Subgroups — #7450

Order 256.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2252	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic
3	#1371	C₂	1	1	yes	maximal, characteristic
4	#500	—	2	1	no	—
5	C₂×C₃₂	—	2	1	no	—
6	#366	—	2	1	no	—
7	#366	C₄	1	2	yes	—
8	C₄×C₁₆	C₂²	1	1	yes	characteristic
9	#335	—	2	1	no	—
10	C₄⋊Q₈	—	4	1	no	—
11	C₂×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₆	D₄	1	1	yes	characteristic
13	#107	—	2	2	no	—
14	#107	—	4	1	no	—
15	C₄⋊C₈	—	4	1	no	—
16	C₄×C₈	D₄	1	1	yes	characteristic
17	C₃₂	—	4	1	no	—
18	C₂×Q₈	—	8	1	no	—
19	C₂×C₈	—	8	1	no	—
20	C₂×C₈	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₈	SD₁₆	1	1	yes	characteristic
22	C₄⋊C₄	—	4	2	no	—
23	C₄⋊C₄	—	8	1	no	—
24	C₄²	D₈	1	1	yes	characteristic
25	C₁₆	—	2	1	no	—
26	C₁₆	SD₁₆	1	1	yes	characteristic
27	C₁₆	Q₁₆	1	1	yes	characteristic
28	Q₈	—	16	1	no	—
29	Q₈	—	16	1	no	—
30	C₂×C₄	—	8	2	no	—
31	C₂×C₄	#102	1	1	yes	characteristic
32	C₂×C₄	D₁₆	1	1	yes	characteristic
33	C₂×C₄	SD₃₂	1	1	yes	characteristic
34	C₈	—	2	1	no	—
35	C₈	—	16	1	no	—
36	C₈	#101	1	1	yes	characteristic
37	C₈	#103	1	1	yes	characteristic
38	C₂²	#357	1	1	yes	characteristic
39	C₄	—	2	1	no	—
40	C₄	—	16	2	no	—
41	C₄	#332	1	1	yes	characteristic
42	C₄	#362	1	1	yes	characteristic
43	C₄	D₃₂	1	1	yes	characteristic
44	C₄	SD₆₄	1	1	yes	characteristic
45	C₂	#1364	1	1	yes	characteristic
46	C₂	#1415	1	1	yes	characteristic
47	C₂	#1420	1	1	yes	characteristic

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