Subgroups — #7052

Order 256.

75 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₁₆	C₂	1	2	yes	maximal
2	C₈×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₆	C₄	1	4	yes	—
4	C₄×C₁₆	C₄	1	2	yes	—
5	C₈²	C₂²	1	1	yes	characteristic
6	C₂×C₁₆	C₈	1	8	yes	—
7	C₂×C₁₆	C₈	1	4	yes	—
8	C₄×C₈	C₂×C₄	1	1	yes	characteristic
9	C₄×C₈	C₂×C₄	1	2	yes	—
10	C₂×C₈	C₂×C₈	1	2	yes	—
11	C₂×C₈	C₂×C₈	1	4	yes	—
12	C₄²	C₄²	1	1	yes	characteristic
13	C₁₆	—	2	8	no	—
14	C₁₆	C₁₆	1	8	yes	complemented
15	C₂×C₄	C₄×C₈	1	1	yes	characteristic
16	C₂×C₄	C₄×C₈	1	2	yes	—
17	C₈	C₂×C₁₆	1	4	yes	—
18	C₈	M₃₂	1	8	yes	—
19	C₂²	C₈²	1	1	yes	characteristic
20	C₄	C₄×C₁₆	1	2	yes	—
21	C₄	#346	1	4	yes	—
22	C₂	C₈×C₁₆	1	1	yes	characteristic
23	C₂	#1311	1	2	yes	—

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

N	H ≅ G/N	type
14. C₁₆	C₁₆	semidirect

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

subgroup	index
C₈×C₁₆	2