Subgroups — #17981560

Order 4352.

574 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545918	C₂	1	2	yes	maximal
2	C₂×#11763893	C₂	1	2	yes	maximal
3	C₂×C₈×#3633	C₂	1	2	yes	maximal
4	C₄×C₈×#595	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×#3633	C₂²	1	4	yes	—
6	(C₂×#3633)⋊C₄	C₄	1	8	yes	—
7	#11763893	C₄	1	8	yes	complemented
8	C₈×#3633	C₄	1	8	yes	complemented
9	C₄×#63242	C₄	1	1	yes	characteristic
10	C₂×C₈×#595	C₄	1	1	yes	characteristic
11	C₂×C₈×#595	C₄	1	1	yes	characteristic
12	C₂×C₈×#595	C₂²	1	1	yes	characteristic
13	C₂×C₈×#595	C₂²	1	1	yes	characteristic
14	C₄²×#595	C₂²	1	1	yes	characteristic
15	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic
16	C₂²×#3633	C₂×C₄	1	8	yes	—
17	C₂×C₄×#595	C₂×C₄	1	4	yes	—
18	C₂×C₄×#595	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×#595	C₂³	1	1	yes	characteristic
20	C₂×#63242	C₂×C₄	1	1	yes	characteristic
21	C₂×#63242	C₂×C₄	1	1	yes	characteristic
22	C₄×#3633	C₂×C₄	1	8	yes	—
23	C₄×#3633	C₂×C₄	1	8	yes	—
24	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
26	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
27	C₄×#3624	C₈	1	4	yes	complemented
28	C₈×#595	C₈	1	4	yes	complemented
29	C₈×#595	C₈	1	4	yes	complemented
30	C₈×#595	C₂×C₄	1	4	yes	—
31	C₈×#595	C₂×C₄	1	4	yes	—
32	C₄×C₈×C₁₇	C₈	1	1	yes	characteristic, complemented
33	C₈×Dic₁₇	C₈	1	1	yes	characteristic, complemented
34	C₈×Dic₁₇	C₈	1	1	yes	characteristic, complemented
35	C₄×#3622	C₈	1	1	yes	characteristic, complemented
36	C₂²×#595	C₄²	1	2	yes	—
37	C₂²×#595	C₂²×C₄	1	2	yes	—
38	C₂×#3633	—	2	16	no	—
39	C₂×#3633	C₄²	1	16	yes	—
40	C₂×C₄×D₁₇	C₄²	1	2	yes	—
41	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
42	C₂×#3624	C₂×C₈	1	2	yes	—
43	C₂×#3624	C₂×C₈	1	2	yes	—
44	C₄×#595	—	2	8	no	—
45	C₄×#595	C₂×C₈	1	2	yes	—
46	C₄×#595	C₂×C₈	1	2	yes	—
47	C₄×#595	C₂²×C₄	1	2	yes	—
48	C₄×#595	C₂²×C₄	1	2	yes	—
49	#63242	C₄²	1	2	yes	—
50	#63242	C₄²	1	2	yes	—
51	#63242	C₂×C₈	1	2	yes	—
52	#63242	C₂×C₈	1	2	yes	—
53	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
54	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
55	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
56	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
57	C₄×Dic₁₇	C₂×C₈	1	2	yes	—
58	C₂×#3622	C₂×C₈	1	1	yes	characteristic
59	C₂×#3622	C₂×C₈	1	1	yes	characteristic
60	C₈×D₁₇	C₄²	1	2	yes	—
61	C₈×D₁₇	C₄²	1	2	yes	—
62	C₈×D₁₇	C₂×C₈	1	2	yes	—
63	C₈×D₁₇	C₂×C₈	1	2	yes	—
64	#7841	—	17	1	no	maximal, Sylow
65	C₂²×D₁₇	C₂×C₄²	1	1	yes	characteristic
66	C₂×#595	—	2	4	no	—
67	C₂×#595	C₄×C₈	1	4	yes	—
68	C₂×#595	C₂×C₄²	1	4	yes	—
69	C₂×#595	#131	1	8	yes	—
70	#3633	—	2	16	no	—
71	C₂×C₄×C₁₇	C₄×C₈	1	2	yes	—
72	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
73	C₂×Dic₁₇	C₄×C₈	1	2	yes	—
74	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
75	C₄×D₁₇	—	2	4	no	—
76	C₄×D₁₇	C₂×C₄²	1	1	yes	characteristic
77	C₄×D₁₇	C₂×C₄²	1	1	yes	characteristic
78	C₄×D₁₇	C₂²×C₈	1	1	yes	characteristic
79	C₄×D₁₇	C₂²×C₈	1	1	yes	characteristic
80	#3624	C₄×C₈	1	4	yes	—
81	#3624	C₄×C₈	1	4	yes	—
82	C₈×C₁₇	C₄×C₈	1	2	yes	—
83	C₈×C₁₇	C₄×C₈	1	2	yes	—
84	#3622	C₄×C₈	1	2	yes	—
85	#3622	C₄×C₈	1	2	yes	—
86	#1744	—	17	2	no	—
87	C₄²×C₈	—	17	1	no	—
88	C₂×#322	—	17	2	no	—
89	C₂×C₈²	—	17	2	no	—
90	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
91	C₂×D₁₇	C₄³	1	1	yes	characteristic
92	C₂×D₁₇	C₂×C₄×C₈	1	1	yes	characteristic
93	C₂×D₁₇	#405	1	4	yes	—
94	#595	—	2	4	no	—
95	#595	#405	1	8	yes	—
96	C₄×C₁₇	—	2	2	no	—
97	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
98	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
99	Dic₁₇	—	2	2	no	—
100	Dic₁₇	C₂×C₄×C₈	1	1	yes	characteristic
101	Dic₁₇	C₂×C₄×C₈	1	1	yes	characteristic
102	C₂×C₄×C₈	—	17	1	no	—
103	C₂×C₄×C₈	—	17	1	no	—
104	C₂×C₄×C₈	—	17	1	no	—
105	C₂×C₄×C₈	—	17	1	no	—
106	C₂×C₄×C₈	—	17	1	no	—
107	C₂×C₄×C₈	—	17	4	no	—
108	C₂×C₄×C₈	—	17	1	no	—
109	C₄³	—	17	1	no	—
110	#336	—	17	8	no	—
111	#322	—	17	8	no	—
112	C₈²	—	17	8	no	—
113	C₂×C₁₇	#1450	1	2	yes	—
114	C₂×C₁₇	C₄²×C₈	1	1	yes	characteristic
115	D₁₇	#1450	1	2	yes	—
116	D₁₇	#1726	1	2	yes	—
117	C₂²×C₈	—	17	1	no	—
118	C₂²×C₈	—	17	1	no	—
119	C₂²×C₈	—	17	1	no	—
120	C₂²×C₈	—	17	1	no	—
121	C₂²×C₈	—	17	8	no	—
122	C₂×C₄²	—	17	1	no	—
123	C₂×C₄²	—	17	1	no	—
124	C₂×C₄²	—	17	1	no	—
125	C₂×C₄²	—	17	4	no	—
126	C₄×C₈	—	17	8	no	—
127	C₄×C₈	—	17	8	no	—
128	C₄×C₈	—	17	4	no	—
129	C₄×C₈	—	17	4	no	—
130	C₄×C₈	—	17	4	no	—
131	C₄×C₈	—	17	4	no	—
132	C₄×C₈	—	17	4	no	—
133	C₄×C₈	—	17	1	no	—
134	C₄×C₈	—	17	1	no	—
135	C₄×C₈	—	17	1	no	—
136	C₄×C₈	#3633	1	1	yes	characteristic, complemented
137	C₁₇	#7841	1	1	yes	characteristic, complemented, Sylow
138	C₂²×C₄	—	17	2	no	—
139	C₂²×C₄	—	17	1	no	—
140	C₂²×C₄	—	17	2	no	—
141	C₂²×C₄	—	17	2	no	—
142	C₂×C₈	—	17	2	no	—
143	C₂×C₈	—	17	2	no	—
144	C₂×C₈	—	17	2	no	—
145	C₂×C₈	—	17	2	no	—
146	C₂×C₈	—	17	2	no	—
147	C₂×C₈	—	17	2	no	—
148	C₂×C₈	—	17	1	no	—
149	C₂×C₈	—	17	1	no	—
150	C₂×C₈	—	17	2	no	—
151	C₂×C₈	—	17	2	no	—
152	C₂×C₈	—	17	2	no	—
153	C₂×C₈	—	17	2	no	—
154	C₂×C₈	—	17	16	no	—
155	C₂×C₈	—	34	16	no	—
156	C₂×C₈	C₂×#3633	1	1	yes	characteristic
157	C₂×C₈	C₂×#3633	1	1	yes	characteristic
158	C₄²	—	17	2	no	—
159	C₄²	—	17	2	no	—
160	C₄²	—	17	2	no	—
161	C₄²	—	17	2	no	—
162	C₄²	—	17	2	no	—
163	C₄²	—	17	1	no	—
164	C₄²	—	34	8	no	—
165	C₄²	C₂×#3633	1	1	yes	characteristic
166	C₂³	—	17	1	no	—
167	C₂×C₄	—	17	4	no	—
168	C₂×C₄	—	17	8	no	—
169	C₂×C₄	—	17	1	no	—
170	C₂×C₄	—	17	1	no	—
171	C₂×C₄	—	17	1	no	—
172	C₂×C₄	—	17	1	no	—
173	C₂×C₄	—	17	1	no	—
174	C₂×C₄	—	17	4	no	—
175	C₂×C₄	—	17	2	no	—
176	C₂×C₄	—	34	4	no	—
177	C₂×C₄	—	34	4	no	—
178	C₂×C₄	C₄×#3633	1	2	yes	—
179	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
180	C₈	—	17	4	no	—
181	C₈	—	17	4	no	—
182	C₈	—	17	2	no	—
183	C₈	—	17	2	no	—
184	C₈	—	34	16	no	—
185	C₈	C₄×#3633	1	2	yes	—
186	C₈	C₄×#3633	1	2	yes	—
187	C₂²	—	17	4	no	—
188	C₂²	—	17	1	no	—
189	C₂²	—	17	1	no	—
190	C₂²	C₂×C₄×#3633	1	1	yes	characteristic
191	C₄	—	2	2	no	—
192	C₄	—	17	8	no	—
193	C₄	—	17	1	no	—
194	C₄	—	17	1	no	—
195	C₄	—	34	4	no	—
196	C₄	—	34	2	no	—
197	C₄	C₂×C₄×#3633	1	1	yes	characteristic
198	C₄	C₂×C₄×#3633	1	1	yes	characteristic
199	C₂	—	17	2	no	—
200	C₂	—	17	2	no	—
201	C₂	#14545893	1	2	yes	—
202	C₂	C₄²×#3633	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×#3633
commutator	C₂×C₁₇	C₄²×C₈
Frattini	C₂×C₄	C₂²×#3633
Fitting	C₄×C₈×C₁₇	C₈
socle	C₂²×C₁₇	C₂×C₄×C₈
prime radical	C₂²×D₁₇	C₂×C₄²
cosocle	C₂×C₄×#595	C₂³
hypercenter	C₄×C₈	#3633
hypocenter	C₁₇	#7841
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
7. #11763893	C₄	semidirect
8. C₈×#3633	C₄	semidirect
27. C₄×#3624	C₈	semidirect
28. C₈×#595	C₈	semidirect
29. C₈×#595	C₈	semidirect
32. C₄×C₈×C₁₇	C₈	semidirect
33. C₈×Dic₁₇	C₈	semidirect
34. C₈×Dic₁₇	C₈	semidirect
35. C₄×#3622	C₈	semidirect
136. C₄×C₈	#3633	semidirect
137. C₁₇	#7841	semidirect

Maximal subgroups

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

subgroup	index
#14545918	2
C₂×#11763893	2
C₂×C₈×#3633	2
C₄×C₈×#595	2
#7841	17