  The origins of coalescing binary black holes (BBHs) detected by the advanced
LIGO/Virgo are still under debate, and clues may be present in the joint
mass-spin distribution of these merger events. Here we construct
phenomenological models containing two sub-populations to investigate the BBH
population detected in gravitational wave observations. We find that our models
can explain the GWTC-3 data rather well, and several constraints to our model
are required by the data: first, the maximum mass for the component with a
stellar-origin, $m_{\rm max}$, is $39.1^{+2.4}_{-2.7}M_{\odot}$ at 90\%
credibility; second, about $15\%$ of the mergers happen in dynamical
environments, in which $7-16\%$ of events are hierarchical mergers, and these
BHs have an average spin magnitude significantly larger than the
first-generation mergers, with ${\rm d}\mu_{\rm a} > 0.4 $ at $99\%$
credibility; third, the dynamical component BHs tend to pair with each other
with larger total mass and higher mass ratio. An independent analysis focusing
on spins is also carried out, and we find that the spin amplitude of component
BHs can be divided into two groups according to a division mass $m_{\rm d} =
46.1^{+5.6}_{-5.1}M_{\odot}$. These constraints can be naturally explained by
current formation channels, and our results suggest that some of the observed
events were likely from AGN disks.
