| Label |
Subgroup |
|
Ambient |
|
Quotient |
| Name |
Order |
norm |
char |
cyc |
ab |
solv |
max |
perf |
cent |
Name |
Order |
Name |
Size |
cyc |
ab |
solv |
max |
| 40320.o.1.a1.a1 |
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
✓ |
✓ |
|
|
|
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
$C_1$ |
$1$ |
✓ |
✓ |
✓ |
|
| 40320.o.2.a1.a1 |
$\PSL(3,4)$ |
$2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ |
✓ |
✓ |
|
|
|
✓ |
✓ |
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
$C_2$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
| 40320.o.42.a1.a1 |
$C_2^4:A_5$ |
$2^{6} \cdot 3 \cdot 5$ |
|
|
|
|
|
|
✓ |
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2 \cdot 3 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.56.a1.b1 |
$A_6.C_2$ |
$2^{4} \cdot 3^{2} \cdot 5$ |
|
|
|
|
|
✓ |
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{3} \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.56.a1.a1 |
$A_6.C_2$ |
$2^{4} \cdot 3^{2} \cdot 5$ |
|
|
|
|
|
✓ |
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{3} \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.56.a1.c1 |
$A_6.C_2$ |
$2^{4} \cdot 3^{2} \cdot 5$ |
|
|
|
|
|
✓ |
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{3} \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.105.a1.a1 |
$C_4^2.S_4$ |
$2^{7} \cdot 3$ |
|
|
|
|
✓ |
✓ |
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$3 \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.112.a1.b1 |
$A_6$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
|
|
|
|
|
|
✓ |
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{4} \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.112.a1.c1 |
$A_6$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
|
|
|
|
|
|
✓ |
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{4} \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.112.a1.a1 |
$A_6$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
|
|
|
|
|
|
✓ |
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{4} \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.120.a1.b1 |
$\PGL(2,7)$ |
$2^{4} \cdot 3 \cdot 7$ |
|
|
|
|
|
✓ |
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{3} \cdot 3 \cdot 5$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.120.a1.a1 |
$\PGL(2,7)$ |
$2^{4} \cdot 3 \cdot 7$ |
|
|
|
|
|
✓ |
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{3} \cdot 3 \cdot 5$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.120.a1.c1 |
$\PGL(2,7)$ |
$2^{4} \cdot 3 \cdot 7$ |
|
|
|
|
|
✓ |
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{3} \cdot 3 \cdot 5$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.210.a1.a1 |
$C_4^2:A_4$ |
$2^{6} \cdot 3$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2 \cdot 3 \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.240.a1.b1 |
$\GL(3,2)$ |
$2^{3} \cdot 3 \cdot 7$ |
|
|
|
|
|
|
✓ |
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{4} \cdot 3 \cdot 5$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.240.a1.a1 |
$\GL(3,2)$ |
$2^{3} \cdot 3 \cdot 7$ |
|
|
|
|
|
|
✓ |
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{4} \cdot 3 \cdot 5$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.240.a1.c1 |
$\GL(3,2)$ |
$2^{3} \cdot 3 \cdot 7$ |
|
|
|
|
|
|
✓ |
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{4} \cdot 3 \cdot 5$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.252.a1.a1 |
$C_2^4:D_5$ |
$2^{5} \cdot 5$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{2} \cdot 3^{2} \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.280.a1.a1 |
$C_2\times \PSU(3,2)$ |
$2^{4} \cdot 3^{2}$ |
|
|
|
|
✓ |
✓ |
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{3} \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.315.a1.a1 |
$C_4^2.D_4$ |
$2^{7}$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$3^{2} \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.336.a1.a1 |
$S_5$ |
$2^{3} \cdot 3 \cdot 5$ |
|
|
|
|
|
✓ |
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{4} \cdot 3 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.420.b1.a1 |
$C_2^2:S_4$ |
$2^{5} \cdot 3$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{2} \cdot 3 \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.420.a1.c1 |
$C_4^2:S_3$ |
$2^{5} \cdot 3$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{2} \cdot 3 \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.420.a1.a1 |
$C_4^2:S_3$ |
$2^{5} \cdot 3$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{2} \cdot 3 \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.420.a1.b1 |
$C_4^2:S_3$ |
$2^{5} \cdot 3$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{2} \cdot 3 \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.504.a1.a1 |
$C_2^4:C_5$ |
$2^{4} \cdot 5$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{3} \cdot 3^{2} \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.560.b1.c1 |
$\PSU(3,2)$ |
$2^{3} \cdot 3^{2}$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{4} \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.560.c1.a1 |
$\PSU(3,2)$ |
$2^{3} \cdot 3^{2}$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{4} \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.560.b1.b1 |
$\PSU(3,2)$ |
$2^{3} \cdot 3^{2}$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{4} \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.560.b1.a1 |
$\PSU(3,2)$ |
$2^{3} \cdot 3^{2}$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{4} \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.560.a1.c1 |
$C_2\times C_3^2:C_4$ |
$2^{3} \cdot 3^{2}$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{4} \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.560.a1.b1 |
$C_2\times C_3^2:C_4$ |
$2^{3} \cdot 3^{2}$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{4} \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.560.a1.a1 |
$C_2\times C_3^2:C_4$ |
$2^{3} \cdot 3^{2}$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{4} \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.630.a1.c1 |
$D_4.D_4$ |
$2^{6}$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2 \cdot 3^{2} \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.630.a1.b1 |
$D_4.D_4$ |
$2^{6}$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2 \cdot 3^{2} \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.630.a1.a1 |
$D_4.D_4$ |
$2^{6}$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2 \cdot 3^{2} \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.630.c1.a1 |
$C_4^2:C_2^2$ |
$2^{6}$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2 \cdot 3^{2} \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.630.b1.a1 |
$C_4^2.C_4$ |
$2^{6}$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2 \cdot 3^{2} \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.630.b1.c1 |
$C_4^2.C_4$ |
$2^{6}$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2 \cdot 3^{2} \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.630.b1.b1 |
$C_4^2.C_4$ |
$2^{6}$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2 \cdot 3^{2} \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.672.a1.a2 |
$A_5$ |
$2^{2} \cdot 3 \cdot 5$ |
|
|
|
|
|
|
✓ |
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{5} \cdot 3 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.672.a1.a3 |
$A_5$ |
$2^{2} \cdot 3 \cdot 5$ |
|
|
|
|
|
|
✓ |
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{5} \cdot 3 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.672.a1.a1 |
$A_5$ |
$2^{2} \cdot 3 \cdot 5$ |
|
|
|
|
|
|
✓ |
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{5} \cdot 3 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.672.a2.a1 |
$A_5$ |
$2^{2} \cdot 3 \cdot 5$ |
|
|
|
|
|
|
✓ |
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{5} \cdot 3 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.840.a1.b1 |
$C_4^2:C_3$ |
$2^{4} \cdot 3$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{3} \cdot 3 \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.840.a1.c1 |
$C_4^2:C_3$ |
$2^{4} \cdot 3$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{3} \cdot 3 \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.840.a1.a1 |
$C_4^2:C_3$ |
$2^{4} \cdot 3$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{3} \cdot 3 \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.840.b1.a1 |
$C_2^2:A_4$ |
$2^{4} \cdot 3$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{3} \cdot 3 \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.960.a1.a1 |
$F_7$ |
$2 \cdot 3 \cdot 7$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{6} \cdot 3 \cdot 5$ |
$-$ |
$-$ |
$-$ |
|
| 40320.o.1120.a1.a1 |
$C_6:S_3$ |
$2^{2} \cdot 3^{2}$ |
|
|
|
|
✓ |
|
|
|
|
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
|
|
$2^{5} \cdot 5 \cdot 7$ |
$-$ |
$-$ |
$-$ |
|
