Subgroups — C₂²×M₁₆ #566

Order 64.

149 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₈	C₂	1	2	yes	maximal, complemented
4	C₂⁴	C₄	1	1	yes	characteristic
5	C₂²×C₄	C₄	1	1	yes	characteristic
6	C₂²×C₄	C₄	1	6	yes	—
7	C₂²×C₄	C₂²	1	6	yes	—
8	C₂²×C₄	C₂²	1	1	yes	characteristic
9	M₁₆	C₂²	1	16	yes	direct product factor
10	C₂×C₈	C₂²	1	12	yes	complemented
11	C₂³	—	2	4	no	—
12	C₂³	C₂×C₄	1	6	yes	—
13	C₂³	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄	C₂×C₄	1	12	yes	—
15	C₂×C₄	C₂×C₄	1	6	yes	—
16	C₂×C₄	C₂×C₄	1	3	yes	—
17	C₂×C₄	C₂³	1	3	yes	—
18	C₂×C₄	C₂³	1	4	yes	—
19	C₈	C₂³	1	8	yes	complemented
20	C₂²	—	2	12	no	—
21	C₂²	M₁₆	1	4	yes	direct product factor
22	C₂²	C₂²×C₄	1	4	yes	—
23	C₂²	C₂²×C₄	1	3	yes	—
24	C₄	C₂²×C₄	1	4	yes	—
25	C₄	C₂²×C₄	1	3	yes	—
26	C₄	C₂⁴	1	1	yes	characteristic
27	C₂	—	2	4	no	—
28	C₂	C₂×M₁₆	1	6	yes	direct product factor
29	C₂	C₂³×C₄	1	1	yes	characteristic

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.