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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 (45 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1327104.di.1.a1 $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ ✓ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_1$ $1$ ✓
1327104.di.2.A $A_4^2.S_4\wr C_2.C_4$ $2^{13} \cdot 3^{4}$ ✓ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2$ $2$ ✓
1327104.di.2.B $A_4^2.S_4\wr C_2.C_4$ $2^{13} \cdot 3^{4}$ ✓ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2$ $2$ ✓
1327104.di.2.C $A_4^2.S_4^2:C_2^3$ $2^{13} \cdot 3^{4}$ ✓ ✓ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2$ $2$ ✓
1327104.di.2.D $A_4^2.(C_2\times S_4^2:C_4)$ $2^{13} \cdot 3^{4}$ ✓ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2$ $2$ ✓
1327104.di.2.E $(C_2\times A_4^2\wr C_2).D_4$ $2^{13} \cdot 3^{4}$ ✓ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2$ $2$ ✓
1327104.di.2.F $C_2^8.C_3^4:C_4^2:C_2$ $2^{13} \cdot 3^{4}$ ✓ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2$ $2$ ✓
1327104.di.4.A $A_4^2.S_4^2:C_2^2$ $2^{12} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1327104.di.4.B $C_2^9.C_3^4:D_4$ $2^{12} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1327104.di.4.C $C_2^9.C_3:S_3^3$ $2^{12} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1327104.di.4.D $A_4^2.(A_4^2:C_4\times C_2^2)$ $2^{12} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1327104.di.4.E $C_2^8.C_3^4.C_2^4$ $2^{12} \cdot 3^{4}$ ✓ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1327104.di.4.F $A_4^2\wr C_2.C_2^3$ $2^{12} \cdot 3^{4}$ ✓ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1327104.di.4.G $C_2^9.C_3^4:D_4$ $2^{12} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1327104.di.4.H $A_4^2.(A_4^2:C_4\times C_2^2)$ $2^{12} \cdot 3^{4}$ ✓ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1327104.di.4.I $C_2^9.C_3^4:D_4$ $2^{12} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1327104.di.4.J $C_2^9.C_3:S_3^3$ $2^{12} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1327104.di.4.K $C_2\times A_4^2\wr C_2.C_4$ $2^{12} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1327104.di.4.L $C_2^8.C_3^4:C_4^2$ $2^{12} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1327104.di.4.M $C_2^9.C_3^4:D_4$ $2^{12} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1327104.di.4.N $C_2^9.C_3^4:Q_8$ $2^{12} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
1327104.di.4.O $A_4^2.S_4^2:C_2^2$ $2^{12} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_4$ $2^{2}$ ✓
1327104.di.8.A $C_2^8.C_3^4.C_2^3$ $2^{11} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^3$ $2^{3}$ ✓
1327104.di.8.B $C_2^8.C_3^4.C_2^3$ $2^{11} \cdot 3^{4}$ ✓ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^3$ $2^{3}$ ✓
1327104.di.8.C $A_4^2\wr C_2.C_2^2$ $2^{11} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^3$ $2^{3}$ ✓
1327104.di.8.D $C_2^9.C_3^2:S_3^2$ $2^{11} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^3$ $2^{3}$ ✓
1327104.di.8.E $C_2^9.C_3^4:C_4$ $2^{11} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^3$ $2^{3}$ ✓
1327104.di.8.F $C_2^9.C_3^4:C_4$ $2^{11} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^3$ $2^{3}$ ✓
1327104.di.8.G $A_4^2.S_4\wr C_2$ $2^{11} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2\times C_4$ $2^{3}$ ✓
1327104.di.8.H $C_2^8.C_3.S_3^3$ $2^{11} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2\times C_4$ $2^{3}$ ✓
1327104.di.8.I $A_4^2\wr C_2.C_2^2$ $2^{11} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2\times C_4$ $2^{3}$ ✓
1327104.di.8.J $A_4^2.(C_2\times A_4^2:C_4)$ $2^{11} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2\times C_4$ $2^{3}$ ✓
1327104.di.16.A $C_2^8.C_3^3.D_6$ $2^{10} \cdot 3^{4}$ ✓ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^4$ $2^{4}$ ✓
1327104.di.16.B $C_2^8.C_3^3.D_6$ $2^{10} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^2\times C_4$ $2^{4}$ ✓
1327104.di.16.C $C_2^8.C_3^3.D_6$ $2^{10} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^2\times C_4$ $2^{4}$ ✓
1327104.di.16.D $A_4^2:\POPlus(4,3)$ $2^{10} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^2\times C_4$ $2^{4}$ ✓
1327104.di.16.E $A_4^2:(A_4^2:C_4)$ $2^{10} \cdot 3^{4}$ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^2\times C_4$ $2^{4}$ ✓
1327104.di.32.A $C_2^8.C_3^4.C_2$ $2^{9} \cdot 3^{4}$ ✓ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $D_4:C_2^2$ $2^{5}$
1327104.di.32.B $C_2^8.C_3^4.C_2$ $2^{9} \cdot 3^{4}$ ✓ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $D_4:C_2^2$ $2^{5}$
1327104.di.32.C $C_2^8.C_3^4.C_2$ $2^{9} \cdot 3^{4}$ ✓ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_2^3\times C_4$ $2^{5}$ ✓
1327104.di.64.A $C_2^8.C_3^4$ $2^{8} \cdot 3^{4}$ ✓ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_4^2:C_2^2$ $2^{6}$
1327104.di.2592.A $C_2^9$ $2^{9}$ ✓ ✓ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_3^4.Q_8:C_2^2$ $2^{5} \cdot 3^{4}$
1327104.di.5184.A $C_2^8$ $2^{8}$ ✓ ✓ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $C_3^4:C_4^2:C_2^2$ $2^{6} \cdot 3^{4}$ ✓
1327104.di.663552.A $C_2$ $2$ ✓ ✓ ✓ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $A_4^2:\POPlus(4,3).C_2^3$ $2^{13} \cdot 3^{4}$ ✓
1327104.di.1327104.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$ $A_4^2\wr C_2.C_2^2.C_2^3$ $2^{14} \cdot 3^{4}$
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