What is the order of the human body systems?

I guess that is an accurate way to group them, but I am not sure what you mean by "order".

Yes, the integumentary system is on the outside, the skeletal system is the inner most, but multiple other organ systems lay in between.  The GI system runs from cranial to caudal.  The lymphatic system is wide-spread through out the body, as is the endocrine system.

Why do you ask?

A group of organs functioning as a unit is called a system, or organ system. For example, the stomach, small intestine, liver, and pancreas are part of the digestive system, and the kidneys, bladder, and connecting tubes constitute the urinary system.

The following are the major systems of the human body.

- Cardiovascular system. The cardiovascular system, or circulatory system, is an organ system that moves substances to and from cells, such as transporting oxygen, nutrients, and waste materials. The human circulatory system consists of the heart, a network of blood vessels, and blood.
 
- Digestive system.  The digestive system, noted above, breaks down food into molecules that the body can use. The alimentary canal, or digestive tract, begins at the mouth and winds through the esophagus, stomach, small intestine, and large intestine, until the anus. The digestive system also includes the liver, located near the stomach in the abdominal cavity. The liver is vital for digesting fats by secreting bile, an emulsifying agent that breaks down fat globules into small droplets. The gallbladder stores and concentrates the bile. The pancreas, also part of the digestive system, secretes pancreatic fluid, which have digestive enzymes for breaking down nutrients.

- Endocrine system. The endocrine system is a control system that transmits chemical messages within the body using hormones, which are chemicals that are produced in one part of the body to impact cells in another part of the body. Major endocrine glands include the pineal gland, pituitary gland, thyroid gland, thymus, adrenal gland, and gonads (the ovary in females, and testis in males). There are also endocrine tissues in such organs as the brain, kidneys, stomach, and pancreas that produce hormones.
 
- Immune system. The immune system involves organs and specialized cells that protect the body against pathogens, such as bacteria and viral infections. This system includes barriers to infection, such as skin and the mucus coating of the gut and airways; phagocytic cells that can ingest and digest foreign substances; and anti-microbrial proteins. The stomach also secretes gastric acid that helps to prevent bacterial colonization, while an adaptive immune system response helps to develop immunity against being infected twice by the same pathogen.

- Integumentary system. The integumentary system includes the skin, hair, nails, and skin glands and their products. This system helps in retention of body fluids, sensing the person's surroundings, regulation of body temperature, elimination of waste products, and offering a protective barrier from the environment outside the body.

- Muscular system. The muscles, which are attached to the skeletal frame, cause the body to move.

- Skeletal system. The skeletal system or skeleton provides structural support and protection by means of bones. There are two basic parts, the axial skeleton (spine, ribs, sacrum, sternum, cranium, and about 80 bones in all) and the appendicular skeleton (bones of the arms, pelvis, legs, and shoulders, totaling 126 bones in all). While at birth a human has about 350 bones, the adult body has about 206 bones, due to the fusing of some bones.

- Lymphatic system. The lymphatic system collects the blood plasma lost from the circulatory system as lymph and returns it to the circulatory system.
 
- Respiratory system. The respiratory system consists of the lungs, airways, and respiratory muscles that mediate the movement of gases (oxygen and carbon dioxide) into and out of the body. Involved in this system are external respiration (exchange of gases between atmosphere and blood), and internal respiration (exchange of gases between cells of the body and the blood).

- Nervous system. The nervous system functions in collecting, transferring, and processing information via cellular communication involving nerve cells, or neurons. The brain and spinal cord comprise the central nervous system and the nerves that radiate out to the rest of the body comprise the peripheral nervous system. The human brain contains approximately 100 billion neurons.

- Reproductive system. The reproductive system involves a group of specialized organs that produce, store, and release gametes for reproduction.

- Urinary system. The urinary system is the organ system that produces, stores, and carries urine. This system includes two kidneys, two ureters, the urinary bladder, two sphincter muscles, and the urethra.

Wish You Best Of Luck !