Subgroups — #1400

Order 128.

37 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂	C₂	1	1	yes	maximal, characteristic
2	M₆₄	C₂	1	2	yes	maximal, complemented
3	C₂²×C₈	C₄	1	1	yes	characteristic
4	M₃₂	—	2	2	no	—
5	C₂×C₁₆	C₄	1	1	yes	characteristic
6	C₂×C₁₆	C₂²	1	1	yes	characteristic
7	C₃₂	—	2	2	no	—
8	C₂²×C₄	C₈	1	1	yes	characteristic
9	C₂×C₈	—	2	1	no	—
10	C₂×C₈	—	2	1	no	—
11	C₂×C₈	C₈	1	1	yes	characteristic
12	C₂×C₈	C₂×C₄	1	1	yes	characteristic
13	C₁₆	—	2	1	no	—
14	C₁₆	D₄	1	2	yes	—
15	C₂³	C₁₆	1	1	yes	characteristic
16	C₂×C₄	—	2	1	no	—
17	C₂×C₄	—	2	1	no	—
18	C₂×C₄	C₁₆	1	1	yes	characteristic
19	C₂×C₄	C₂×C₈	1	1	yes	characteristic
20	C₈	—	2	1	no	—
21	C₈	C₂²⋊C₄	1	1	yes	characteristic
22	C₈	M₁₆	1	1	yes	characteristic
23	C₂²	—	2	1	no	—
24	C₂²	—	4	1	no	—
25	C₂²	C₂×C₁₆	1	1	yes	characteristic
26	C₄	—	2	1	no	—
27	C₄	C₂²⋊C₈	1	1	yes	characteristic
28	C₄	M₃₂	1	1	yes	characteristic
29	C₂	—	2	1	no	—
30	C₂	—	4	1	no	—
31	C₂	C₂²⋊C₁₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. M₆₄	C₂	semidirect

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

subgroup	index
C₂×M₃₂	2
M₆₄	2