Subgroups — #7510

Order 256.

41 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	C₄	1	4	yes	complemented
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	C₈	1	2	yes	—
11	C₃₂	C₂×C₄	1	2	yes	—
12	C₂×C₈	C₁₆	1	1	yes	characteristic
13	C₂×C₈	C₂×C₈	1	1	yes	characteristic
14	C₄²	C₁₆	1	1	yes	characteristic
15	C₁₆	C₁₆	1	2	yes	—
16	C₁₆	C₄²	1	1	yes	characteristic
17	C₁₆	C₂×C₈	1	1	yes	characteristic
18	C₂×C₄	C₃₂	1	2	yes	—
19	C₂×C₄	C₂×C₁₆	1	1	yes	characteristic
20	C₈	C₃₂	1	2	yes	—
21	C₈	C₄×C₈	1	1	yes	characteristic
22	C₈	C₂×C₁₆	1	1	yes	characteristic
23	C₂²	C₂×C₃₂	1	1	yes	characteristic
24	C₄	—	2	2	no	—
25	C₄	C₄×C₁₆	1	1	yes	characteristic
26	C₄	C₂×C₃₂	1	1	yes	characteristic
27	C₂	C₄×C₃₂	1	1	yes	characteristic
28	C₂	M₁₂₈	1	2	yes	—

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

N	H ≅ G/N	type
6. C₆₄	C₄	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