Subgroups — #7272

Order 256.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#364	C₂	1	2	yes	maximal
2	#1848	C₂	1	1	yes	maximal, characteristic
3	C₂×M₃₂	—	2	2	no	—
4	C₂×#108	—	2	2	no	—
5	#423	C₄	1	2	yes	—
6	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
7	#364	—	2	2	no	—
8	#364	C₄	1	4	yes	—
9	C₂×M₁₆	—	2	2	no	—
10	C₂²×C₈	D₄	1	2	yes	—
11	C₂×C₄²	C₂×C₄	1	1	yes	characteristic
12	M₃₂	—	2	4	no	—
13	M₃₂	—	4	2	no	—
14	C₂×C₁₆	—	4	2	no	—
15	#108	—	4	2	no	—
16	#108	—	4	2	no	—
17	C₄⋊C₈	—	4	2	no	—
18	C₄×C₈	C₂×C₄	1	2	yes	—
19	C₄×C₈	D₄	1	1	yes	characteristic
20	C₄×C₈	Q₈	1	1	yes	characteristic
21	C₂²×C₄	—	2	1	no	—
22	C₂²×C₄	C₂²⋊C₄	1	1	yes	characteristic
23	M₁₆	—	4	4	no	—
24	C₂×C₈	—	4	2	no	—
25	C₂×C₈	C₂²⋊C₄	1	2	yes	—
26	C₂×C₈	C₄⋊C₄	1	2	yes	—
27	C₂×C₈	D₈	1	2	yes	—
28	C₂×C₈	SD₁₆	1	2	yes	—
29	C₂×C₈	SD₁₆	1	2	yes	—
30	C₂×C₈	Q₁₆	1	2	yes	—
31	C₄²	—	2	1	no	—
32	C₄²	C₄²	1	1	yes	characteristic
33	C₄²	C₄⋊C₄	1	1	yes	characteristic
34	C₁₆	—	4	4	no	—
35	C₂³	#101	1	1	yes	characteristic
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	—	4	2	no	—
39	C₂×C₄	#95	1	1	yes	characteristic
40	C₂×C₄	#100	1	1	yes	characteristic
41	C₂×C₄	#102	1	2	yes	—
42	C₂×C₄	#103	1	2	yes	—
43	C₈	—	8	2	no	—
44	C₈	#102	1	2	yes	—
45	C₈	#103	1	2	yes	—
46	C₈	#106	1	2	yes	—
47	C₈	#107	1	2	yes	—
48	C₂²	—	4	1	no	—
49	C₂²	#332	1	2	yes	—
50	C₂²	#343	1	1	yes	characteristic
51	C₄	—	2	2	no	—
52	C₄	—	4	1	no	—
53	C₄	#331	1	1	yes	characteristic
54	C₄	#333	1	1	yes	characteristic
55	C₄	#340	1	2	yes	—
56	C₂	—	2	1	no	—
57	C₂	—	2	2	no	—
58	C₂	#1296	1	1	yes	characteristic

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

subgroup	index
C₂×#364	2
#1848	2