Subgroups — #7539

Order 256.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2262	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#1425	C₂	1	1	yes	maximal, characteristic, complemented
4	#508	—	2	1	no	—
5	Q₆₄	C₄	1	1	yes	characteristic
6	SD₆₄	—	2	1	no	—
7	D₃₂	C₄	1	1	yes	characteristic
8	C₂×C₃₂	C₂²	1	1	yes	characteristic
9	#368	—	2	1	no	—
10	C₆₄	—	2	1	no	—
11	#135	—	4	1	no	—
12	Q₃₂	—	2	1	no	—
13	SD₃₂	—	4	1	no	—
14	D₁₆	—	2	1	no	—
15	C₂×C₁₆	D₄	1	1	yes	characteristic
16	#108	—	4	1	no	—
17	C₃₂	C₂×C₄	1	1	yes	characteristic
18	C₃₂	D₄	1	1	yes	characteristic
19	#41	—	8	1	no	—
20	Q₁₆	—	4	1	no	—
21	SD₁₆	—	8	1	no	—
22	D₈	—	4	1	no	—
23	M₁₆	—	8	1	no	—
24	C₂×C₈	D₈	1	1	yes	characteristic
25	C₁₆	C₂²⋊C₄	1	1	yes	characteristic
26	C₁₆	SD₁₆	1	1	yes	characteristic
27	Q₈	—	8	1	no	—
28	D₄	—	8	1	no	—
29	D₄	—	16	1	no	—
30	C₂×C₄	—	16	1	no	—
31	C₂×C₄	D₁₆	1	1	yes	characteristic
32	C₈	—	16	1	no	—
33	C₈	#102	1	1	yes	characteristic
34	C₈	SD₃₂	1	1	yes	characteristic
35	C₂²	—	16	1	no	—
36	C₂²	SD₆₄	1	1	yes	characteristic
37	C₄	—	16	1	no	—
38	C₄	#357	1	1	yes	characteristic
39	C₄	D₃₂	1	1	yes	characteristic
40	C₂	—	2	1	no	—
41	C₂	—	32	1	no	—
42	C₂	#1415	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₂×C₆₄	C₂	semidirect
3. #1425	C₂	semidirect

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