Subgroups — #16955350

Order 4352.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14531058	C₂	1	2	yes	maximal
2	#14526986	C₂	1	1	yes	maximal, characteristic
3	#14526985	C₂	1	2	yes	maximal
4	C₃₂×Dic₁₇	C₂	1	1	yes	maximal, characteristic
5	C₁₇×#1424	C₂	1	1	yes	maximal, characteristic
6	#11763213	—	2	2	no	—
7	C₂×#10587465	C₂²	1	1	yes	characteristic
8	#11762635	C₂²	1	2	yes	—
9	#11762634	—	2	2	no	—
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	#10587574	—	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	#10587478	—	4	2	no	—
20	C₁₇×C₃₂	Q₈	1	2	yes	complemented
21	#10587465	Q₈	1	2	yes	complemented
22	C₂×Dic₃₄	—	8	2	no	—
23	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
24	C₄⋊C₄×C₁₇	—	4	2	no	—
25	C₄⋊Dic₁₇	—	4	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	#13733	—	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	Dic₃₄	—	16	4	no	—
38	C₈×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
39	C₈×C₁₇	C₂×Q₁₆	1	1	yes	characteristic
40	#3622	Q₃₂	1	2	yes	—
41	#2252	—	17	2	no	—
42	#1424	—	17	1	no	—
43	#1424	—	17	2	no	—
44	#1424	D₁₇	1	1	yes	characteristic
45	C₄×C₃₂	—	17	1	no	—
46	C₂²×C₁₇	C₂×D₁₆	1	1	yes	characteristic
47	C₄×C₁₇	—	16	2	no	—
48	C₄×C₁₇	#500	1	1	yes	characteristic
49	C₄×C₁₇	C₂×Q₃₂	1	1	yes	characteristic
50	Dic₁₇	—	16	2	no	—
51	Dic₁₇	SD₆₄	1	4	yes	—
52	#500	—	34	2	no	—
53	C₂×C₃₂	—	17	1	no	—
54	C₂×C₃₂	C₂×D₁₇	1	1	yes	characteristic
55	#366	—	17	2	no	—
56	#366	—	34	2	no	—
57	#366	C₂×D₁₇	1	2	yes	—
58	C₄×C₁₆	—	17	1	no	—
59	C₂×C₁₇	#2252	1	1	yes	characteristic
60	C₂×C₁₇	C₂×SD₆₄	1	2	yes	—
61	C₄⋊Q₈	—	68	2	no	—
62	C₂×C₁₆	—	17	1	no	—
63	C₂×C₁₆	C₂²×D₁₇	1	1	yes	characteristic
64	#107	—	2	2	no	—
65	#107	—	34	2	no	—
66	#107	—	68	2	no	—
67	C₄×C₈	—	17	1	no	—
68	C₃₂	—	17	2	no	—
69	C₃₂	Dic₃₄	1	2	yes	complemented
70	C₁₇	#13733	1	1	yes	characteristic, complemented, Sylow
71	C₂×Q₈	—	136	2	no	—
72	C₂×C₈	—	17	1	no	—
73	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
74	C₄⋊C₄	—	4	2	no	—
75	C₄⋊C₄	—	68	2	no	—
76	C₄⋊C₄	—	136	2	no	—
77	C₄²	—	17	1	no	—
78	C₁₆	—	17	2	no	—
79	C₁₆	C₂×Dic₃₄	1	1	yes	characteristic
80	C₁₆	Q₈×D₁₇	1	1	yes	characteristic
81	Q₈	—	272	4	no	—
82	C₂×C₄	—	8	2	no	—
83	C₂×C₄	—	17	2	no	—
84	C₂×C₄	—	136	2	no	—
85	C₂×C₄	D₈×D₁₇	1	1	yes	characteristic
86	C₈	—	17	2	no	—
87	C₈	#10587574	1	1	yes	characteristic
88	C₈	Q₁₆×D₁₇	1	1	yes	characteristic
89	C₂²	D₁₆×D₁₇	1	1	yes	characteristic
90	C₄	—	16	2	no	—
91	C₄	—	272	2	no	—
92	C₄	—	17	4	no	—
93	C₄	#11763213	1	1	yes	characteristic
94	C₄	Q₃₂×D₁₇	1	1	yes	characteristic
95	C₂	#14531058	1	1	yes	characteristic
96	C₂	D₁₇×SD₆₄	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	#13733
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
20. C₁₇×C₃₂	Q₈	semidirect
21. #10587465	Q₈	semidirect
69. C₃₂	Dic₃₄	semidirect
70. C₁₇	#13733	semidirect

Maximal subgroups

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

subgroup	index
#14531058	2
#14526986	2
#14526985	2
C₃₂×Dic₁₇	2
C₁₇×#1424	2
#13733	17