Subgroups — #17948599

Order 4352.

282 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11763695	C₂	1	1	yes	maximal, characteristic
2	C₂×#11763672	C₂	1	1	yes	maximal, characteristic
3	#107×Dic₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×#63216	—	2	1	no	—
5	C₂×C₄⋊#3624	—	2	1	no	—
6	#11763695	—	2	1	no	—
7	#11763695	C₄	1	2	yes	complemented
8	#11763672	—	2	1	no	—
9	#11763672	C₄	1	2	yes	complemented
10	C₂×#10587489	C₄	1	1	yes	characteristic
11	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×Dic₁₇	—	2	1	no	—
13	#11762571	—	2	1	no	—
14	C₂×C₁₇×#107	C₄	1	1	yes	characteristic
15	C₂²×#3624	—	4	1	no	—
16	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
18	C₂×C₄⋊Dic₁₇	—	2	1	no	—
19	C₂×C₄×Dic₁₇	—	4	1	no	—
20	C₂×C₄×Dic₁₇	D₄	1	1	yes	characteristic
21	C₂²×#3622	D₄	1	1	yes	characteristic
22	C₄⋊#3624	—	2	2	no	—
23	C₄⋊#3624	—	4	1	no	—
24	C₂×#63216	—	2	2	no	—
25	C₂×#63216	—	2	2	no	—
26	C₂×#63216	—	2	2	no	—
27	C₁₇×#107	—	2	1	no	—
28	C₁₇×#107	C₈	1	2	yes	complemented
29	#10587502	—	4	1	no	—
30	#10587489	—	2	1	no	—
31	#10587489	C₈	1	2	yes	complemented
32	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
33	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
34	C₈×Dic₁₇	D₄	1	1	yes	characteristic
35	C₈×Dic₁₇	Q₈	1	1	yes	characteristic
36	C₂²×C₄×C₁₇	—	4	1	no	—
37	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
38	C₂²×Dic₁₇	—	4	1	no	—
39	C₂²×Dic₁₇	D₈	1	1	yes	characteristic
40	C₂²×Dic₁₇	SD₁₆	1	1	yes	characteristic
41	C₂×#3624	—	4	2	no	—
42	C₂×#3624	—	8	1	no	—
43	C₂×#3624	—	8	1	no	—
44	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
45	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
47	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
48	C₂×C₈×C₁₇	M₁₆	1	1	yes	characteristic
49	C₂×C₈×C₁₇	M₁₆	1	1	yes	characteristic
50	C₄⋊C₄×C₁₇	—	2	2	no	—
51	C₄⋊C₄×C₁₇	—	4	1	no	—
52	C₄⋊Dic₁₇	—	2	2	no	—
53	C₄⋊Dic₁₇	—	4	1	no	—
54	C₄×Dic₁₇	—	8	1	no	—
55	C₄×Dic₁₇	—	8	1	no	—
56	C₄×Dic₁₇	C₂²⋊C₄	1	1	yes	characteristic
57	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
58	C₄×Dic₁₇	SD₁₆	1	1	yes	characteristic
59	C₄×Dic₁₇	Q₁₆	1	1	yes	characteristic
60	C₂×#3622	—	2	1	no	—
61	C₂×#3622	—	2	1	no	—
62	C₂×#3622	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
64	#63216	—	2	4	no	—
65	#7171	—	17	1	no	maximal, Sylow
66	C₂³×C₁₇	#102	1	1	yes	characteristic
67	C₂×C₄×C₁₇	—	4	2	no	—
68	C₂×C₄×C₁₇	—	8	1	no	—
69	C₂×C₄×C₁₇	—	8	1	no	—
70	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
71	C₂×C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
72	C₂×C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
73	C₂×C₄×C₁₇	#103	1	1	yes	characteristic
74	C₂×C₄×C₁₇	#104	1	1	yes	characteristic
75	C₂×C₄×C₁₇	#104	1	1	yes	characteristic
76	C₂×Dic₁₇	—	2	1	no	—
77	C₂×Dic₁₇	—	2	1	no	—
78	C₂×Dic₁₇	—	4	2	no	—
79	C₂×Dic₁₇	—	8	1	no	—
80	C₂×Dic₁₇	—	8	1	no	—
81	C₂×Dic₁₇	#102	1	1	yes	characteristic
82	C₂×Dic₁₇	#103	1	1	yes	characteristic
83	C₂×Dic₁₇	#106	1	1	yes	characteristic
84	C₂×Dic₁₇	#107	1	1	yes	characteristic
85	C₂×Dic₁₇	D₁₆	1	1	yes	characteristic
86	C₂×Dic₁₇	SD₃₂	1	1	yes	characteristic
87	C₂×Dic₁₇	SD₃₂	1	1	yes	characteristic
88	C₂×Dic₁₇	Q₃₂	1	1	yes	characteristic
89	#3624	—	8	2	no	—
90	C₈×C₁₇	C₄×C₈	1	1	yes	characteristic
91	C₈×C₁₇	#97	1	1	yes	characteristic
92	C₈×C₁₇	C₄⋊C₈	1	1	yes	characteristic
93	C₈×C₁₇	C₄⋊C₈	1	1	yes	characteristic
94	#3622	—	2	1	no	—
95	#3622	—	2	1	no	—
96	C₂×C₄×C₁₆	—	17	1	no	—
97	C₄×#107	—	17	1	no	—
98	C₂×#335	—	17	1	no	—
99	C₂²×C₁₇	D₄⋊C₈	1	1	yes	characteristic
100	C₂²×C₁₇	D₄⋊C₈	1	1	yes	characteristic
101	C₂²×C₁₇	#340	1	1	yes	characteristic
102	C₂²×C₁₇	#357	1	1	yes	characteristic
103	C₂²×C₁₇	#358	1	1	yes	characteristic
104	C₂²×C₁₇	#359	1	1	yes	characteristic
105	C₂²×C₁₇	#359	1	1	yes	characteristic
106	C₄×C₁₇	—	8	2	no	—
107	C₄×C₁₇	Q₈⋊C₈	1	1	yes	characteristic
108	C₄×C₁₇	Q₈⋊C₈	1	1	yes	characteristic
109	C₄×C₁₇	#336	1	1	yes	characteristic
110	C₄×C₁₇	#339	1	1	yes	characteristic
111	Dic₁₇	—	2	1	no	—
112	Dic₁₇	—	2	1	no	—
113	Dic₁₇	—	8	2	no	—
114	Dic₁₇	#357	1	1	yes	characteristic
115	Dic₁₇	#358	1	1	yes	characteristic
116	Dic₁₇	#366	1	1	yes	characteristic
117	Dic₁₇	#367	1	1	yes	characteristic
118	C₂²×C₁₆	—	34	1	no	—
119	C₂×#107	—	17	1	no	—
120	C₂×#107	#595	1	1	yes	characteristic
121	C₂×C₄⋊C₈	—	34	1	no	—
122	C₂×C₄×C₈	—	17	1	no	—
123	C₄×C₄⋊C₄	—	34	1	no	—
124	C₄×C₁₆	—	17	2	no	—
125	C₄×C₁₆	—	34	1	no	—
126	#340	—	34	1	no	—
127	#335	—	17	2	no	—
128	#335	—	34	1	no	—
129	C₂×C₁₇	#1279	1	1	yes	characteristic
130	C₂×C₁₇	#1331	1	1	yes	characteristic
131	C₂×C₁₇	#1331	1	1	yes	characteristic
132	C₂×C₁₇	#1332	1	1	yes	characteristic
133	C₂×C₁₇	#1332	1	1	yes	characteristic
134	C₂×C₁₇	#1380	1	1	yes	characteristic
135	C₂×C₁₇	#1382	1	1	yes	characteristic
136	C₂²×C₈	—	17	1	no	—
137	C₂²×C₈	—	68	1	no	—
138	C₂²×C₈	C₂×#595	1	1	yes	characteristic
139	C₂×C₄⋊C₄	—	2	1	no	—
140	C₂×C₄⋊C₄	—	34	1	no	—
141	C₂×C₄²	—	17	1	no	—
142	C₂×C₄²	—	68	1	no	—
143	C₂×C₁₆	—	34	2	no	—
144	C₂×C₁₆	—	34	2	no	—
145	C₂×C₁₆	—	34	2	no	—
146	#107	—	2	1	no	—
147	#107	—	17	2	no	—
148	#107	—	34	1	no	—
149	#107	#3624	1	2	yes	complemented
150	C₄⋊C₈	—	34	2	no	—
151	C₄⋊C₈	—	68	1	no	—
152	C₄×C₈	—	17	1	no	—
153	C₄×C₈	—	17	1	no	—
154	C₄×C₈	—	17	1	no	—
155	C₄×C₈	—	17	1	no	—
156	#95	—	68	1	no	—
157	C₁₇	#7171	1	1	yes	characteristic, complemented, Sylow
158	C₂²×C₄	—	4	1	no	—
159	C₂²×C₄	—	17	1	no	—
160	C₂²×C₄	—	17	1	no	—
161	C₂²×C₄	—	68	1	no	—
162	C₂²×C₄	C₂²⋊#595	1	1	yes	characteristic
163	C₂×C₈	—	17	1	no	—
164	C₂×C₈	—	17	1	no	—
165	C₂×C₈	—	34	1	no	—
166	C₂×C₈	—	34	1	no	—
167	C₂×C₈	—	68	2	no	—
168	C₂×C₈	—	136	1	no	—
169	C₂×C₈	—	136	1	no	—
170	C₂×C₈	#63242	1	1	yes	characteristic
171	C₂×C₈	#63243	1	1	yes	characteristic
172	C₂×C₈	C₄×#595	1	1	yes	characteristic
173	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
174	C₂×C₈	C₂×#3624	1	1	yes	characteristic
175	C₂×C₈	#63247	1	1	yes	characteristic
176	C₄⋊C₄	—	2	2	no	—
177	C₄⋊C₄	—	4	1	no	—
178	C₄⋊C₄	—	34	2	no	—
179	C₄⋊C₄	—	68	1	no	—
180	C₄²	—	17	1	no	—
181	C₄²	—	17	1	no	—
182	C₄²	—	17	1	no	—
183	C₄²	—	17	1	no	—
184	C₄²	—	136	1	no	—
185	C₄²	—	136	1	no	—
186	C₁₆	—	34	4	no	—
187	C₂³	#10587547	1	1	yes	characteristic
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	—	8	1	no	—
190	C₂×C₄	—	8	1	no	—
191	C₂×C₄	—	17	1	no	—
192	C₂×C₄	—	17	1	no	—
193	C₂×C₄	—	17	1	no	—
194	C₂×C₄	—	17	1	no	—
195	C₂×C₄	—	17	1	no	—
196	C₂×C₄	—	17	1	no	—
197	C₂×C₄	—	17	1	no	—
198	C₂×C₄	—	17	1	no	—
199	C₂×C₄	—	34	1	no	—
200	C₂×C₄	—	34	1	no	—
201	C₂×C₄	—	68	2	no	—
202	C₂×C₄	—	136	1	no	—
203	C₂×C₄	—	136	1	no	—
204	C₂×C₄	#10587543	1	1	yes	characteristic
205	C₂×C₄	(C₂×#595)⋊C₄	1	1	yes	characteristic
206	C₂×C₄	#10587548	1	1	yes	characteristic
207	C₂×C₄	#10587549	1	1	yes	characteristic
208	C₂×C₄	#10587550	1	1	yes	characteristic
209	C₂×C₄	C₂²⋊#3624	1	1	yes	characteristic
210	C₈	—	34	1	no	—
211	C₈	—	34	1	no	—
212	C₈	—	136	2	no	—
213	C₈	C₄×#3624	1	1	yes	characteristic
214	C₈	C₄⋊#3624	1	1	yes	characteristic
215	C₈	#10587542	1	1	yes	characteristic
216	C₈	#10587544	1	1	yes	characteristic
217	C₂²	D₄⋊#3624	1	1	yes	characteristic
218	C₂²	#11763657	1	1	yes	characteristic
219	C₂²	#11763682	1	1	yes	characteristic
220	C₂²	#11763721	1	1	yes	characteristic
221	C₂²	#11763722	1	1	yes	characteristic
222	C₂²	#11763723	1	1	yes	characteristic
223	C₂²	#11763724	1	1	yes	characteristic
224	C₄	—	8	2	no	—
225	C₄	—	17	1	no	—
226	C₄	—	17	1	no	—
227	C₄	—	17	1	no	—
228	C₄	—	17	1	no	—
229	C₄	—	34	1	no	—
230	C₄	—	34	1	no	—
231	C₄	—	136	2	no	—
232	C₄	Q₈⋊#3624	1	1	yes	characteristic
233	C₄	#11763659	1	1	yes	characteristic
234	C₄	#11763675	1	1	yes	characteristic
235	C₄	#11763679	1	1	yes	characteristic
236	C₂	#14543620	1	1	yes	characteristic
237	C₂	#14543738	1	1	yes	characteristic
238	C₂	#14543739	1	1	yes	characteristic
239	C₂	#14543740	1	1	yes	characteristic
240	C₂	#14543741	1	1	yes	characteristic
241	C₂	#14543841	1	1	yes	characteristic
242	C₂	#14543845	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10587547
commutator	C₈×C₁₇	C₄×C₈
Frattini	C₂²×C₈	C₂×#595
Fitting	C₂×C₁₇×#107	C₄
socle, prime radical	C₂³×C₁₇	#102
cosocle	C₂×C₈×Dic₁₇	C₂²
hypercenter	C₂×#107	#595
hypocenter	C₁₇	#7171
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#107

Complements

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

N	H ≅ G/N	type
7. #11763695	C₄	semidirect
9. #11763672	C₄	semidirect
28. C₁₇×#107	C₈	semidirect
31. #10587489	C₈	semidirect
149. #107	#3624	semidirect
157. C₁₇	#7171	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11763695	2
C₂×#11763672	2
#107×Dic₁₇	2
#7171	17