An integer is called "octal" if it is divisible by $8$ or if at least one of its digits is $8$. 
How many integers between $1$ and $100$ are octal?

(A): $22$, (B): $24$, (C): $27$, (D): $30$, (E): $33$
1. **Identify numbers with a digit of $8$ between $1$ and $100$:**
   - The numbers are: $8, 18, 28, 38, 48, 58, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 98$.
   - There are $19$ such numbers.

2. **Identify numbers divisible by $8$ between $1$ and $100$:**
   - These numbers are: $8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96$.
   - There are $\left\lfloor \frac{100}{8} \right\rfloor = 12$ such numbers.

3. **Identify overcounted numbers (numbers that are both divisible by $8$ and have a digit $8$):**
   - These numbers are: $8, 48, 88$.
   - There are $3$ such numbers.

4. **Calculate the total number of octal numbers:**
   - Total octal numbers = (Numbers with a digit $8$) + (Numbers divisible by $8$) - (Overcounted numbers)
   - Total octal numbers = $19 + 12 - 3 = 28$.

The final answer is $\boxed{28}$.