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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 79 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
20736.ig.20736.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
41472.fz.20736.A $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_2\times C_6^3).\GL(2,\mathbb{Z}/4)$ $2^{9} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$ ✓
41472.ga.20736.A $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{12}:D_6^2.S_4$ $2^{9} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$ ✓
41472.gb.20736.A $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6^3:D_4.S_4$ $2^{9} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$ ✓
41472.gc.20736.A $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{12}:D_6^2.S_4$ $2^{9} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$ ✓
82944.da.20736.A $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_6^3.C_2^2\wr S_3$ $2^{10} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
559872.fk.20736._.B $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$ ✓
559872.ju.20736.A $C_3^3$ $3^{3}$ ✓ ✓ $C_3^6.C_2^5:S_4$ $2^{8} \cdot 3^{7}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$ ✓
1119744.ei.20736.B $C_3^2\times C_6$ $2 \cdot 3^{3}$ ✓ ✓ ✓ $C_6^3.C_6^3:S_4$ $2^{9} \cdot 3^{7}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
1119744.ej.20736.A $C_3^2\times C_6$ $2 \cdot 3^{3}$ ✓ ✓ ✓ $C_6^3.C_6^3:S_4$ $2^{9} \cdot 3^{7}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
1119744.ek.20736.B $C_3^2\times C_6$ $2 \cdot 3^{3}$ ✓ ✓ ✓ $C_6^3.C_6^3:S_4$ $2^{9} \cdot 3^{7}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
1119744.gl.20736.A $C_3^2\times C_6$ $2 \cdot 3^{3}$ ✓ ✓ $C_6^3.C_6^3:S_4$ $2^{9} \cdot 3^{7}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
1119744.gx.20736.A $C_3^2\times C_6$ $2 \cdot 3^{3}$ ✓ ✓ ✓ $C_6^3.C_6^3:S_4$ $2^{9} \cdot 3^{7}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
1119744.ke.20736.B $C_3^2\times C_6$ $2 \cdot 3^{3}$ ✓ ✓ ✓ $C_6^3.C_6^3:S_4$ $2^{9} \cdot 3^{7}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
1119744.kk.20736.B $C_3^2\times C_6$ $2 \cdot 3^{3}$ ✓ ✓ ✓ $C_6^3.C_6^3:S_4$ $2^{9} \cdot 3^{7}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
1327104.jd.20736.A $C_2^6$ $2^{6}$ ✓ ✓ ✓ $A_4^3.C_2^5:S_4$ $2^{14} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$ ✓
2239488.bo.20736.B $C_3\times C_6^2$ $2^{2} \cdot 3^{3}$ ✓ ✓ ✓ $C_6^3.D_6\wr S_3$ $2^{10} \cdot 3^{7}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
2239488.fe.20736.A $C_3^2:D_6$ $2^{2} \cdot 3^{3}$ ✓ ✓ $C_6^3.D_6\wr S_3$ $2^{10} \cdot 3^{7}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
2654208.kw.20736.A $C_2^7$ $2^{7}$ ✓ ✓ ✓ $A_4^3.C_2^4:\GL(2,\mathbb{Z}/4)$ $2^{15} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
2654208.kx.20736.A $C_2^7$ $2^{7}$ ✓ ✓ ✓ $A_4^3.C_2^6:D_{12}$ $2^{15} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
2654208.ky.20736.A $C_2^7$ $2^{7}$ ✓ ✓ ✓ $A_4^3.C_2^6:S_4$ $2^{15} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
2654208.kz.20736.A $C_2^7$ $2^{7}$ ✓ ✓ ✓ $A_4^3.(C_2^7.D_6)$ $2^{15} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
5308416.iy.20736.A $C_2^8$ $2^{8}$ ✓ ✓ ✓ $C_2^{10}.C_6^3:S_4$ $2^{16} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
15116544.cy.20736.A $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$ ✓
15116544.de.20736.A $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^9.C_2^6.D_6$ $2^{8} \cdot 3^{10}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$ ✓
30233088.bj.20736.A $C_3^5:S_3$ $2 \cdot 3^{6}$ ✓ ✓ $C_3^6:C_2^3.C_6^3:S_4$ $2^{9} \cdot 3^{10}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
30233088.cf.20736.A $C_3^5:S_3$ $2 \cdot 3^{6}$ ✓ ✓ $C_3^6.((C_2\times C_6^3).\GL(2,\mathbb{Z}/4))$ $2^{9} \cdot 3^{10}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
30233088.ct.20736.A $C_3^5:S_3$ $2 \cdot 3^{6}$ ✓ ✓ $C_3^9.C_2^6.D_{12}$ $2^{9} \cdot 3^{10}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
30233088.cy.20736.A $C_3^5:S_3$ $2 \cdot 3^{6}$ ✓ ✓ $(C_3:S_3)^3.C_6^3:S_4$ $2^{9} \cdot 3^{10}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
60466176.bc.20736._.B $C_3^5.D_6$ $2^{2} \cdot 3^{6}$ ✓ ✓ $C_3^6.(C_6^3.C_2^2\wr S_3)$ $2^{10} \cdot 3^{10}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
84934656.ha.20736._.A $C_2^{12}$ $2^{12}$ ✓ ✓ ✓ $C_2^{10}.(C_2\times A_4^3:S_4)$ $2^{20} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
84934656.mr.20736._.A $C_2^{12}$ $2^{12}$ ✓ ✓ ✓ $C_2^{10}.(C_2\times A_4^3:S_4)$ $2^{20} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
84934656.ru.20736._.A $C_4^6$ $2^{12}$ ✓ ✓ ✓ $C_2^{10}.(C_2\times A_4^3:S_4)$ $2^{20} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
169869312.gr.20736._.A $C_2^{13}$ $2^{13}$ ✓ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
169869312.gs.20736._.A $C_2^{13}$ $2^{13}$ ✓ ✓ ✓ $C_2^{10}.(C_4\times A_4^3:S_4)$ $2^{21} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
169869312.gt.20736._.A $C_2^{13}$ $2^{13}$ ✓ ✓ ✓ $C_2^{10}.(A_4^3.\GL(2,\mathbb{Z}/4))$ $2^{21} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
169869312.gu.20736._.A $C_2^{13}$ $2^{13}$ ✓ ✓ ✓ $C_2^{10}.(C_2^2\times A_4^3:S_4)$ $2^{21} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
169869312.jp.20736._.A $C_2^{13}$ $2^{13}$ ✓ ✓ ✓ $C_2^{10}.(A_4^3.\GL(2,\mathbb{Z}/4))$ $2^{21} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
169869312.jz.20736._.A $C_2^{13}$ $2^{13}$ ✓ ✓ ✓ $C_2^{10}.(C_2^2\times A_4^3:S_4)$ $2^{21} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
169869312.nb.20736._.A $C_2^{13}$ $2^{13}$ ✓ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
169869312.nh.20736._.A $C_2^{13}$ $2^{13}$ ✓ ✓ ✓ $C_2^{10}.(C_4\times A_4^3:S_4)$ $2^{21} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
169869312.st.20736._.A $C_2\times C_4^6$ $2^{13}$ ✓ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
169869312.su.20736._.A $C_2\times C_4^6$ $2^{13}$ ✓ ✓ ✓ $C_2^{10}.(C_4\times A_4^3:S_4)$ $2^{21} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
169869312.sv.20736._.A $C_2\times C_4^6$ $2^{13}$ ✓ ✓ ✓ $C_2^{10}.(A_4^3.\GL(2,\mathbb{Z}/4))$ $2^{21} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
169869312.sw.20736._.A $C_2\times C_4^6$ $2^{13}$ ✓ ✓ ✓ $C_2^{10}.(C_2^2\times A_4^3:S_4)$ $2^{21} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
339738624.bq.20736._.A $C_2^{14}$ $2^{14}$ ✓ ✓ ✓ $C_2^{10}.(D_4\times A_4^3:S_4)$ $2^{22} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
339738624.hf.20736._.B $C_2^{13}.C_2$ $2^{14}$ ✓ ✓ $C_2^{10}.(D_4\times A_4^3:S_4)$ $2^{22} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
339738624.ke.20736._.A $C_2^6.C_2^6.C_2^2$ $2^{14}$ ✓ ✓ $C_2^{10}.(D_4\times A_4^3:S_4)$ $2^{22} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
408146688.wp.20736._.B $C_3^9$ $3^{9}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
408146688.wu.20736._.B $C_3^9$ $3^{9}$ ✓ ✓ ✓ $C_3^{12}.C_2^6.D_6$ $2^{8} \cdot 3^{13}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
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