# \Subset with line beneath it

The command \Subset produces an inclusion symbol \subset with a small inclusion inside of it. I have two related questions:

1. How can I draw a line under \Subset just like the one under \subseteq?

2. How can I make \Subset the same size as \subseteq?

I'd superimpose \Subset to \subseteq.

\documentclass{article}
\usepackage{amsmath,amssymb}

\makeatletter
\newcommand{\Subseteq}{\mathrel{\mathpalette\SubSupseteq@{\Subset\subseteq}}}
\newcommand{\Supseteq}{\mathrel{\mathpalette\SubSupseteq@{\Supset\supseteq}}}
\newcommand{\SubSupseteq@}[2]{\SubSupseteq@@#1#2}
\newcommand{\SubSupseteq@@}[3]{%
\vcenter{%
\sbox\z@{$#1#3$}%
\sbox\tw@{$#1#2$}%
\hbox{\ooalign{\raisebox{\dimexpr\ht\z@-\ht\tw@}{$\m@th#1#2$}\cr$\m@th#1#3$\cr}}%
}%
}
\makeatother

\begin{document}

$A\subseteq B \Subseteq C$
$A\supseteq B \Supseteq C$

$\scriptstyle A\subseteq B \Subseteq C$
$\scriptstyle A\supseteq B \Supseteq C$

$\scriptscriptstyle A\subseteq B \Subseteq C$
$\scriptscriptstyle A\supseteq B \Supseteq C$

\end{document}