In Office 365 SharePoint admin can disable SubSites creation:

Well, agree, SubSites are not really disabled, but the button to create subsites is hidden: “This controls whether the Subsite command appears on the New menu on the Site contents page”.

Anyway, the result is: you are not able to create a SubSite (web) in SharePoint Online:

Actually there are at least 3 options to create a SubSite:

Option 1. Create a SubSite in Classic mode.

Step 1: Select “Site Contents” page
Step 2: Click “Return to classic SharePoint”
Step 3: Create SubSite

Option 2. Create a SubSite from “Sites and Workspaces” page

Step 1: Go to “Site Settings”
Step 2: Select “Sites and Workspaces” page (site/_layouts/15/mngsubwebs.aspx)
Step 3: Create a SubSite

Option 3: use PowerShell PnP

Step 1: Install PowerShell PnP
Step 2: Connect to your site with PnP
Step 3: create a SubSite

Install-Module SharePointPnPPowerShellOnline
Connect-PnPOnline -Url <your site Url> -UseWebLogin
New-PnPWeb -Url "<new Web Url>" -Title "MySubSite" -Template "STS#3"

References:

• Microsoft PowerShell PnP

See also: How to create a SharePoint Site in Office 365 if site creation is disabled