Subgroups — #1398

Order 128.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₆₄	C₂	1	2	yes	maximal
2	#346	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆	C₄	1	1	yes	characteristic
4	C₂×C₁₆	C₂²	1	1	yes	characteristic
5	C₄×C₈	C₄	1	1	yes	characteristic
6	C₃₂	C₄	1	4	yes	complemented
7	C₂×C₈	C₈	1	1	yes	characteristic
8	C₂×C₈	C₂×C₄	1	1	yes	characteristic
9	C₄²	C₈	1	1	yes	characteristic
10	C₁₆	C₈	1	2	yes	—
11	C₁₆	C₂×C₄	1	2	yes	—
12	C₂×C₄	—	2	1	no	—
13	C₂×C₄	C₂×C₈	1	1	yes	characteristic
14	C₈	—	2	1	no	—
15	C₈	C₄²	1	1	yes	characteristic
16	C₈	C₂×C₈	1	1	yes	characteristic
17	C₂²	M₃₂	1	1	yes	characteristic
18	C₄	—	4	1	no	—
19	C₄	C₄×C₈	1	1	yes	characteristic
20	C₄	M₃₂	1	1	yes	characteristic
21	C₂	—	2	1	no	—
22	C₂	#346	1	1	yes	characteristic

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

N	H ≅ G/N	type
6. C₃₂	C₄	semidirect

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

subgroup	index
M₆₄	2
#346	2