Though Shogakukan has been one of the biggest forces in the manga industry since the earliest days of the form, originally it founded the subsidiary Shueisha in the 1920's to be the entertainment division. Though they often partner together in things (such as jointly owning Viz Media, which translates both of their works for an English market), individually they are both among the most successful publishers in the manga market and most of their manga magazines are competitive with each other, aiming at the same demographics.
Though where Shueisha is often known for Weekly Shonen Jump, which was at its peak the most successful manga magazine of all time, Shogakukan is not as easily defined by a single magazine with decades-old classic magazines in a number of demographics.
In shonen manga, Shogakukan's best known magazine is Weekly Shonen Sunday which launched in 1959, almost ten years before Weekly Shonen Jump (though 1959 was the same year Weekly Shonen Magazine launched).
In its earliest decades, before collections were as commonplace, it serialized many creators that would be seen as some of the biggest in the era (including Osamu Tezuka, Fujio Akatsuka, Fujiko Fujio, Shotaro Ishimori, Sanpei Shirato, Shigeru Mizuki, Takao Saito, Kazuo Umezu, George Akiyama and Go Nagai). However, especially in the 60's, because of the way publishing in manga worked and how many creators worked for numerous publishers, the collections of these serials were not necessarily ever published by Shogakukan.
Since the late 1970's, when shonen serials began running much longer, Sunday has been home to some hugely successful creators who would follow up one big decade-long success with another such as Mitsuru Adachi and Rumiko Takahashi (the best-selling female comic creator in history) and since 1994, it has been serializing what has become its longest-running and best-selling series (Meitantei Conan).
For even younger children, Shogakukan is also one of the biggest publishers of popular children's manga (many of them being serialized in CoroCoro Comic as well as various other magazines) and is the publisher of hugely successful franchises like Doraemon, Pokemon Adventures and Super Mario-kun.
Shogakukan launched Big Comic in 1968, which was one of the first major seinen manga magazines and within a year it began the Golgo 13 serialization. While the series has been a major force in the magazine ever since and gone on to be one of the longest-running manga and the best-selling seinen manga, the collections of the series where it gets the majority of its sales are self-published by the author's company, Leed Publishing and Shogakukan only prints the serialized chapters.
However, Big Comic itself was successful enough to get a spin-off magazine in the form of Big Comic Original in 1972, which itself has had multiple serializations last over 100 volumes and in time even become more popular than Big Comic itself. Since the 80's, the Big Comic seinen manga division has been successful enough to support three biweeklies (Big Comic, Big Comic Original and Big Comic Superior) and one weekly (Big Comic Spirits). All four magazines have produced multiple series that are among the longest-running in manga and the best-selling (and generally have a higher circulation than Shonen Sunday). A fifth magazine in Monthly! Big Comic Spirits currently fills out the Big Comic brand though in the 80's it also attempted to branch into shonen (Shonen Big Comic) and josei (Big Comic for Lady).
Though Shogakukan has long-running magazines and serials that have had success in the female demographics, they are a much smaller portion of the publisher's market and unlike their shonen and seinen manga, their flagship magazines are not definitively among the oldest or most successful.