Subgroups — C₄×M₁₆ #404

Order 64.

71 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₄²	C₂	1	1	yes	maximal, characteristic
3	#97	C₂	1	2	yes	maximal, complemented
4	C₄×C₈	C₂	1	2	yes	maximal, complemented
5	C₂²×C₄	C₄	1	2	yes	—
6	C₂²×C₄	C₂²	1	1	yes	characteristic
7	M₁₆	C₄	1	8	yes	direct product factor
8	C₂×C₈	C₂²	1	4	yes	—
9	C₄²	C₄	1	2	yes	—
10	C₄²	C₂²	1	1	yes	characteristic
11	C₄²	C₂²	1	1	yes	characteristic
12	C₂³	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄	—	2	4	no	—
14	C₂×C₄	C₂×C₄	1	2	yes	—
15	C₂×C₄	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄	C₂×C₄	1	4	yes	—
17	C₂×C₄	C₂×C₄	1	2	yes	—
18	C₂×C₄	C₂³	1	1	yes	characteristic
19	C₈	C₂×C₄	1	8	yes	complemented
20	C₂²	—	2	2	no	—
21	C₂²	C₄²	1	2	yes	—
22	C₂²	C₂²×C₄	1	1	yes	characteristic
23	C₄	—	2	2	no	—
24	C₄	C₄²	1	2	yes	—
25	C₄	M₁₆	1	4	yes	direct product factor
26	C₄	C₂²×C₄	1	2	yes	—
27	C₂	—	2	2	no	—
28	C₂	C₂×C₄²	1	1	yes	characteristic
29	C₂	C₂×M₁₆	1	2	yes	—

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.