↑

Learn more

Note: Search results may be incomplete due to uncomputed quantities: Characteristic (9102698 objects)

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 (19 matches)

  displayed columns for results
Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
37044.e.1.a1 $\He_7:(C_3^2\times D_6)$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ ✓ ✓ $\He_7:(C_3^2\times D_6)$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ $C_1$ $1$ ✓
37044.e.2.a1 $C_7^2:(C_3^2\times F_7)$ $2 \cdot 3^{3} \cdot 7^{3}$ ✓ ✓ ✓ $\He_7:(C_3^2\times D_6)$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ $C_2$ $2$ ✓
37044.e.3.a1 $C_3\times \He_7:D_6$ $2^{2} \cdot 3^{2} \cdot 7^{3}$ ✓ ✓ ✓ $\He_7:(C_3^2\times D_6)$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ $C_3$ $3$ ✓
37044.e.4.a1 $\He_7:C_3^3$ $3^{3} \cdot 7^{3}$ ✓ ✓ $\He_7:(C_3^2\times D_6)$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ $C_2^2$ $2^{2}$ ✓
37044.e.6.a1 $C_3\times C_7^2:F_7$ $2 \cdot 3^{2} \cdot 7^{3}$ ✓ ✓ $\He_7:(C_3^2\times D_6)$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ $C_6$ $2 \cdot 3$ ✓
37044.e.6.b1 $C_3\times C_7^2:F_7$ $2 \cdot 3^{2} \cdot 7^{3}$ ✓ ✓ $\He_7:(C_3^2\times D_6)$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ $S_3$ $2 \cdot 3$
37044.e.9.a1 $\He_7:D_6$ $2^{2} \cdot 3 \cdot 7^{3}$ ✓ ✓ $\He_7:(C_3^2\times D_6)$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ $C_3^2$ $3^{2}$ ✓
37044.e.12.a1 $\He_7:C_3^2$ $3^{2} \cdot 7^{3}$ ✓ ✓ $\He_7:(C_3^2\times D_6)$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
37044.e.12.b1 $\He_7:C_3^2$ $3^{2} \cdot 7^{3}$ ✓ ✓ $\He_7:(C_3^2\times D_6)$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ $D_6$ $2^{2} \cdot 3$
37044.e.18.a1 $\He_7:C_6$ $2 \cdot 3 \cdot 7^{3}$ ✓ ✓ $\He_7:(C_3^2\times D_6)$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ $C_3\times S_3$ $2 \cdot 3^{2}$
37044.e.18.b1 $C_7^2:F_7$ $2 \cdot 3 \cdot 7^{3}$ ✓ ✓ $\He_7:(C_3^2\times D_6)$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ $C_3\times C_6$ $2 \cdot 3^{2}$ ✓
37044.e.36.a1 $C_3\times \He_7$ $3 \cdot 7^{3}$ ✓ ✓ $\He_7:(C_3^2\times D_6)$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ $C_6\times S_3$ $2^{2} \cdot 3^{2}$
37044.e.36.b1 $\He_7:C_3$ $3 \cdot 7^{3}$ ✓ ✓ $\He_7:(C_3^2\times D_6)$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ $C_6^2$ $2^{2} \cdot 3^{2}$ ✓
37044.e.54.a1 $C_7^2:D_7$ $2 \cdot 7^{3}$ ✓ ✓ $\He_7:(C_3^2\times D_6)$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ $S_3\times C_3^2$ $2 \cdot 3^{3}$
37044.e.108.a1 $\He_7$ $7^{3}$ $7$ ✓ ✓ $\He_7:(C_3^2\times D_6)$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ $C_3^2\times D_6$ $2^{2} \cdot 3^{3}$
37044.e.1764.a1 $C_{21}$ $3 \cdot 7$ ✓ ✓ ✓ $\He_7:(C_3^2\times D_6)$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ $C_7^2:(C_6\times S_3)$ $2^{2} \cdot 3^{2} \cdot 7^{2}$
37044.e.5292.a1 $C_7$ $7$ ✓ ✓ ✓ $\He_7:(C_3^2\times D_6)$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ $C_7^2:(C_3^2\times D_6)$ $2^{2} \cdot 3^{3} \cdot 7^{2}$ ✓
37044.e.12348.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $\He_7:(C_3^2\times D_6)$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ $\He_7:(C_6\times S_3)$ $2^{2} \cdot 3^{2} \cdot 7^{3}$ ✓
37044.e.37044.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $\He_7:(C_3^2\times D_6)$ $2^{2} \cdot 3^{3} \cdot 7^{3}$ $\He_7:(C_3^2\times D_6)$ $2^{2} \cdot 3^{3} \cdot 7^{3}$
  displayed columns for results