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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 57 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
7776.cc.7776.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
23328.bd.7776.A $C_3$ $3$ ✓ ✓ ✓ ✓ $(C_3\times S_3^2)\wr C_2$ $2^{5} \cdot 3^{6}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$ ✓
69984.hf.7776.B $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3^5.D_6\wr C_2$ $2^{5} \cdot 3^{7}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$ ✓
69984.io.7776.B $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3^3.S_3^2\wr C_2$ $2^{5} \cdot 3^{7}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$ ✓
69984.ir.7776.A $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3^5:D_6\wr C_2$ $2^{5} \cdot 3^{7}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$ ✓
209952.k.7776.A $C_3^3$ $3^{3}$ ✓ ✓ $C_3^2\wr C_2^2.D_4$ $2^{5} \cdot 3^{8}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
209952.fq.7776.A $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^6.D_6\wr C_2$ $2^{5} \cdot 3^{8}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
209952.ki.7776.A $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^6.D_6\wr C_2$ $2^{5} \cdot 3^{8}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
629856.bw.7776.B $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^4.S_3^4:S_3$ $2^{5} \cdot 3^{9}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
629856.bx.7776.B $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^4.S_3^4:S_3$ $2^{5} \cdot 3^{9}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
629856.im.7776.A $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^7.D_6\wr C_2$ $2^{5} \cdot 3^{9}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
629856.ir.7776._.A $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
629856.iy.7776.A $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
629856.jg.7776.B $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
629856.ka.7776._.B $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^5.S_3^2\wr C_2$ $2^{5} \cdot 3^{9}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
1889568.em.7776.A $C_3^4:C_3$ $3^{5}$ ✓ ✓ $C_3^8.C_6^2:D_4$ $2^{5} \cdot 3^{10}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
1889568.en.7776.A $C_3^5$ $3^{5}$ ✓ ✓ ✓ $C_3^5.S_3^4:C_6$ $2^{5} \cdot 3^{10}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
1889568.nc.7776.A $C_3^5$ $3^{5}$ ✓ ✓ ✓ $C_3^8.D_6\wr C_2$ $2^{5} \cdot 3^{10}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
1889568.nk.7776.A $C_3^5$ $3^{5}$ ✓ ✓ ✓ $C_3^6.S_3^2\wr C_2$ $2^{5} \cdot 3^{10}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
1889568.nl.7776.A $C_3^5$ $3^{5}$ ✓ ✓ ✓ $C_3^6.S_3^2\wr C_2$ $2^{5} \cdot 3^{10}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
1889568.ox.7776.A $C_3^5$ $3^{5}$ ✓ ✓ ✓ $C_3^6.S_3^2\wr C_2$ $2^{5} \cdot 3^{10}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
5668704.s.7776._.A $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^6.S_3^4:S_3$ $2^{5} \cdot 3^{11}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
5668704.hm.7776.A $C_3^6$ $3^{6}$ ✓ ✓ $C_3^7.S_3^2\wr C_2$ $2^{5} \cdot 3^{11}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
5668704.hm.7776.B $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^7.S_3^2\wr C_2$ $2^{5} \cdot 3^{11}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
5668704.il.7776.A $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^7.S_3^2\wr C_2$ $2^{5} \cdot 3^{11}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
5668704.it.7776.B $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^7.S_3^2\wr C_2$ $2^{5} \cdot 3^{11}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
5668704.km.7776.A $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^7.S_3^2\wr C_2$ $2^{5} \cdot 3^{11}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
5668704.kn.7776.A $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_9^4.D_6^2:S_3$ $2^{5} \cdot 3^{11}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
17006112.bb.7776._.B $C_3^2\times C_3^4:C_3$ $3^{7}$ ✓ ✓ $C_3^{10}.C_6^2.C_2^3$ $2^{5} \cdot 3^{12}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
17006112.gf.7776._.A $C_3^7$ $3^{7}$ ✓ ✓ ✓ $C_3^8.S_3^2\wr C_2$ $2^{5} \cdot 3^{12}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
17006112.gg.7776._.A $C_3^7$ $3^{7}$ ✓ ✓ ✓ $C_3^8.S_3^2\wr C_2$ $2^{5} \cdot 3^{12}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
17006112.gq.7776.A $C_3^7$ $3^{7}$ ✓ ✓ ✓ $C_3^7.S_3^4:C_6$ $2^{5} \cdot 3^{12}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
17006112.hv.7776._.B $C_3^7$ $3^{7}$ ✓ ✓ ✓ $C_3^8.S_3^2\wr C_2$ $2^{5} \cdot 3^{12}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
17006112.hv.7776._.C $C_3^2\times C_3^4:C_3$ $3^{7}$ ✓ $C_3^8.S_3^2\wr C_2$ $2^{5} \cdot 3^{12}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
17006112.hv.7776._.D $C_3^2\times C_3^4:C_3$ $3^{7}$ ✓ $C_3^8.S_3^2\wr C_2$ $2^{5} \cdot 3^{12}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
17006112.lu.7776.A $C_3^7$ $3^{7}$ ✓ ✓ ✓ $C_3^7.S_3^4:C_6$ $2^{5} \cdot 3^{12}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
17006112.lw.7776.A $C_3^7$ $3^{7}$ ✓ ✓ ✓ $C_3^7.S_3^4:C_6$ $2^{5} \cdot 3^{12}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
51018336.df.7776._.B $C_3^8$ $3^{8}$ ✓ ✓ ✓ $C_3^8.S_3^4:S_3$ $2^{5} \cdot 3^{13}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
51018336.hr.7776._.A $C_3^8$ $3^{8}$ ✓ ✓ ✓ $C_3^8.S_3^4:S_3$ $2^{5} \cdot 3^{13}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
51018336.hx.7776._.B $C_3^8$ $3^{8}$ ✓ ✓ ✓ $C_3^8.S_3^4:S_3$ $2^{5} \cdot 3^{13}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
51018336.ko.7776._.C $C_3^8$ $3^{8}$ ✓ ✓ ✓ $C_3^8.S_3^4:S_3$ $2^{5} \cdot 3^{13}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
153055008.bt.7776._.B $C_3^8.C_3$ $3^{9}$ ✓ ✓ $C_3^{12}.C_6^2.C_2^3$ $2^{5} \cdot 3^{14}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
153055008.eh.7776._.A $C_3^9$ $3^{9}$ ✓ ✓ ✓ $C_3^8.(C_3\times S_3^2)\wr C_2$ $2^{5} \cdot 3^{14}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
153055008.ev.7776._.B $C_3^8.C_3$ $3^{9}$ ✓ ✓ $C_3^8.(C_3\times S_3^2)\wr C_2$ $2^{5} \cdot 3^{14}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
153055008.ix.7776._.B $C_3^9$ $3^{9}$ ✓ ✓ ✓ $C_3^8.(C_3\times S_3^2)\wr C_2$ $2^{5} \cdot 3^{14}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
459165024.l.7776._.A $C_3^{10}$ $3^{10}$ ✓ ✓ $C_3^4.(C_3^7.S_3^2\wr C_2)$ $2^{5} \cdot 3^{15}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
459165024.l.7776._.B $C_3^8.C_3^2$ $3^{10}$ ✓ ✓ $C_3^4.(C_3^7.S_3^2\wr C_2)$ $2^{5} \cdot 3^{15}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
459165024.l.7776._.C $C_3^{10}$ $3^{10}$ ✓ ✓ $C_3^4.(C_3^7.S_3^2\wr C_2)$ $2^{5} \cdot 3^{15}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
459165024.cy.7776._.A $C_3^8.C_3^2$ $3^{10}$ ✓ $C_3^8.C_3^7:C_2^2\wr C_2$ $2^{5} \cdot 3^{15}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
459165024.cy.7776._.B $C_3^{10}$ $3^{10}$ ✓ ✓ ✓ $C_3^8.C_3^7:C_2^2\wr C_2$ $2^{5} \cdot 3^{15}$ $S_3^4:S_3$ $2^{5} \cdot 3^{5}$
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