Subgroups — #17034604

Order 4352.

1062 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14528927	C₂	1	2	yes	maximal, complemented
2	#14528901	C₂	1	2	yes	maximal, complemented
3	#14528852	C₂	1	2	yes	maximal
4	#14528764	C₂	1	2	yes	maximal
5	C₄×C₄⋊#3622	C₂	1	2	yes	maximal, complemented
6	C₄×C₂²⋊#3622	C₂	1	2	yes	maximal
7	#14528530	C₂	1	2	yes	maximal, complemented
8	C₂×C₄³×C₁₇	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄⋊#3622	C₂²	1	4	yes	—
10	C₂×C₂²⋊#3622	C₂²	1	4	yes	—
11	C₂×C₄×#3622	C₂²	1	4	yes	—
12	#11762564	C₂²	1	4	yes	—
13	#11762564	C₂²	1	4	yes	—
14	#11762564	C₂²	1	4	yes	—
15	#11762564	C₂²	1	4	yes	—
16	C₂²×C₄²×C₁₇	C₄	1	1	yes	characteristic
17	C₂²×C₄²×C₁₇	C₄	1	1	yes	characteristic
18	C₂²×C₄²×C₁₇	C₄	1	1	yes	characteristic
19	C₂²×C₄²×C₁₇	C₄	1	1	yes	characteristic
20	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
23	C₄³×C₁₇	C₄	1	1	yes	characteristic
24	C₄³×C₁₇	C₄	1	1	yes	characteristic
25	C₄³×C₁₇	C₄	1	1	yes	characteristic
26	C₄³×C₁₇	C₄	1	1	yes	characteristic
27	C₄³×C₁₇	C₂²	1	1	yes	characteristic
28	C₄³×C₁₇	C₂²	1	1	yes	characteristic
29	C₄³×C₁₇	C₂²	1	1	yes	characteristic
30	C₄³×C₁₇	C₂²	1	1	yes	characteristic
31	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
38	C₂×C₄²×C₁₇	—	2	4	no	—
39	C₂×C₄²×C₁₇	—	2	4	no	—
40	C₂×C₄²×C₁₇	—	2	4	no	—
41	C₂×C₄²×C₁₇	—	2	4	no	—
42	C₂×C₄²×C₁₇	—	2	4	no	—
43	C₂×C₄²×C₁₇	—	2	4	no	—
44	C₂×C₄²×C₁₇	C₈	1	8	yes	complemented
45	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
73	C₂²×#3622	C₂³	1	8	yes	—
74	C₂²⋊#3622	—	2	8	no	—
75	C₄⋊#3622	—	2	8	no	—
76	C₄×#3622	—	2	8	no	—
77	C₂⁴×C₁₇	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₇	—	2	2	no	—
79	C₂²×C₄×C₁₇	—	2	2	no	—
80	C₂²×C₄×C₁₇	—	2	2	no	—
81	C₂²×C₄×C₁₇	—	2	2	no	—
82	C₂²×C₄×C₁₇	—	2	2	no	—
83	C₂²×C₄×C₁₇	—	2	2	no	—
84	C₂²×C₄×C₁₇	—	2	2	no	—
85	C₂²×C₄×C₁₇	—	2	2	no	—
86	C₂²×C₄×C₁₇	—	2	2	no	—
87	C₂²×C₄×C₁₇	—	2	2	no	—
88	C₂²×C₄×C₁₇	—	2	2	no	—
89	C₂²×C₄×C₁₇	—	2	2	no	—
90	C₂²×C₄×C₁₇	—	2	2	no	—
91	C₂²×C₄×C₁₇	—	2	2	no	—
92	C₂²×C₄×C₁₇	—	2	2	no	—
93	C₂²×C₄×C₁₇	—	2	2	no	—
94	C₂²×C₄×C₁₇	C₂×C₈	1	4	yes	—
95	C₂²×C₄×C₁₇	C₂×C₈	1	4	yes	—
96	C₂²×C₄×C₁₇	C₂×C₈	1	4	yes	—
97	C₂²×C₄×C₁₇	M₁₆	1	4	yes	—
98	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₇	#41	1	4	yes	—
112	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
113	C₄²×C₁₇	—	2	2	no	—
114	C₄²×C₁₇	—	2	2	no	—
115	C₄²×C₁₇	—	2	2	no	—
116	C₄²×C₁₇	—	2	2	no	—
117	C₄²×C₁₇	—	2	2	no	—
118	C₄²×C₁₇	—	2	2	no	—
119	C₄²×C₁₇	—	2	2	no	—
120	C₄²×C₁₇	—	2	2	no	—
121	C₄²×C₁₇	—	2	2	no	—
122	C₄²×C₁₇	—	2	2	no	—
123	C₄²×C₁₇	—	2	2	no	—
124	C₄²×C₁₇	—	2	2	no	—
125	C₄²×C₁₇	—	2	2	no	—
126	C₄²×C₁₇	—	2	2	no	—
127	C₄²×C₁₇	—	2	2	no	—
128	C₄²×C₁₇	—	2	2	no	—
129	C₄²×C₁₇	—	2	2	no	—
130	C₄²×C₁₇	—	2	2	no	—
131	C₄²×C₁₇	—	2	2	no	—
132	C₄²×C₁₇	—	2	2	no	—
133	C₄²×C₁₇	C₂×C₈	1	4	yes	—
134	C₄²×C₁₇	C₂×C₈	1	4	yes	—
135	C₄²×C₁₇	C₂×C₈	1	4	yes	—
136	C₄²×C₁₇	C₂×C₈	1	4	yes	—
137	C₄²×C₁₇	M₁₆	1	4	yes	—
138	C₄²×C₁₇	M₁₆	1	4	yes	—
139	C₄²×C₁₇	#41	1	4	yes	—
140	C₄²×C₁₇	#41	1	4	yes	—
141	C₂×#3622	—	2	8	no	—
142	C₂×#3622	—	2	8	no	—
143	C₂×#3622	—	2	8	no	—
144	#20777	—	17	1	no	maximal, Sylow
145	C₂³×C₁₇	—	2	1	no	—
146	C₂³×C₁₇	—	2	1	no	—
147	C₂³×C₁₇	—	2	1	no	—
148	C₂³×C₁₇	—	2	1	no	—
149	C₂³×C₁₇	#117	1	2	yes	—
150	C₂³×C₁₇	C₂²×C₈	1	2	yes	—
151	C₂³×C₁₇	C₂×M₁₆	1	2	yes	—
152	C₂³×C₁₇	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₇	—	2	8	no	—
154	C₂×C₄×C₁₇	—	2	8	no	—
155	C₂×C₄×C₁₇	—	2	1	no	—
156	C₂×C₄×C₁₇	—	2	1	no	—
157	C₂×C₄×C₁₇	—	2	1	no	—
158	C₂×C₄×C₁₇	—	2	1	no	—
159	C₂×C₄×C₁₇	—	2	1	no	—
160	C₂×C₄×C₁₇	—	2	1	no	—
161	C₂×C₄×C₁₇	—	2	1	no	—
162	C₂×C₄×C₁₇	—	2	1	no	—
163	C₂×C₄×C₁₇	—	2	1	no	—
164	C₂×C₄×C₁₇	—	2	1	no	—
165	C₂×C₄×C₁₇	—	2	1	no	—
166	C₂×C₄×C₁₇	—	2	1	no	—
167	C₂×C₄×C₁₇	—	2	1	no	—
168	C₂×C₄×C₁₇	—	2	1	no	—
169	C₂×C₄×C₁₇	—	2	1	no	—
170	C₂×C₄×C₁₇	—	2	1	no	—
171	C₂×C₄×C₁₇	—	2	1	no	—
172	C₂×C₄×C₁₇	—	2	1	no	—
173	C₂×C₄×C₁₇	—	2	1	no	—
174	C₂×C₄×C₁₇	—	2	1	no	—
175	C₂×C₄×C₁₇	—	2	8	no	—
176	C₂×C₄×C₁₇	—	2	8	no	—
177	C₂×C₄×C₁₇	—	2	8	no	—
178	C₂×C₄×C₁₇	—	2	8	no	—
179	C₂×C₄×C₁₇	—	2	8	no	—
180	C₂×C₄×C₁₇	#117	1	2	yes	—
181	C₂×C₄×C₁₇	#117	1	2	yes	—
182	C₂×C₄×C₁₇	#117	1	2	yes	—
183	C₂×C₄×C₁₇	#117	1	2	yes	—
184	C₂×C₄×C₁₇	#117	1	2	yes	—
185	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
186	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
187	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
188	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
189	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
190	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
191	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
192	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
193	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
194	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
195	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
196	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
197	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
198	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
199	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
200	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
201	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
202	#3622	—	4	8	no	—
203	C₂×C₄³	D₁₇	1	1	yes	characteristic
204	#1839	—	17	2	no	—
205	#1831	—	17	2	no	—
206	#1817	—	17	2	no	—
207	#1797	—	17	2	no	—
208	C₄×C₄⋊C₈	—	17	2	no	—
209	C₄×C₂²⋊C₈	—	17	2	no	—
210	#1744	—	17	2	no	—
211	C₂²×C₁₇	—	2	2	no	—
212	C₂²×C₁₇	—	2	2	no	—
213	C₂²×C₁₇	—	2	2	no	—
214	C₂²×C₁₇	—	2	2	no	—
215	C₂²×C₁₇	—	2	2	no	—
216	C₂²×C₁₇	—	2	2	no	—
217	C₂²×C₁₇	#431	1	4	yes	—
218	C₂²×C₁₇	C₂×#117	1	1	yes	characteristic
219	C₂²×C₁₇	C₂×#117	1	1	yes	characteristic
220	C₂²×C₁₇	C₂×#117	1	1	yes	characteristic
221	C₂²×C₁₇	C₂³×C₈	1	1	yes	characteristic
222	C₂²×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
223	C₂²×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
224	C₂²×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
225	C₄×C₁₇	—	2	2	no	—
226	C₄×C₁₇	—	2	2	no	—
227	C₄×C₁₇	—	2	2	no	—
228	C₄×C₁₇	—	2	2	no	—
229	C₄×C₁₇	—	2	2	no	—
230	C₄×C₁₇	—	2	2	no	—
231	C₄×C₁₇	—	2	2	no	—
232	C₄×C₁₇	—	2	2	no	—
233	C₄×C₁₇	—	2	2	no	—
234	C₄×C₁₇	—	2	2	no	—
235	C₄×C₁₇	#431	1	4	yes	—
236	C₄×C₁₇	#431	1	4	yes	—
237	C₄×C₁₇	#432	1	4	yes	—
238	C₄×C₁₇	#529	1	4	yes	—
239	C₂²×C₄²	Dic₁₇	1	1	yes	characteristic
240	C₂²×C₄²	Dic₁₇	1	1	yes	characteristic
241	C₂²×C₄²	Dic₁₇	1	1	yes	characteristic
242	C₂²×C₄²	Dic₁₇	1	1	yes	characteristic
243	C₂²×C₄²	C₂×D₁₇	1	1	yes	characteristic
244	C₂²×C₄²	C₂×D₁₇	1	1	yes	characteristic
245	C₂²×C₄²	C₂×D₁₇	1	1	yes	characteristic
246	C₂×C₄⋊C₈	—	17	4	no	—
247	C₂×C₂²⋊C₈	—	17	4	no	—
248	C₂×C₄×C₈	—	17	4	no	—
249	C₄³	Dic₁₇	1	1	yes	characteristic
250	C₄³	Dic₁₇	1	1	yes	characteristic
251	C₄³	Dic₁₇	1	1	yes	characteristic
252	C₄³	Dic₁₇	1	1	yes	characteristic
253	C₄³	C₂×D₁₇	1	1	yes	characteristic
254	C₄³	C₂×D₁₇	1	1	yes	characteristic
255	C₄³	C₂×D₁₇	1	1	yes	characteristic
256	C₄³	C₂×D₁₇	1	1	yes	characteristic
257	#336	—	17	4	no	—
258	#336	—	17	4	no	—
259	#336	—	17	4	no	—
260	#336	—	17	4	no	—
261	C₂×C₁₇	—	2	4	no	—
262	C₂×C₁₇	#2283	1	1	yes	characteristic
263	C₂×C₁₇	C₂×#431	1	1	yes	characteristic
264	C₂×C₁₇	C₂×#431	1	1	yes	characteristic
265	C₂×C₁₇	C₂×#431	1	1	yes	characteristic
266	C₂×C₁₇	C₂×#432	1	1	yes	characteristic
267	C₂×C₁₇	#2920	1	1	yes	characteristic
268	C₂×C₁₇	#2920	1	1	yes	characteristic
269	C₂³×C₄	C₂×Dic₁₇	1	1	yes	characteristic
270	C₂³×C₄	C₂×Dic₁₇	1	1	yes	characteristic
271	C₂³×C₄	C₂×Dic₁₇	1	1	yes	characteristic
272	C₂³×C₄	C₂×Dic₁₇	1	1	yes	characteristic
273	C₂³×C₄	C₂×Dic₁₇	1	1	yes	characteristic
274	C₂³×C₄	C₂×Dic₁₇	1	1	yes	characteristic
275	C₂³×C₄	C₂²×D₁₇	1	1	yes	characteristic
276	C₂²×C₈	—	17	8	no	—
277	C₂×C₄²	—	2	4	no	—
278	C₂×C₄²	—	2	4	no	—
279	C₂×C₄²	—	2	4	no	—
280	C₂×C₄²	—	2	4	no	—
281	C₂×C₄²	—	2	4	no	—
282	C₂×C₄²	—	2	4	no	—
283	C₂×C₄²	#3622	1	8	yes	complemented
284	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
285	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
286	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
287	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
288	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
289	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
290	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
291	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
292	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
293	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
294	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
295	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
296	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
297	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
298	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
299	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
300	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
301	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
302	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
303	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
304	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
305	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
306	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
307	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
308	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
309	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
310	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
311	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
312	C₄⋊C₈	—	34	8	no	—
313	C₂²⋊C₈	—	34	8	no	—
314	C₄×C₈	—	34	8	no	—
315	C₁₇	#20777	1	1	yes	characteristic, complemented, Sylow
316	C₂⁴	C₂²×Dic₁₇	1	1	yes	characteristic
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	C₂×#3622	1	4	yes	—
334	C₂²×C₄	C₂×#3622	1	4	yes	—
335	C₂²×C₄	C₂×#3622	1	4	yes	—
336	C₂²×C₄	#63223	1	4	yes	—
337	C₂²×C₄	#63252	1	4	yes	—
338	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
339	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
340	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
341	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
342	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
343	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
344	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
345	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
346	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
347	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
348	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
349	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
350	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
351	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
352	C₂×C₈	—	34	8	no	—
353	C₂×C₈	—	34	8	no	—
354	C₂×C₈	—	34	8	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	C₂×#3622	1	4	yes	—
376	C₄²	C₂×#3622	1	4	yes	—
377	C₄²	C₂×#3622	1	4	yes	—
378	C₄²	C₂×#3622	1	4	yes	—
379	C₄²	#63223	1	4	yes	—
380	C₄²	#63223	1	4	yes	—
381	C₄²	#63252	1	4	yes	—
382	C₄²	#63252	1	4	yes	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	C₂²×#3622	1	2	yes	—
388	C₂³	C₂×#63223	1	2	yes	—
389	C₂³	#10587612	1	2	yes	—
390	C₂³	C₂³×Dic₁₇	1	1	yes	characteristic
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	2	8	no	—
418	C₂×C₄	C₂²×#3622	1	2	yes	—
419	C₂×C₄	C₂²×#3622	1	2	yes	—
420	C₂×C₄	C₂²×#3622	1	2	yes	—
421	C₂×C₄	C₂²×#3622	1	2	yes	—
422	C₂×C₄	C₂²×#3622	1	2	yes	—
423	C₂×C₄	C₂²×#3622	1	2	yes	—
424	C₂×C₄	C₂×#63223	1	2	yes	—
425	C₂×C₄	C₂×#63223	1	2	yes	—
426	C₂×C₄	C₂×#63223	1	2	yes	—
427	C₂×C₄	C₂×#63223	1	2	yes	—
428	C₂×C₄	C₂×#63223	1	2	yes	—
429	C₂×C₄	C₂×#63223	1	2	yes	—
430	C₂×C₄	C₂×#63223	1	2	yes	—
431	C₂×C₄	C₂×#63223	1	2	yes	—
432	C₂×C₄	#10587612	1	2	yes	—
433	C₂×C₄	#10587612	1	2	yes	—
434	C₂×C₄	#10587612	1	2	yes	—
435	C₂×C₄	#10587612	1	2	yes	—
436	C₂×C₄	#10587612	1	2	yes	—
437	C₂×C₄	C₂×#63252	1	2	yes	—
438	C₂×C₄	C₂×#63252	1	2	yes	—
439	C₂×C₄	C₂×#63252	1	2	yes	—
440	C₈	—	68	8	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	#11762862	1	4	yes	—
448	C₂²	C₂×#10587612	1	1	yes	characteristic
449	C₂²	C₂×#10587612	1	1	yes	characteristic
450	C₂²	C₂×#10587612	1	1	yes	characteristic
451	C₂²	C₂³×#3622	1	1	yes	characteristic
452	C₂²	C₂²×#63223	1	1	yes	characteristic
453	C₂²	C₂²×#63223	1	1	yes	characteristic
454	C₂²	C₂²×#63223	1	1	yes	characteristic
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	#11762862	1	4	yes	—
466	C₄	#11762862	1	4	yes	—
467	C₄	#11762866	1	4	yes	—
468	C₄	#11763343	1	4	yes	—
469	C₂	—	2	4	no	—
470	C₂	#14531182	1	1	yes	characteristic
471	C₂	C₂×#11762862	1	1	yes	characteristic
472	C₂	C₂×#11762862	1	1	yes	characteristic
473	C₂	C₂×#11762862	1	1	yes	characteristic
474	C₂	C₂×#11762866	1	1	yes	characteristic
475	C₂	#14537417	1	1	yes	characteristic
476	C₂	#14537417	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²	C₂²×D₁₇
commutator	C₂²×C₁₇	C₂³×C₈
Frattini	C₂²×C₄	C₂³×D₁₇
Fitting	C₂×C₄³×C₁₇	C₂
socle	C₂³×C₁₇	C₂³×C₄
prime radical	C₂⁴×C₁₇	C₂²×C₄
cosocle	C₂²×C₄×C₁₇	C₂⁴
hypercenter	C₂×C₄³	D₁₇
hypocenter	C₁₇	#20777
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄³

Complements

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

N	H ≅ G/N	type
1. #14528927	C₂	semidirect
2. #14528901	C₂	semidirect
5. C₄×C₄⋊#3622	C₂	semidirect
7. #14528530	C₂	semidirect
44. C₂×C₄²×C₁₇	C₈	semidirect
283. C₂×C₄²	#3622	semidirect
315. C₁₇	#20777	semidirect

Maximal subgroups

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

subgroup	index
#14528927	2
#14528901	2
#14528852	2
#14528764	2
C₄×C₄⋊#3622	2
C₄×C₂²⋊#3622	2
#14528530	2
C₂×C₄³×C₁₇	2
#20777	17