Subgroups — #93885

Order 512.

57 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#7459	C₂	1	2	yes	maximal
2	#7329	C₂	1	1	yes	maximal, characteristic
3	#1422	—	2	2	no	—
4	C₄×C₃₂	C₄	1	1	yes	characteristic
5	C₄×C₃₂	C₄	1	1	yes	characteristic
6	C₈×C₁₆	C₂²	1	1	yes	characteristic
7	M₆₄	—	4	2	no	—
8	C₂×C₃₂	—	2	1	no	—
9	C₂×C₃₂	C₈	1	1	yes	characteristic
10	C₂×C₃₂	C₈	1	1	yes	characteristic
11	C₄×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₄×C₁₆	D₄	1	1	yes	characteristic
13	C₈²	Q₈	1	1	yes	characteristic
14	C₂×C₁₆	C₂×C₈	1	1	yes	characteristic
15	C₂×C₁₆	M₁₆	1	1	yes	characteristic
16	C₂×C₁₆	D₈	1	1	yes	characteristic
17	C₂×C₁₆	Q₁₆	1	1	yes	characteristic
18	C₄×C₈	—	2	1	no	—
19	C₄×C₈	C₄⋊C₄	1	1	yes	characteristic
20	C₃₂	—	2	2	no	—
21	C₃₂	—	2	1	no	—
22	C₃₂	—	8	2	no	—
23	C₃₂	C₁₆	1	2	yes	—
24	C₂×C₈	—	2	2	no	—
25	C₂×C₈	C₄⋊C₈	1	1	yes	characteristic
26	C₂×C₈	#107	1	1	yes	characteristic
27	C₄²	#108	1	1	yes	characteristic
28	C₁₆	—	2	1	no	—
29	C₁₆	—	2	1	no	—
30	C₁₆	C₂×C₁₆	1	1	yes	characteristic
31	C₁₆	M₃₂	1	1	yes	characteristic
32	C₁₆	SD₃₂	1	2	yes	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	#335	1	1	yes	characteristic
35	C₈	—	4	2	no	—
36	C₈	C₄⋊C₁₆	1	1	yes	characteristic
37	C₈	#364	1	1	yes	characteristic
38	C₈	#367	1	1	yes	characteristic
39	C₈	#368	1	1	yes	characteristic
40	C₂²	#1373	1	1	yes	characteristic
41	C₄	—	2	2	no	—
42	C₄	#1370	1	1	yes	characteristic
43	C₄	#1372	1	1	yes	characteristic
44	C₂	—	2	1	no	—
45	C₂	#7101	1	1	yes	characteristic

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

subgroup	index
#7459	2
#7329	2