Subgroups — #94509

Order 512.

57 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#7511	C₂	1	2	yes	maximal
2	#7330	C₂	1	1	yes	maximal, characteristic
3	M₁₂₈	C₄	1	4	yes	—
4	#1397	C₄	1	1	yes	characteristic
5	#1397	C₂²	1	1	yes	characteristic
6	#1311	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	—	2	1	no	—
14	C₂×C₁₆	C₄²	1	1	yes	characteristic
15	C₂×C₁₆	C₂×C₈	1	1	yes	characteristic
16	C₄×C₈	—	2	1	no	—
17	C₄×C₈	C₂×C₈	1	1	yes	characteristic
18	C₃₂	C₁₆	1	4	yes	—
19	C₃₂	M₁₆	1	4	yes	—
20	C₂×C₈	—	4	1	no	—
21	C₂×C₈	C₄×C₈	1	1	yes	characteristic
22	C₂×C₈	M₃₂	1	1	yes	characteristic
23	C₄²	M₃₂	1	1	yes	characteristic
24	C₁₆	—	4	1	no	—
25	C₁₆	#97	1	2	yes	—
26	C₁₆	C₂×C₁₆	1	2	yes	—
27	C₂×C₄	—	2	1	no	—
28	C₂×C₄	#346	1	1	yes	characteristic
29	C₈	—	2	1	no	—
30	C₈	—	8	1	no	—
31	C₈	#322	1	1	yes	characteristic
32	C₈	C₄×C₁₆	1	1	yes	characteristic
33	C₂²	#1398	1	1	yes	characteristic
34	C₄	—	4	1	no	—
35	C₄	#1312	1	1	yes	characteristic
36	C₄	#1398	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#7332	1	1	yes	characteristic

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

subgroup	index
#7511	2
#7330	2