Do massive bolide entries coincide with meteor showers? Are exceptionally large, bright, meteors (such as Tunguska or Chelyabinsk) more common during common meteor showers like the Perseids, or the Leonids? 

If not, why is that? Do the meteor showers simply not carry any more massive pieces?
In historical times we do not have enough data to do serious statistics about meteors of the size of the Chelyabinsk meteor.

In Wikipedia's list of meteor air bursts there are only six events within two orders of magnitude of the Chelyabinsk meteor.

$$\begin{array}{lll}
\hline
\text{Date} &amp; \text{Location} &amp; \text{Energy [TJ]}\\
\hline
\text{1490-04-04} &amp; \text{Qingyang district, China} &amp; unknown\\
\text{1908-06-30} &amp; \text{Tunguska event} &amp; 42000–63000\\
\text{1930-08-13} &amp; \text{Curuca River Area, Brazil} &amp; 38–20920\\
\text{1963-08-03} &amp; \text{Prince Edward Islands} &amp; 740–1490\\
\text{2009-10-08} &amp; \text{South Sulawesi, Indonesia} &amp; 130–210\\
\text{2013-02-15} &amp; \text{Chelyabinsk meteor} &amp; 2100\\
\hline
\end{array}$$

Note that for the Tunguska event it is not proven to date that it had been caused by a meteor.