↑

Learn more

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 84 matches)

Next   displayed columns for results
Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
3024.r.3024.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
6048.q.3024.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $\SL(2,8):C_{12}$ $2^{5} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$ ✓
6048.r.3024.a1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_2^2\times {}^2G(2,3)$ $2^{5} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$ ✓
6048.r.3024.a1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_2^2\times {}^2G(2,3)$ $2^{5} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$ ✓
6048.r.3024.a1.c1 $C_2$ $2$ ✓ ✓ ✓ $C_2^2\times {}^2G(2,3)$ $2^{5} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$ ✓
9072.b.3024.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $S_3\times {}^2G(2,3)$ $2^{4} \cdot 3^{4} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$ ✓
9072.c.3024.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_6\times {}^2G(2,3)$ $2^{4} \cdot 3^{4} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$ ✓
12096.br.3024.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^3\times {}^2G(2,3)$ $2^{6} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
12096.bt.3024.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^3:{}^2G(2,3)$ $2^{6} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$ ✓
12096.bu.3024.a1.a1 $C_2^2$ $2^{2}$ ✓ ✓ ✓ ✓ $C_2\times \SL(2,8):C_{12}$ $2^{6} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
12096.bu.3024.b1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_2\times \SL(2,8):C_{12}$ $2^{6} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
12096.bu.3024.b1.b1 $C_4$ $2^{2}$ ✓ ✓ ✓ $C_2\times \SL(2,8):C_{12}$ $2^{6} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
15120.k.3024.a1.a1 $C_5$ $5$ $5$ ✓ ✓ ✓ $D_5\times {}^2G(2,3)$ $2^{4} \cdot 3^{3} \cdot 5 \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$ ✓
18144.b.3024.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ $D_6\times {}^2G(2,3)$ $2^{5} \cdot 3^{4} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
18144.b.3024.b1.a1 $S_3$ $2 \cdot 3$ ✓ $D_6\times {}^2G(2,3)$ $2^{5} \cdot 3^{4} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
18144.b.3024.b1.b1 $S_3$ $2 \cdot 3$ ✓ $D_6\times {}^2G(2,3)$ $2^{5} \cdot 3^{4} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
24192.u.3024.a1 $C_2^3$ $2^{3}$ ✓ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
24192.u.3024.b1 $C_2\times C_4$ $2^{3}$ ✓ ✓ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
24192.u.3024.c1 $D_4$ $2^{3}$ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
27216.a.3024.a1.a1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $C_3\times S_3\times {}^2G(2,3)$ $2^{4} \cdot 3^{5} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
27216.b.3024.a1 $C_3^2$ $3^{2}$ ✓ ✓ ✓ $(C_3^2\times \SL(2,8)):C_6$ $2^{4} \cdot 3^{5} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
30240.i.3024.a1.a1 $D_5$ $2 \cdot 5$ ✓ ✓ $F_5\times {}^2G(2,3)$ $2^{5} \cdot 3^{3} \cdot 5 \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
36288.c.3024.a1.a1 $A_4$ $2^{2} \cdot 3$ ✓ ✓ $S_4\times {}^2G(2,3)$ $2^{6} \cdot 3^{4} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
36288.d.3024.a1.a1 $A_4$ $2^{2} \cdot 3$ ✓ ✓ $A_4\times \SL(2,8):C_6$ $2^{6} \cdot 3^{4} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
54432.a.3024.a1.a1 $C_3\times S_3$ $2 \cdot 3^{2}$ ✓ $S_3^2\times {}^2G(2,3)$ $2^{5} \cdot 3^{5} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
54432.a.3024.a1.b1 $C_3\times S_3$ $2 \cdot 3^{2}$ ✓ $S_3^2\times {}^2G(2,3)$ $2^{5} \cdot 3^{5} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
54432.a.3024.b1.a1 $C_3:S_3$ $2 \cdot 3^{2}$ ✓ ✓ $S_3^2\times {}^2G(2,3)$ $2^{5} \cdot 3^{5} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
54432.b.3024.a1.a1 $C_3:S_3$ $2 \cdot 3^{2}$ ✓ ✓ $(C_3^2\times \SL(2,8)):C_{12}$ $2^{5} \cdot 3^{5} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
72576.a.3024.a1 $C_2\times A_4$ $2^{3} \cdot 3$ ✓ ✓ $S_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{4} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
72576.a.3024.b1 $S_4$ $2^{3} \cdot 3$ ✓ $S_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{4} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
108864.a.3024.a1.a1 $S_3^2$ $2^{2} \cdot 3^{2}$ ✓ ${}^2G(2,3)\times \SOPlus(4,2)$ $2^{6} \cdot 3^{5} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
108864.a.3024.a1.b1 $S_3^2$ $2^{2} \cdot 3^{2}$ ✓ ${}^2G(2,3)\times \SOPlus(4,2)$ $2^{6} \cdot 3^{5} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
108864.a.3024.b1.a1 $C_3^2:C_4$ $2^{2} \cdot 3^{2}$ ✓ ✓ ${}^2G(2,3)\times \SOPlus(4,2)$ $2^{6} \cdot 3^{5} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
181440.h.3024.a1.a1 $A_5$ $2^{2} \cdot 3 \cdot 5$ ✓ ✓ $S_5\times {}^2G(2,3)$ $2^{6} \cdot 3^{4} \cdot 5 \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$ ✓
774144.a.3024.A $C_2^8$ $2^{8}$ ✓ ✓ ✓ $C_2^9.{}^2G(2,3)$ $2^{12} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$ ✓
1088640.d.3024.a1 $A_6$ $2^{3} \cdot 3^{2} \cdot 5$ ✓ ✓ $S_6\times {}^2G(2,3)$ $2^{7} \cdot 3^{5} \cdot 5 \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$ ✓
1548288.a.3024.A $C_2^9$ $2^{9}$ ✓ ✓ ✓ $C_4\times C_2^8:{}^2G(2,3)$ $2^{13} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
1548288.b.3024.A $C_2^9$ $2^{9}$ ✓ ✓ $C_2^{10}.{}^2G(2,3)$ $2^{13} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
3096576.a.3024.A $C_2^{10}$ $2^{10}$ ✓ ✓ $D_4\times C_2^8:{}^2G(2,3)$ $2^{14} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
3096576.a.3024.B $C_2^8\times C_4$ $2^{10}$ ✓ ✓ ✓ $D_4\times C_2^8:{}^2G(2,3)$ $2^{14} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
19840464.a.3024.A $C_3^8$ $3^{8}$ ✓ ✓ ✓ $C_3^8.\SL(2,8):C_6$ $2^{4} \cdot 3^{11} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
59521392.a.3024._.A $C_3^9$ $3^{9}$ ✓ ✓ ✓ $C_3^8.(S_3\times {}^2G(2,3))$ $2^{4} \cdot 3^{12} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
198180864.a.3024._.A $C_2^{16}$ $2^{16}$ ✓ ✓ ✓ $C_2^{16}.\SL(2,8).C_6$ $2^{20} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
198180864.b.3024._.A $C_4^8$ $2^{16}$ ✓ ✓ ✓ $C_4^8.\SL(2,8).C_6$ $2^{20} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
198180864.c.3024._.A $C_4^8$ $2^{16}$ ✓ ✓ ✓ $C_4^8.\SL(2,8).C_6$ $2^{20} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
198180864.d.3024._.A $C_2^{16}$ $2^{16}$ ✓ ✓ ✓ $C_2^{16}.\SL(2,8).C_6$ $2^{20} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
396361728.a.3024._.A $C_2^{17}$ $2^{17}$ ✓ ✓ ✓ $C_2^{16}.\SL(2,8).C_{12}$ $2^{21} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
396361728.b.3024._.A $C_2^{16}.C_2$ $2^{17}$ ✓ $C_2^{17}.\SL(2,8).C_6$ $2^{21} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
396361728.b.3024._.B $C_2^{17}$ $2^{17}$ ✓ ✓ ✓ $C_2^{17}.\SL(2,8).C_6$ $2^{21} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
396361728.b.3024._.C $C_2^{16}.C_2$ $2^{17}$ ✓ $C_2^{17}.\SL(2,8).C_6$ $2^{21} \cdot 3^{3} \cdot 7$ $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$
Next   displayed columns for results