The following Captain and lieutenant listings (names of all known captains and lieutenants, current and former, in the Gotei 13 in chronological order) Every division has its own own symbol that represents the division's primary role, which all seem to be based on flowers:
1st division - Chrysanthemum, Truth and innocence
2nd Division - Tulip, Seek nothing
3rd Division - Marigold, Despair
4th Division - Bellflower, Those who grieve are loved
5th Division - Lily of the Valley, Sacrifice, danger, pure love
6th Division - Camellia, Noble reason
7th Division - Iris, Courage
8th Division - Bird of paradise flower, Everything is obtained
9th Division - Buttercup, Oblivion
10th Division - Daffodil, Mystery, egoism
11th Division - Yarrow, Fight
12th Division - Thistle, Vengeance
13th Division - Summer snowflake, Hope

The current structure of soul society = the 13 divisons + all the Lieutenants and Soul Reapers. The Captain of 1st division also known as Captain/ General Commander, who in-charge of the whole soul society. Then follow by 12 more divisions that in-charge of the other tasks due to their specializations:
2rd Division - Take charge of the milltary - Special Force
4th Division - medical/supply division
9th Division - newspaper and magazine-related duties
11th Division - the combat division (swords-only combat)
12th Division - the research/scientific division

* There are 3 captain: Aizen (leader), Tosen & Gin leave soul society and become Arrancar

The Arrancar chart (still not complete)

Soul Reapers Vs Arrancar - this chart based on the latest story in the Manga.