Subgroups — #94507

Order 512.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₆₄	C₂	1	2	yes	maximal
2	C₈×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₄	C₄	1	4	yes	—
4	C₄×C₃₂	C₄	1	1	yes	characteristic
5	C₄×C₃₂	C₂²	1	1	yes	characteristic
6	C₈×C₁₆	C₄	1	1	yes	characteristic
7	C₂×C₃₂	C₈	1	2	yes	—
8	C₂×C₃₂	C₂×C₄	1	2	yes	—
9	C₄×C₁₆	C₈	1	1	yes	characteristic
10	C₄×C₁₆	C₂×C₄	1	1	yes	characteristic
11	C₈²	C₈	1	1	yes	characteristic
12	C₆₄	—	2	4	no	—
13	C₂×C₁₆	C₁₆	1	2	yes	—
14	C₂×C₁₆	C₄²	1	1	yes	characteristic
15	C₂×C₁₆	C₂×C₈	1	1	yes	characteristic
16	C₄×C₈	C₁₆	1	1	yes	characteristic
17	C₄×C₈	C₁₆	1	1	yes	characteristic
18	C₄×C₈	C₂×C₈	1	1	yes	characteristic
19	C₃₂	—	2	2	no	—
20	C₃₂	M₁₆	1	4	yes	—
21	C₂×C₈	C₃₂	1	2	yes	—
22	C₂×C₈	C₃₂	1	2	yes	—
23	C₂×C₈	C₄×C₈	1	1	yes	characteristic
24	C₂×C₈	C₂×C₁₆	1	1	yes	characteristic
25	C₄²	C₂×C₁₆	1	1	yes	characteristic
26	C₁₆	—	2	2	no	—
27	C₁₆	#97	1	2	yes	—
28	C₁₆	M₃₂	1	2	yes	—
29	C₂×C₄	C₄×C₁₆	1	1	yes	characteristic
30	C₂×C₄	C₂×C₃₂	1	1	yes	characteristic
31	C₂×C₄	C₂×C₃₂	1	1	yes	characteristic
32	C₈	—	2	2	no	—
33	C₈	C₆₄	1	4	yes	complemented
34	C₈	#322	1	1	yes	characteristic
35	C₈	#346	1	1	yes	characteristic
36	C₈	M₆₄	1	2	yes	—
37	C₂²	C₄×C₃₂	1	1	yes	characteristic
38	C₄	#1312	1	1	yes	characteristic
39	C₄	#1397	1	1	yes	characteristic
40	C₄	C₂×C₆₄	1	2	yes	—
41	C₄	M₁₂₈	1	2	yes	—
42	C₂	#7331	1	1	yes	characteristic
43	C₂	C₄×C₆₄	1	1	yes	characteristic
44	C₂	#7510	1	1	yes	characteristic

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

N	H ≅ G/N	type
33. C₈	C₆₄	semidirect

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

subgroup	index
C₄×C₆₄	2
C₈×C₃₂	2