Subgroups — C₂×Q₃₂ #507

Order 64.

41 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆	C₂	1	2	yes	maximal
2	Q₃₂	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈	—	2	2	no	—
5	Q₁₆	—	2	2	no	—
6	Q₁₆	C₂²	1	4	yes	—
7	C₂×C₈	C₂²	1	1	yes	characteristic
8	C₁₆	C₂²	1	2	yes	—
9	Q₈	—	2	4	no	—
10	Q₈	—	4	2	no	—
11	C₂×C₄	—	4	2	no	—
12	C₂×C₄	D₄	1	1	yes	characteristic
13	C₈	D₄	1	1	yes	characteristic
14	C₈	C₂³	1	1	yes	characteristic
15	C₂²	D₈	1	1	yes	characteristic
16	C₄	—	4	4	no	—
17	C₄	D₈	1	1	yes	characteristic
18	C₄	C₂×D₄	1	1	yes	characteristic
19	C₂	Q₃₂	1	2	yes	direct product factor
20	C₂	C₂×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²	D₈
commutator, Frattini, cosocle	C₈	C₂³
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ G
LECS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

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

N	H ≅ G/N	type
2. Q₃₂	C₂	direct (N × H)
19. C₂	Q₃₂	direct (N × H)

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