Subgroups — C₆₄×#595 #17949540

Order 4352.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543952	C₂	1	1	yes	maximal, characteristic
2	C₃₂×#595	C₂	1	1	yes	maximal, characteristic
3	D₁₇×C₆₄	C₂	1	1	yes	maximal, characteristic
4	#11763740	C₄	1	1	yes	characteristic
5	C₁₆×#595	C₄	1	1	yes	characteristic
6	#11763648	C₄	1	2	yes	complemented
7	C₃₂×D₁₇	C₂²	1	1	yes	characteristic
8	#11762528	C₄	1	1	yes	characteristic, complemented
9	C₁₇×C₆₄	C₄	1	1	yes	characteristic, complemented
10	C₈×#595	C₈	1	1	yes	characteristic
11	#10587529	C₈	1	1	yes	characteristic
12	C₁₆×D₁₇	C₂×C₄	1	1	yes	characteristic
13	#10587467	C₈	1	2	yes	—
14	C₁₇×C₃₂	C₂×C₄	1	1	yes	characteristic
15	#10587465	C₂×C₄	1	1	yes	characteristic
16	C₄×#595	C₁₆	1	1	yes	characteristic
17	#63242	C₁₆	1	1	yes	characteristic
18	C₈×D₁₇	C₂×C₈	1	1	yes	characteristic
19	#63216	C₁₆	1	2	yes	—
20	C₁₆×C₁₇	C₄²	1	1	yes	characteristic
21	#63214	C₂×C₈	1	1	yes	characteristic
22	C₄×C₆₄	—	17	1	no	maximal, Sylow
23	C₂×#595	C₃₂	1	2	yes	—
24	C₄×D₁₇	C₂×C₁₆	1	1	yes	characteristic
25	#3624	C₃₂	1	2	yes	—
26	C₈×C₁₇	C₄×C₈	1	1	yes	characteristic
27	#3622	C₂×C₁₆	1	1	yes	characteristic
28	C₂×C₆₄	—	17	1	no	—
29	C₂×C₆₄	—	17	1	no	—
30	C₄×C₃₂	—	17	1	no	—
31	C₂×D₁₇	C₂×C₃₂	1	1	yes	characteristic
32	#595	C₆₄	1	4	yes	direct product factor
33	C₄×C₁₇	C₄×C₁₆	1	1	yes	characteristic
34	Dic₁₇	C₂×C₃₂	1	1	yes	characteristic
35	C₂×C₃₂	—	17	1	no	—
36	C₂×C₃₂	—	17	1	no	—
37	C₄×C₁₆	—	17	1	no	—
38	C₆₄	—	17	2	no	—
39	C₆₄	—	17	1	no	—
40	C₆₄	#595	1	1	yes	characteristic, direct product factor
41	C₂×C₁₇	C₄×C₃₂	1	1	yes	characteristic
42	D₁₇	C₂×C₆₄	1	2	yes	—
43	C₂×C₁₆	—	17	1	no	—
44	C₂×C₁₆	—	17	1	no	—
45	C₄×C₈	—	17	1	no	—
46	C₃₂	—	17	2	no	—
47	C₃₂	—	17	1	no	—
48	C₃₂	C₂×#595	1	1	yes	characteristic
49	C₁₇	C₄×C₆₄	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₈	—	17	1	no	—
51	C₂×C₈	—	17	1	no	—
52	C₄²	—	17	1	no	—
53	C₁₆	—	17	2	no	—
54	C₁₆	—	17	1	no	—
55	C₁₆	C₄×#595	1	1	yes	characteristic
56	C₂×C₄	—	17	2	no	—
57	C₂×C₄	—	17	1	no	—
58	C₈	—	17	2	no	—
59	C₈	—	17	1	no	—
60	C₈	C₈×#595	1	1	yes	characteristic
61	C₂²	—	17	1	no	—
62	C₄	—	17	4	no	—
63	C₄	—	17	1	no	—
64	C₄	C₁₆×#595	1	1	yes	characteristic
65	C₂	—	17	2	no	—
66	C₂	C₃₂×#595	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₆₄	#595
commutator, hypocenter	C₁₇	C₄×C₆₄
Frattini	C₃₂	C₂×#595
Fitting	C₁₇×C₆₄	C₄
socle	C₂×C₁₇	C₄×C₃₂
prime radical	C₂×D₁₇	C₂×C₃₂
cosocle	C₃₂×D₁₇	C₂²
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₆₄

Complements

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

N	H ≅ G/N	type
6. #11763648	C₄	semidirect
8. #11762528	C₄	semidirect
9. C₁₇×C₆₄	C₄	semidirect
32. #595	C₆₄	direct (N × H)
40. C₆₄	#595	direct (N × H)
49. C₁₇	C₄×C₆₄	semidirect

Maximal subgroups

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

subgroup	index
#14543952	2
C₃₂×#595	2
D₁₇×C₆₄	2
C₄×C₆₄	17

Subgroups — C64×#595 #17949540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₄×#595 #17949540