Subgroups — #7246

Order 256.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2150	C₂	1	1	yes	maximal, characteristic
2	#1568	C₂	1	2	yes	maximal
3	C₂×M₃₂	C₄	1	2	yes	—
4	#432	—	2	2	no	—
5	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
6	C₄⋊C₁₆	—	2	2	no	—
7	#335	—	2	2	no	—
8	#334	C₄	1	4	yes	—
9	C₂²×C₈	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₈	Q₈	1	1	yes	characteristic
11	C₂×C₄²	D₄	1	1	yes	characteristic
12	M₃₂	—	4	2	no	—
13	C₂×C₁₆	—	2	2	no	—
14	C₄⋊C₈	—	2	4	no	—
15	C₂²⋊C₈	—	4	2	no	—
16	#97	—	4	2	no	—
17	C₄×C₈	C₂×C₄	1	2	yes	—
18	C₄×C₈	D₄	1	2	yes	—
19	C₂²×C₄	C₄⋊C₄	1	1	yes	characteristic
20	C₂²×C₄	SD₁₆	1	2	yes	—
21	C₂×C₈	—	2	1	no	—
22	C₂×C₈	—	2	1	no	—
23	C₂×C₈	—	4	1	no	—
24	C₂×C₈	—	4	4	no	—
25	C₂×C₈	C₄²	1	1	yes	characteristic
26	C₂×C₈	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₈	C₄⋊C₄	1	2	yes	—
28	C₄²	C₂²⋊C₄	1	2	yes	—
29	C₄²	D₈	1	1	yes	characteristic
30	C₄²	Q₁₆	1	1	yes	characteristic
31	C₁₆	—	4	2	no	—
32	C₂³	#106	1	1	yes	characteristic
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	4	2	no	—
36	C₂×C₄	#95	1	1	yes	characteristic
37	C₂×C₄	#102	1	2	yes	—
38	C₂×C₄	#103	1	2	yes	—
39	C₂×C₄	#107	1	1	yes	characteristic
40	C₈	—	2	2	no	—
41	C₈	—	2	1	no	—
42	C₈	—	8	4	no	—
43	C₈	#100	1	1	yes	characteristic
44	C₈	#101	1	1	yes	characteristic
45	C₂²	—	2	1	no	—
46	C₂²	—	2	2	no	—
47	C₂²	#340	1	1	yes	characteristic
48	C₄	—	2	1	no	—
49	C₄	—	2	2	no	—
50	C₄	—	2	2	no	—
51	C₄	#338	1	1	yes	characteristic
52	C₄	#343	1	1	yes	characteristic
53	C₂	—	4	1	no	—
54	C₂	#1292	1	1	yes	characteristic
55	C₂	#1389	1	2	yes	—

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

subgroup	index
#2150	2
#1568	2