Subgroups — #16955347

Order 4352.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14531061	C₂	1	2	yes	maximal
2	#14526986	C₂	1	1	yes	maximal, characteristic
3	#14526983	C₂	1	2	yes	maximal
4	C₃₂×Dic₁₇	C₂	1	1	yes	maximal, characteristic
5	C₁₇×#1424	C₂	1	1	yes	maximal, characteristic
6	#11763210	—	2	2	no	—
7	C₂×#10587465	C₂²	1	1	yes	characteristic
8	#11762636	—	2	2	no	—
9	#11762635	C₂²	1	2	yes	—
10	C₁₆×Dic₁₇	C₂²	1	1	yes	characteristic
11	C₂×C₁₇×C₃₂	C₂²	1	1	yes	characteristic
12	C₁₇×#366	C₂²	1	2	yes	—
13	#10587576	—	4	2	no	—
14	C₂×C₁₆×C₁₇	C₂³	1	1	yes	characteristic
15	C₁₇×#107	—	2	2	no	—
16	#10587489	—	2	2	no	—
17	C₈×Dic₁₇	D₄	1	1	yes	characteristic
18	C₂×#63214	D₄	1	1	yes	characteristic
19	#10587479	—	4	2	no	—
20	C₁₇×C₃₂	Q₈	1	2	yes	—
21	#10587465	Q₈	1	2	yes	—
22	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
23	C₄⋊C₄×C₁₇	—	4	2	no	—
24	C₄⋊Dic₁₇	—	4	2	no	—
25	C₄⋊Dic₁₇	—	8	2	no	—
26	#63225	—	8	2	no	—
27	C₄×Dic₁₇	D₈	1	1	yes	characteristic
28	C₂×#3622	D₈	1	1	yes	characteristic
29	C₁₆×C₁₇	C₂×Q₈	1	1	yes	characteristic
30	C₁₆×C₁₇	C₂×Q₈	1	1	yes	characteristic
31	#63214	Q₁₆	1	2	yes	—
32	#13732	—	17	1	no	maximal, Sylow
33	C₂×C₄×C₁₇	—	8	2	no	—
34	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
35	C₂×Dic₁₇	—	8	2	no	—
36	C₂×Dic₁₇	D₁₆	1	2	yes	—
37	C₈×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
38	C₈×C₁₇	C₂×Q₁₆	1	1	yes	characteristic
39	#3622	Q₃₂	1	2	yes	—
40	#2253	—	17	2	no	—
41	#1424	—	17	1	no	—
42	#1424	D₁₇	1	1	yes	characteristic
43	#1423	—	17	2	no	—
44	C₄×C₃₂	—	17	1	no	—
45	C₂²×C₁₇	C₂×D₁₆	1	1	yes	characteristic
46	C₄×C₁₇	—	16	2	no	—
47	C₄×C₁₇	#500	1	1	yes	characteristic
48	C₄×C₁₇	C₂×Q₃₂	1	1	yes	characteristic
49	Dic₁₇	—	2	2	no	—
50	Dic₁₇	—	16	2	no	—
51	#499	—	34	2	no	—
52	C₂×C₃₂	—	17	1	no	—
53	C₂×C₃₂	C₂×D₁₇	1	1	yes	characteristic
54	#367	—	34	2	no	—
55	#366	—	17	2	no	—
56	#366	C₂×D₁₇	1	2	yes	—
57	C₄×C₁₆	—	17	1	no	—
58	C₂×C₁₇	#2252	1	1	yes	characteristic
59	C₂×C₁₇	#2262	1	2	yes	—
60	#125	—	68	2	no	—
61	C₂×C₁₆	—	17	1	no	—
62	C₂×C₁₆	C₂²×D₁₇	1	1	yes	characteristic
63	#107	—	2	2	no	—
64	#107	—	34	2	no	—
65	#106	—	68	2	no	—
66	C₄×C₈	—	17	1	no	—
67	C₃₂	—	17	2	no	—
68	C₃₂	Dic₃₄	1	2	yes	—
69	C₁₇	#13732	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₈	—	17	1	no	—
71	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
72	C₄⋊C₄	—	4	2	no	—
73	C₄⋊C₄	—	68	2	no	—
74	C₄⋊C₄	—	136	2	no	—
75	C₄⋊C₄	—	136	2	no	—
76	C₄²	—	17	1	no	—
77	C₁₆	—	17	2	no	—
78	C₁₆	C₂×Dic₃₄	1	1	yes	characteristic
79	C₁₆	Q₈×D₁₇	1	1	yes	characteristic
80	C₂×C₄	—	8	2	no	—
81	C₂×C₄	—	17	2	no	—
82	C₂×C₄	—	136	2	no	—
83	C₂×C₄	D₈×D₁₇	1	1	yes	characteristic
84	C₈	—	17	2	no	—
85	C₈	#10587574	1	1	yes	characteristic
86	C₈	Q₁₆×D₁₇	1	1	yes	characteristic
87	C₂²	D₁₆×D₁₇	1	1	yes	characteristic
88	C₄	—	16	2	no	—
89	C₄	—	272	2	no	—
90	C₄	—	34	2	no	—
91	C₄	#11763213	1	1	yes	characteristic
92	C₄	Q₃₂×D₁₇	1	1	yes	characteristic
93	C₂	#14531058	1	1	yes	characteristic
94	C₂	#14531092	1	2	yes	—

	subgroup	G/H
center	C₂²	D₁₆×D₁₇
commutator, cosocle	C₂×C₁₆×C₁₇	C₂³
Frattini	C₂×C₁₆	C₂²×D₁₇
Fitting	C₁₇×#1424	C₂
socle, prime radical	C₂²×C₁₇	C₂×D₁₆
hypercenter	#1424	D₁₇
hypocenter	C₁₇	#13732
LCS	G ▷ C₂×C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #1424

Complements

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

N	H ≅ G/N	type
69. C₁₇	#13732	semidirect

Maximal subgroups

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

subgroup	index
#14531061	2
#14526986	2
#14526983	2
C₃₂×Dic₁₇	2
C₁₇×#1424	2
#13732	17