Subgroups — #1369

Order 128.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#364	C₂	1	2	yes	maximal
2	#346	C₂	1	1	yes	maximal, characteristic
3	M₃₂	—	2	2	no	—
4	C₂×C₁₆	C₄	1	1	yes	characteristic
5	C₂×C₁₆	C₄	1	1	yes	characteristic
6	C₄×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₈	C₂×C₄	1	1	yes	characteristic
8	C₂×C₈	D₄	1	1	yes	characteristic
9	C₄²	Q₈	1	1	yes	characteristic
10	C₁₆	—	2	1	no	—
11	C₁₆	—	4	2	no	—
12	C₁₆	C₈	1	2	yes	—
13	C₂×C₄	—	2	1	no	—
14	C₂×C₄	C₄⋊C₄	1	1	yes	characteristic
15	C₈	C₂×C₈	1	1	yes	characteristic
16	C₈	M₁₆	1	1	yes	characteristic
17	C₈	SD₁₆	1	2	yes	—
18	C₂²	#108	1	1	yes	characteristic
19	C₄	—	4	1	no	—
20	C₄	C₄⋊C₈	1	1	yes	characteristic
21	C₄	#106	1	1	yes	characteristic
22	C₂	—	2	1	no	—
23	C₂	#334	1	1	yes	characteristic

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

subgroup	index
#364	2
#346	2