Subgroups — M₁₂₈ #1428

Order 128.

19 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₆₄	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₆	C₄	1	1	yes	characteristic
4	C₃₂	C₄	1	1	yes	characteristic
5	C₃₂	C₂²	1	1	yes	characteristic
6	C₂×C₈	C₈	1	1	yes	characteristic
7	C₁₆	C₈	1	1	yes	characteristic
8	C₁₆	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄	C₁₆	1	1	yes	characteristic
10	C₈	C₁₆	1	1	yes	characteristic
11	C₈	C₂×C₈	1	1	yes	characteristic
12	C₂²	C₃₂	1	1	yes	characteristic
13	C₄	C₃₂	1	1	yes	characteristic
14	C₄	C₂×C₁₆	1	1	yes	characteristic
15	C₂	—	2	1	no	—
16	C₂	C₂×C₃₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₆₄	C₂	semidirect

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

subgroup	index
C₂×C₃₂	2
C₆₄	2