  We present LOFAR observations at 120-168 MHz of 42 systems with possible
X-ray cavities in their hot atmosphere, of which 17 are groups or ellipticals,
19 are nearby clusters (z<0.3), and six are higher-redshift clusters (z>0.3).
The X-ray cavities, formed by the radio lobes of the central active galactic
nucleus (AGN), are evidence of radio-mode AGN feedback. In the groups and
ellipticals sample, more than half of the systems have X-ray cavities for which
no associated lobe emission was detected. Conversely, we report the discovery
of large radio lobes in NGC 6338, extending far beyond the emission reported
previously in the literature. In the case of the nearby clusters, our
observations show that there is little low-frequency radio emission that
extends beyond the cavities (e.g., MS 0735.6+7421 and A2052). For the first
time, we report secure cavity-radio associations in 2A 0335+096, ZwCl 2701, and
ZwCl 8276 that strengthens their interpretation as AGN-created cavities.
However, in some known cavity systems (e.g., A1795 and ZwCl 3146) we report the
lack of detectable low-frequency radio emission associated with the cavities.
Our sample of higher-redshift systems is small, and unfortunately the present
LOFAR observations are not able to resolve the lobes in many of them.
Nevertheless, our sample represents one of the best available for investigating
the connection between radio and jet power in radio-mode AGN feedback.
