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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 (43 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
2916.it.2916.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
8748.jt.2916.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_3^6.D_6$ $2^{2} \cdot 3^{7}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$ ✓
26244.gw.2916.B $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3^7.D_6$ $2^{2} \cdot 3^{8}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
26244.gw.2916.C $C_3^2$ $3^{2}$ ✓ ✓ $C_3^7.D_6$ $2^{2} \cdot 3^{8}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
26244.he.2916.D $C_3^2$ $3^{2}$ ✓ ✓ $C_3^6.D_{18}$ $2^{2} \cdot 3^{8}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
26244.hw.2916.D $C_3^2$ $3^{2}$ ✓ ✓ $C_3^7.D_6$ $2^{2} \cdot 3^{8}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
26244.is.2916.B $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3^6.S_3^2$ $2^{2} \cdot 3^{8}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
26244.nl.2916.a1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_9^2.C_3^2.S_3^2$ $2^{2} \cdot 3^{8}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
78732.fp.2916.B $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
78732.fp.2916.C $C_3^3$ $3^{3}$ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
78732.gb.2916.I $C_3^3$ $3^{3}$ ✓ ✓ $C_3^8.D_6$ $2^{2} \cdot 3^{9}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
236196.ep.2916._.BU $C_3^4$ $3^{4}$ ✓ ✓ $C_3^8.S_3^2$ $2^{2} \cdot 3^{10}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
236196.ep.2916._.BV $C_3^4$ $3^{4}$ ✓ ✓ $C_3^8.S_3^2$ $2^{2} \cdot 3^{10}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
236196.ep.2916._.BW $C_3^4$ $3^{4}$ ✓ ✓ $C_3^8.S_3^2$ $2^{2} \cdot 3^{10}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
236196.ep.2916._.BX $C_3^4$ $3^{4}$ ✓ ✓ $C_3^8.S_3^2$ $2^{2} \cdot 3^{10}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
236196.ep.2916._.CB $C_3^4$ $3^{4}$ ✓ ✓ $C_3^8.S_3^2$ $2^{2} \cdot 3^{10}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
236196.ep.2916._.CC $C_3^4$ $3^{4}$ ✓ ✓ $C_3^8.S_3^2$ $2^{2} \cdot 3^{10}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
236196.ep.2916._.CD $C_3^4$ $3^{4}$ ✓ ✓ $C_3^8.S_3^2$ $2^{2} \cdot 3^{10}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
236196.ep.2916._.CE $C_3^4$ $3^{4}$ ✓ ✓ $C_3^8.S_3^2$ $2^{2} \cdot 3^{10}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
236196.ep.2916._.CI $C_3^4$ $3^{4}$ ✓ ✓ $C_3^8.S_3^2$ $2^{2} \cdot 3^{10}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
236196.ep.2916._.CJ $C_3^4$ $3^{4}$ ✓ ✓ $C_3^8.S_3^2$ $2^{2} \cdot 3^{10}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
236196.ep.2916._.CK $C_3^4$ $3^{4}$ ✓ ✓ $C_3^8.S_3^2$ $2^{2} \cdot 3^{10}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
236196.ep.2916._.CL $C_3^4$ $3^{4}$ ✓ ✓ $C_3^8.S_3^2$ $2^{2} \cdot 3^{10}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
236196.eu.2916._.X $C_3^4$ $3^{4}$ ✓ ✓ $C_3^8.D_{18}$ $2^{2} \cdot 3^{10}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
236196.eu.2916._.BA $C_3^4$ $3^{4}$ ✓ ✓ $C_3^8.D_{18}$ $2^{2} \cdot 3^{10}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
236196.eu.2916._.BB $C_3^4$ $3^{4}$ ✓ ✓ $C_3^8.D_{18}$ $2^{2} \cdot 3^{10}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
236196.eu.2916._.BC $C_3^4$ $3^{4}$ ✓ ✓ $C_3^8.D_{18}$ $2^{2} \cdot 3^{10}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
236196.eu.2916._.BG $C_3^4$ $3^{4}$ ✓ ✓ $C_3^8.D_{18}$ $2^{2} \cdot 3^{10}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
236196.eu.2916._.BK $C_3^4$ $3^{4}$ ✓ ✓ $C_3^8.D_{18}$ $2^{2} \cdot 3^{10}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
236196.eu.2916._.BO $C_3^4$ $3^{4}$ ✓ ✓ $C_3^8.D_{18}$ $2^{2} \cdot 3^{10}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
236196.eu.2916._.BR $C_3^4$ $3^{4}$ ✓ ✓ $C_3^8.D_{18}$ $2^{2} \cdot 3^{10}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
708588.db.2916._.V $C_3^5$ $3^{5}$ ✓ ✓ $C_3^4.C_3\wr D_6$ $2^{2} \cdot 3^{11}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
708588.db.2916._.W $C_3^5$ $3^{5}$ ✓ ✓ $C_3^4.C_3\wr D_6$ $2^{2} \cdot 3^{11}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
708588.db.2916._.X $C_3^5$ $3^{5}$ ✓ ✓ $C_3^4.C_3\wr D_6$ $2^{2} \cdot 3^{11}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
708588.db.2916._.Y $C_3^5$ $3^{5}$ ✓ ✓ $C_3^4.C_3\wr D_6$ $2^{2} \cdot 3^{11}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
708588.db.2916._.CM $C_3^5$ $3^{5}$ ✓ ✓ $C_3^4.C_3\wr D_6$ $2^{2} \cdot 3^{11}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
708588.db.2916._.CN $C_3^5$ $3^{5}$ ✓ ✓ $C_3^4.C_3\wr D_6$ $2^{2} \cdot 3^{11}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
708588.db.2916._.CO $C_3^5$ $3^{5}$ ✓ ✓ $C_3^4.C_3\wr D_6$ $2^{2} \cdot 3^{11}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
708588.db.2916._.CP $C_3^5$ $3^{5}$ ✓ ✓ $C_3^4.C_3\wr D_6$ $2^{2} \cdot 3^{11}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
708588.db.2916._.DA $C_3^5$ $3^{5}$ ✓ ✓ $C_3^4.C_3\wr D_6$ $2^{2} \cdot 3^{11}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
708588.db.2916._.DB $C_3^5$ $3^{5}$ ✓ ✓ $C_3^4.C_3\wr D_6$ $2^{2} \cdot 3^{11}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
708588.db.2916._.DC $C_3^5$ $3^{5}$ ✓ ✓ $C_3^4.C_3\wr D_6$ $2^{2} \cdot 3^{11}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
708588.db.2916._.DD $C_3^5$ $3^{5}$ ✓ ✓ $C_3^4.C_3\wr D_6$ $2^{2} \cdot 3^{11}$ $C_3^5.D_6$ $2^{2} \cdot 3^{6}$
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