Subgroups — C₂×SD₃₂ #506

Order 64.

45 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₈	C₂	1	1	yes	maximal, characteristic
3	SD₃₂	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈	—	2	1	no	—
6	C₂×D₄	—	2	1	no	—
7	Q₁₆	—	2	1	no	—
8	Q₁₆	C₂²	1	2	yes	complemented
9	D₈	—	2	1	no	—
10	D₈	C₂²	1	2	yes	—
11	C₂×C₈	C₂²	1	1	yes	characteristic
12	C₁₆	C₂²	1	2	yes	complemented
13	C₂³	—	4	1	no	—
14	Q₈	—	2	2	no	—
15	Q₈	—	4	1	no	—
16	D₄	—	2	2	no	—
17	D₄	—	4	1	no	—
18	C₂×C₄	—	4	1	no	—
19	C₂×C₄	D₄	1	1	yes	characteristic
20	C₈	D₄	1	1	yes	characteristic
21	C₈	C₂³	1	1	yes	characteristic
22	C₂²	—	4	2	no	—
23	C₂²	—	8	2	no	—
24	C₂²	D₈	1	1	yes	characteristic
25	C₄	—	4	2	no	—
26	C₄	D₈	1	1	yes	characteristic
27	C₄	C₂×D₄	1	1	yes	characteristic
28	C₂	—	8	2	no	—
29	C₂	SD₃₂	1	2	yes	direct product factor
30	C₂	C₂×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	D₈
commutator, Frattini, cosocle	C₈	C₂³
prime radical	C₂×D₈	C₂
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.

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