  We analyze a three-dimensional (3D) magnetic structure and its stability in
large solar active region(AR) 12192, using the 3D coronal magnetic field
constructed under a nonlinear force-free field (NLFFF) approximation. In
particular, we focus on the magnetic structure that produced an X3.1-class
flare which is one of the X-class flares observed in AR 12192. According to our
analysis, the AR contains multiple-flux-tube system, {\it e.g.}, a large flux
tube, both of whose footpoints are anchored to the large bipole field, under
which other tubes exist close to a polarity inversion line (PIL). These various
flux tubes of different sizes and shapes coexist there. In particular, the
later are embedded along the PIL, which produces a favorable shape for the
tether-cutting reconnection and is related to the X-class solar flare. We
further found that most of magnetic twists are not released even after the
flare, which is consistent with the fact that no observational evidence for
major eruptions was found. On the other hand, the upper part of the flux tube
is beyond a critical decay index, essential for the excitation of torus
instability before the flare, even though no coronal mass ejections (CMEs) were
observed. We discuss the stability of the complicated flux tube system and
suggest the reason for the existence of the stable flux tube. In addition, we
further point out a possibility for tracing the shape of flare ribbons, on the
basis of a detailed structural analysis of the NLFFF before a flare.
