Subgroups — #7449

Order 256.

63 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2247	C₂	1	1	yes	maximal, characteristic
2	#1422	C₂	1	1	yes	maximal, characteristic
3	#1373	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₃₂	—	2	1	no	—
5	C₂×Q₃₂	C₄	1	2	yes	—
6	#494	—	2	1	no	—
7	M₆₄	—	2	1	no	—
8	#364	—	2	1	no	—
9	C₄×C₁₆	C₂²	1	1	yes	characteristic
10	C₂×Q₁₆	—	2	2	no	—
11	C₂×Q₁₆	—	4	1	no	—
12	C₄⋊Q₈	—	4	1	no	—
13	Q₃₂	—	4	2	no	—
14	Q₃₂	—	4	1	no	—
15	Q₃₂	—	4	1	no	—
16	M₃₂	—	4	1	no	—
17	C₂×C₁₆	C₂×C₄	1	1	yes	characteristic
18	C₂×C₁₆	D₄	1	1	yes	characteristic
19	C₄×C₈	D₄	1	1	yes	characteristic
20	C₃₂	—	4	1	no	—
21	C₂×Q₈	—	4	2	no	—
22	Q₁₆	—	4	2	no	—
23	Q₁₆	—	4	2	no	—
24	Q₁₆	—	8	1	no	—
25	Q₁₆	—	8	1	no	—
26	C₂×C₈	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₈	D₈	1	1	yes	characteristic
28	C₄⋊C₄	—	8	2	no	—
29	C₄²	SD₁₆	1	1	yes	characteristic
30	C₁₆	—	2	1	no	—
31	C₁₆	—	8	1	no	—
32	C₁₆	D₈	1	1	yes	characteristic
33	C₁₆	SD₁₆	1	1	yes	characteristic
34	Q₈	—	8	2	no	—
35	Q₈	—	8	2	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	8	2	no	—
38	C₂×C₄	#102	1	1	yes	characteristic
39	C₈	#100	1	1	yes	characteristic
40	C₈	#102	1	1	yes	characteristic
41	C₈	D₁₆	1	1	yes	characteristic
42	C₈	SD₃₂	1	1	yes	characteristic
43	C₂²	#361	1	1	yes	characteristic
44	C₄	—	2	2	no	—
45	C₄	—	16	2	no	—
46	C₄	#331	1	1	yes	characteristic
47	C₄	#357	1	1	yes	characteristic
48	C₂	—	2	1	no	—
49	C₂	#1361	1	1	yes	characteristic

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