The letter C can make a s-sound, a k-sound, a sh-sound (/ʃ/), a ch-sound (/ʧ/) and can be silent. C makes an sh-sound in various suffixes.
The suffix -ician uses C and makes the sound . It refers to someone highly skilled in that profession; for example: electrician, mathematician, musician, technician... The origin is the Latin suffix -ianus (as in mathematicianus = mathematician). Even words not from Latin were constructed by adding the suffix in English. For example, the word electrician was formed from electric + -ician in the mid-18th century. Both parts of the word do have Latin origins; electrum means the stone amber.1 The construction and this messy C-pronunciation is English.
The suffix -cial is a variant of -al. It forms adjectives from nouns or other adjectives, and has the meaning: of, related to, similar to. The origin is the Latin suffix -alis and many of the words with this suffix come from Latin. (For simplicity the Latin spelling is in brackets.) For example2: beneficial (beneficialis), glacial (glacialis), judicial (iudicalis3), official (officialis), provincial (provincialis), sacrificial (sacrificium), social (socialis), special (specialis)... This unusual C-pronunciation comes from English's heavy borrowing from Latin.
The English suffix -cious has another letter C making the sound /ʃ/. It is a variant of -ous. This suffix forms adjectives from nouns meaning: having / full of / associated with / tends to. The origin is the Latin suffix -iosus. For example1: delicious (deliciosus), gracious (gratiosus), precious (pretiosus), spacious (spatiosus)... Several other Latin words were modified to match this spelling pattern. For example: audacious (audacia), auspicious (auspicium), tenacious (tenax).
C is silent before T in a very few words such as indict. This example was borrowed from the Old French word enditer about 700 years ago. The modern spelling is about 400 years old, when it was changed to match the Latin word indictus. The US state of Connecticut and river of the same name also have a silent C before T; but in this case the spelling was similar to connect and also never matched the pronunciation. Fortunately there are only a few such cases.
The letter C has many pronunciations in English words of Italian origin. Some words such as cappuccino, cello and ciao are borrowed from Italian and pronounce C as a ch-sound /ʧ/. The word crescendo has C pronounced /k/ and /ʃ/. We get an s-sound /s/ in words like concert and citadel. Other words, such as macaroni, concert and replica use the /k/ pronunciation.
To get a general guideline for English words of Italian origin we can fall back on the old rule that C makes a /s/ before the vowels E and I. We must turn it around: In words of Italian origin C (usually) has a /k/ pronunciation when before the vowels A, O and U; otherwise the pronunciation is /ʧ/, /ʃ/ or /s/. Many English words come from Latin and C before I in a Latin suffix is usually pronounced /ʃ/. Next week double C will be covered.