Subgroups — C₄⋊Q₈ #128

Order 32.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈	C₂	1	2	yes	maximal
2	C₄⋊C₄	C₂	1	4	yes	maximal
3	C₄²	C₂	1	1	yes	maximal, characteristic
4	Q₈	—	2	4	no	—
5	C₂×C₄	C₂²	1	4	yes	—
6	C₂×C₄	C₂²	1	1	yes	characteristic
7	C₂×C₄	C₂²	1	2	yes	—
8	C₂²	C₂³	1	1	yes	characteristic
9	C₄	—	2	4	no	—
10	C₄	D₄	1	2	yes	—
11	C₄	Q₈	1	4	yes	complemented
12	C₂	C₂×D₄	1	1	yes	characteristic
13	C₂	C₂×Q₈	1	2	yes	—

	subgroup	G/H
center, commutator, Frattini, socle, prime radical, cosocle	C₂²	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ G
LECS	G ▷ C₂² ▷ C₁

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

N	H ≅ G/N	type
11. C₄	Q₈	semidirect

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