Subgroups — C₄⋊C₈ #105

Order 32.

19 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

N	H ≅ G/N	type
9. C₄	C₈	semidirect

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

subgroup	index
C₂×C₈	2
C₄²	2