Abstract Background The consolidated framework for implementation research states that personal leadership matters in quality management implementation. However, it remains to be answered which characteristics of plural leadership in hospital management boards make them impactful. The present study focuses on social determinants of implementation power of hospital boards using Talcott Parsons’ sociological concept of adaptation, goal attainment, integration, and latency (AGIL), focusing on the G (goal attainment) and I (integration) factors of this concept. The study aims to test the hypothesis that hospitals with management boards that are oriented toward the quality goal (G) and socially integrated (I) (GI boards) are better at implementing quality management than hospitals with boards lacking these characteristics (non-GI boards). Methods A cross-sectional mixed-method design was used for data collection in 109 randomly selected hospitals in seven European countries. Data is based on the study “Deepening our understanding of quality improvement in Europe” (DUQUE). We used responses from (a) hospitals’ chief executive officers to measure the variable social integration and the variable quality orientation of the board and (b) responses from quality managers to measure the degree of implementation of the quality management system. We developed the GI index measuring the combination of goal-orientation and integration. A multiple linear regression analysis was performed. Results Hospitals with management boards that are quality oriented and socially integrated (GI boards) had significantly higher scores on the quality management system index than hospitals with boards scoring low on these features, when controlled for several context factors. Conclusions Our findings suggest that the implementation power of hospital management boards is higher if there is a sense of unity and purpose within the boards. Thus, to improve quality management, it could be worthwhile to increase boards’ social capital and to increase time designated for quality management in board meetings.