This study aims to improve the accuracy of Hungarian automatic speech recognition (ASR) by applying large amounts of Hungarian training data both for self-supervised learning (SSL) and traditional supervised learning methods. In our experiments, the effectiveness of self-supervised pretraining on both smaller public and larger proprietary datasets was tested. Introducing SSL techniques to small Hungarian training sets resulted in noticeable improvements in model accuracy. When fine-tuning on large datasets containing thousands of hours of Hungarian speech, SSL accelerated training convergence, but fine-tuned models pretrained in English in a supervised way could not be outperformed in terms of word error rate. However, models trained or fine-tuned on a larger-than-ever purely Hungarian dataset achieved state-of-the-art accuracy across multiple independent evaluation sets.