Subgroups — #349

Order 64.

29 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

N	H ≅ G/N	type
2. M₃₂	C₂	semidirect

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

subgroup	index
C₂×M₁₆	2
M₃₂	2