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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 753 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
6144.hg.1.a1 $C_2^8.S_4$ $2^{11} \cdot 3$ ✓ ✓ $C_2^8.S_4$ $2^{11} \cdot 3$ $C_1$ $1$ ✓
6144.hg.2.A $C_2^8.A_4$ $2^{10} \cdot 3$ ✓ ✓ ✓ $C_2^8.S_4$ $2^{11} \cdot 3$ $C_2$ $2$ ✓
6144.hg.2.B $C_2^7:S_4$ $2^{10} \cdot 3$ ✓ ✓ $C_2^8.S_4$ $2^{11} \cdot 3$ $C_2$ $2$ ✓
6144.hg.3.a1 $C_2^5.C_2^5.C_2$ $2^{11}$ $2$ ✓ $C_2^8.S_4$ $2^{11} \cdot 3$ $3$ $-$
6144.hg.4.A $C_2^7:A_4$ $2^{9} \cdot 3$ ✓ ✓ $C_2^8.S_4$ $2^{11} \cdot 3$ $C_2^2$ $2^{2}$ ✓
6144.hg.4.B $C_2^6:S_4$ $2^{9} \cdot 3$ ✓ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{2}$ $-$
6144.hg.4.C $C_2^6:S_4$ $2^{9} \cdot 3$ ✓ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{2}$ $-$
6144.hg.4.D $C_2\wr S_4$ $2^{9} \cdot 3$ ✓ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{2}$ $-$
6144.hg.4.E $C_2^6.S_4$ $2^{9} \cdot 3$ ✓ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{2}$ $-$
6144.hg.4.F $C_2^6:S_4$ $2^{9} \cdot 3$ ✓ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{2}$ $-$
6144.hg.6.A $C_2^8.C_2^2$ $2^{10}$ ✓ ✓ $C_2^8.S_4$ $2^{11} \cdot 3$ $S_3$ $2 \cdot 3$
6144.hg.6.B $C_2^5.C_2^5$ $2^{10}$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2 \cdot 3$ $-$
6144.hg.6.C $C_2.C_2^6.C_2^3$ $2^{10}$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2 \cdot 3$ $-$
6144.hg.6.D $C_2^4.C_2^5.C_2$ $2^{10}$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2 \cdot 3$ $-$
6144.hg.6.E $C_2.C_2^6.C_2^3$ $2^{10}$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2 \cdot 3$ $-$
6144.hg.6.F $C_2^7:D_4$ $2^{10}$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2 \cdot 3$ $-$
6144.hg.6.G $C_2^4.C_2^4.C_2^2$ $2^{10}$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2 \cdot 3$ $-$
6144.hg.6.H $C_2^7:D_4$ $2^{10}$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2 \cdot 3$ $-$
6144.hg.6.I $C_2.C_2^6.C_2^3$ $2^{10}$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2 \cdot 3$ $-$
6144.hg.6.J $C_2^8.C_2^2$ $2^{10}$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2 \cdot 3$ $-$
6144.hg.6.K $C_2^5.C_2^4.C_2$ $2^{10}$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2 \cdot 3$ $-$
6144.hg.6.L $C_2^5.C_2^4.C_2$ $2^{10}$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2 \cdot 3$ $-$
6144.hg.6.M $C_2^5.C_2^4.C_2$ $2^{10}$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2 \cdot 3$ $-$
6144.hg.6.N $C_2^5.C_2^4.C_2$ $2^{10}$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2 \cdot 3$ $-$
6144.hg.6.O $C_2^5.C_2^4.C_2$ $2^{10}$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2 \cdot 3$ $-$
6144.hg.6.P $C_2^4.C_2^4.C_2^2$ $2^{10}$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2 \cdot 3$ $-$
6144.hg.6.Q $C_2^5.C_2^4.C_2$ $2^{10}$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2 \cdot 3$ $-$
6144.hg.8.A $C_2^6:A_4$ $2^{8} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{3}$ $-$
6144.hg.8.B $C_2^6:A_4$ $2^{8} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{3}$ $-$
6144.hg.8.C $C_2^5:\SL(2,3)$ $2^{8} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{3}$ $-$
6144.hg.8.D $C_2\wr A_4$ $2^{8} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{3}$ $-$
6144.hg.8.E $C_2^6.A_4$ $2^{8} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{3}$ $-$
6144.hg.8.F $C_2^6.A_4$ $2^{8} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{3}$ $-$
6144.hg.8.G $C_2^6:A_4$ $2^{8} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{3}$ $-$
6144.hg.8.H $C_2^6.A_4$ $2^{8} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{3}$ $-$
6144.hg.8.I $C_2^6.A_4$ $2^{8} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{3}$ $-$
6144.hg.8.J $C_2^6:A_4$ $2^{8} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{3}$ $-$
6144.hg.8.K $C_2^5:S_4$ $2^{8} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{3}$ $-$
6144.hg.8.L $C_2^5:S_4$ $2^{8} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{3}$ $-$
6144.hg.8.M $C_2^5.S_4$ $2^{8} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{3}$ $-$
6144.hg.8.N $C_2^5:S_4$ $2^{8} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{3}$ $-$
6144.hg.8.O $C_2^5:S_4$ $2^{8} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{3}$ $-$
6144.hg.8.P $C_2^5:S_4$ $2^{8} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{3}$ $-$
6144.hg.8.Q $C_2^5:S_4$ $2^{8} \cdot 3$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{3}$ $-$
6144.hg.12.A $C_2^7.C_2^2$ $2^{9}$ ✓ ✓ $C_2^8.S_4$ $2^{11} \cdot 3$ $D_6$ $2^{2} \cdot 3$
6144.hg.12.B $C_2^7.C_2^2$ $2^{9}$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{2} \cdot 3$ $-$
6144.hg.12.C $C_2^7.C_2^2$ $2^{9}$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{2} \cdot 3$ $-$
6144.hg.12.D $C_2^4.C_2^5$ $2^{9}$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{2} \cdot 3$ $-$
6144.hg.12.E $(C_2^2\times D_4).C_2^4$ $2^{9}$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{2} \cdot 3$ $-$
6144.hg.12.F $C_2^6.C_2^3$ $2^{9}$ $C_2^8.S_4$ $2^{11} \cdot 3$ $2^{2} \cdot 3$ $-$
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