Subgroups — C₂²×SD₁₆ #570

Order 64.

149 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄	C₂	1	1	yes	maximal, characteristic
3	C₂×SD₁₆	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁴	—	2	1	no	—
6	C₂×Q₈	—	2	3	no	—
7	C₂×Q₈	C₂²	1	6	yes	complemented
8	C₂×D₄	—	2	3	no	—
9	C₂×D₄	C₂²	1	6	yes	—
10	C₂²×C₄	—	2	1	no	—
11	C₂²×C₄	C₂²	1	1	yes	characteristic
12	SD₁₆	C₂²	1	16	yes	direct product factor
13	C₂×C₈	C₂²	1	6	yes	complemented
14	C₂³	—	2	6	no	—
15	C₂³	—	4	4	no	—
16	C₂³	D₄	1	1	yes	characteristic
17	Q₈	—	2	6	no	—
18	Q₈	C₂³	1	4	yes	complemented
19	D₄	—	2	6	no	—
20	D₄	C₂³	1	4	yes	—
21	C₂×C₄	—	2	6	no	—
22	C₂×C₄	D₄	1	3	yes	—
23	C₂×C₄	C₂³	1	3	yes	—
24	C₈	C₂³	1	4	yes	complemented
25	C₂²	—	2	4	no	—
26	C₂²	—	4	12	no	—
27	C₂²	SD₁₆	1	4	yes	direct product factor
28	C₂²	C₂×D₄	1	3	yes	—
29	C₄	—	2	4	no	—
30	C₄	C₂×D₄	1	3	yes	—
31	C₄	C₂⁴	1	1	yes	characteristic
32	C₂	—	4	4	no	—
33	C₂	C₂×SD₁₆	1	6	yes	direct product factor
34	C₂	C₂²×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	D₄
commutator, Frattini, cosocle	C₄	C₂⁴
prime radical	C₂²×D₄	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂²×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.