Subgroups — C₄⋊C₆₄ #7543

Order 256.

37 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₄	C₂	1	2	yes	maximal
2	C₄×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₂	C₄	1	1	yes	characteristic
4	C₂×C₃₂	C₂²	1	1	yes	characteristic
5	C₄×C₁₆	C₄	1	1	yes	characteristic
6	C₆₄	—	2	2	no	—
7	C₂×C₁₆	C₈	1	1	yes	characteristic
8	C₂×C₁₆	C₂×C₄	1	1	yes	characteristic
9	C₄×C₈	C₈	1	1	yes	characteristic
10	C₃₂	—	2	1	no	—
11	C₃₂	D₄	1	1	yes	characteristic
12	C₃₂	Q₈	1	1	yes	characteristic
13	C₂×C₈	C₁₆	1	1	yes	characteristic
14	C₂×C₈	C₂×C₈	1	1	yes	characteristic
15	C₄²	C₁₆	1	1	yes	characteristic
16	C₁₆	—	2	1	no	—
17	C₁₆	C₄⋊C₄	1	1	yes	characteristic
18	C₁₆	M₁₆	1	1	yes	characteristic
19	C₂×C₄	C₃₂	1	1	yes	characteristic
20	C₂×C₄	C₃₂	1	1	yes	characteristic
21	C₂×C₄	C₂×C₁₆	1	1	yes	characteristic
22	C₈	—	2	1	no	—
23	C₈	C₄⋊C₈	1	1	yes	characteristic
24	C₈	M₃₂	1	1	yes	characteristic
25	C₂²	C₂×C₃₂	1	1	yes	characteristic
26	C₄	—	2	1	no	—
27	C₄	C₆₄	1	2	yes	complemented
28	C₄	C₄⋊C₁₆	1	1	yes	characteristic
29	C₄	M₆₄	1	1	yes	characteristic
30	C₂	C₄⋊C₃₂	1	1	yes	characteristic
31	C₂	C₂×C₆₄	1	1	yes	characteristic
32	C₂	M₁₂₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
27. C₄	C₆₄	semidirect

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

subgroup	index
C₂×C₆₄	2
C₄×C₃₂	2