Ask Mr. Smarty Plants

For millennia humankind has been trying to classify living things.  Botanists for hundreds of years have worked on developing a classification system for flowering plants (angiosperms) that reflects the natural world.  Other important criteria for a classification system are that it be consistent, easy to use, and predictable.  The relationships of plants to one another is the rationale for most classification systems. A. L. de Jussieu in his Genera Plantarum (1789) was the first to introduce genera belonging to families that were then assigned to classes—a hierarchical system that is still the basis for our classification systems today.  Bentham & Hooker's Genera Plantarum (1862-1883) created a classification that arranged families by a few essential characteristics from what they considered to be the most primitive to the more complex.  This was published before Darwin's Origin of Species even though it sounds as if it has aspects of evolution in its structure.  Evolutionary relationships have certainly been the foundation in subsequent classification schemes. Changes to our understanding of these relationships are ongoing as we learn more about them by modern genetic methods such as the sequencing of the DNA of plant genomes.

You can read about the history of botanical classification in Classification Systems in Flowering Plants:  Historical Background (Chapter 3 in Judd, Walter S.  2002.  Plant Systematics: a Phylogenetic Approach. 2d ed. Sinauer Press.)  You can also see an outline for a course with Professional Educational, Testing and Certification Program that gives more information about the history of botanical classification.

Here are a few of the modern classification systems:

Cronquist System: named for Arthur John Cronquist (1919-1992)

Thorne System: created by Robert Thorne (1920–  )

Takhtajan System: created by Armen Takhtajan in 1997.

Kartesz System: John Kartesz published the Synonymized Checklist of the Vascular Flora of the United States, Canada and Greenland in 1994.  It is now a part of the Biota of North American, North American Plant Atlas and is constantly updated.

Angiosperm Phylogeny Group (APG): created by an informal international group of systematic botanists using new genetic information to establish relationships.  There have been two upgrades to the first APGI (1998)—APGII (2002) and APGIII (2009).  Many herbaria are switching to this system.

The various systems differ in how they arrange the families, sub-classes and orders.  For instance, Cronquist has 388 families, Thorne has 454 and Takhjatan has 592.

The USDA Plants Database uses the Cronquist System that includes Alliaceae under the Family Liliaceae and not as a separate family.  Kartesz also includes the Alliaceae within the Family Liliaceae.

The Wildflower Center's Native Plant Database follows Cronquist and Kartesz.

The Thorne System and Takhtajan System have the Family Alliaceae as a distinct and separate family.

APGIII puts Alliaceae under the Family Amaryllidaceae, not under Family Liliaceae and not as a separate family.  The Amaryllidaceae is within the Family Liliaceae in Cronquist and Kartesz and not used as a distinct and separate family.

So, the answer to your question is that it depends on the classification system being used whether Allium cernuum (Nodding onion) is placed in the Family Liliaceae or the Family Alliaceae or even another family (e.g., the Plants of Canada database shows Lilium cernuum under the Family Amaryllidaceae).

The classification of flowering plants doesn't have one single authority, nor is it likely to in the near future.  Some ongoing confusion about the classification of plants can be expected in the future—like many areas of life, it is a complex subject with many opinions about which system is the best.