^{3}$ ✓
1296.879.8.c1.d1 $C_3^2:D_9$ $2 \cdot 3^{4}$ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $C_2\times C_4$ $2^{3}$ ✓
1296.879.9.a1.a1 $D_6.D_6$ $2^{4} \cdot 3^{2}$ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $3^{2}$ $-$
1296.879.9.b1.a1 $D_6.D_6$ $2^{4} \cdot 3^{2}$ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $3^{2}$ $-$
1296.879.9.c1.a1 $C_2^2.S_3^2$ $2^{4} \cdot 3^{2}$ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $3^{2}$ $-$
1296.879.9.d1.a1 $C_4\times D_{18}$ $2^{4} \cdot 3^{2}$ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $3^{2}$ $-$
1296.879.12.a1.a1 $C_3\times C_6^2$ $2^{2} \cdot 3^{3}$ ✓ ✓ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
1296.879.12.b1.a1 $C_6\times C_{18}$ $2^{2} \cdot 3^{3}$ ✓ ✓ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
1296.879.12.c1.a1 $C_3^2:C_{12}$ $2^{2} \cdot 3^{3}$ ✓ $C_6^2.D_{18}$ $2^{4} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
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