Subgroups — #17949366

Order 4352.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543944	C₂	1	1	yes	maximal, characteristic
2	#14543820	C₂	1	1	yes	maximal, characteristic
3	#14531062	C₂	1	1	yes	maximal, characteristic
4	#11763741	—	2	1	no	—
5	#11763731	—	2	1	no	—
6	#11763210	—	2	1	no	—
7	#11762637	C₄	1	1	yes	characteristic
8	#11762634	—	2	1	no	—
9	C₁₆×Dic₁₇	C₂²	1	1	yes	characteristic
10	C₁₇×#367	C₄	1	1	yes	characteristic
11	#10587576	—	4	1	no	—
12	#10587538	—	4	1	no	—
13	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
14	C₁₇×#107	—	2	1	no	—
15	#10587489	—	2	1	no	—
16	C₈×Dic₁₇	D₄	1	1	yes	characteristic
17	C₂×#63214	D₄	1	1	yes	characteristic
18	#10587479	—	4	1	no	—
19	#10587467	—	4	1	no	—
20	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄⋊C₄×C₁₇	—	4	1	no	—
22	C₄⋊Dic₁₇	—	4	1	no	—
23	C₄⋊Dic₁₇	—	8	1	no	—
24	#63225	—	8	1	no	—
25	C₄×Dic₁₇	SD₁₆	1	1	yes	characteristic
26	C₂×#3622	D₈	1	1	yes	characteristic
27	#63216	—	8	1	no	—
28	C₁₆×C₁₇	—	2	1	no	—
29	#63214	SD₁₆	1	1	yes	characteristic
30	#63214	Q₁₆	1	1	yes	characteristic
31	#7454	—	17	1	no	maximal, Sylow
32	C₂×C₄×C₁₇	—	8	1	no	—
33	C₂×C₄×C₁₇	#102	1	1	yes	characteristic
34	C₂×Dic₁₇	—	2	1	no	—
35	C₂×Dic₁₇	—	8	1	no	—
36	C₈×C₁₇	#101	1	1	yes	characteristic
37	C₈×C₁₇	#103	1	1	yes	characteristic
38	#3622	SD₃₂	1	1	yes	characteristic
39	#3622	Q₃₂	1	1	yes	characteristic
40	#2253	—	17	1	no	—
41	#1422	—	17	1	no	—
42	#1373	—	17	1	no	—
43	C₂²×C₁₇	#361	1	1	yes	characteristic
44	C₄×C₁₇	—	16	1	no	—
45	C₄×C₁₇	#332	1	1	yes	characteristic
46	C₄×C₁₇	#358	1	1	yes	characteristic
47	Dic₁₇	—	4	1	no	—
48	Dic₁₇	—	16	1	no	—
49	#499	—	34	1	no	—
50	M₆₄	—	34	1	no	—
51	#367	—	17	1	no	—
52	#367	#595	1	1	yes	characteristic
53	#366	—	34	1	no	—
54	#364	—	34	1	no	—
55	C₄×C₁₆	—	17	1	no	—
56	C₂×C₁₇	—	2	1	no	—
57	C₂×C₁₇	#1365	1	1	yes	characteristic
58	#125	—	68	1	no	—
59	M₃₂	—	68	1	no	—
60	C₂×C₁₆	—	17	1	no	—
61	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
62	#107	—	2	1	no	—
63	#107	—	34	1	no	—
64	#106	—	68	1	no	—
65	C₄×C₈	—	17	1	no	—
66	C₃₂	—	68	1	no	—
67	C₁₇	#7454	1	1	yes	characteristic, complemented, Sylow
68	C₂×C₈	—	17	1	no	—
69	C₂×C₈	C₂²⋊#595	1	1	yes	characteristic
70	C₄⋊C₄	—	4	1	no	—
71	C₄⋊C₄	—	68	1	no	—
72	C₄⋊C₄	—	136	1	no	—
73	C₄⋊C₄	—	136	1	no	—
74	C₄²	—	17	1	no	—
75	C₁₆	—	2	1	no	—
76	C₁₆	—	17	1	no	—
77	C₁₆	—	17	1	no	—
78	C₁₆	—	136	1	no	—
79	C₂×C₄	—	8	1	no	—
80	C₂×C₄	—	34	1	no	—
81	C₂×C₄	—	136	1	no	—
82	C₂×C₄	#10587547	1	1	yes	characteristic
83	C₈	—	17	1	no	—
84	C₈	—	17	1	no	—
85	C₈	#10587545	1	1	yes	characteristic
86	C₈	#10587549	1	1	yes	characteristic
87	C₂²	#11763727	1	1	yes	characteristic
88	C₄	—	16	1	no	—
89	C₄	—	272	1	no	—
90	C₄	—	68	1	no	—
91	C₄	#11763668	1	1	yes	characteristic
92	C₄	#11763722	1	1	yes	characteristic
93	C₂	—	2	1	no	—
94	C₂	#14543803	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14543803
commutator	C₂×C₁₆×C₁₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×#595
Fitting	C₁₇×#367	C₄
socle	C₂×C₁₇	#1365
prime radical	C₂²×C₁₇	#361
cosocle	C₁₆×Dic₁₇	C₂²
hypercenter	#367	#595
hypocenter	C₁₇	#7454
LCS	G ▷ C₂×C₁₆×C₁₇ ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #367

Complements

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

N	H ≅ G/N	type
67. C₁₇	#7454	semidirect

Maximal subgroups

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

subgroup	index
#14543944	2
#14543820	2
#14531062	2
#7454	17