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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 (46 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
17496.ln.1.a1 $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_1$ $1$ ✓
17496.ln.2.a1 $C_3^6:D_6$ $2^{2} \cdot 3^{7}$ ✓ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_2$ $2$ ✓
17496.ln.2.b1 $C_3^6.C_6.C_2$ $2^{2} \cdot 3^{7}$ ✓ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_2$ $2$ ✓
17496.ln.2.c1 $(C_3^3\times \He_3):C_{12}$ $2^{2} \cdot 3^{7}$ ✓ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_2$ $2$ ✓
17496.ln.4.a1 $C_3^6.C_6$ $2 \cdot 3^{7}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_2^2$ $2^{2}$ ✓
17496.ln.6.a1 $C_3^5:D_6$ $2^{2} \cdot 3^{6}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $S_3$ $2 \cdot 3$
17496.ln.6.b1 $C_3^5.D_6$ $2^{2} \cdot 3^{6}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $S_3$ $2 \cdot 3$
17496.ln.6.c1 $(C_3^3\times \He_3):C_4$ $2^{2} \cdot 3^{6}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $S_3$ $2 \cdot 3$
17496.ln.8.a1 $C_3^2\times C_3^4:C_3$ $3^{7}$ $3$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $D_4$ $2^{3}$
17496.ln.12.a1 $C_3^5:C_6$ $2 \cdot 3^{6}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $D_6$ $2^{2} \cdot 3$
17496.ln.12.b1 $C_3^5:C_6$ $2 \cdot 3^{6}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $D_6$ $2^{2} \cdot 3$
17496.ln.12.c1 $C_3^5:C_6$ $2 \cdot 3^{6}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $D_6$ $2^{2} \cdot 3$
17496.ln.24.a1 $C_3^6$ $3^{6}$ ✓ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_3:D_4$ $2^{3} \cdot 3$
17496.ln.24.b1 $C_3^3\times \He_3$ $3^{6}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $D_{12}$ $2^{3} \cdot 3$
17496.ln.24.c1 $C_3^3\times \He_3$ $3^{6}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_3:D_4$ $2^{3} \cdot 3$
17496.ln.36.a1 $C_3^4:C_6$ $2 \cdot 3^{5}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $S_3^2$ $2^{2} \cdot 3^{2}$
17496.ln.36.b1 $C_3^4:C_6$ $2 \cdot 3^{5}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $S_3^2$ $2^{2} \cdot 3^{2}$
17496.ln.36.c1 $C_3^4:C_6$ $2 \cdot 3^{5}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $S_3^2$ $2^{2} \cdot 3^{2}$
17496.ln.72.a1 $C_3^5$ $3^{5}$ ✓ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_3:D_{12}$ $2^{3} \cdot 3^{2}$
17496.ln.72.b1 $C_3^5$ $3^{5}$ ✓ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $D_6:S_3$ $2^{3} \cdot 3^{2}$
17496.ln.72.c1 $C_3^5$ $3^{5}$ ✓ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_3:D_{12}$ $2^{3} \cdot 3^{2}$
17496.ln.72.d1 $C_3^4:C_3$ $3^{5}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $\SOPlus(4,2)$ $2^{3} \cdot 3^{2}$
17496.ln.108.a1 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_3:S_3^2$ $2^{2} \cdot 3^{3}$
17496.ln.108.b1 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$
17496.ln.108.c1 $C_3^2\wr C_2$ $2 \cdot 3^{4}$ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$
17496.ln.216.a1 $C_3^4$ $3^{4}$ ✓ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_3^2:D_{12}$ $2^{3} \cdot 3^{3}$
17496.ln.216.b1 $C_3^4$ $3^{4}$ ✓ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $S_3^2:S_3$ $2^{3} \cdot 3^{3}$
17496.ln.216.c1 $C_3\times \He_3$ $3^{4}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_3^2:D_{12}$ $2^{3} \cdot 3^{3}$
17496.ln.216.d1 $C_3\times \He_3$ $3^{4}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $S_3^2:S_3$ $2^{3} \cdot 3^{3}$
17496.ln.216.e1 $C_3^4$ $3^{4}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $\He_3:D_4$ $2^{3} \cdot 3^{3}$
17496.ln.216.f1 $C_3^4$ $3^{4}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_3^2:D_{12}$ $2^{3} \cdot 3^{3}$
17496.ln.324.a1 $C_3^2:C_6$ $2 \cdot 3^{3}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$
17496.ln.324.b1 $C_3^2:C_6$ $2 \cdot 3^{3}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_3^2:S_3^2$ $2^{2} \cdot 3^{4}$
17496.ln.648.a1 $C_3^3$ $3^{3}$ ✓ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$
17496.ln.648.b1 $C_3^3$ $3^{3}$ ✓ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_3^4:D_4$ $2^{3} \cdot 3^{4}$
17496.ln.648.c1 $C_3^3$ $3^{3}$ ✓ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$
17496.ln.648.d1 $C_3^3$ $3^{3}$ ✓ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $\He_3:D_{12}$ $2^{3} \cdot 3^{4}$
17496.ln.648.e1 $C_3^3$ $3^{3}$ ✓ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_3^3:D_{12}$ $2^{3} \cdot 3^{4}$
17496.ln.972.a1 $C_3:S_3$ $2 \cdot 3^{2}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_3^3:S_3^2$ $2^{2} \cdot 3^{5}$
17496.ln.1944.a1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_3^4:D_{12}$ $2^{3} \cdot 3^{5}$
17496.ln.1944.b1 $C_3^2$ $3^{2}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $\He_3:\SOPlus(4,2)$ $2^{3} \cdot 3^{5}$
17496.ln.1944.c1 $C_3^2$ $3^{2}$ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_3^4:D_{12}$ $2^{3} \cdot 3^{5}$
17496.ln.1944.d1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $(C_3\times \He_3):D_{12}$ $2^{3} \cdot 3^{5}$ ✓
17496.ln.5832.a1 $C_3$ $3$ ✓ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_3.C_3^5.D_4$ $2^{3} \cdot 3^{6}$ ✓
17496.ln.5832.b1 $C_3$ $3$ ✓ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $C_3^5.C_3.D_4$ $2^{3} \cdot 3^{6}$ ✓
17496.ln.17496.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$ $(C_3^3\times \He_3):D_{12}$ $2^{3} \cdot 3^{7}$
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