Subgroups — C₂×#131 #567

Order 64.

133 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41	C₂	1	1	yes	maximal, characteristic
2	#131	C₂	1	8	yes	maximal, direct product factor
3	C₂×M₁₆	C₂	1	3	yes	maximal, complemented
4	C₂²×C₈	C₂	1	3	yes	maximal, complemented
5	#41	C₄	1	4	yes	—
6	#41	C₂²	1	4	yes	—
7	C₂×Q₈	C₄	1	1	yes	characteristic
8	C₂×D₄	C₄	1	3	yes	—
9	C₂²×C₄	C₂²	1	3	yes	—
10	M₁₆	C₂²	1	12	yes	complemented
11	C₂×C₈	C₂²	1	3	yes	—
12	C₂×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₈	C₂²	1	12	yes	complemented
14	C₂³	C₂×C₄	1	3	yes	—
15	Q₈	C₂×C₄	1	4	yes	—
16	D₄	C₂×C₄	1	12	yes	—
17	C₂×C₄	C₂×C₄	1	3	yes	—
18	C₂×C₄	C₂×C₄	1	6	yes	—
19	C₂×C₄	C₂³	1	1	yes	characteristic
20	C₂×C₄	C₂³	1	6	yes	—
21	C₈	C₂³	1	6	yes	—
22	C₈	C₂³	1	2	yes	—
23	C₂²	—	2	6	no	—
24	C₂²	C₂²×C₄	1	6	yes	—
25	C₂²	C₂²×C₄	1	1	yes	characteristic
26	C₄	C₂²×C₄	1	1	yes	characteristic
27	C₄	C₂²×C₄	1	6	yes	—
28	C₄	C₂⁴	1	1	yes	characteristic
29	C₂	—	2	6	no	—
30	C₂	#131	1	2	yes	direct product factor
31	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.