Subgroups — #93255

Order 512.

183 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#12593	C₂	1	3	yes	maximal
2	C₄×M₃₂	C₄	1	6	yes	—
3	#1726	C₂²	1	1	yes	characteristic
4	#1375	—	2	6	no	—
5	C₂×M₃₂	—	2	6	no	—
6	C₂×#97	D₄	1	3	yes	—
7	C₂×C₄×C₈	C₂×C₄	1	3	yes	—
8	#376	Q₈	1	1	yes	characteristic
9	#346	—	2	6	no	—
10	C₄×C₁₆	C₈	1	12	yes	—
11	C₂²×C₈	C₄²	1	1	yes	characteristic
12	C₂²×C₈	C₂²⋊C₄	1	3	yes	—
13	C₂×C₄²	C₄⋊C₄	1	3	yes	—
14	M₃₂	—	4	12	no	—
15	C₂×C₁₆	—	2	12	no	—
16	#97	—	4	3	no	—
17	C₄×C₈	C₂×C₈	1	6	yes	—
18	C₄×C₈	M₁₆	1	6	yes	—
19	#95	—	4	1	no	—
20	C₂²×C₄	—	2	3	no	—
21	C₂²×C₄	#95	1	1	yes	characteristic
22	C₂×C₈	—	2	6	no	—
23	C₂×C₈	C₄×C₈	1	3	yes	—
24	C₂×C₈	#97	1	3	yes	—
25	C₂×C₈	C₂²⋊C₈	1	6	yes	—
26	C₄²	—	2	3	no	—
27	C₄²	C₄⋊C₈	1	6	yes	—
28	C₁₆	—	4	12	no	—
29	C₂³	#338	1	1	yes	characteristic
30	C₂×C₄	—	2	6	no	—
31	C₂×C₄	—	8	3	no	—
32	C₂×C₄	#336	1	3	yes	—
33	C₂×C₄	H(3,ℤ/4)	1	3	yes	—
34	C₈	—	2	6	no	—
35	C₈	C₈²	1	1	yes	characteristic
36	C₈	#322	1	3	yes	—
37	C₂²	—	4	1	no	—
38	C₂²	#1275	1	3	yes	—
39	C₄	—	4	6	no	—
40	C₄	#1273	1	1	yes	characteristic
41	C₄	#1274	1	3	yes	—
42	C₂	—	2	3	no	—
43	C₂	#7014	1	1	yes	characteristic

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

subgroup	index
#12593	2