So this is Nate's response to my query about the Ostii/suffruticosa cross designation as Suffruticosa. Anya, I mentioned your comment about hybrid vs Lacti so you'll see your name mentioned in the 2nd comment.
Liz, Internet is working for the moment! Yeah! Suffruticosas...APS doesn't act as a taxonomic entity, thus doesn't get caught up in all of the species classifications. However, some taxonomic rules are followed to place cultivars into categories. Since Suffruticosa group plants are not actually species (those found in the wild) they are a collection of plants which have a highly variable genetic background. All Suffruticosa plants are hybrids which have the following the following species in their genetic make up: P. rockii, P. decomposita, P. jishanensis, P. cathayana, P. ostii, P. rotundiloba and P. qiui; which are all taxonomically part of the Section "Moutan". Genetic marker technology has allowed scientists to identify these species in Suffruticosa cultivars, thus all Suffruticosas are hybrids. Thus Suffruticosa Group plants are part of a hybrid swarm of 1000's cultivars. Any species within the Section Moutan and/or hybrids of these species (all Suffruticosa cultivars) which are crossed within the group are considered Suffruticosa Group plants. To answer your question in short... a cross of P. ostii x Suffruticosa ends up being a Suffruticosa Group cultivar since it is a cross within the Section Moutan. It is no longer simply P. ostii because it has other Suffruticosa genes in its ancestory. Since P. ostii makes up 50% or more in this cross it may have more traits which are similar to P. ostii, but it no longer can be considered that species. We might say call these plants "P. ostii" lineage/influence cultivars, to note the similarities. The same can be said for any other species crossed with Suffruticosa Group cultivars. I've to noting cultivars which heavily favor P. rockii as Rockii lineage or influence cultivars. Very few people actually own true species P. rockii, but actually have Suffruticosa cultivars with Rockii lineage/influence. APS doesn't want to create new categories for all of the possible combinations, but does recommend that hybridizers and originators include parental information in their descriptions. Thus a description may include information about the influence/lineage and this is helpful to people looking for certain traits in Suffruticosa Group cultivars. This all gets complex and Reiner has done a great job sorting it out, but getting the peony world at large to understand the subtleties will be challenging. Your question has been asked numerous times in the last year, but I'm not sure those who receive the answer have the foundational knowledge to understand.
I'm not sure which Lactiflora Group cultivars Anya is referring to, but can supply the following... Some hybrids may end up being classified as Lactiflora Group cultivars because there is no discernible difference that would place them in the Hybrid Group. I never liked this classification since they genetically are hybrids, but look like lactifloras. Don Hollingsworth has a number of plants that are hybrids which look exactly like lactiflora cultivars; "Show Girl" is an example and is listed as a lactiflora of hybrid origin. I agree "Show Girl" looks and behaves exactly like a lactiflora, but it is still a hybrid. I guess the Lactiflora Group is heavily based on visual and behavioral characteristics, rather than genetics. I've mentioned this on a number of occasions, but there doesn't seem to be the desire to make changes as it would alter many past introductions. In essence we need to remember that the Peony Registry acts as a historical record and not a perfectly scientific reflection of the genus. The science of genetics and taxonomy are changing rapidly, thus the disconnect in the Peony Registry.