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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 (4 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
2688.dt.1344.a1 $C_2$ $2$ ✓ ✓ ✓ $F_7\times D_4^2$ $2^{7} \cdot 3 \cdot 7$ $C_2^2\times D_4\times F_7$ $2^{6} \cdot 3 \cdot 7$ ✓
2688.eh.1344.b1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_8:C_2^3\times F_7$ $2^{7} \cdot 3 \cdot 7$ $C_2^2\times D_4\times F_7$ $2^{6} \cdot 3 \cdot 7$ ✓
2688.ej.1344.b1 $C_2$ $2$ ✓ ✓ ✓ $C_2^3:D_4\times F_7$ $2^{7} \cdot 3 \cdot 7$ $C_2^2\times D_4\times F_7$ $2^{6} \cdot 3 \cdot 7$ ✓
2688.ek.1344.A $C_2$ $2$ ✓ ✓ ✓ $D_4\times C_2^3\times F_7$ $2^{7} \cdot 3 \cdot 7$ $C_2^2\times D_4\times F_7$ $2^{6} \cdot 3 \cdot 7$ ✓
  displayed columns for results