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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 737 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
165888.bz.1.a1 $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ ✓ ✓ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $C_1$ $1$ ✓
165888.bz.2.A $A_4^2.A_4^2.C_2^2$ $2^{10} \cdot 3^{4}$ ✓ ✓ ✓ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $C_2$ $2$ ✓
165888.bz.2.B $C_2.A_4^2\wr C_2$ $2^{10} \cdot 3^{4}$ ✓ ✓ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $C_2$ $2$ ✓
165888.bz.3.A $A_4^2:C_2^4.S_4$ $2^{11} \cdot 3^{3}$ ✓ ✓ ✓ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $C_3$ $3$ ✓
165888.bz.3.B $C_2^9.(C_3\times S_3^2)$ $2^{11} \cdot 3^{3}$ ✓ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $3$ $-$
165888.bz.3.C $C_2^7.(A_4\times S_3^2)$ $2^{11} \cdot 3^{3}$ ✓ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $3$ $-$
165888.bz.4.A $C_2^8.C_3^4.C_2$ $2^{9} \cdot 3^{4}$ ✓ ✓ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
165888.bz.4.B $A_4^2.A_4^2.C_2$ $2^{9} \cdot 3^{4}$ ✓ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $C_4$ $2^{2}$ ✓
165888.bz.6.A $A_4^2.C_2^4.C_6.C_2$ $2^{10} \cdot 3^{3}$ ✓ ✓ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
165888.bz.6.B $A_4^2.C_2^4.C_6.C_2$ $2^{10} \cdot 3^{3}$ ✓ ✓ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $C_6$ $2 \cdot 3$ ✓
165888.bz.6.C $(C_2^3\times A_4^2).S_4$ $2^{10} \cdot 3^{3}$ ✓ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
165888.bz.6.D $(C_2^3\times A_4^2).S_4$ $2^{10} \cdot 3^{3}$ ✓ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $C_6$ $2 \cdot 3$ ✓
165888.bz.6.E $A_4.C_2^5.C_6^2.C_2$ $2^{10} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2 \cdot 3$ $-$
165888.bz.6.F $C_2^4:C_3.A_4^2.C_2^2$ $2^{10} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2 \cdot 3$ $-$
165888.bz.6.G $A_4^2.A_4.C_2^4$ $2^{10} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2 \cdot 3$ $-$
165888.bz.6.H $C_2^9.(S_3\times C_3^2)$ $2^{10} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2 \cdot 3$ $-$
165888.bz.6.I $C_2^9.(S_3\times C_3^2)$ $2^{10} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2 \cdot 3$ $-$
165888.bz.6.J $C_2^9.(S_3\times C_3^2)$ $2^{10} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2 \cdot 3$ $-$
165888.bz.6.K $C_2^4:A_4^2.C_{12}$ $2^{10} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2 \cdot 3$ $-$
165888.bz.8.A $C_2^8.C_3^4$ $2^{8} \cdot 3^{4}$ ✓ ✓ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $C_2\times C_4$ $2^{3}$ ✓
165888.bz.8.B $(C_3\times A_4).A_4^2.C_2^2$ $2^{8} \cdot 3^{4}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2^{3}$ $-$
165888.bz.8.C $A_4^2.C_2^2.C_6^2$ $2^{8} \cdot 3^{4}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2^{3}$ $-$
165888.bz.9.A $C_2^4.(C_6^2\times D_4).C_2^2$ $2^{11} \cdot 3^{2}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $3^{2}$ $-$
165888.bz.9.B $C_2^6.(C_{12}\times S_4)$ $2^{11} \cdot 3^{2}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $3^{2}$ $-$
165888.bz.9.C $C_2^5.S_4^2$ $2^{11} \cdot 3^{2}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $3^{2}$ $-$
165888.bz.9.D $A_4^2.C_2^6.C_2$ $2^{11} \cdot 3^{2}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $3^{2}$ $-$
165888.bz.12.A $C_2^8.C_3^3.C_2$ $2^{9} \cdot 3^{3}$ ✓ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
165888.bz.12.B $C_2^8.C_3^3.C_2$ $2^{9} \cdot 3^{3}$ ✓ ✓ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
165888.bz.12.C $C_2^8.C_3^3.C_2$ $2^{9} \cdot 3^{3}$ ✓ ✓ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
165888.bz.12.D $A_4^2.C_2^4.C_6$ $2^{9} \cdot 3^{3}$ ✓ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $C_3:C_4$ $2^{2} \cdot 3$
165888.bz.12.E $A_4^2.C_2^4.C_6$ $2^{9} \cdot 3^{3}$ ✓ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $C_{12}$ $2^{2} \cdot 3$ ✓
165888.bz.12.F $A_4.A_4^2.C_2^3$ $2^{9} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
165888.bz.12.G $A_4.A_4^2.C_2^2.C_2$ $2^{9} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
165888.bz.12.H $C_2\times A_4^2.A_4.C_2^2$ $2^{9} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
165888.bz.12.I $C_2\times A_4^2.A_4.C_2^2$ $2^{9} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
165888.bz.12.J $C_2^8.C_3^3.C_2$ $2^{9} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
165888.bz.12.K $C_2^6.C_6^3$ $2^{9} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
165888.bz.12.L $C_2^8.C_3^3.C_2$ $2^{9} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
165888.bz.12.M $C_2^6.C_6^3$ $2^{9} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
165888.bz.12.N $C_2^8.C_3^3.C_2$ $2^{9} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
165888.bz.12.O $C_2^8.C_3^3.C_2$ $2^{9} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
165888.bz.12.P $C_2^8.C_3^3.C_2$ $2^{9} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
165888.bz.12.Q $C_2^8.C_3^3.C_2$ $2^{9} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
165888.bz.12.R $A_4^3:(C_2\times C_4)$ $2^{9} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
165888.bz.12.S $A_4^3:(C_2\times C_4)$ $2^{9} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
165888.bz.12.T $A_4^2:C_4\times S_4$ $2^{9} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
165888.bz.12.U $A_4.C_2^5.C_6^2$ $2^{9} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
165888.bz.12.V $A_4^2.A_4.C_2^3$ $2^{9} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
165888.bz.12.W $A_4.C_2^5.C_6^2$ $2^{9} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
165888.bz.12.X $C_2^4:C_3.A_4^2.C_2$ $2^{9} \cdot 3^{3}$ $C_2^9.C_3\wr C_2^2$ $2^{11} \cdot 3^{4}$ $2^{2} \cdot 3$ $-$
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