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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 110 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
78732.fx.1.a1 $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_1$ $1$ ✓
78732.fx.2.A $C_3^8.C_6$ $2 \cdot 3^{9}$ ✓ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_2$ $2$ ✓
78732.fx.2.B $C_3^5.\He_3.C_6$ $2 \cdot 3^{9}$ ✓ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_2$ $2$ ✓
78732.fx.2.C $C_3^7.C_3.C_6$ $2 \cdot 3^{9}$ ✓ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_2$ $2$ ✓
78732.fx.3.A $C_3^7.D_6$ $2^{2} \cdot 3^{8}$ ✓ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_3$ $3$ ✓
78732.fx.3.B $C_3^7.D_6$ $2^{2} \cdot 3^{8}$ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $3$ $-$
78732.fx.3.C $C_3^8.C_2^2$ $2^{2} \cdot 3^{8}$ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $3$ $-$
78732.fx.3.D $C_3^7.D_6$ $2^{2} \cdot 3^{8}$ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $3$ $-$
78732.fx.3.E $C_3^7.D_6$ $2^{2} \cdot 3^{8}$ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $3$ $-$
78732.fx.4.a1 $C_3^8.C_3$ $3^{9}$ $3$ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_2^2$ $2^{2}$ ✓
78732.fx.6.A $C_3^8.C_2$ $2 \cdot 3^{8}$ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $S_3$ $2 \cdot 3$
78732.fx.6.B $C_3^7.C_6$ $2 \cdot 3^{8}$ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $S_3$ $2 \cdot 3$
78732.fx.6.C $C_3^7.C_6$ $2 \cdot 3^{8}$ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $S_3$ $2 \cdot 3$
78732.fx.6.D $C_3^7.C_6$ $2 \cdot 3^{8}$ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_6$ $2 \cdot 3$ ✓
78732.fx.6.E $C_3^6.C_3.C_6$ $2 \cdot 3^{8}$ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $S_3$ $2 \cdot 3$
78732.fx.6.F $C_3^6.C_3.C_6$ $2 \cdot 3^{8}$ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_6$ $2 \cdot 3$ ✓
78732.fx.6.G $C_3^7.S_3$ $2 \cdot 3^{8}$ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_6$ $2 \cdot 3$ ✓
78732.fx.6.H $C_3^7.C_6$ $2 \cdot 3^{8}$ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $2 \cdot 3$ $-$
78732.fx.6.I $C_3^7.C_6$ $2 \cdot 3^{8}$ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $2 \cdot 3$ $-$
78732.fx.6.J $C_3^7.C_6$ $2 \cdot 3^{8}$ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $2 \cdot 3$ $-$
78732.fx.6.K $C_3^7.C_6$ $2 \cdot 3^{8}$ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $2 \cdot 3$ $-$
78732.fx.6.L $C_3^8.C_2$ $2 \cdot 3^{8}$ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $2 \cdot 3$ $-$
78732.fx.6.M $C_3^4.C_3^4.C_2$ $2 \cdot 3^{8}$ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $2 \cdot 3$ $-$
78732.fx.6.N $C_3^4.C_3^4.C_2$ $2 \cdot 3^{8}$ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $2 \cdot 3$ $-$
78732.fx.6.O $C_3^6.C_3.C_6$ $2 \cdot 3^{8}$ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $2 \cdot 3$ $-$
78732.fx.6.P $C_3^8.C_2$ $2 \cdot 3^{8}$ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $2 \cdot 3$ $-$
78732.fx.6.Q $C_3^5.C_3^3.C_2$ $2 \cdot 3^{8}$ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $2 \cdot 3$ $-$
78732.fx.6.R $C_3^4.\He_3.C_6$ $2 \cdot 3^{8}$ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $2 \cdot 3$ $-$
78732.fx.6.S $C_3^5.C_3^3.C_2$ $2 \cdot 3^{8}$ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $2 \cdot 3$ $-$
78732.fx.6.T $C_3^5.C_3^3.C_2$ $2 \cdot 3^{8}$ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $2 \cdot 3$ $-$
78732.fx.6.U $C_3^4.\He_3.C_6$ $2 \cdot 3^{8}$ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $2 \cdot 3$ $-$
78732.fx.6.V $C_3^5.C_3^3.C_2$ $2 \cdot 3^{8}$ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $2 \cdot 3$ $-$
78732.fx.12.A $C_3^8$ $3^{8}$ ✓ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $D_6$ $2^{2} \cdot 3$
78732.fx.12.B $C_3^7.C_3$ $3^{8}$ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $D_6$ $2^{2} \cdot 3$
78732.fx.12.C $C_3^7.C_3$ $3^{8}$ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $D_6$ $2^{2} \cdot 3$
78732.fx.12.D $C_3\times C_3^6.C_3$ $3^{8}$ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $D_6$ $2^{2} \cdot 3$
78732.fx.12.E $C_3^7.C_3$ $3^{8}$ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
78732.fx.18.A $C_3^7.C_2$ $2 \cdot 3^{7}$ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_3:S_3$ $2 \cdot 3^{2}$
78732.fx.18.B $C_3^7.C_2$ $2 \cdot 3^{7}$ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_3\times S_3$ $2 \cdot 3^{2}$
78732.fx.18.C $C_3^6.C_6$ $2 \cdot 3^{7}$ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_3\times S_3$ $2 \cdot 3^{2}$
78732.fx.18.D $C_3^6.C_6$ $2 \cdot 3^{7}$ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_3\times S_3$ $2 \cdot 3^{2}$
78732.fx.18.E $C_3^6.S_3$ $2 \cdot 3^{7}$ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_3\times S_3$ $2 \cdot 3^{2}$
78732.fx.36.A $C_3^7$ $3^{7}$ ✓ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_6:S_3$ $2^{2} \cdot 3^{2}$
78732.fx.36.B $C_3^7$ $3^{7}$ ✓ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $S_3^2$ $2^{2} \cdot 3^{2}$
78732.fx.36.C $C_3^6.C_3$ $3^{7}$ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $S_3^2$ $2^{2} \cdot 3^{2}$
78732.fx.36.D $C_3\times C_3^5.C_3$ $3^{7}$ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $S_3^2$ $2^{2} \cdot 3^{2}$
78732.fx.36.E $C_3^7$ $3^{7}$ ✓ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_6\times S_3$ $2^{2} \cdot 3^{2}$
78732.fx.36.F $C_3^6.C_3$ $3^{7}$ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_6\times S_3$ $2^{2} \cdot 3^{2}$
78732.fx.36.G $C_3^6.C_3$ $3^{7}$ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_6\times S_3$ $2^{2} \cdot 3^{2}$
78732.fx.36.H $C_3^6.C_3$ $3^{7}$ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_6\times S_3$ $2^{2} \cdot 3^{2}$
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