파일:Subgroup lattice of D4.png

\begin{tikzpicture}[node distance=2.5cm,line width=0.7pt]
\title{Subgroup lattice of $D_4$}
\node(D4) at (0,0)     {$D_4$};
\node(F2)      [below=1.5cm of D4]  {$\langle \sigma \rangle$};
\node(F1)      [left of=F2]       {$\langle \sigma^2,\tau \rangle$};
\node(F3)      [right of=F2]       {$\langle \sigma^2, \sigma\tau \rangle$};
\node(T3)      [below=1.5cm of F2]       {$\langle \sigma^2 \rangle$};
\node(T2)      [left of=T3]       {$\langle\tau\rangle$};
\node(T1)      [left of=T2]       {$\langle\sigma^2\tau\rangle$};
\node(T4)      [right of=T3]      {$\langle\sigma\tau\rangle$};
\node(T5)      [right of=T4]      {$\langle\sigma^3\tau\rangle$};
\node(1)        [below=1.5cm of T3]   {$\left\{1\right\}$};
\draw(D4)       -- (F1);
\draw(D4)       -- (F2);
\draw(D4)       -- (F3);
\draw(F1)       -- (T1);
\draw(F1)       -- (T2);
\draw(F1)       -- (T3);
\draw(F2)       -- (T3);
\draw(F3)       -- (T3);
\draw(F3)       -- (T4);
\draw(F3)       -- (T5);
\draw(T1)       -- (1);
\draw(T2)       -- (1);
\draw(T3)       -- (1);
\draw(T4)       -- (1);
\draw(T5)       -- (1);
\end{tikzpicture}