We explore the spin states in the quantum spin chain compound SrCo$_{2}$V$_{2}$O$_{8}$ up to 14.9 T and down to 50 mK, using single-crystal neutron diffraction. Upon cooling in zero-field, antiferromagnetic (AFM) order of Neel type develops at $T_mathrm{{N}}$ $simeq$ 5.0 K. Applying an external magnetic field ($H$ $parallel$ $c$-axis) destabilizes the Neel order, leading to an order-disorder transition when applying a field between $T_mathrm{{N}}$ and $sim$ 1.5 K. Below 1.5 K, we observe a Neel to longitudinal spin density wave (LSDW) order transition at 3.9 T, and a LSDW to emergent AFM order transition at 7.0 T. Our results also reveal several unique signatures for the states of the spins that are not present in the isostructural counterpart BaCo$_{2}$V$_{2}$O$_{8}$.