Subgroups — C₂×M₆₄ #2257

Order 128.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆	C₂	1	1	yes	maximal, characteristic
2	M₆₄	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃₂	C₂	1	2	yes	maximal, complemented
4	C₂²×C₈	C₄	1	1	yes	characteristic
5	C₂×C₁₆	C₄	1	1	yes	characteristic
6	C₂×C₁₆	C₄	1	2	yes	—
7	C₂×C₁₆	C₂²	1	2	yes	—
8	C₂×C₁₆	C₂²	1	1	yes	characteristic
9	C₃₂	C₂²	1	4	yes	complemented
10	C₂²×C₄	C₈	1	1	yes	characteristic
11	C₂×C₈	C₈	1	1	yes	characteristic
12	C₂×C₈	C₈	1	2	yes	—
13	C₂×C₈	C₂×C₄	1	2	yes	—
14	C₂×C₈	C₂×C₄	1	1	yes	characteristic
15	C₁₆	C₂×C₄	1	2	yes	—
16	C₁₆	C₂×C₄	1	1	yes	characteristic
17	C₁₆	C₂³	1	1	yes	characteristic
18	C₂³	C₁₆	1	1	yes	characteristic
19	C₂×C₄	C₁₆	1	2	yes	—
20	C₂×C₄	C₁₆	1	1	yes	characteristic
21	C₂×C₄	C₂×C₈	1	2	yes	—
22	C₂×C₄	C₂×C₈	1	1	yes	characteristic
23	C₈	C₂×C₈	1	2	yes	—
24	C₈	C₂×C₈	1	1	yes	characteristic
25	C₈	C₂²×C₄	1	1	yes	characteristic
26	C₂²	—	2	2	no	—
27	C₂²	C₂×C₁₆	1	2	yes	—
28	C₂²	C₂×C₁₆	1	1	yes	characteristic
29	C₄	C₂×C₁₆	1	1	yes	characteristic
30	C₄	C₂×C₁₆	1	2	yes	—
31	C₄	C₂²×C₈	1	1	yes	characteristic
32	C₂	—	2	2	no	—
33	C₂	M₆₄	1	2	yes	direct product factor
34	C₂	C₂²×C₁₆	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.