Subgroups — #1422

Order 128.

29 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₆₄	C₂	1	2	yes	maximal
2	C₄×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆	C₄	1	1	yes	characteristic
4	C₂×C₁₆	C₂²	1	1	yes	characteristic
5	C₄×C₈	C₄	1	1	yes	characteristic
6	C₃₂	—	2	2	no	—
7	C₂×C₈	C₈	1	1	yes	characteristic
8	C₂×C₈	C₂×C₄	1	1	yes	characteristic
9	C₄²	C₈	1	1	yes	characteristic
10	C₁₆	—	2	1	no	—
11	C₁₆	D₄	1	1	yes	characteristic
12	C₁₆	Q₈	1	1	yes	characteristic
13	C₂×C₄	—	2	1	no	—
14	C₂×C₄	C₂×C₈	1	1	yes	characteristic
15	C₈	C₁₆	1	2	yes	—
16	C₈	C₄⋊C₄	1	1	yes	characteristic
17	C₈	M₁₆	1	1	yes	characteristic
18	C₂²	M₃₂	1	1	yes	characteristic
19	C₄	—	2	2	no	—
20	C₄	C₄⋊C₈	1	1	yes	characteristic
21	C₄	C₂×C₁₆	1	1	yes	characteristic
22	C₂	—	2	1	no	—
23	C₂	C₄⋊C₁₆	1	1	yes	characteristic

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
M₆₄	2
C₄×C₁₆	2