Subgroups — #7267

Order 256.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#347	C₂	1	2	yes	maximal
2	#1838	C₂	1	1	yes	maximal, characteristic
3	C₂×M₃₂	—	2	2	no	—
4	#423	C₄	1	1	yes	characteristic
5	#423	C₄	1	1	yes	characteristic
6	C₂×#97	C₂²	1	1	yes	characteristic
7	#347	—	2	2	no	—
8	#347	C₄	1	4	yes	—
9	#341	—	2	2	no	—
10	C₂×M₁₆	—	2	1	no	—
11	C₂×M₁₆	—	2	1	no	—
12	C₂²×C₈	D₄	1	2	yes	—
13	C₂×C₄²	C₂×C₄	1	1	yes	characteristic
14	M₃₂	—	2	4	no	—
15	M₃₂	—	2	4	no	—
16	C₂×C₁₆	—	2	4	no	—
17	C₄⋊C₈	—	4	1	no	—
18	C₄⋊C₈	—	4	1	no	—
19	#97	C₂×C₄	1	2	yes	—
20	#97	D₄	1	1	yes	characteristic
21	#97	Q₈	1	1	yes	characteristic
22	C₂²×C₄	—	2	1	no	—
23	C₂²×C₄	C₂²⋊C₄	1	1	yes	characteristic
24	M₁₆	—	4	2	no	—
25	M₁₆	—	4	2	no	—
26	C₂×C₈	—	2	2	no	—
27	C₂×C₈	—	2	2	no	—
28	C₂×C₈	—	4	1	no	—
29	C₂×C₈	—	4	1	no	—
30	C₂×C₈	C₂²⋊C₄	1	2	yes	—
31	C₂×C₈	C₄⋊C₄	1	2	yes	—
32	C₄²	—	2	1	no	—
33	C₄²	C₄²	1	1	yes	characteristic
34	C₄²	C₄⋊C₄	1	1	yes	characteristic
35	C₁₆	—	2	8	no	—
36	C₂³	#101	1	1	yes	characteristic
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	—	2	1	no	—
39	C₂×C₄	—	8	1	no	—
40	C₂×C₄	#95	1	1	yes	characteristic
41	C₂×C₄	#100	1	1	yes	characteristic
42	C₂×C₄	#104	1	2	yes	—
43	C₂×C₄	#104	1	2	yes	—
44	C₈	—	2	2	no	—
45	C₈	—	2	2	no	—
46	C₈	—	8	1	no	—
47	C₈	—	8	1	no	—
48	C₂²	—	4	1	no	—
49	C₂²	#330	1	2	yes	—
50	C₂²	#343	1	1	yes	characteristic
51	C₄	—	4	1	no	—
52	C₄	—	4	1	no	—
53	C₄	#329	1	1	yes	characteristic
54	C₄	#329	1	1	yes	characteristic
55	C₄	#339	1	2	yes	—
56	C₂	—	2	1	no	—
57	C₂	—	2	2	no	—
58	C₂	#1295	1	1	yes	characteristic

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

subgroup	index
C₂×#347	2
#1838	2