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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 833 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
110592.cy.1.a1 $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_1$ $1$ ✓
110592.cy.2.A $C_2^4:C_3.A_4^2.C_2^3$ $2^{11} \cdot 3^{3}$ ✓ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_2$ $2$ ✓
110592.cy.2.B $A_4^2.C_2\wr C_6$ $2^{11} \cdot 3^{3}$ ✓ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_2$ $2$ ✓
110592.cy.2.C $(C_2^2\times A_4^2).\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3^{3}$ ✓ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_2$ $2$ ✓
110592.cy.2.D $C_2^8.(C_6\times S_3^2)$ $2^{11} \cdot 3^{3}$ ✓ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_2$ $2$ ✓
110592.cy.2.E $C_2^9.(C_3\times S_3^2)$ $2^{11} \cdot 3^{3}$ ✓ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_2$ $2$ ✓
110592.cy.2.F $(C_2^2\times A_4^2).\GL(2,\mathbb{Z}/4)$ $2^{11} \cdot 3^{3}$ ✓ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_2$ $2$ ✓
110592.cy.2.G $C_2^9.(C_3\times S_3^2)$ $2^{11} \cdot 3^{3}$ ✓ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_2$ $2$ ✓
110592.cy.3.A $C_2^6.S_4^2$ $2^{12} \cdot 3^{2}$ ✓ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_3$ $3$ ✓
110592.cy.3.B $C_2^4:C_3.C_2^4.C_6.C_2^3$ $2^{12} \cdot 3^{2}$ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $3$ $-$
110592.cy.3.C $C_2^8.(C_6\times S_4)$ $2^{12} \cdot 3^{2}$ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $3$ $-$
110592.cy.4.A $C_2^8.C_3.C_6^2$ $2^{10} \cdot 3^{3}$ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
110592.cy.4.B $C_2^4:C_3.A_4^2.C_2^2$ $2^{10} \cdot 3^{3}$ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
110592.cy.4.C $C_2^4:C_3.A_4^2.C_2^2$ $2^{10} \cdot 3^{3}$ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
110592.cy.4.D $C_2^8.(C_3^2\times D_6)$ $2^{10} \cdot 3^{3}$ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
110592.cy.4.E $(C_2^3\times A_4^2).S_4$ $2^{10} \cdot 3^{3}$ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
110592.cy.4.F $C_2^9.(S_3\times C_3^2)$ $2^{10} \cdot 3^{3}$ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
110592.cy.4.G $(C_2^3\times A_4^2).S_4$ $2^{10} \cdot 3^{3}$ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_2^2$ $2^{2}$ ✓
110592.cy.4.H $S_4\times A_4^2:D_4$ $2^{10} \cdot 3^{3}$ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2^{2}$ $-$
110592.cy.4.I $C_2^4:C_3.A_4^2.C_2^2$ $2^{10} \cdot 3^{3}$ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2^{2}$ $-$
110592.cy.4.J $C_2^8.(C_3\times S_3^2)$ $2^{10} \cdot 3^{3}$ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2^{2}$ $-$
110592.cy.6.A $C_2^6.(A_4\times S_4)$ $2^{11} \cdot 3^{2}$ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $S_3$ $2 \cdot 3$
110592.cy.6.B $C_2^6.(A_4\times S_4)$ $2^{11} \cdot 3^{2}$ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
110592.cy.6.C $C_2^4.(C_2\times C_6^2).C_2^4$ $2^{11} \cdot 3^{2}$ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $S_3$ $2 \cdot 3$
110592.cy.6.D $C_2^4.(A_4\times \GL(2,\mathbb{Z}/4))$ $2^{11} \cdot 3^{2}$ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
110592.cy.6.E $C_2^6.\PSOPlus(4,3)$ $2^{11} \cdot 3^{2}$ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
110592.cy.6.F $C_2^5.S_4^2$ $2^{11} \cdot 3^{2}$ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
110592.cy.6.G $C_2^5.S_4^2$ $2^{11} \cdot 3^{2}$ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
110592.cy.6.H $C_2^5.S_4^2$ $2^{11} \cdot 3^{2}$ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
110592.cy.6.I $C_2^5.S_4^2$ $2^{11} \cdot 3^{2}$ ✓ ✓ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $C_6$ $2 \cdot 3$ ✓
110592.cy.6.J $C_2^4.C_6^2.C_2^5$ $2^{11} \cdot 3^{2}$ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2 \cdot 3$ $-$
110592.cy.6.K $C_2^4:C_3.C_2^3.C_6.C_2^3$ $2^{11} \cdot 3^{2}$ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2 \cdot 3$ $-$
110592.cy.6.L $C_2^4:C_3.C_2^3.C_6.C_2^3$ $2^{11} \cdot 3^{2}$ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2 \cdot 3$ $-$
110592.cy.6.M $C_2^4:C_3.C_2^3.C_6.C_2^3$ $2^{11} \cdot 3^{2}$ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2 \cdot 3$ $-$
110592.cy.6.N $C_2^6.C_6^2.C_2^3$ $2^{11} \cdot 3^{2}$ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2 \cdot 3$ $-$
110592.cy.6.O $C_2\times C_2^2.A_4^2.C_2^4$ $2^{11} \cdot 3^{2}$ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2 \cdot 3$ $-$
110592.cy.6.P $C_2^9.C_6^2$ $2^{11} \cdot 3^{2}$ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2 \cdot 3$ $-$
110592.cy.6.Q $C_2^7.(A_4\times D_6)$ $2^{11} \cdot 3^{2}$ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2 \cdot 3$ $-$
110592.cy.6.R $C_2^4.(C_2\times C_6^2).C_2^4$ $2^{11} \cdot 3^{2}$ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2 \cdot 3$ $-$
110592.cy.6.S $C_2^4.(A_4\times \GL(2,\mathbb{Z}/4))$ $2^{11} \cdot 3^{2}$ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2 \cdot 3$ $-$
110592.cy.6.T $C_2^7.(C_6\times S_4)$ $2^{11} \cdot 3^{2}$ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2 \cdot 3$ $-$
110592.cy.6.U $C_2^4.(C_2\times C_6^2).C_2^4$ $2^{11} \cdot 3^{2}$ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2 \cdot 3$ $-$
110592.cy.6.V $C_2^4:C_3.C_2^3.C_6.C_2^3$ $2^{11} \cdot 3^{2}$ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2 \cdot 3$ $-$
110592.cy.6.W $C_2^4:C_3.C_2^4.C_6.C_2^2$ $2^{11} \cdot 3^{2}$ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2 \cdot 3$ $-$
110592.cy.6.X $C_2^4:C_3.C_2^4.C_6.C_2^2$ $2^{11} \cdot 3^{2}$ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2 \cdot 3$ $-$
110592.cy.6.Y $C_2^4.(C_2\times C_6^2).C_2^4$ $2^{11} \cdot 3^{2}$ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2 \cdot 3$ $-$
110592.cy.6.Z $C_2^4:C_3.C_2^3.C_6.C_2^3$ $2^{11} \cdot 3^{2}$ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2 \cdot 3$ $-$
110592.cy.6.BA $C_2^6.(A_4\times S_4)$ $2^{11} \cdot 3^{2}$ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2 \cdot 3$ $-$
110592.cy.6.BB $C_2^6.(C_{12}\times S_4)$ $2^{11} \cdot 3^{2}$ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2 \cdot 3$ $-$
110592.cy.6.BC $C_2^4:C_3.C_2^4.C_6.C_2^2$ $2^{11} \cdot 3^{2}$ $A_4^2.C_2\wr D_6$ $2^{12} \cdot 3^{3}$ $2 \cdot 3$ $-$
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