Subgroups — #106

Order 32.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄	C₂	1	2	yes	maximal
3	C₂×C₄	—	2	2	no	—
4	C₂×C₄	C₂²	1	1	yes	characteristic
5	C₈	C₄	1	2	yes	complemented
6	C₂²	D₄	1	1	yes	characteristic
7	C₄	—	4	2	no	—
8	C₄	C₂×C₄	1	1	yes	characteristic
9	C₄	Q₈	1	1	yes	characteristic
10	C₂	C₄⋊C₄	1	1	yes	characteristic
11	C₂	SD₁₆	1	2	yes	—

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

N	H ≅ G/N	type
5. C₈	C₄	semidirect

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

subgroup	index
C₂×C₈	2
C₄⋊C₄	2