Subgroups — #7329

Order 256.

63 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₃₂	C₂	1	2	yes	maximal
2	C₈×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₂	C₄	1	4	yes	—
4	C₄×C₁₆	C₄	1	1	yes	characteristic
5	C₄×C₁₆	C₂²	1	1	yes	characteristic
6	C₈²	C₄	1	1	yes	characteristic
7	C₂×C₁₆	C₈	1	2	yes	—
8	C₂×C₁₆	C₂×C₄	1	2	yes	—
9	C₄×C₈	C₈	1	2	yes	—
10	C₄×C₈	C₂×C₄	1	1	yes	characteristic
11	C₃₂	C₈	1	8	yes	complemented
12	C₂×C₈	C₁₆	1	4	yes	—
13	C₂×C₈	C₄²	1	1	yes	characteristic
14	C₂×C₈	C₂×C₈	1	1	yes	characteristic
15	C₄²	C₂×C₈	1	1	yes	characteristic
16	C₁₆	C₁₆	1	4	yes	—
17	C₁₆	C₂×C₈	1	4	yes	—
18	C₂×C₄	C₄×C₈	1	1	yes	characteristic
19	C₂×C₄	C₂×C₁₆	1	2	yes	—
20	C₈	—	2	4	no	—
21	C₈	C₄×C₈	1	2	yes	—
22	C₈	C₂×C₁₆	1	2	yes	—
23	C₂²	C₄×C₁₆	1	1	yes	characteristic
24	C₄	C₈²	1	1	yes	characteristic
25	C₄	C₄×C₁₆	1	1	yes	characteristic
26	C₄	M₆₄	1	4	yes	—
27	C₂	C₈×C₁₆	1	1	yes	characteristic
28	C₂	#1397	1	2	yes	—

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

N	H ≅ G/N	type
11. C₃₂	C₈	semidirect

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

subgroup	index
C₄×C₃₂	2
C₈×C₁₆	2