Subgroups — C₂×#106 #425

Order 64.

65 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄	C₂	1	2	yes	maximal
3	#106	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄	—	2	2	no	—
5	C₂²×C₄	C₂²	1	1	yes	characteristic
6	C₂×C₈	C₄	1	4	yes	complemented
7	C₂×C₈	C₂²	1	2	yes	—
8	C₄⋊C₄	—	2	2	no	—
9	C₄⋊C₄	C₂²	1	4	yes	—
10	C₂³	D₄	1	1	yes	characteristic
11	C₂×C₄	—	2	4	no	—
12	C₂×C₄	—	4	4	no	—
13	C₂×C₄	C₂×C₄	1	2	yes	—
14	C₂×C₄	D₄	1	1	yes	characteristic
15	C₂×C₄	Q₈	1	2	yes	—
16	C₂×C₄	C₂³	1	1	yes	characteristic
17	C₈	C₂×C₄	1	4	yes	complemented
18	C₂²	C₄⋊C₄	1	2	yes	—
19	C₂²	SD₁₆	1	4	yes	—
20	C₂²	C₂×D₄	1	1	yes	characteristic
21	C₄	—	4	4	no	—
22	C₄	C₄⋊C₄	1	2	yes	—
23	C₄	C₂²×C₄	1	1	yes	characteristic
24	C₄	C₂×Q₈	1	1	yes	characteristic
25	C₂	#106	1	4	yes	direct product factor
26	C₂	C₂×C₄⋊C₄	1	1	yes	characteristic
27	C₂	C₂×SD₁₆	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.