Refine search

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
Sort order Select

Results (1-50 of 143 matches)

Next   displayed columns for results
Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
660.13.660.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
1320.13.660.a1.a1 $C_2$ $2$ ✓ ✓ ✓ $\SL(2,11)$ $2^{3} \cdot 3 \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$ ✓
1320.134.660.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2\times \PSL(2,11)$ $2^{3} \cdot 3 \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$ ✓
1980.57.660.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_3\times \PSL(2,11)$ $2^{2} \cdot 3^{2} \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$ ✓
2640.d.660.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_2\times \SL(2,11)$ $2^{4} \cdot 3 \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
2640.l.660.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $\SL(2,11):C_2$ $2^{4} \cdot 3 \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
2640.bs.660.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_4\times \PSL(2,11)$ $2^{4} \cdot 3 \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
2640.bt.660.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_2^2\times \PSL(2,11)$ $2^{4} \cdot 3 \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
3960.a.660.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_3\times \SL(2,11)$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
3960.o.660.a1.a1 $S_3$ $2 \cdot 3$ ✓ ✓ $S_3\times \PSL(2,11)$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
5280.d.660.a1.a1 $C_8$ $2^{3}$ ✓ ✓ ✓ ✓ $C_8.\PSL(2,11)$ $2^{5} \cdot 3 \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
5280.p.660.a1.a1 $D_4$ $2^{3}$ ✓ ✓ $D_4.\PSL(2,11)$ $2^{5} \cdot 3 \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
5280.q.660.a1.a1 $C_2\times C_4$ $2^{3}$ ✓ ✓ ✓ ✓ $C_4\times \SL(2,11)$ $2^{5} \cdot 3 \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
5280.r.660.a1 $Q_8$ $2^{3}$ ✓ ✓ $\SL(2,11):C_2^2$ $2^{5} \cdot 3 \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
5280.x.660.a1.a1 $D_4$ $2^{3}$ ✓ ✓ $D_4\times \PSL(2,11)$ $2^{5} \cdot 3 \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
6600.a.660.a1.a1 $C_{10}$ $2 \cdot 5$ ✓ ✓ ✓ ✓ $C_5\times \SL(2,11)$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
7920.b.660.a1.a1 $D_6$ $2^{2} \cdot 3$ ✓ ✓ $S_3\times \SL(2,11)$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
7920.i.660.a1.a1 $C_{12}$ $2^{2} \cdot 3$ ✓ ✓ ✓ ✓ $\SL(2,11):C_6$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
7920.n.660.a1.a1 $C_2\times C_6$ $2^{2} \cdot 3$ ✓ ✓ ✓ ✓ $C_6\times \SL(2,11)$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
7920.o.660.a1.a1 $C_3:C_4$ $2^{2} \cdot 3$ ✓ ✓ $\SL(2,11):S_3$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
7920.r.660.a1.a1 $A_4$ $2^{2} \cdot 3$ ✓ ✓ $A_4\times \PSL(2,11)$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
10560.c.660.a1.a1 $\SD_{16}$ $2^{4}$ ✓ ✓ $\SL(2,11).D_4$ $2^{6} \cdot 3 \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
10560.f.660.a1 $C_2\times Q_8$ $2^{4}$ ✓ ✓ $Q_8\times \SL(2,11)$ $2^{6} \cdot 3 \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
13200.c.660.a1.a1 $C_2\times C_{10}$ $2^{2} \cdot 5$ ✓ ✓ ✓ ✓ $C_{10}\times \SL(2,11)$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
13200.f.660.a1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ ✓ $\SL(2,11):C_{10}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
13200.t.660.a1.a1 $D_{10}$ $2^{2} \cdot 5$ ✓ ✓ $D_5\times \SL(2,11)$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
13200.u.660.a1.a1 $C_5:C_4$ $2^{2} \cdot 5$ ✓ ✓ $\SL(2,11):D_5$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
14520.bt.660.a1.a1 $C_{22}$ $2 \cdot 11$ ✓ ✓ ✓ ✓ $C_{11}\times \SL(2,11)$ $2^{3} \cdot 3 \cdot 5 \cdot 11^{2}$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
15840.d.660.a1.a1 $C_{24}$ $2^{3} \cdot 3$ ✓ ✓ ✓ ✓ $C_{24}.\PSL(2,11)$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
15840.g.660.a1.a1 $C_2\times C_{12}$ $2^{3} \cdot 3$ ✓ ✓ ✓ ✓ $C_{12}\times \SL(2,11)$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
15840.h.660.a1.a1 $C_6:C_4$ $2^{3} \cdot 3$ ✓ ✓ $C_3:C_4\times \SL(2,11)$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
15840.j.660.a1.a1 $C_3:Q_8$ $2^{3} \cdot 3$ ✓ ✓ $\SL(2,11):D_6$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
15840.k.660.a1.a1 $D_{12}$ $2^{3} \cdot 3$ ✓ ✓ $D_{12}.\PSL(2,11)$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
15840.r.660.a1.a1 $S_4$ $2^{3} \cdot 3$ ✓ ✓ $S_4\times \PSL(2,11)$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
19800.a.660.a1.a1 $C_{30}$ $2 \cdot 3 \cdot 5$ ✓ ✓ ✓ ✓ $C_{15}\times \SL(2,11)$ $2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
26400.c.660.a1.a1 $C_{40}$ $2^{3} \cdot 5$ ✓ ✓ ✓ ✓ $C_{40}.\PSL(2,11)$ $2^{5} \cdot 3 \cdot 5^{2} \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
26400.g.660.a1.a1 $C_5\times D_4$ $2^{3} \cdot 5$ ✓ ✓ $(C_2\times \SL(2,11)):C_{10}$ $2^{5} \cdot 3 \cdot 5^{2} \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
26400.l.660.a1.a1 $C_2\times C_{20}$ $2^{3} \cdot 5$ ✓ ✓ ✓ ✓ $C_{20}\times \SL(2,11)$ $2^{5} \cdot 3 \cdot 5^{2} \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
26400.n.660.a1 $C_5\times Q_8$ $2^{3} \cdot 5$ ✓ ✓ $C_5\times \SL(2,11):C_2^2$ $2^{5} \cdot 3 \cdot 5^{2} \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
26400.s.660.a1.a1 $C_5:D_4$ $2^{3} \cdot 5$ ✓ ✓ $\SL(2,11).D_{10}$ $2^{5} \cdot 3 \cdot 5^{2} \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
26400.t.660.a1.a1 $C_{10}:C_4$ $2^{3} \cdot 5$ ✓ ✓ $C_5:C_4\times \SL(2,11)$ $2^{5} \cdot 3 \cdot 5^{2} \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
29040.z.660.a1.a1 $C_2\times C_{22}$ $2^{2} \cdot 11$ ✓ ✓ ✓ ✓ $C_{22}\times \SL(2,11)$ $2^{4} \cdot 3 \cdot 5 \cdot 11^{2}$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
31680.b.660.a1.a1 $C_{24}:C_2$ $2^{4} \cdot 3$ ✓ ✓ $\SL(2,11).D_{12}$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
31680.c.660.a1.a1 $C_6:Q_8$ $2^{4} \cdot 3$ ✓ ✓ $C_3:Q_8\times \SL(2,11)$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
31680.f.660.a1.a1 $C_2\times \SL(2,3)$ $2^{4} \cdot 3$ ✓ ✓ $\SL(2,11)\times \SL(2,3)$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
33000.a.660.a1 $C_5\times C_{10}$ $2 \cdot 5^{2}$ ✓ ✓ ✓ $C_5^2\times \SL(2,11)$ $2^{3} \cdot 3 \cdot 5^{3} \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
39600.a.660.a1.a1 $A_5$ $2^{2} \cdot 3 \cdot 5$ ✓ ✓ $A_5\times \PSL(2,11)$ $2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$ ✓
39600.b.660.a1.a1 $S_3\times C_{10}$ $2^{2} \cdot 3 \cdot 5$ ✓ ✓ $C_5\times S_3\times \SL(2,11)$ $2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
39600.e.660.a1.a1 $C_{60}$ $2^{2} \cdot 3 \cdot 5$ ✓ ✓ ✓ ✓ $\SL(2,11):C_{30}$ $2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
39600.j.660.a1.a1 $C_2\times C_{30}$ $2^{2} \cdot 3 \cdot 5$ ✓ ✓ ✓ ✓ $C_{30}\times \SL(2,11)$ $2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11$ $\PSL(2,11)$ $2^{2} \cdot 3 \cdot 5 \cdot 11$
Next   displayed columns for results