A given convolution call is not necessarily supported by all the algos: it depends on the tensor data type, layout, among other things. Here cudnnGetConvolutionForwardAlgorithm_v7 and cudnnFindConvolutionForwardAlgorithm are simply reporting the returned cudnnStatus_t for each algo.
For the support matrix of each algo, please consult the API documentation API Reference :: NVIDIA Deep Learning cuDNN Documentation and the various tables in that section.
algo3 CUDNN_CONVOLUTION_FWD_ALGO_DIRECT is not implemented.
algo6 CUDNN_CONVOLUTION_FWD_ALGO_WINOGRAD requires 3x3 filter.