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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 55 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
663552.jo.663552.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
1327104.lb.663552.A $C_2$ $2$ ✓ ✓ ✓ $C_2^6.A_4^3:A_4$ $2^{14} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$ ✓
5308416.jf.663552.A $C_2^3$ $2^{3}$ ✓ ✓ ✓ $A_4^3.C_2^8:A_4$ $2^{16} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
5308416.kc.663552.A $C_2^3$ $2^{3}$ ✓ ✓ ✓ $A_4^3.(C_2^2\times C_4^3):A_4$ $2^{16} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
10616832.ko.663552._.A $C_2^4$ $2^{4}$ ✓ ✓ $D_4^3.A_4^3:A_4$ $2^{17} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
10616832.ko.663552._.B $C_2^2\times C_4$ $2^{4}$ ✓ ✓ ✓ $D_4^3.A_4^3:A_4$ $2^{17} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
10616832.ko.663552._.C $C_2^4$ $2^{4}$ ✓ ✓ $D_4^3.A_4^3:A_4$ $2^{17} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
42467328.oa.663552._.A $C_2^6$ $2^{6}$ ✓ ✓ ✓ $C_2\times C_2^{10}.A_4^3:A_4$ $2^{19} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$ ✓
42467328.ot.663552._.A $C_2^6$ $2^{6}$ ✓ ✓ ✓ $C_2^{10}.(C_2\times A_4^3:A_4)$ $2^{19} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$ ✓
42467328.re.663552._.A $C_2^6$ $2^{6}$ ✓ ✓ ✓ $C_2^{10}.(C_2\times A_4^3:A_4)$ $2^{19} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$ ✓
42467328.rf.663552._.A $C_2^6$ $2^{6}$ ✓ ✓ ✓ $C_2^{10}.(C_2\times A_4^3:A_4)$ $2^{19} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$ ✓
42467328.xm.663552._.A $C_2^6$ $2^{6}$ ✓ ✓ $C_2^{10}.(C_2\times A_4^3:A_4)$ $2^{19} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$ ✓
42467328.xm.663552._.B $C_2^6$ $2^{6}$ ✓ ✓ $C_2^{10}.(C_2\times A_4^3:A_4)$ $2^{19} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$ ✓
42467328.xm.663552._.C $C_2^6$ $2^{6}$ ✓ ✓ $C_2^{10}.(C_2\times A_4^3:A_4)$ $2^{19} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$ ✓
84934656.kt.663552._.A $C_2^7$ $2^{7}$ ✓ ✓ $C_2^{12}.A_4^3:A_4$ $2^{20} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
84934656.kt.663552._.B $C_2^7$ $2^{7}$ ✓ ✓ $C_2^{12}.A_4^3:A_4$ $2^{20} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
84934656.kt.663552._.C $C_2^7$ $2^{7}$ ✓ ✓ ✓ $C_2^{12}.A_4^3:A_4$ $2^{20} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
84934656.oe.663552._.A $C_2^7$ $2^{7}$ ✓ ✓ $C_2^{12}.A_4^3:A_4$ $2^{20} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
84934656.oe.663552._.B $C_2^7$ $2^{7}$ ✓ ✓ $C_2^{12}.A_4^3:A_4$ $2^{20} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
84934656.oe.663552._.C $C_2^7$ $2^{7}$ ✓ ✓ ✓ $C_2^{12}.A_4^3:A_4$ $2^{20} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
84934656.tt.663552._.A $C_2^7$ $2^{7}$ ✓ ✓ $C_2^{12}.A_4^3:A_4$ $2^{20} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
84934656.tt.663552._.B $C_2^7$ $2^{7}$ ✓ ✓ $C_2^{12}.A_4^3:A_4$ $2^{20} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
84934656.tt.663552._.C $C_2^7$ $2^{7}$ ✓ ✓ $C_2^{12}.A_4^3:A_4$ $2^{20} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
84934656.tt.663552._.D $C_2^7$ $2^{7}$ ✓ ✓ $C_2^{12}.A_4^3:A_4$ $2^{20} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
84934656.tt.663552._.E $C_2^7$ $2^{7}$ ✓ ✓ $C_2^{12}.A_4^3:A_4$ $2^{20} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
84934656.tt.663552._.F $C_2^7$ $2^{7}$ ✓ ✓ $C_2^{12}.A_4^3:A_4$ $2^{20} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
84934656.tt.663552._.G $C_2^7$ $2^{7}$ ✓ ✓ $C_2^{12}.A_4^3:A_4$ $2^{20} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
84934656.tt.663552._.H $C_2^7$ $2^{7}$ ✓ ✓ $C_2^{12}.A_4^3:A_4$ $2^{20} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
84934656.tt.663552._.I $C_2^7$ $2^{7}$ ✓ ✓ $C_2^{12}.A_4^3:A_4$ $2^{20} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
339738624.bz.663552._.C $C_2^9$ $2^{9}$ ✓ ✓ ✓ $C_2^{12}.(A_4:S_4^2.A_4)$ $2^{22} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
339738624.fy.663552._.A $C_2^9$ $2^{9}$ ✓ ✓ ✓ $C_2^{12}.(C_{12}^3.C_2^2:A_4)$ $2^{22} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
339738624.fz.663552._.B $C_2^9$ $2^{9}$ ✓ ✓ ✓ $C_2^{12}.(A_4:S_4^2.A_4)$ $2^{22} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
339738624.kg.663552._.B $C_2^9$ $2^{9}$ ✓ ✓ ✓ $C_2^{12}.(A_4:S_4^2.A_4)$ $2^{22} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
339738624.ld.663552._.A $C_2^9$ $2^{9}$ ✓ ✓ ✓ $C_4^3.(C_2^8.A_4^3:A_4)$ $2^{22} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
679477248.bf.663552._.A $C_2^{10}$ $2^{10}$ ✓ ✓ ✓ $C_2^6.(D_4^3.A_4^3:A_4)$ $2^{23} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
679477248.bf.663552._.B $C_2^{10}$ $2^{10}$ ✓ ✓ ✓ $C_2^6.(D_4^3.A_4^3:A_4)$ $2^{23} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
679477248.bf.663552._.C $C_2^8\times C_4$ $2^{10}$ ✓ ✓ ✓ $C_2^6.(D_4^3.A_4^3:A_4)$ $2^{23} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
679477248.fm.663552._.A $C_2^8\times C_4$ $2^{10}$ ✓ ✓ ✓ $C_2^6.(D_4^3.A_4^3:A_4)$ $2^{23} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
679477248.fm.663552._.B $C_2^{10}$ $2^{10}$ ✓ ✓ $C_2^6.(D_4^3.A_4^3:A_4)$ $2^{23} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
679477248.fm.663552._.C $C_2^{10}$ $2^{10}$ ✓ ✓ $C_2^6.(D_4^3.A_4^3:A_4)$ $2^{23} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
21743271936.w.663552._.A $C_2^{15}$ $2^{15}$ ✓ ✓ ✓ $C_2^{10}.(C_2^{10}.A_4^3:A_4)$ $2^{28} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
21743271936.w.663552._.B $C_2^3\times C_4^6$ $2^{15}$ ✓ ✓ ✓ $C_2^{10}.(C_2^{10}.A_4^3:A_4)$ $2^{28} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
21743271936.w.663552._.C $C_2^{15}$ $2^{15}$ ✓ ✓ ✓ $C_2^{10}.(C_2^{10}.A_4^3:A_4)$ $2^{28} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
21743271936.bt.663552._.A $C_2^{15}$ $2^{15}$ ✓ ✓ $C_2^9.(C_2^{10}.(C_2\times A_4^3:A_4))$ $2^{28} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
21743271936.bt.663552._.B $C_2^3\times C_4^6$ $2^{15}$ ✓ ✓ ✓ $C_2^9.(C_2^{10}.(C_2\times A_4^3:A_4))$ $2^{28} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
21743271936.bt.663552._.C $C_2^{15}$ $2^{15}$ ✓ ✓ $C_2^9.(C_2^{10}.(C_2\times A_4^3:A_4))$ $2^{28} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
43486543872.ce.663552._.A $C_2^{10}.C_2^6$ $2^{16}$ ✓ $C_2^{12}.(C_2^9.A_4^3:A_4)$ $2^{29} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
43486543872.ce.663552._.B $C_2^{15}.C_2$ $2^{16}$ ✓ $C_2^{12}.(C_2^9.A_4^3:A_4)$ $2^{29} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
43486543872.ce.663552._.C $C_2^{10}.C_2^6$ $2^{16}$ ✓ $C_2^{12}.(C_2^9.A_4^3:A_4)$ $2^{29} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
43486543872.ce.663552._.D $C_2^{10}.C_2^6$ $2^{16}$ ✓ $C_2^{12}.(C_2^9.A_4^3:A_4)$ $2^{29} \cdot 3^{4}$ $C_2^5.A_4^3:A_4$ $2^{13} \cdot 3^{4}$
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