Subgroups — #17960425

Order 4352.

478 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11763696	C₂	1	2	yes	maximal
2	C₄×#10587529	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×#595	C₂	1	2	yes	maximal
4	#14544440	C₂	1	1	yes	maximal, characteristic
5	D₁₇×#346	C₂	1	1	yes	maximal, characteristic
6	C₂×#10587529	C₂²	1	1	yes	characteristic
7	C₂×#10587529	C₂²	1	1	yes	characteristic
8	#11763768	C₄	1	1	yes	characteristic
9	C₂×#10587532	C₄	1	2	yes	—
10	C₂×C₈×#595	C₂²	1	2	yes	—
11	#11763745	C₄	1	1	yes	characteristic
12	#11763696	C₄	1	8	yes	complemented
13	#11763695	C₄	1	2	yes	complemented
14	C₄×#63216	C₄	1	2	yes	complemented
15	C₁₆×#595	C₄	1	8	yes	complemented
16	C₂×C₁₆×D₁₇	C₂²	1	2	yes	—
17	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
18	#11762585	C₄	1	1	yes	characteristic, complemented
19	#11762584	C₄	1	2	yes	complemented
20	C₁₇×#346	C₄	1	1	yes	characteristic, complemented
21	C₂×C₄×#595	C₂×C₄	1	2	yes	—
22	C₂×#63242	C₂×C₄	1	2	yes	—
23	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
25	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
26	(C₂×#595)⋊C₄	C₈	1	4	yes	—
27	#10587542	C₈	1	4	yes	—
28	C₂×#63216	C₂×C₄	1	2	yes	—
29	C₂×#63216	C₂×C₄	1	2	yes	—
30	#10587532	C₈	1	8	yes	—
31	C₈×#595	C₂×C₄	1	4	yes	—
32	C₈×#595	C₂×C₄	1	4	yes	—
33	#10587529	C₂×C₄	1	4	yes	—
34	#10587529	C₂×C₄	1	4	yes	—
35	C₂×C₁₆×C₁₇	C₂×C₄	1	2	yes	—
36	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
37	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
38	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
39	C₂×#63214	C₂×C₄	1	2	yes	—
40	C₄×#3622	C₂×C₄	1	1	yes	characteristic
41	C₁₆×D₁₇	C₂×C₄	1	4	yes	—
42	C₁₆×D₁₇	C₂×C₄	1	4	yes	—
43	C₂²×#595	C₂×C₈	1	4	yes	—
44	C₂×C₄×D₁₇	C₂×C₈	1	2	yes	—
45	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
46	C₂×#3624	C₂×C₈	1	4	yes	—
47	C₄×#595	C₄²	1	4	yes	—
48	C₄×#595	C₂×C₈	1	4	yes	—
49	#63242	C₄²	1	4	yes	—
50	#63242	C₂×C₈	1	4	yes	—
51	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
52	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
53	C₄²×C₁₇	C₄²	1	1	yes	characteristic
54	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
55	C₄×Dic₁₇	C₂×C₈	1	2	yes	—
56	C₂×#3622	C₄²	1	1	yes	characteristic
57	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
58	C₈×D₁₇	C₂×C₈	1	4	yes	—
59	C₈×D₁₇	C₂²×C₄	1	2	yes	—
60	C₈×D₁₇	C₂²×C₄	1	2	yes	—
61	#63216	C₄²	1	4	yes	—
62	#63216	C₄²	1	4	yes	—
63	C₁₆×C₁₇	C₄²	1	4	yes	—
64	#63214	C₄²	1	4	yes	—
65	#12539	—	17	1	no	maximal, Sylow
66	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
67	C₂×#595	—	2	8	no	—
68	C₂×#595	C₄×C₈	1	8	yes	—
69	C₂×C₄×C₁₇	C₄×C₈	1	2	yes	—
70	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
71	C₂×Dic₁₇	C₄×C₈	1	2	yes	—
72	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
73	C₄×D₁₇	—	2	4	no	—
74	C₄×D₁₇	C₂×C₄²	1	2	yes	—
75	C₄×D₁₇	C₂²×C₈	1	2	yes	—
76	#3624	C₄×C₈	1	8	yes	—
77	C₈×C₁₇	C₄×C₈	1	2	yes	—
78	C₈×C₁₇	C₂×C₄²	1	2	yes	—
79	#3622	C₄×C₈	1	2	yes	—
80	#3622	C₂×C₄²	1	1	yes	characteristic
81	#3622	C₂×C₄²	1	1	yes	characteristic
82	C₂×#346	—	17	2	no	—
83	C₂×#346	—	17	1	no	—
84	C₂×C₄×C₁₆	—	17	2	no	—
85	C₂×C₄×C₁₆	—	17	1	no	—
86	#1726	—	17	1	no	—
87	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
88	C₂×D₁₇	C₂×C₄×C₈	1	2	yes	—
89	C₂×D₁₇	#504	1	4	yes	—
90	#595	—	2	8	no	—
91	C₄×C₁₇	—	2	2	no	—
92	C₄×C₁₇	C₄³	1	1	yes	characteristic
93	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
94	Dic₁₇	—	2	2	no	—
95	Dic₁₇	C₂×C₄×C₈	1	2	yes	—
96	C₂²×C₁₆	—	17	1	no	—
97	C₂²×C₁₆	—	17	1	no	—
98	C₂²×C₁₆	—	17	2	no	—
99	C₂×#97	—	17	2	no	—
100	C₂×#97	—	17	1	no	—
101	C₂×C₄×C₈	—	17	2	no	—
102	C₂×C₄×C₈	—	17	1	no	—
103	#376	—	17	1	no	—
104	#346	—	17	8	no	—
105	#346	—	17	2	no	—
106	#346	—	17	1	no	—
107	#346	#595	1	1	yes	characteristic, complemented
108	C₄×C₁₆	—	17	8	no	—
109	C₄×C₁₆	—	17	2	no	—
110	C₄×C₁₆	—	17	2	no	—
111	C₂×C₁₇	C₄²×C₈	1	1	yes	characteristic
112	C₂×C₁₇	#2108	1	2	yes	—
113	D₁₇	#2108	1	4	yes	—
114	C₂²×C₈	—	17	2	no	—
115	C₂²×C₈	—	17	1	no	—
116	C₂²×C₈	—	17	1	no	—
117	C₂×C₄²	—	17	2	no	—
118	C₂×C₄²	—	17	1	no	—
119	C₂×C₁₆	—	17	4	no	—
120	C₂×C₁₆	—	17	2	no	—
121	C₂×C₁₆	—	17	2	no	—
122	C₂×C₁₆	—	17	4	no	—
123	C₂×C₁₆	—	17	2	no	—
124	C₂×C₁₆	—	17	4	no	—
125	C₂×C₁₆	—	17	4	no	—
126	C₂×C₁₆	C₂×#595	1	2	yes	—
127	#97	—	17	8	no	—
128	#97	—	17	4	no	—
129	C₄×C₈	—	17	4	no	—
130	C₄×C₈	—	17	4	no	—
131	C₄×C₈	—	17	1	no	—
132	C₄×C₈	—	17	1	no	—
133	C₄×C₈	—	17	1	no	—
134	C₄×C₈	C₂×#595	1	1	yes	characteristic
135	#95	—	17	4	no	—
136	C₁₇	#12539	1	1	yes	characteristic, complemented, Sylow
137	C₂²×C₄	—	17	1	no	—
138	C₂²×C₄	—	17	4	no	—
139	C₂²×C₄	—	17	2	no	—
140	C₂×C₈	—	17	4	no	—
141	C₂×C₈	—	17	4	no	—
142	C₂×C₈	—	17	4	no	—
143	C₂×C₈	—	17	1	no	—
144	C₂×C₈	—	17	1	no	—
145	C₂×C₈	—	17	2	no	—
146	C₂×C₈	—	17	2	no	—
147	C₂×C₈	—	17	4	no	—
148	C₂×C₈	C₄×#595	1	1	yes	characteristic
149	C₂×C₈	C₂²×#595	1	1	yes	characteristic
150	C₄²	—	17	4	no	—
151	C₄²	—	17	4	no	—
152	C₄²	—	17	1	no	—
153	C₄²	—	17	2	no	—
154	C₄²	C₄×#595	1	1	yes	characteristic
155	C₁₆	—	17	4	no	—
156	C₁₆	—	17	4	no	—
157	C₁₆	—	17	4	no	—
158	C₁₆	C₄×#595	1	4	yes	—
159	C₂³	—	17	1	no	—
160	C₂×C₄	—	17	1	no	—
161	C₂×C₄	—	17	2	no	—
162	C₂×C₄	—	17	2	no	—
163	C₂×C₄	—	17	8	no	—
164	C₂×C₄	—	17	2	no	—
165	C₂×C₄	—	34	4	no	—
166	C₂×C₄	—	34	8	no	—
167	C₂×C₄	C₈×#595	1	2	yes	—
168	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
169	C₈	—	17	8	no	—
170	C₈	—	17	1	no	—
171	C₈	—	17	1	no	—
172	C₈	—	17	2	no	—
173	C₈	C₈×#595	1	2	yes	—
174	C₈	C₂×C₄×#595	1	2	yes	—
175	C₂²	—	17	2	no	—
176	C₂²	—	17	4	no	—
177	C₂²	C₂×C₈×#595	1	1	yes	characteristic
178	C₄	—	2	2	no	—
179	C₄	—	17	2	no	—
180	C₄	—	34	8	no	—
181	C₄	—	34	2	no	—
182	C₄	C₄²×#595	1	1	yes	characteristic
183	C₄	C₂×C₈×#595	1	1	yes	characteristic
184	C₂	—	17	4	no	—
185	C₂	C₄×C₈×#595	1	1	yes	characteristic
186	C₂	#14544996	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×#595
commutator	C₂×C₁₇	C₄²×C₈
Fitting	C₁₇×#346	C₄
socle	C₂²×C₁₇	C₂×C₄×C₈
prime radical	C₂²×D₁₇	C₂²×C₈
cosocle	C₂×C₈×D₁₇	C₂³
hypercenter	#346	#595
hypocenter	C₁₇	#12539
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
12. #11763696	C₄	semidirect
13. #11763695	C₄	semidirect
14. C₄×#63216	C₄	semidirect
15. C₁₆×#595	C₄	semidirect
18. #11762585	C₄	semidirect
19. #11762584	C₄	semidirect
20. C₁₇×#346	C₄	semidirect
107. #346	#595	semidirect
136. C₁₇	#12539	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11763696	2
C₄×#10587529	2
C₂×C₁₆×#595	2
#14544440	2
D₁₇×#346	2
#12539	17