floatssubfloats
Is it possible to get two figure environments side by side across the top of a page, where both (or at least 1) contains subfloats? IE: 
And if so, how? I am currently using the subfig package with a combination of figure/subfloat in my document.
The caption package version you use is too old to work fine with the actual version of hyperref.
That's explaining both issues, the wired behaviour when used with the subfig package, and the error you get when using the subcaption package. So updating the caption package (or even better: your whole TeX system) should help.
(Current versions of the hyperref package need at least caption v3.1m from 2010/01/09)
Addendum: The very next version 1.1b of the subcaption package will typeout a more reasonable error message.
It seems the starred environment version subfloatrow* produces the correct numbering. The floatrow manual isn't too verbose, though, about why is so -- quoting from section 6.2:
subfloatrow*The starred form loads settings for creation captions of float parts, but in this environment the
\captioncommand restores its meaning. Thus, you need the\subcaptioncommand for typesetting sub-captions.
\documentclass[11pt]{article}
\usepackage{subfig}
\usepackage{tikz}
\usepackage[]{floatrow}
\floatsetup[figure]{floatrowsep=qquad,valign=c }
\floatsetup[subfloat]{subfloatrowsep=qquad,valign=c}
\usepackage{graphicx}
\begin{document}
\begin{figure}[htbp]
\centering
\ffigbox{
\begin{subfloatrow*}[3]
\subfloat[First, we see an empty green circle]{
\begin{tikzpicture}[scale=1] \draw[green] (0,0) circle (1.2cm);\end{tikzpicture}
}
\subfloat[A large orange circle is the middle picture]{
\begin{tikzpicture}[scale=1]\draw[orange] (0,0) circle (2cm);\end{tikzpicture}}
\subfloat[Finally, a beautiful red circle with a black border]{
\begin{tikzpicture}[scale=1]\draw[fill=red] (0,0) circle (.75cm);\end{tikzpicture}}
\end{subfloatrow*}
}
{\caption{``Gadgets'' in reduced Levi graphs found as a consequence of using the construction in the configuration construction lemma.}
\label{CCLvolt}
}
\end{figure}
\end{document}
Best Answer
You can do it by using the packages
floatrowandsubfigtogether.