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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 139 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
972.445.972.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
1944.1307.972.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3^3:(S_3\times C_{12})$ $2^{3} \cdot 3^{5}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$ ✓
1944.1308.972.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3^3:(S_3\times C_{12})$ $2^{3} \cdot 3^{5}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$ ✓
1944.1309.972.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $\He_3.(S_3\times C_{12})$ $2^{3} \cdot 3^{5}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$ ✓
1944.1310.972.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3^3:(C_3\times D_{12})$ $2^{3} \cdot 3^{5}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$ ✓
1944.1311.972.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_3\times \He_3):D_{12}$ $2^{3} \cdot 3^{5}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$ ✓
1944.1312.972.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3^3:C_6\wr C_2$ $2^{3} \cdot 3^{5}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$ ✓
1944.1313.972.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $(C_3^2\times C_6).S_3^2$ $2^{3} \cdot 3^{5}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$ ✓
1944.2700.972.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_3^3:(C_6\times D_6)$ $2^{3} \cdot 3^{5}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$ ✓
2916.ef.972.b1.a1 $C_3$ $3$ ✓ ✓ ✓ $C_3^4.S_3^2$ $2^{2} \cdot 3^{6}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$ ✓
2916.mc.972.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_3^4.S_3^2$ $2^{2} \cdot 3^{6}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$ ✓
3888.kf.972.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_3^3:(C_6\times S_4)$ $2^{4} \cdot 3^{5}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$ ✓
3888.le.972.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_3^3.D_6^2$ $2^{4} \cdot 3^{5}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
5832.gj.972.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_3^3\times C_6).S_3^2$ $2^{3} \cdot 3^{6}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
5832.gk.972.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $C_2\times C_3^4.S_3^2$ $2^{3} \cdot 3^{6}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
5832.gl.972.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_3^3\times C_6).S_3^2$ $2^{3} \cdot 3^{6}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
5832.gm.972.b1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $(C_3^3\times C_6).S_3^2$ $2^{3} \cdot 3^{6}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
5832.oe.972.a1 $S_3$ $2 \cdot 3$ ✓ ✓ $C_3^3.S_3^3$ $2^{3} \cdot 3^{6}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
7776.jp.972.a1 $C_2^3$ $2^{3}$ ✓ ✓ ✓ $C_6^3.S_3^2$ $2^{5} \cdot 3^{5}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
8748.fn.972.a1.a1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3^5.S_3^2$ $2^{2} \cdot 3^{7}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
8748.fq.972.a1 $C_3^2$ $3^{2}$ ✓ ✓ $C_3^5.S_3^2$ $2^{2} \cdot 3^{7}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
8748.ge.972.a1 $C_3^2$ $3^{2}$ ✓ ✓ $C_3^5.S_3^2$ $2^{2} \cdot 3^{7}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
8748.gm.972.b1.a1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3^5.S_3^2$ $2^{2} \cdot 3^{7}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
8748.kr.972.b1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3^5.S_3^2$ $2^{2} \cdot 3^{7}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
8748.kw.972.b1.a1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3^5.S_3^2$ $2^{2} \cdot 3^{7}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
8748.nt.972.d1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3^5.S_3^2$ $2^{2} \cdot 3^{7}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
8748.nu.972.c1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3^5.S_3^2$ $2^{2} \cdot 3^{7}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
11664.fq.972.b1 $C_2\times C_6$ $2^{2} \cdot 3$ ✓ ✓ ✓ $(C_3^2\times C_6^2).S_3^2$ $2^{4} \cdot 3^{6}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
11664.lh.972.b1 $A_4$ $2^{2} \cdot 3$ ✓ ✓ $(A_4\times C_3^3).S_3^2$ $2^{4} \cdot 3^{6}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
15552.ma.972.a1 $C_2^4$ $2^{4}$ ✓ ✓ ✓ $C_6^3:(C_6\times D_6)$ $2^{6} \cdot 3^{5}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
17496.no.972.b1 $C_3\times S_3$ $2 \cdot 3^{2}$ ✓ ✓ $C_3^4.S_3^3$ $2^{3} \cdot 3^{7}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
17496.ru.972.A $C_3:S_3$ $2 \cdot 3^{2}$ ✓ ✓ $C_3^4.S_3^3$ $2^{3} \cdot 3^{7}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
26244.ed.972.a1 $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^6.S_3^2$ $2^{2} \cdot 3^{8}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
26244.ei.972.a1 $C_3^3$ $3^{3}$ ✓ ✓ $C_3^6.S_3^2$ $2^{2} \cdot 3^{8}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
26244.eu.972.b1 $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^5:C_{18}:C_6$ $2^{2} \cdot 3^{8}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
26244.fe.972.C $C_3^3$ $3^{3}$ ✓ ✓ $C_3^6:(C_6\times S_3)$ $2^{2} \cdot 3^{8}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
26244.fg.972.a1.a1 $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^5:C_3.S_3^2$ $2^{2} \cdot 3^{8}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
26244.fi.972.A $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^6:(C_6\times S_3)$ $2^{2} \cdot 3^{8}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
26244.fi.972.D $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^6:(C_6\times S_3)$ $2^{2} \cdot 3^{8}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
26244.jc.972.C $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^6.S_3^2$ $2^{2} \cdot 3^{8}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
26244.nk.972.D $\He_3$ $3^{3}$ ✓ ✓ $(C_3\times \He_3^2):D_6$ $2^{2} \cdot 3^{8}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
46656.eq.972.b1 $C_2^3\times C_6$ $2^{4} \cdot 3$ ✓ ✓ ✓ $C_6^4.S_3^2$ $2^{6} \cdot 3^{6}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
52488.mx.972.A $C_3^2:C_6$ $2 \cdot 3^{3}$ ✓ ✓ $C_3^5.S_3^3$ $2^{3} \cdot 3^{8}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
52488.nn.972.B $C_3^2:C_6$ $2 \cdot 3^{3}$ ✓ ✓ $C_3^6.C_3:D_{12}$ $2^{3} \cdot 3^{8}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
52488.no.972.A $C_3^2:C_6$ $2 \cdot 3^{3}$ ✓ ✓ $C_3^6.C_3:D_{12}$ $2^{3} \cdot 3^{8}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
52488.nw.972.A $C_3^2:C_6$ $2 \cdot 3^{3}$ ✓ ✓ $C_3^5:C_6.S_3^2$ $2^{3} \cdot 3^{8}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
52488.sv.972.BD $C_3^2:C_6$ $2 \cdot 3^{3}$ ✓ ✓ $C_3^5.S_3^3$ $2^{3} \cdot 3^{8}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
52488.sx.972.A $C_3^2:C_6$ $2 \cdot 3^{3}$ ✓ ✓ $C_3^5.S_3^3$ $2^{3} \cdot 3^{8}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
78732.hu.972.B $C_3^4$ $3^{4}$ ✓ ✓ $C_3^7.S_3^2$ $2^{2} \cdot 3^{9}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
78732.hv.972.E $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^7.S_3^2$ $2^{2} \cdot 3^{9}$ $C_3^3.S_3^2$ $2^{2} \cdot 3^{5}$
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