Subgroups — #94750

Order 512.

51 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₆₄	C₂	1	1	yes	maximal, characteristic
2	#7460	C₂	1	2	yes	maximal
3	C₂×C₆₄	C₄	1	1	yes	characteristic
4	C₂×C₆₄	C₄	1	1	yes	characteristic
5	C₄×C₃₂	C₂²	1	1	yes	characteristic
6	#1371	—	2	2	no	—
7	C₂×C₃₂	C₂×C₄	1	1	yes	characteristic
8	C₂×C₃₂	Q₈	1	1	yes	characteristic
9	C₄×C₁₆	D₄	1	1	yes	characteristic
10	#335	—	4	2	no	—
11	C₆₄	—	2	1	no	—
12	C₆₄	C₈	1	2	yes	complemented
13	C₂×C₁₆	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₁₆	Q₁₆	1	1	yes	characteristic
15	C₄⋊C₈	—	8	2	no	—
16	C₄×C₈	D₈	1	1	yes	characteristic
17	C₃₂	—	2	1	no	—
18	C₃₂	C₂×C₈	1	1	yes	characteristic
19	C₃₂	M₁₆	1	1	yes	characteristic
20	C₂×C₈	—	16	2	no	—
21	C₂×C₈	#107	1	1	yes	characteristic
22	C₂×C₈	Q₃₂	1	1	yes	characteristic
23	C₄²	D₁₆	1	1	yes	characteristic
24	C₁₆	—	2	1	no	—
25	C₁₆	C₄⋊C₈	1	1	yes	characteristic
26	C₁₆	#108	1	1	yes	characteristic
27	C₂×C₄	#366	1	1	yes	characteristic
28	C₂×C₄	D₃₂	1	1	yes	characteristic
29	C₂×C₄	Q₆₄	1	1	yes	characteristic
30	C₈	—	2	1	no	—
31	C₈	—	32	2	no	—
32	C₈	#335	1	1	yes	characteristic
33	C₈	#368	1	1	yes	characteristic
34	C₂²	#1423	1	1	yes	characteristic
35	C₄	—	2	1	no	—
36	C₄	#1371	1	1	yes	characteristic
37	C₄	#1425	1	1	yes	characteristic
38	C₄	SD₁₂₈	1	2	yes	—
39	C₂	#7460	1	1	yes	characteristic
40	C₂	#7546	1	1	yes	characteristic
41	C₂	#7547	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. C₆₄	C₈	semidirect

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

subgroup	index
C₄×C₆₄	2
#7460	2