Subgroups — #17949101

Order 4352.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543896	C₂	1	1	yes	maximal, characteristic
2	#14543700	C₂	1	1	yes	maximal, characteristic
3	#14526919	C₂	1	1	yes	maximal, characteristic
4	#11763741	C₄	1	2	yes	—
5	#11763698	C₄	1	1	yes	characteristic
6	#11763650	C₄	1	1	yes	characteristic
7	#11762643	C₄	1	1	yes	characteristic
8	#11762584	C₂²	1	1	yes	characteristic
9	C₁₇×M₆₄	C₄	1	1	yes	characteristic
10	C₄×#3624	—	2	1	no	—
11	C₂×#63216	—	2	1	no	—
12	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
13	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
14	C₂×#63214	C₂×C₄	1	1	yes	characteristic
15	#10587467	—	2	2	no	—
16	C₁₇×C₃₂	C₈	1	2	yes	complemented
17	#10587465	C₈	1	2	yes	complemented
18	C₂×#3624	—	4	1	no	—
19	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
20	C₄×Dic₁₇	M₁₆	1	1	yes	characteristic
21	C₂×#3622	M₁₆	1	1	yes	characteristic
22	#63216	—	4	1	no	—
23	C₁₆×C₁₇	C₂×C₈	1	1	yes	characteristic
24	C₁₆×C₁₇	C₂×C₈	1	1	yes	characteristic
25	#63214	M₁₆	1	2	yes	—
26	#7333	—	17	1	no	maximal, Sylow
27	C₂×C₄×C₁₇	#97	1	1	yes	characteristic
28	C₂×Dic₁₇	—	2	1	no	—
29	#3624	—	8	1	no	—
30	C₈×C₁₇	C₄×C₈	1	1	yes	characteristic
31	C₈×C₁₇	#97	1	1	yes	characteristic
32	#3622	—	2	1	no	—
33	#1398	—	17	1	no	—
34	#1398	—	17	1	no	—
35	#1313	—	17	1	no	—
36	C₂²×C₁₇	#347	1	1	yes	characteristic
37	C₄×C₁₇	#322	1	1	yes	characteristic
38	C₄×C₁₇	#347	1	1	yes	characteristic
39	Dic₁₇	—	4	1	no	—
40	M₆₄	—	17	1	no	—
41	M₆₄	—	17	2	no	—
42	M₆₄	#595	1	1	yes	characteristic
43	#346	—	17	1	no	—
44	#346	—	17	1	no	—
45	#322	—	17	1	no	—
46	C₂×C₁₇	—	2	1	no	—
47	C₂×C₁₇	#1313	1	1	yes	characteristic
48	C₂×C₁₆	—	17	1	no	—
49	C₂×C₁₆	—	34	1	no	—
50	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
51	C₄×C₈	—	17	1	no	—
52	C₄×C₈	—	34	1	no	—
53	C₃₂	—	17	2	no	—
54	C₃₂	—	34	2	no	—
55	C₃₂	#3624	1	2	yes	complemented
56	C₁₇	#7333	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₈	—	17	1	no	—
58	C₂×C₈	—	68	1	no	—
59	C₂×C₈	C₄×#595	1	1	yes	characteristic
60	C₄²	—	17	1	no	—
61	C₁₆	—	17	2	no	—
62	C₁₆	—	68	1	no	—
63	C₁₆	#63242	1	1	yes	characteristic
64	C₁₆	C₂×#3624	1	1	yes	characteristic
65	C₂×C₄	—	34	1	no	—
66	C₂×C₄	#10587532	1	1	yes	characteristic
67	C₈	—	34	1	no	—
68	C₈	—	136	1	no	—
69	C₈	#10587532	1	1	yes	characteristic
70	C₈	C₄×#3624	1	1	yes	characteristic
71	C₂²	#11763699	1	1	yes	characteristic
72	C₄	—	68	1	no	—
73	C₄	#11763650	1	1	yes	characteristic
74	C₄	#11763699	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	#14543700	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11763650
commutator	C₈×C₁₇	C₄×C₈
Frattini	C₂×C₁₆	C₂×#595
Fitting	C₁₇×M₆₄	C₄
socle	C₂×C₁₇	#1313
prime radical	C₂²×C₁₇	#347
cosocle	#11762584	C₂²
hypercenter	M₆₄	#595
hypocenter	C₁₇	#7333
LCS	G ▷ C₈×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
16. C₁₇×C₃₂	C₈	semidirect
17. #10587465	C₈	semidirect
55. C₃₂	#3624	semidirect
56. C₁₇	#7333	semidirect

Maximal subgroups

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

subgroup	index
#14543896	2
#14543700	2
#14526919	2
#7333	17