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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 544 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
24192.u.1.a1 $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ ✓ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $C_1$ $1$ ✓
24192.u.2.a1 $C_2^3\times {}^2G(2,3)$ $2^{6} \cdot 3^{3} \cdot 7$ ✓ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $C_2$ $2$ ✓
24192.u.2.b1 $C_2\times \SL(2,8):C_{12}$ $2^{6} \cdot 3^{3} \cdot 7$ ✓ ✓ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $C_2$ $2$ ✓
24192.u.2.c1 $D_4\times {}^2G(2,3)$ $2^{6} \cdot 3^{3} \cdot 7$ ✓ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $C_2$ $2$ ✓
24192.u.3.a1 $C_2\times D_4\times \SL(2,8)$ $2^{7} \cdot 3^{2} \cdot 7$ ✓ ✓ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $C_3$ $3$ ✓
24192.u.4.a1 $C_2^2\times {}^2G(2,3)$ $2^{5} \cdot 3^{3} \cdot 7$ ✓ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $C_2^2$ $2^{2}$ ✓
24192.u.4.b1 $C_2^2\times {}^2G(2,3)$ $2^{5} \cdot 3^{3} \cdot 7$ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $C_2^2$ $2^{2}$ ✓
24192.u.4.c1 $\SL(2,8):C_{12}$ $2^{5} \cdot 3^{3} \cdot 7$ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $C_2^2$ $2^{2}$ ✓
24192.u.4.d1 $C_2^2\times {}^2G(2,3)$ $2^{5} \cdot 3^{3} \cdot 7$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2^{2}$ $-$
24192.u.6.a1 $C_2^3\times \SL(2,8)$ $2^{6} \cdot 3^{2} \cdot 7$ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $C_6$ $2 \cdot 3$ ✓
24192.u.6.b1 $C_2\times C_4\times \SL(2,8)$ $2^{6} \cdot 3^{2} \cdot 7$ ✓ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $C_6$ $2 \cdot 3$ ✓
24192.u.6.c1 $D_4\times \SL(2,8)$ $2^{6} \cdot 3^{2} \cdot 7$ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $C_6$ $2 \cdot 3$ ✓
24192.u.8.a1 $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $D_4$ $2^{3}$
24192.u.8.b1 $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$ ✓ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $C_2^3$ $2^{3}$ ✓
24192.u.8.c1 $\SL(2,8):C_6$ $2^{4} \cdot 3^{3} \cdot 7$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2^{3}$ $-$
24192.u.9.a1 $D_4\times F_8:C_6$ $2^{7} \cdot 3 \cdot 7$ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $3^{2}$ $-$
24192.u.12.a1 $C_2^2\times \SL(2,8)$ $2^{5} \cdot 3^{2} \cdot 7$ ✓ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
24192.u.12.b1 $C_2^2\times \SL(2,8)$ $2^{5} \cdot 3^{2} \cdot 7$ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
24192.u.12.c1 $C_4\times \SL(2,8)$ $2^{5} \cdot 3^{2} \cdot 7$ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
24192.u.12.d1 $C_2^2\times \SL(2,8)$ $2^{5} \cdot 3^{2} \cdot 7$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2^{2} \cdot 3$ $-$
24192.u.16.a1 ${}^2G(2,3)$ $2^{3} \cdot 3^{3} \cdot 7$ ✓ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $C_2\times D_4$ $2^{4}$
24192.u.18.a1 $C_2^2\times F_8:C_6$ $2^{6} \cdot 3 \cdot 7$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2 \cdot 3^{2}$ $-$
24192.u.18.b1 $C_2\times F_8:C_{12}$ $2^{6} \cdot 3 \cdot 7$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2 \cdot 3^{2}$ $-$
24192.u.18.c1 $D_4\times F_8:C_3$ $2^{6} \cdot 3 \cdot 7$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2 \cdot 3^{2}$ $-$
24192.u.24.a1 $C_2\times \SL(2,8)$ $2^{4} \cdot 3^{2} \cdot 7$ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $C_3\times D_4$ $2^{3} \cdot 3$
24192.u.24.b1 $C_2\times \SL(2,8)$ $2^{4} \cdot 3^{2} \cdot 7$ ✓ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $C_2^2\times C_6$ $2^{3} \cdot 3$ ✓
24192.u.24.c1 $C_2\times \SL(2,8)$ $2^{4} \cdot 3^{2} \cdot 7$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2^{3} \cdot 3$ $-$
24192.u.27.a1 $C_2^6:C_{14}$ $2^{7} \cdot 7$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $3^{3}$ $-$
24192.u.28.a1 $C_2\times D_{36}:C_6$ $2^{5} \cdot 3^{3}$ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2^{2} \cdot 7$ $-$
24192.u.36.a1 $C_2\times F_8:C_6$ $2^{5} \cdot 3 \cdot 7$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2^{2} \cdot 3^{2}$ $-$
24192.u.36.b1 $C_2\times D_4\times F_7$ $2^{5} \cdot 3 \cdot 7$ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2^{2} \cdot 3^{2}$ $-$
24192.u.36.c1 $C_2\times F_8:C_6$ $2^{5} \cdot 3 \cdot 7$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2^{2} \cdot 3^{2}$ $-$
24192.u.36.d1 $C_2\times F_8:C_6$ $2^{5} \cdot 3 \cdot 7$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2^{2} \cdot 3^{2}$ $-$
24192.u.36.e1 $F_8:C_{12}$ $2^{5} \cdot 3 \cdot 7$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2^{2} \cdot 3^{2}$ $-$
24192.u.48.a1 $\SL(2,8)$ $2^{3} \cdot 3^{2} \cdot 7$ ✓ ✓ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $C_6\times D_4$ $2^{4} \cdot 3$ ✓
24192.u.54.a1 $C_2^3\times F_8$ $2^{6} \cdot 7$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2 \cdot 3^{3}$ $-$
24192.u.54.b1 $C_2^4:C_{28}$ $2^{6} \cdot 7$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2 \cdot 3^{3}$ $-$
24192.u.54.c1 $D_4\times F_8$ $2^{6} \cdot 7$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2 \cdot 3^{3}$ $-$
24192.u.56.a1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2^{3} \cdot 7$ $-$
24192.u.56.b1 $C_6^2.D_6$ $2^{4} \cdot 3^{3}$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2^{3} \cdot 7$ $-$
24192.u.56.c1 $C_{12}.C_6^2$ $2^{4} \cdot 3^{3}$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2^{3} \cdot 7$ $-$
24192.u.56.d1 $D_{18}:C_{12}$ $2^{4} \cdot 3^{3}$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2^{3} \cdot 7$ $-$
24192.u.56.e1 $D_{36}:C_6$ $2^{4} \cdot 3^{3}$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2^{3} \cdot 7$ $-$
24192.u.56.f1 $D_{36}:C_6$ $2^{4} \cdot 3^{3}$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2^{3} \cdot 7$ $-$
24192.u.56.g1 $D_{36}:C_6$ $2^{4} \cdot 3^{3}$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2^{3} \cdot 7$ $-$
24192.u.63.a1 $C_2^6:C_6$ $2^{7} \cdot 3$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $3^{2} \cdot 7$ $-$
24192.u.72.a1 $F_8:C_6$ $2^{4} \cdot 3 \cdot 7$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2^{3} \cdot 3^{2}$ $-$
24192.u.72.b1 $C_2^3\times F_7$ $2^{4} \cdot 3 \cdot 7$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2^{3} \cdot 3^{2}$ $-$
24192.u.72.c1 $C_2^3:F_7$ $2^{4} \cdot 3 \cdot 7$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2^{3} \cdot 3^{2}$ $-$
24192.u.72.d1 $C_2\times C_{28}:C_6$ $2^{4} \cdot 3 \cdot 7$ $D_4\times \SL(2,8):C_6$ $2^{7} \cdot 3^{3} \cdot 7$ $2^{3} \cdot 3^{2}$ $-$
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