Subgroups — #7475

Order 256.

85 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₆₄	C₂	1	1	yes	maximal, characteristic
2	#2158	C₂	1	2	yes	maximal
3	C₂²×C₁₆	C₂²	1	1	yes	characteristic
4	#427	—	2	2	no	—
5	M₆₄	—	2	2	no	—
6	C₂×C₃₂	C₄	1	2	yes	complemented
7	#367	C₄	1	4	yes	complemented
8	#366	—	2	2	no	—
9	C₂²×C₈	D₄	1	1	yes	characteristic
10	#117	—	4	2	no	—
11	C₂×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₆	C₂×C₄	1	2	yes	—
13	C₂×C₁₆	D₄	1	2	yes	—
14	C₂×C₁₆	Q₈	1	1	yes	characteristic
15	#107	—	2	4	no	—
16	#106	—	4	2	no	—
17	C₃₂	—	2	2	no	—
18	C₂²×C₄	D₈	1	1	yes	characteristic
19	C₂×C₈	C₂²⋊C₄	1	2	yes	—
20	C₂×C₈	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₈	SD₁₆	1	2	yes	—
22	C₂×C₈	Q₁₆	1	1	yes	characteristic
23	C₄⋊C₄	—	4	4	no	—
24	C₂²⋊C₄	—	8	2	no	—
25	C₄²	—	8	2	no	—
26	C₁₆	C₄²	1	1	yes	characteristic
27	C₁₆	C₂²⋊C₄	1	1	yes	characteristic
28	C₁₆	C₄⋊C₄	1	2	yes	—
29	C₂³	D₁₆	1	1	yes	characteristic
30	C₂×C₄	—	8	4	no	—
31	C₂×C₄	#102	1	2	yes	—
32	C₂×C₄	#107	1	1	yes	characteristic
33	C₂×C₄	SD₃₂	1	2	yes	—
34	C₂×C₄	Q₃₂	1	1	yes	characteristic
35	C₈	#95	1	1	yes	characteristic
36	C₈	#103	1	2	yes	—
37	C₈	#106	1	1	yes	characteristic
38	C₂²	—	4	1	no	—
39	C₂²	#357	1	2	yes	—
40	C₂²	#366	1	1	yes	characteristic
41	C₄	—	16	4	no	—
42	C₄	#340	1	1	yes	characteristic
43	C₄	#358	1	2	yes	—
44	C₄	#367	1	1	yes	characteristic
45	C₂	—	2	2	no	—
46	C₂	—	2	1	no	—
47	C₂	#1380	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
6. C₂×C₃₂	C₄	semidirect
7. #367	C₄	semidirect

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

subgroup	index
C₂×M₆₄	2
#2158	2