Subgroups — #341

Order 64.

45 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆	C₂	1	2	yes	maximal
2	C₂²×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄	C₂²	1	1	yes	characteristic
4	M₁₆	—	2	2	no	—
5	M₁₆	C₄	1	4	yes	—
6	C₂×C₈	—	2	2	no	—
7	C₂×C₈	—	2	2	no	—
8	C₂×C₈	C₄	1	2	yes	—
9	C₂³	Q₈	1	1	yes	characteristic
10	C₂×C₄	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄	C₂×C₄	1	2	yes	—
12	C₂×C₄	D₄	1	2	yes	—
13	C₂×C₄	D₄	1	1	yes	characteristic
14	C₈	—	2	2	no	—
15	C₈	—	2	4	no	—
16	C₂²	—	2	2	no	—
17	C₂²	C₄⋊C₄	1	2	yes	—
18	C₂²	C₄⋊C₄	1	1	yes	characteristic
19	C₄	C₄²	1	1	yes	characteristic
20	C₄	C₂²⋊C₄	1	1	yes	characteristic
21	C₄	C₂²⋊C₄	1	2	yes	—
22	C₂	—	2	2	no	—
23	C₂	#95	1	1	yes	characteristic
24	C₂	#108	1	2	yes	—

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

subgroup	index
C₂×M₁₆	2
C₂²×C₈	2