Subgroups — #17953801

Order 4352.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543651	C₂	1	3	yes	maximal
2	#14543644	C₂	1	3	yes	maximal
3	#14527086	C₂	1	1	yes	maximal, characteristic
4	#11763832	C₂²	1	3	yes	—
5	#11763754	C₂²	1	1	yes	characteristic
6	C₄×#63218	C₂²	1	3	yes	—
7	#11762530	C₄	1	3	yes	complemented
8	C₈²×C₁₇	C₄	1	1	yes	characteristic, complemented
9	C₂×#63218	—	2	3	no	—
10	C₄²×D₁₇	C₂³	1	1	yes	characteristic
11	(C₂×#595)⋊C₄	—	2	3	no	—
12	#10587544	—	2	3	no	—
13	#10587543	—	2	3	no	—
14	#10587542	—	2	3	no	—
15	C₄×C₈×C₁₇	C₂×C₄	1	3	yes	—
16	#10587486	—	2	3	no	—
17	C₄×#3622	C₂×C₄	1	3	yes	—
18	C₂²×#595	—	4	1	no	—
19	C₂×C₄×D₁₇	#41	1	3	yes	—
20	C₂×#3624	—	4	3	no	—
21	C₂×C₈×C₁₇	—	2	3	no	—
22	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
23	C₄×Dic₁₇	#41	1	3	yes	—
24	C₂×#3622	—	2	3	no	—
25	#63218	—	4	6	no	—
26	#8803	—	17	1	no	maximal, Sylow
27	C₂²×D₁₇	#126	1	1	yes	characteristic
28	C₂×#595	—	8	3	no	—
29	C₂×C₄×C₁₇	#117	1	3	yes	—
30	C₂×Dic₁₇	#126	1	3	yes	—
31	C₄×D₁₇	—	4	3	no	—
32	#3624	—	8	3	no	—
33	C₈×C₁₇	—	2	6	no	—
34	#3622	—	4	3	no	—
35	#1455	—	17	1	no	—
36	#1291	—	17	3	no	—
37	#1288	—	17	3	no	—
38	C₂²×C₁₇	#383	1	1	yes	characteristic
39	C₂×D₁₇	—	2	3	no	—
40	#595	—	16	1	no	—
41	C₄×C₁₇	—	2	3	no	—
42	Dic₁₇	—	2	3	no	—
43	#432	—	17	3	no	—
44	C₄×M₁₆	—	17	3	no	—
45	#383	—	17	1	no	—
46	#322	—	17	3	no	—
47	C₈²	#595	1	1	yes	characteristic, complemented
48	C₂×C₁₇	#1841	1	3	yes	—
49	D₁₇	—	4	1	no	—
50	C₂×M₁₆	—	34	3	no	—
51	C₂×C₄²	—	17	1	no	—
52	C₄⋊C₈	—	34	3	no	—
53	C₂²⋊C₈	—	34	3	no	—
54	#97	—	34	3	no	—
55	#97	—	34	3	no	—
56	C₄×C₈	—	17	3	no	—
57	C₄×C₈	C₂×#595	1	3	yes	—
58	#95	—	34	3	no	—
59	C₁₇	#8803	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₄	—	17	3	no	—
61	C₂²×C₄	—	68	1	no	—
62	M₁₆	—	68	6	no	—
63	C₂×C₈	—	2	3	no	—
64	C₂×C₈	—	34	3	no	—
65	C₂×C₈	—	68	3	no	—
66	C₄²	—	17	3	no	—
67	C₄²	C₂²×#595	1	1	yes	characteristic
68	C₂³	—	17	1	no	—
69	C₂×C₄	—	17	3	no	—
70	C₂×C₄	—	68	3	no	—
71	C₂×C₄	—	136	3	no	—
72	C₂×C₄	#10587677	1	3	yes	—
73	C₈	—	2	6	no	—
74	C₈	—	68	3	no	—
75	C₈	—	136	3	no	—
76	C₂²	—	34	3	no	—
77	C₂²	#11763754	1	1	yes	characteristic
78	C₄	—	2	3	no	—
79	C₄	—	272	1	no	—
80	C₄	—	34	3	no	—
81	C₂	—	68	1	no	—
82	C₂	#14544714	1	3	yes	—

	subgroup	G/H
center	C₂²	#11763754
commutator	C₄²×C₁₇	C₂²×C₄
Frattini	C₄²	C₂²×#595
Fitting	C₈²×C₁₇	C₄
socle	C₂²×C₁₇	#383
prime radical	C₂²×D₁₇	#126
cosocle	C₄²×D₁₇	C₂³
hypercenter	C₈²	#595
hypocenter	C₁₇	#8803
LCS	G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
7. #11762530	C₄	semidirect
8. C₈²×C₁₇	C₄	semidirect
47. C₈²	#595	semidirect
59. C₁₇	#8803	semidirect

Maximal subgroups

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

subgroup	index
#14543651	2
#14543644	2
#14527086	2
#8803	17