Subgroups — #94751

Order 512.

47 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	#7462	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	#1373	—	2	2	no	—
7	C₂×C₃₂	C₂×C₄	1	1	yes	characteristic
8	C₂×C₃₂	Q₈	1	1	yes	characteristic
9	#364	—	4	2	no	—
10	C₄×C₁₆	D₄	1	1	yes	characteristic
11	C₆₄	—	2	1	no	—
12	C₆₄	C₈	1	2	yes	—
13	M₃₂	—	8	2	no	—
14	C₂×C₁₆	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₁₆	Q₁₆	1	1	yes	characteristic
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	#107	1	1	yes	characteristic
21	C₂×C₈	D₁₆	1	1	yes	characteristic
22	C₄²	Q₃₂	1	1	yes	characteristic
23	C₁₆	—	2	1	no	—
24	C₁₆	—	16	2	no	—
25	C₁₆	C₄⋊C₈	1	1	yes	characteristic
26	C₁₆	#108	1	1	yes	characteristic
27	C₂×C₄	—	2	1	no	—
28	C₂×C₄	#366	1	1	yes	characteristic
29	C₈	#335	1	1	yes	characteristic
30	C₈	#368	1	1	yes	characteristic
31	C₈	D₃₂	1	1	yes	characteristic
32	C₈	Q₆₄	1	1	yes	characteristic
33	C₂²	#1425	1	1	yes	characteristic
34	C₄	—	2	2	no	—
35	C₄	#1371	1	1	yes	characteristic
36	C₄	#1423	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#7460	1	1	yes	characteristic

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

subgroup	index
C₄×C₆₄	2
#7462	2