Can a tenant sublet their apartment without the landlord’s consent?

You did not indicate whether your building contains four or more residential units. If it does not, then the lease provision regarding subletting controls. If it does have four or more residential units, then subletting is governed by NY Real Property Law §226-b, which gives a residential tenant the right to sublet or assign & sets forth specific requirements. The law states as follows:

"Right  to sublease or assign...2.(a) A tenant renting a residence pursuant to an existing lease in a dwelling  having four or more residential units shall have the right to sublease his premises subject to the written consent of the landlord in advance of the subletting. Such consent shall not be unreasonably withheld.
(b) The tenant shall inform the landlord of his intent to sublease by mailing a notice of such intent by certified mail, return receipt requested. Such request shall be accompanied by the following information: (i) the term of the sublease, (ii) the name of the proposed sublessee, (iii) the business and permanent home address of the proposed sublessee, (iv) the tenant's reason for subletting, (v) the tenant's address for the term of the sublease, (vi) the written consent of any cotenant or guarantor of the lease, and (vii) a copy of the proposed
sublease, to which a copy of the tenant's lease shall be attached if available, acknowledged by the tenant and proposed subtenant as being a true copy of such sublease.
(c) Within ten days after the mailing of such request, the  landlord may ask the tenant for additional information as will enable the landlord to determine if rejection of such request shall be unreasonable. Any such request for additional information shall not be unduly burdensome.  Within thirty days after the mailing of the request for consent, or of the additional information reasonably asked for by the landlord, whichever is later, the landlord shall send a notice to the tenant of his consent or, if he does not consent, his reasons therefor. Landlord's failure to send such a notice shall be deemed to be a consent to the proposed subletting. If the landlord consents, the premises may be sublet in accordance with the request, but the tenant thereunder, shall nevertheless remain  liable for the performance of tenant's obligations under said lease. If the landlord reasonably withholds consent, there shall be no subletting and the tenant shall not
be released from the lease. If the landlord unreasonably  withholds consent, the tenant may sublet in accordance with the request and may recover the costs of the proceeding and attorneys fees if it is found that the owner acted in bad faith by withholding consent.

This law is detailed and involves specific time limits and may result in legal consequences for a landlord or a tenant if there is non-compliance with the law. Since you did not indicate whether the apartment is rent stabilized or rent controlled, you should be aware that §226-b(4) provides that units covered under the rent stabilization law or emergency tenant protection act "... shall be subject to the applicable provisions of such laws..."  Also, this law does not affect the rights of any rent controlled tenant.

If the lease provides that all of the tenants are jointly & severally liable for the rent, you also have the option of bringing a nonpayment proceeding against the remaining tenant when she fails to pay the monthly rent in full. If she is unable to pay the judgment amount entered by the court within the time fixed by law or within any extension of time granted by the judge, then you would be entitled to have a warrant of eviction issued by the court and then have the warrant executed by the sheriff or marshal according to law.