Subgroups — #7547

Order 256.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₄	C₂	1	1	yes	maximal, characteristic
2	#1425	C₂	1	2	yes	maximal
3	C₂×C₃₂	C₂²	1	1	yes	characteristic
4	#368	—	2	2	no	—
5	C₆₄	C₄	1	2	yes	—
6	C₂×C₁₆	D₄	1	1	yes	characteristic
7	#108	—	4	2	no	—
8	C₃₂	C₂×C₄	1	1	yes	characteristic
9	C₃₂	Q₈	1	1	yes	characteristic
10	M₁₆	—	8	2	no	—
11	C₂×C₈	D₈	1	1	yes	characteristic
12	C₁₆	C₄⋊C₄	1	1	yes	characteristic
13	C₁₆	Q₁₆	1	1	yes	characteristic
14	C₂×C₄	D₁₆	1	1	yes	characteristic
15	C₈	—	16	2	no	—
16	C₈	#107	1	1	yes	characteristic
17	C₈	Q₃₂	1	1	yes	characteristic
18	C₂²	Q₆₄	1	1	yes	characteristic
19	C₄	#366	1	1	yes	characteristic
20	C₄	D₃₂	1	1	yes	characteristic
21	C₂	—	2	1	no	—
22	C₂	#1423	1	1	yes	characteristic

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

subgroup	index
C₂×C₆₄	2
#1425	2