Subgroups — C₄⋊C₁₆ #363

Order 64.

25 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
15. C₄	C₁₆	semidirect

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

subgroup	index
C₂×C₁₆	2
C₄×C₈	2