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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 65 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
648.702.648.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
1296.3491.648.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_6\times \PU(3,2)$ $2^{4} \cdot 3^{4}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$ ✓
1944.3440.648.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_9\times \PU(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$ ✓
1944.3441.648.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $(C_3^2\times C_9):\SL(2,3)$ $2^{3} \cdot 3^{5}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$ ✓
1944.3442.648.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $\SU(3,2):C_3^2$ $2^{3} \cdot 3^{5}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$ ✓
1944.3443.648.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $\SU(3,2):C_3^2$ $2^{3} \cdot 3^{5}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$ ✓
1944.3444.648.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $\SU(3,2).C_3^2$ $2^{3} \cdot 3^{5}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$ ✓
1944.3445.648.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $\SU(3,2).C_3^2$ $2^{3} \cdot 3^{5}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$ ✓
1944.3446.648.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_3\times \Unitary(3,2)$ $2^{3} \cdot 3^{5}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$ ✓
1944.3447.648.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $\Unitary(3,2):C_3$ $2^{3} \cdot 3^{5}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$ ✓
1944.3448.648.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $\Unitary(3,2):C_3$ $2^{3} \cdot 3^{5}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$ ✓
1944.3449.648.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $\Unitary(3,2):C_3$ $2^{3} \cdot 3^{5}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$ ✓
1944.3450.648.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_3^4.\SL(2,3)$ $2^{3} \cdot 3^{5}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$ ✓
1944.3451.648.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_3^4.\SL(2,3)$ $2^{3} \cdot 3^{5}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$ ✓
1944.3452.648.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_3^4:\SL(2,3)$ $2^{3} \cdot 3^{5}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$ ✓
1944.3874.648.a1 $C_3$ $3$ ✓ ✓ ✓ $C_3^4:\SL(2,3)$ $2^{3} \cdot 3^{5}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$ ✓
2592.lr.648.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $A_4\times \PU(3,2)$ $2^{5} \cdot 3^{4}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$ ✓
3888.ks.648.a1.a1 $S_3$ $2 \cdot 3$ ✓ ✓ $S_3\times C_3^3:\SL(2,3)$ $2^{4} \cdot 3^{5}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
5184.qo.648.a1.a1 $C_2^3$ $2^{3}$ ✓ ✓ ✓ $C_6^2:(C_6\times \SL(2,3))$ $2^{6} \cdot 3^{4}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
5832.dp.648.a1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3^5:\SL(2,3)$ $2^{3} \cdot 3^{6}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$ ✓
5832.el.648.a1.a1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3^4:(C_3\times \SL(2,3))$ $2^{3} \cdot 3^{6}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$ ✓
17496.cz.648.b1 $C_3^3$ $3^{3}$ ✓ ✓ ✓ $C_3^6:\SL(2,3)$ $2^{3} \cdot 3^{7}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$ ✓
52488.cm.648.A $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^6:(C_3\times \SL(2,3))$ $2^{3} \cdot 3^{8}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
52488.ky.648.a1 $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^6:(C_3\times \SL(2,3))$ $2^{3} \cdot 3^{8}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
52488.kz.648.A $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^6.(C_3\times \SL(2,3))$ $2^{3} \cdot 3^{8}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
52488.kz.648.B $C_3^4$ $3^{4}$ ✓ ✓ $C_3^6.(C_3\times \SL(2,3))$ $2^{3} \cdot 3^{8}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
52488.rc.648.a1 $C_3^4$ $3^{4}$ ✓ ✓ ✓ $C_3^5.\PU(3,2)$ $2^{3} \cdot 3^{8}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
157464.x.648.B $C_3^5$ $3^{5}$ ✓ ✓ ✓ $C_3^8.\SL(2,3)$ $2^{3} \cdot 3^{9}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
157464.sf.648.A $C_3^5$ $3^{5}$ ✓ ✓ $C_3^6:\PU(3,2)$ $2^{3} \cdot 3^{9}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
157464.si.648.A $C_3^5$ $3^{5}$ ✓ ✓ ✓ $C_3^6.\PU(3,2)$ $2^{3} \cdot 3^{9}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
157464.sj.648.a1 $C_3^5$ $3^{5}$ ✓ ✓ ✓ $C_3^6:\PU(3,2)$ $2^{3} \cdot 3^{9}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
472392.hx.648.A $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^8.(C_3\times \SL(2,3))$ $2^{3} \cdot 3^{10}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
472392.hy.648.A $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^8.(C_3\times \SL(2,3))$ $2^{3} \cdot 3^{10}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
472392.ia.648.A $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^8.(C_3\times \SL(2,3))$ $2^{3} \cdot 3^{10}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
472392.ia.648.B $C_3^6$ $3^{6}$ ✓ ✓ $C_3^8.(C_3\times \SL(2,3))$ $2^{3} \cdot 3^{10}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
472392.ia.648.C $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^8.(C_3\times \SL(2,3))$ $2^{3} \cdot 3^{10}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
472392.rq.648.A $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^7.\PU(3,2)$ $2^{3} \cdot 3^{10}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
472392.rq.648.B $C_3^6$ $3^{6}$ ✓ ✓ $C_3^7.\PU(3,2)$ $2^{3} \cdot 3^{10}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
472392.rr.648.A $C_3^6$ $3^{6}$ ✓ ✓ ✓ $C_3^6.\Unitary(3,2)$ $2^{3} \cdot 3^{10}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
472392.ty.648._.A $C_3^2\times C_9^2$ $3^{6}$ ✓ ✓ ✓ $C_9^4.(C_3\times \SL(2,3))$ $2^{3} \cdot 3^{10}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
1417176.qb.648.B $C_3^7$ $3^{7}$ ✓ ✓ ✓ $C_3^8.\PU(3,2)$ $2^{3} \cdot 3^{11}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
1417176.qc.648.B $C_3^7$ $3^{7}$ ✓ ✓ ✓ $C_3^8.\PU(3,2)$ $2^{3} \cdot 3^{11}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
1889568.pd.648.A $C_3^5:D_6$ $2^{2} \cdot 3^{6}$ ✓ ✓ $C_3^8.(A_4\times \SL(2,3))$ $2^{5} \cdot 3^{10}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
4251528.v.648.A $C_3^8$ $3^{8}$ ✓ ✓ ✓ $C_3^8.C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{12}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
4251528.dt.648._.A $C_3^8$ $3^{8}$ ✓ ✓ $C_3^8.C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{12}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
4251528.dt.648._.B $C_3^8$ $3^{8}$ ✓ ✓ ✓ $C_3^8.C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{12}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
4251528.dt.648._.C $C_3^8$ $3^{8}$ ✓ ✓ ✓ $C_3^8.C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{12}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
4251528.dt.648._.D $C_3^8$ $3^{8}$ ✓ ✓ $C_3^8.C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{12}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
4251528.kp.648.A $C_3^8$ $3^{8}$ ✓ ✓ ✓ $C_3^7.C_3^4:\SL(2,3)$ $2^{3} \cdot 3^{12}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
4251528.kp.648.B $C_3\times C_3^4.C_3^3$ $3^{8}$ ✓ ✓ $C_3^7.C_3^4:\SL(2,3)$ $2^{3} \cdot 3^{12}$ $C_3^3:\SL(2,3)$ $2^{3} \cdot 3^{4}$
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