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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 121 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
746496.n.1.a1 $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_1$ $1$ ✓
746496.n.2.A $C_3^4.D_4^3:C_3^2$ $2^{9} \cdot 3^{6}$ ✓ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2$ $2$ ✓
746496.n.2.B $C_3^5.C_2\wr S_4$ $2^{9} \cdot 3^{6}$ ✓ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2$ $2$ ✓
746496.n.2.C $C_3^5.C_2\wr S_4$ $2^{9} \cdot 3^{6}$ ✓ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2$ $2$ ✓
746496.n.2.D $C_3^5.C_2\wr S_4$ $2^{9} \cdot 3^{6}$ ✓ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2$ $2$ ✓
746496.n.2.E $C_3^5.C_2\wr S_4$ $2^{9} \cdot 3^{6}$ ✓ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2$ $2$ ✓
746496.n.2.F $C_3^5.C_4^3:S_4$ $2^{9} \cdot 3^{6}$ ✓ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2$ $2$ ✓
746496.n.2.G $C_3^5.C_4^3:S_4$ $2^{9} \cdot 3^{6}$ ✓ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2$ $2$ ✓
746496.n.4.A $C_3^5.C_2\wr A_4$ $2^{8} \cdot 3^{6}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
746496.n.4.B $C_3^5.C_2\wr A_4$ $2^{8} \cdot 3^{6}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
746496.n.4.C $C_3^5.C_4^3:A_4$ $2^{8} \cdot 3^{6}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
746496.n.4.D $C_6^2.C_6^3:S_4$ $2^{8} \cdot 3^{6}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
746496.n.4.E $C_6^2.C_6^3:S_4$ $2^{8} \cdot 3^{6}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
746496.n.4.F $C_6^2.C_6^3:S_4$ $2^{8} \cdot 3^{6}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
746496.n.4.G $C_6^3.C_6^2:S_4$ $2^{8} \cdot 3^{6}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2^2$ $2^{2}$ ✓
746496.n.6.A $C_6^5.C_2^4$ $2^{9} \cdot 3^{5}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $S_3$ $2 \cdot 3$
746496.n.8.A $C_6^2.C_6^3:A_4$ $2^{7} \cdot 3^{6}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2^3$ $2^{3}$ ✓
746496.n.12.A $C_6^5.C_2^3$ $2^{8} \cdot 3^{5}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $D_6$ $2^{2} \cdot 3$
746496.n.12.C $C_6^5.C_2^3$ $2^{8} \cdot 3^{5}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $D_6$ $2^{2} \cdot 3$
746496.n.12.E $C_6^5.C_2^3$ $2^{8} \cdot 3^{5}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $D_6$ $2^{2} \cdot 3$
746496.n.18.A $C_6^4.C_2^5$ $2^{9} \cdot 3^{4}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_3:S_3$ $2 \cdot 3^{2}$
746496.n.24.A $C_6^5.C_2^2$ $2^{7} \cdot 3^{5}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $S_4$ $2^{3} \cdot 3$
746496.n.24.B $C_6^3.C_6^2.C_2^2$ $2^{7} \cdot 3^{5}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $S_4$ $2^{3} \cdot 3$
746496.n.24.C $C_6^3.C_6^2.C_2^2$ $2^{7} \cdot 3^{5}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $S_4$ $2^{3} \cdot 3$
746496.n.24.D $C_6^5.C_2^2$ $2^{7} \cdot 3^{5}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2\times D_6$ $2^{3} \cdot 3$
746496.n.36.A $C_6^4.C_2^4$ $2^{8} \cdot 3^{4}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_6:S_3$ $2^{2} \cdot 3^{2}$
746496.n.36.B $C_6^4.C_2^4$ $2^{8} \cdot 3^{4}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_6:S_3$ $2^{2} \cdot 3^{2}$
746496.n.36.C $C_6^4.C_2^4$ $2^{8} \cdot 3^{4}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_6:S_3$ $2^{2} \cdot 3^{2}$
746496.n.48.A $C_2\times C_6^5$ $2^{6} \cdot 3^{5}$ ✓ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2\times S_4$ $2^{4} \cdot 3$
746496.n.48.B $(C_3\times C_6^4).C_2^2$ $2^{6} \cdot 3^{5}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2\times S_4$ $2^{4} \cdot 3$
746496.n.48.C $(C_3\times C_6^4).C_2^2$ $2^{6} \cdot 3^{5}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2\times S_4$ $2^{4} \cdot 3$
746496.n.48.D $C_6^5.C_2$ $2^{6} \cdot 3^{5}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2\times S_4$ $2^{4} \cdot 3$
746496.n.48.E $C_6^5.C_2$ $2^{6} \cdot 3^{5}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2\times S_4$ $2^{4} \cdot 3$
746496.n.48.F $C_3^5.C_2^6$ $2^{6} \cdot 3^{5}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2\times S_4$ $2^{4} \cdot 3$
746496.n.48.G $(C_3^2\times C_6^3).C_2^3$ $2^{6} \cdot 3^{5}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2\times S_4$ $2^{4} \cdot 3$
746496.n.48.H $(C_3^2\times C_6^3).C_2^3$ $2^{6} \cdot 3^{5}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2\times S_4$ $2^{4} \cdot 3$
746496.n.48.I $C_3^5.C_4^3$ $2^{6} \cdot 3^{5}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2\times S_4$ $2^{4} \cdot 3$
746496.n.54.A $C_6^3.C_2^6$ $2^{9} \cdot 3^{3}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_3^2:S_3$ $2 \cdot 3^{3}$
746496.n.72.A $C_6^4.C_2^3$ $2^{7} \cdot 3^{4}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_3:S_4$ $2^{3} \cdot 3^{2}$
746496.n.72.B $C_6^4.C_2^3$ $2^{7} \cdot 3^{4}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_3:S_4$ $2^{3} \cdot 3^{2}$
746496.n.72.C $C_6^4.C_2^3$ $2^{7} \cdot 3^{4}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_3:S_4$ $2^{3} \cdot 3^{2}$
746496.n.72.D $C_6^4.C_2^3$ $2^{7} \cdot 3^{4}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_6:D_6$ $2^{3} \cdot 3^{2}$
746496.n.96.A $(C_3\times C_6^4).C_2$ $2^{5} \cdot 3^{5}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2^2:S_4$ $2^{5} \cdot 3$
746496.n.96.B $C_6^5$ $2^{5} \cdot 3^{5}$ ✓ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2^2\times S_4$ $2^{5} \cdot 3$
746496.n.96.C $C_3^5.C_2^5$ $2^{5} \cdot 3^{5}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2^2\times S_4$ $2^{5} \cdot 3$
746496.n.96.D $C_3^5.(C_2\times C_4^2)$ $2^{5} \cdot 3^{5}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_2^2\times S_4$ $2^{5} \cdot 3$
746496.n.108.A $C_6^3.C_2^5$ $2^{8} \cdot 3^{3}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$
746496.n.108.B $C_6^3.C_2^5$ $2^{8} \cdot 3^{3}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$
746496.n.108.C $C_6^3.C_2^5$ $2^{8} \cdot 3^{3}$ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_3^2:D_6$ $2^{2} \cdot 3^{3}$
746496.n.144.A $C_2^2\times C_6^4$ $2^{6} \cdot 3^{4}$ ✓ ✓ ✓ $C_3^5.D_4^3:S_3$ $2^{10} \cdot 3^{6}$ $C_6:S_4$ $2^{4} \cdot 3^{2}$
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