Subgroups — C₂²⋊C₈ #98

Order 32.

25 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈	C₂	1	2	yes	maximal, complemented
3	C₂³	C₄	1	1	yes	characteristic
4	C₂×C₄	—	2	2	no	—
5	C₂×C₄	C₄	1	1	yes	characteristic
6	C₂×C₄	C₂²	1	1	yes	characteristic
7	C₈	—	2	2	no	—
8	C₂²	—	2	1	no	—
9	C₂²	—	2	1	no	—
10	C₂²	C₈	1	2	yes	complemented
11	C₂²	C₂×C₄	1	1	yes	characteristic
12	C₄	—	2	1	no	—
13	C₄	D₄	1	2	yes	—
14	C₂	—	2	2	no	—
15	C₂	C₂²⋊C₄	1	1	yes	characteristic
16	C₂	C₂×C₈	1	1	yes	characteristic
17	C₂	M₁₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₂×C₈	C₂	semidirect
10. C₂²	C₈	semidirect

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

subgroup	index
C₂²×C₄	2
C₂×C₈	2