Subgroups — #7454

Order 256.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2253	C₂	1	1	yes	maximal, characteristic
2	#1422	C₂	1	1	yes	maximal, characteristic
3	#1373	C₂	1	1	yes	maximal, characteristic
4	#499	—	2	1	no	—
5	M₆₄	—	2	1	no	—
6	#367	C₄	1	2	yes	—
7	#366	—	2	1	no	—
8	#364	—	2	1	no	—
9	C₄×C₁₆	C₂²	1	1	yes	characteristic
10	#125	—	4	1	no	—
11	M₃₂	—	4	1	no	—
12	C₂×C₁₆	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₆	D₄	1	1	yes	characteristic
14	#107	—	2	2	no	—
15	#106	—	4	1	no	—
16	C₄×C₈	D₄	1	1	yes	characteristic
17	C₃₂	—	4	1	no	—
18	C₂×C₈	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₈	D₈	1	1	yes	characteristic
20	C₄⋊C₄	—	4	2	no	—
21	C₄⋊C₄	—	8	2	no	—
22	C₄²	SD₁₆	1	1	yes	characteristic
23	C₁₆	—	2	1	no	—
24	C₁₆	—	8	1	no	—
25	C₁₆	SD₁₆	1	1	yes	characteristic
26	C₁₆	Q₁₆	1	1	yes	characteristic
27	C₂×C₄	—	2	1	no	—
28	C₂×C₄	—	8	2	no	—
29	C₂×C₄	#102	1	1	yes	characteristic
30	C₈	#101	1	1	yes	characteristic
31	C₈	#103	1	1	yes	characteristic
32	C₈	SD₃₂	1	1	yes	characteristic
33	C₈	Q₃₂	1	1	yes	characteristic
34	C₂²	#361	1	1	yes	characteristic
35	C₄	—	4	1	no	—
36	C₄	—	16	2	no	—
37	C₄	#332	1	1	yes	characteristic
38	C₄	#358	1	1	yes	characteristic
39	C₂	—	2	1	no	—
40	C₂	#1365	1	1	yes	characteristic

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