Subgroups — #17949547

Order 4352.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543954	C₂	1	1	yes	maximal, characteristic
2	#14543890	C₂	1	1	yes	maximal, characteristic
3	#14526994	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	#7511	—	17	1	no	maximal, Sylow
23	C₂×#595	—	2	1	no	—
24	C₄×D₁₇	C₂×C₁₆	1	1	yes	characteristic
25	#3624	—	2	1	no	—
26	C₈×C₁₇	C₄×C₈	1	1	yes	characteristic
27	#3622	C₂×C₁₆	1	1	yes	characteristic
28	M₁₂₈	—	17	1	no	—
29	M₁₂₈	—	17	1	no	—
30	#1397	—	17	1	no	—
31	C₂×D₁₇	M₆₄	1	1	yes	characteristic
32	#595	—	4	1	no	—
33	C₄×C₁₇	C₄×C₁₆	1	1	yes	characteristic
34	Dic₁₇	M₆₄	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, complemented
41	C₂×C₁₇	#1397	1	1	yes	characteristic
42	D₁₇	—	2	1	no	—
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	#7511	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	1	no	—
57	C₂×C₄	—	34	1	no	—
58	C₈	—	17	1	no	—
59	C₈	—	34	1	no	—
60	C₈	C₈×#595	1	1	yes	characteristic
61	C₂²	—	17	1	no	—
62	C₄	—	17	1	no	—
63	C₄	—	68	1	no	—
64	C₄	C₁₆×#595	1	1	yes	characteristic
65	C₂	—	34	1	no	—
66	C₂	#14543890	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₄×#595
commutator	C₄×C₁₇	C₄×C₁₆
Frattini	C₃₂	C₂×#595
Fitting	C₁₇×C₆₄	C₄
socle	C₂×C₁₇	#1397
prime radical	C₂×D₁₇	M₆₄
cosocle	C₃₂×D₁₇	C₂²
hypercenter	C₆₄	#595
hypocenter	C₁₇	#7511
LCS	G ▷ C₄×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₁₆ ◁ 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
40. C₆₄	#595	semidirect
49. C₁₇	#7511	semidirect

Maximal subgroups

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

subgroup	index
#14543954	2
#14543890	2
#14526994	2
#7511	17