Subgroups — #7544

Order 256.

35 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₁₂₈	C₂	1	2	yes	maximal
2	C₄×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₂	C₄	1	1	yes	characteristic
4	C₂×C₃₂	C₂²	1	1	yes	characteristic
5	C₄×C₁₆	C₄	1	1	yes	characteristic
6	C₆₄	—	2	2	no	—
7	C₂×C₁₆	C₈	1	1	yes	characteristic
8	C₂×C₁₆	C₂×C₄	1	1	yes	characteristic
9	C₄×C₈	C₈	1	1	yes	characteristic
10	C₃₂	—	2	1	no	—
11	C₃₂	D₄	1	1	yes	characteristic
12	C₃₂	Q₈	1	1	yes	characteristic
13	C₂×C₈	C₁₆	1	1	yes	characteristic
14	C₂×C₈	C₂×C₈	1	1	yes	characteristic
15	C₄²	C₁₆	1	1	yes	characteristic
16	C₁₆	—	2	1	no	—
17	C₁₆	C₄⋊C₄	1	1	yes	characteristic
18	C₁₆	M₁₆	1	1	yes	characteristic
19	C₂×C₄	—	2	1	no	—
20	C₂×C₄	C₂×C₁₆	1	1	yes	characteristic
21	C₈	C₃₂	1	2	yes	—
22	C₈	C₄⋊C₈	1	1	yes	characteristic
23	C₈	M₃₂	1	1	yes	characteristic
24	C₂²	M₆₄	1	1	yes	characteristic
25	C₄	—	2	2	no	—
26	C₄	C₄⋊C₁₆	1	1	yes	characteristic
27	C₄	C₂×C₃₂	1	1	yes	characteristic
28	C₂	—	2	1	no	—
29	C₂	C₄⋊C₃₂	1	1	yes	characteristic

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

subgroup	index
M₁₂₈	2
C₄×C₃₂	2