Subgroups — #7331

Order 256.

59 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	1	yes	characteristic
10	C₄×C₈	C₈	1	1	yes	characteristic
11	C₄×C₈	C₂×C₄	1	1	yes	characteristic
12	C₃₂	—	2	4	no	—
13	C₂×C₈	C₁₆	1	2	yes	—
14	C₂×C₈	C₁₆	1	2	yes	—
15	C₂×C₈	C₄²	1	1	yes	characteristic
16	C₂×C₈	C₂×C₈	1	1	yes	characteristic
17	C₄²	C₂×C₈	1	1	yes	characteristic
18	C₁₆	—	2	2	no	—
19	C₁₆	M₁₆	1	4	yes	—
20	C₂×C₄	C₄×C₈	1	1	yes	characteristic
21	C₂×C₄	C₂×C₁₆	1	1	yes	characteristic
22	C₂×C₄	C₂×C₁₆	1	1	yes	characteristic
23	C₈	—	2	2	no	—
24	C₈	C₃₂	1	4	yes	complemented
25	C₈	#97	1	2	yes	—
26	C₈	M₃₂	1	2	yes	—
27	C₂²	C₄×C₁₆	1	1	yes	characteristic
28	C₄	#322	1	1	yes	characteristic
29	C₄	#346	1	1	yes	characteristic
30	C₄	C₂×C₃₂	1	2	yes	—
31	C₄	M₆₄	1	2	yes	—
32	C₂	#1312	1	1	yes	characteristic
33	C₂	C₄×C₃₂	1	1	yes	characteristic
34	C₂	#1397	1	1	yes	characteristic

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

N	H ≅ G/N	type
24. C₈	C₃₂	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