Subgroups — #7445

Order 256.

66 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	C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic
3	#1371	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	C₂×C₃₂	—	2	1	no	—
8	C₄×C₁₆	C₂²	1	1	yes	characteristic
9	#335	—	2	1	no	—
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	C₂×C₁₆	C₂×C₄	1	1	yes	characteristic
17	C₂×C₁₆	D₄	1	1	yes	characteristic
18	C₄⋊C₈	—	4	1	no	—
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	2	no	—
25	C₂×C₈	—	8	1	no	—
26	C₂×C₈	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₈	SD₁₆	1	1	yes	characteristic
28	C₄⋊C₄	—	8	1	no	—
29	C₄⋊C₄	—	8	1	no	—
30	C₄²	D₈	1	1	yes	characteristic
31	C₁₆	—	2	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	—	8	2	no	—
37	C₂×C₄	#102	1	1	yes	characteristic
38	C₂×C₄	D₁₆	1	1	yes	characteristic
39	C₂×C₄	SD₃₂	1	1	yes	characteristic
40	C₈	—	2	1	no	—
41	C₈	—	16	1	no	—
42	C₈	#100	1	1	yes	characteristic
43	C₈	#102	1	1	yes	characteristic
44	C₂²	#357	1	1	yes	characteristic
45	C₄	—	2	1	no	—
46	C₄	—	16	2	no	—
47	C₄	#331	1	1	yes	characteristic
48	C₄	#361	1	1	yes	characteristic
49	C₄	SD₆₄	1	1	yes	characteristic
50	C₄	Q₆₄	1	1	yes	characteristic
51	C₂	#1361	1	1	yes	characteristic
52	C₂	#1416	1	1	yes	characteristic
53	C₂	#1420	1	1	yes	characteristic

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