  We systematically construct tetraquark currents of $I^GJ^{PC}=1^-1^{++}$ and
classify them into types $\mathbf{A}$ (antisymmetric), $\mathbf{S}$ (symmetric)
and $\mathbf{M}$ (mixed), based on flavor symmetries of diquarks and
antidiquarks composing the tetra quark currents. We use tetraquark currents of
type $\mathbf{M}$ to perform QCD sum rule analyses, and find a tetraquark
current $\eta^M_{5\mu}$ with quark contents $q s\bar q \bar s$($q=u$ or $d$)
leading to a mass of $1.44 \pm 0.08$ GeV consistent with the $a_1(1420)$ state
recently observed by the COMPASS collaboration. Our results support tetraquark
explanations for both $a_1(1420)$ and $f_1(1420)$, assuming that they are
isospin partners. We also study their possible decay patterns. As tetraquark
candidates, the possible decay modes of $a_1(1420)$ are $S$-wave $a_1(1420)
\rightarrow K^*(892)K$ and $P$-wave $a_1(1420)\rightarrow f_0(980) \pi$ while
the possible decay patterns of $f_1(1420)$ are $S$-wave $f_1(1420) \rightarrow
K^*(892)K$ and $P$-wave $f_1(1420) \rightarrow a_0(980) \pi$. We speculate that
$a_1(1420)$ is partly responsible for the large isospin violation in the
$\eta(1405)\to f_0(980)\pi_0$ decay mode which is reported by BESIII
collaboration in the $J/\psi\to\gamma 3\pi$ process.
