Subgroups — C₂×SD₁₆ #133

Order 32.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄	C₂	1	1	yes	maximal, characteristic
3	SD₁₆	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³	—	2	1	no	—
6	Q₈	—	2	1	no	—
7	Q₈	C₂²	1	2	yes	complemented
8	D₄	—	2	1	no	—
9	D₄	C₂²	1	2	yes	—
10	C₂×C₄	—	2	1	no	—
11	C₂×C₄	C₂²	1	1	yes	characteristic
12	C₈	C₂²	1	2	yes	complemented
13	C₂²	—	2	2	no	—
14	C₂²	—	4	2	no	—
15	C₂²	D₄	1	1	yes	characteristic
16	C₄	—	2	2	no	—
17	C₄	D₄	1	1	yes	characteristic
18	C₄	C₂³	1	1	yes	characteristic
19	C₂	—	4	2	no	—
20	C₂	SD₁₆	1	2	yes	direct product factor
21	C₂	C₂×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	D₄
commutator, Frattini, cosocle	C₄	C₂³
prime radical	C₂×D₄	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ G
LECS	G ▷ 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.