Subgroups — C₂×#101 #412

Order 64.

73 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
2	C₂×M₁₆	C₂	1	2	yes	maximal
3	#101	C₂	1	4	yes	maximal, direct product factor
4	C₂×Q₈	—	2	2	no	—
5	C₂×Q₈	—	2	2	no	—
6	C₂×Q₈	C₄	1	2	yes	—
7	C₂×Q₈	C₂²	1	2	yes	—
8	C₂²×C₄	C₄	1	2	yes	—
9	C₂²×C₄	C₂²	1	1	yes	characteristic
10	M₁₆	—	2	2	no	—
11	M₁₆	C₂²	1	4	yes	—
12	C₂×C₈	—	2	2	no	—
13	C₂³	C₂×C₄	1	1	yes	characteristic
14	Q₈	—	2	4	no	—
15	Q₈	—	2	4	no	—
16	C₂×C₄	—	2	2	no	—
17	C₂×C₄	—	2	2	no	—
18	C₂×C₄	C₂×C₄	1	4	yes	—
19	C₂×C₄	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄	D₄	1	2	yes	—
21	C₂×C₄	D₄	1	2	yes	—
22	C₂×C₄	C₂³	1	1	yes	characteristic
23	C₈	—	2	4	no	—
24	C₂²	—	2	2	no	—
25	C₂²	C₂²⋊C₄	1	1	yes	characteristic
26	C₂²	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²	C₂²×C₄	1	1	yes	characteristic
28	C₄	—	2	4	no	—
29	C₄	C₂²⋊C₄	1	2	yes	—
30	C₄	C₂×D₄	1	2	yes	—
31	C₂	—	2	1	no	—
32	C₂	—	2	1	no	—
33	C₂	#101	1	2	yes	direct product factor
34	C₂	C₂×C₂²⋊C₄	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. #101	C₂	direct (N × H)
33. C₂	#101	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.