Abstract Let G G be a finite nonabelian group. For any integer m ≥ 2 m\ge 2 , let A 1 , … , A m {A}_{1},\ldots ,{A}_{m} be nonempty subsets of G G . If A 1 , … , A m {A}_{1},\ldots ,{A}_{m} are mutually disjoint and if the subset product A 1 … A m = { α 1 … α m ∣ α v ∈ A v , v = 1 , 2 , … , m } {A}_{1}\ldots {A}_{m}=\left\{{\alpha }_{1}\ldots {\alpha }_{m}| {\alpha }_{v}\in {A}_{v},v=1,2,\ldots ,m\right\} coincides with G G , then ( A 1 , … , A m ) \left({A}_{1},\ldots ,{A}_{m}) is called a complete decomposition of G G of order m m . In this article, we let G G be the generalized quaternion groups Q 2 n {Q}_{{2}^{n}} , which is a finite nonabelian group of order 2 n {2}^{n} with group presentation given by ⟨ x , y ∣ x 2 n − 1 = 1 , y 2 = x 2 n − 2 , y x = x 2 n − 1 − 1 y ⟩ \langle x,y| {x}^{{2}^{n-1}}=1,{y}^{2}={x}^{{2}^{n-2}},yx={x}^{{2}^{n-1}-1}y\rangle for positive integer n ≥ 3 n\ge 3 . We determine the existence of complete decompositions of Q 2 n {Q}_{{2}^{n}} of order k k , for k ∈ { 2 , 3 , … , 2 n − 1 } k\in \left\{2,3,\ldots ,{2}^{n-1}\right\} , and show that Q 2 n {Q}_{{2}^{n}} can be written in the product of 2 n − 1 {2}^{n-1} subsets, i.e., Q 2 n = A 1 A 2 ⋯ A 2 n − 1 {Q}_{{2}^{n}}={A}_{1}{A}_{2}\cdots {A}_{{2}^{n-1}} , where ∣ A j ∣ = 2 | {A}_{j}| =2 , for j ∈ { 1 , 2 , … , 2 n − 1 } j\in \left\{1,2,\ldots ,{2}^{n-1}\right\} . In addition, we construct the non-complete decomposition of Q 2 n {Q}_{{2}^{n}} of order k k , for k ∈ { 2 , 3 , … , 2 n − 1 } k\in \left\{2,3,\ldots ,{2}^{n-1}\right\} , using the non-exhaustive subsets of Q 2 n {Q}_{2n} .