Subgroups — C₁₇×#8063 #16865807

Order 4352.

652 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#2920	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₇×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×M₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#1299	C₂	1	4	yes	maximal, complemented
5	C₂²×M₁₆×C₁₇	—	2	1	no	—
6	C₂²×M₁₆×C₁₇	C₄	1	2	yes	—
7	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
8	C₁₇×#432	—	2	1	no	—
9	C₁₇×#432	C₄	1	2	yes	—
10	C₁₇×#431	—	2	1	no	—
11	C₁₇×#431	C₂²	1	2	yes	—
12	C₁₇×#423	—	2	1	no	—
13	C₁₇×#423	—	2	1	no	—
14	C₁₇×#423	C₄	1	2	yes	—
15	C₁₇×#423	C₄	1	2	yes	—
16	C₁₇×#423	C₂²	1	2	yes	—
17	C₂×C₁₇×C₄⋊C₈	—	2	1	no	—
18	C₂×C₁₇×C₄⋊C₈	—	2	1	no	—
19	C₁₇×#407	—	2	1	no	—
20	C₄×M₁₆×C₁₇	—	2	1	no	—
21	C₄×M₁₆×C₁₇	—	2	1	no	—
22	C₄×M₁₆×C₁₇	—	2	1	no	—
23	C₄×M₁₆×C₁₇	C₄	1	2	yes	—
24	C₄×M₁₆×C₁₇	C₂²	1	2	yes	—
25	C₂×C₁₇×#97	C₄	1	2	yes	—
26	C₂×C₄×C₈×C₁₇	—	2	1	no	—
27	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₇	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₇	Q₈	1	1	yes	characteristic
30	C₂×M₁₆×C₁₇	—	2	8	no	—
31	C₂×M₁₆×C₁₇	—	2	2	no	—
32	C₂×M₁₆×C₁₇	—	2	2	no	—
33	C₂×M₁₆×C₁₇	—	2	2	no	—
34	C₂×M₁₆×C₁₇	—	2	2	no	—
35	C₂×M₁₆×C₁₇	—	4	4	no	—
36	C₂×M₁₆×C₁₇	C₂×C₄	1	4	yes	—
37	C₂²×C₈×C₁₇	—	2	2	no	—
38	C₂²×C₈×C₁₇	—	2	2	no	—
39	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₇	Q₈	1	1	yes	characteristic
50	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
51	C₁₇×C₄⋊C₈	—	2	2	no	—
52	C₁₇×C₄⋊C₈	—	2	2	no	—
53	C₁₇×C₄⋊C₈	—	2	2	no	—
54	C₁₇×C₄⋊C₈	—	2	2	no	—
55	C₁₇×C₄⋊C₈	—	2	2	no	—
56	C₁₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
57	C₁₇×C₂²⋊C₈	—	2	2	no	—
58	C₁₇×C₂²⋊C₈	—	2	2	no	—
59	C₁₇×#97	—	2	2	no	—
60	C₁₇×#97	—	2	2	no	—
61	C₁₇×#97	C₂×C₄	1	4	yes	—
62	C₄×C₈×C₁₇	—	2	2	no	—
63	C₄×C₈×C₁₇	—	2	2	no	—
64	C₄×C₈×C₁₇	—	2	2	no	—
65	C₂⁴×C₁₇	C₄⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₇	—	2	2	no	—
67	C₂²×C₄×C₁₇	—	2	2	no	—
68	C₂²×C₄×C₁₇	—	2	4	no	—
69	C₂²×C₄×C₁₇	—	4	2	no	—
70	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
88	M₁₆×C₁₇	—	2	8	no	—
89	M₁₆×C₁₇	—	2	8	no	—
90	M₁₆×C₁₇	—	4	4	no	—
91	M₁₆×C₁₇	—	4	4	no	—
92	M₁₆×C₁₇	—	4	4	no	—
93	C₂×C₈×C₁₇	—	2	8	no	—
94	C₂×C₈×C₁₇	—	2	4	no	—
95	C₂×C₈×C₁₇	—	2	4	no	—
96	C₂×C₈×C₁₇	—	2	4	no	—
97	C₂×C₈×C₁₇	—	4	4	no	—
98	C₄²×C₁₇	C₄²	1	1	yes	characteristic
99	C₄²×C₁₇	C₄²	1	1	yes	characteristic
100	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
106	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
114	#8063	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂³×C₁₇	—	2	2	no	—
116	C₂³×C₁₇	—	2	2	no	—
117	C₂³×C₁₇	—	4	1	no	—
118	C₂³×C₁₇	#95	1	1	yes	characteristic
119	C₂³×C₁₇	#95	1	1	yes	characteristic
120	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₁₇	—	2	2	no	—
122	C₂×C₄×C₁₇	—	2	2	no	—
123	C₂×C₄×C₁₇	—	2	2	no	—
124	C₂×C₄×C₁₇	—	2	2	no	—
125	C₂×C₄×C₁₇	—	2	2	no	—
126	C₂×C₄×C₁₇	—	2	2	no	—
127	C₂×C₄×C₁₇	—	2	1	no	—
128	C₂×C₄×C₁₇	—	2	1	no	—
129	C₂×C₄×C₁₇	—	2	1	no	—
130	C₂×C₄×C₁₇	—	2	1	no	—
131	C₂×C₄×C₁₇	—	2	2	no	—
132	C₂×C₄×C₁₇	—	2	2	no	—
133	C₂×C₄×C₁₇	—	2	2	no	—
134	C₂×C₄×C₁₇	—	2	2	no	—
135	C₂×C₄×C₁₇	—	2	2	no	—
136	C₂×C₄×C₁₇	—	4	1	no	—
137	C₂×C₄×C₁₇	—	4	1	no	—
138	C₂×C₄×C₁₇	—	4	1	no	—
139	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
140	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
141	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
142	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
143	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
144	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
145	C₂×C₄×C₁₇	#100	1	2	yes	—
146	C₂×C₄×C₁₇	#101	1	2	yes	—
147	C₂×C₄×C₁₇	#104	1	4	yes	—
148	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
149	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₈×C₁₇	—	2	8	no	—
155	C₈×C₁₇	—	4	4	no	—
156	C₈×C₁₇	—	4	4	no	—
157	#2920	C₂×C₁₇	1	1	yes	characteristic
158	C₂×#423	C₂×C₁₇	1	1	yes	characteristic
159	C₂×C₄×M₁₆	C₂×C₁₇	1	1	yes	characteristic
160	#1299	C₂×C₁₇	1	4	yes	complemented
161	C₂²×C₁₇	—	2	1	no	—
162	C₂²×C₁₇	—	2	1	no	—
163	C₂²×C₁₇	—	2	1	no	—
164	C₂²×C₁₇	—	2	1	no	—
165	C₂²×C₁₇	—	2	1	no	—
166	C₂²×C₁₇	—	2	1	no	—
167	C₂²×C₁₇	—	2	1	no	—
168	C₂²×C₁₇	—	4	4	no	—
169	C₂²×C₁₇	#339	1	2	yes	—
170	C₂²×C₁₇	#343	1	2	yes	—
171	C₂²×C₁₇	C₂×#95	1	1	yes	characteristic
172	C₄×C₁₇	—	2	1	no	—
173	C₄×C₁₇	—	2	1	no	—
174	C₄×C₁₇	—	2	1	no	—
175	C₄×C₁₇	—	2	1	no	—
176	C₄×C₁₇	—	2	1	no	—
177	C₄×C₁₇	—	2	1	no	—
178	C₄×C₁₇	—	2	1	no	—
179	C₄×C₁₇	#339	1	2	yes	—
180	C₄×C₁₇	#343	1	2	yes	—
181	C₄×C₁₇	C₂×#100	1	1	yes	characteristic
182	C₄×C₁₇	C₂×#101	1	1	yes	characteristic
183	C₄×C₁₇	C₂×#104	1	2	yes	—
184	C₄×C₁₇	#430	1	2	yes	—
185	C₂²×M₁₆	—	2	1	no	—
186	C₂²×M₁₆	C₄×C₁₇	1	2	yes	—
187	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic
188	#432	—	2	1	no	—
189	#432	C₄×C₁₇	1	2	yes	—
190	#431	—	2	1	no	—
191	#431	C₂²×C₁₇	1	2	yes	—
192	#423	—	2	1	no	—
193	#423	—	2	1	no	—
194	#423	C₄×C₁₇	1	2	yes	—
195	#423	C₄×C₁₇	1	2	yes	—
196	#423	C₂²×C₁₇	1	2	yes	—
197	C₂×C₄⋊C₈	—	2	1	no	—
198	C₂×C₄⋊C₈	—	2	1	no	—
199	#407	—	2	1	no	—
200	C₄×M₁₆	—	2	1	no	—
201	C₄×M₁₆	—	2	1	no	—
202	C₄×M₁₆	—	2	1	no	—
203	C₄×M₁₆	C₄×C₁₇	1	2	yes	—
204	C₄×M₁₆	C₂²×C₁₇	1	2	yes	—
205	C₂×#97	C₄×C₁₇	1	2	yes	—
206	C₂×C₄×C₈	—	2	1	no	—
207	C₂×C₁₇	—	2	2	no	—
208	C₂×C₁₇	—	2	2	no	—
209	C₂×C₁₇	—	4	1	no	—
210	C₂×C₁₇	C₂×#339	1	1	yes	characteristic
211	C₂×C₁₇	#1738	1	1	yes	characteristic
212	C₂×C₁₇	C₂×#343	1	1	yes	characteristic
213	C₂³×C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
214	C₂³×C₄	D₄×C₁₇	1	1	yes	characteristic
215	C₂³×C₄	Q₈×C₁₇	1	1	yes	characteristic
216	C₂×M₁₆	—	2	8	no	—
217	C₂×M₁₆	—	2	2	no	—
218	C₂×M₁₆	—	2	2	no	—
219	C₂×M₁₆	—	2	2	no	—
220	C₂×M₁₆	—	2	2	no	—
221	C₂×M₁₆	—	4	4	no	—
222	C₂×M₁₆	C₂×C₄×C₁₇	1	4	yes	—
223	C₂²×C₈	—	2	2	no	—
224	C₂²×C₈	—	2	2	no	—
225	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
226	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
227	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
228	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
229	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
230	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
231	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
232	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
233	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
234	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
235	C₂×C₄²	Q₈×C₁₇	1	1	yes	characteristic
236	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
237	C₄⋊C₈	—	2	2	no	—
238	C₄⋊C₈	—	2	2	no	—
239	C₄⋊C₈	—	2	2	no	—
240	C₄⋊C₈	—	2	2	no	—
241	C₄⋊C₈	—	2	2	no	—
242	C₄⋊C₈	C₂×C₄×C₁₇	1	4	yes	—
243	C₂²⋊C₈	—	2	2	no	—
244	C₂²⋊C₈	—	2	2	no	—
245	#97	—	2	2	no	—
246	#97	—	2	2	no	—
247	#97	C₂×C₄×C₁₇	1	4	yes	—
248	C₄×C₈	—	2	2	no	—
249	C₄×C₈	—	2	2	no	—
250	C₄×C₈	—	2	2	no	—
251	C₁₇	#8063	1	1	yes	characteristic, direct product factor, Sylow
252	C₂⁴	C₄⋊C₄×C₁₇	1	1	yes	characteristic
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	4	2	no	—
257	C₂²×C₄	C₄²×C₁₇	1	1	yes	characteristic
258	C₂²×C₄	C₄²×C₁₇	1	1	yes	characteristic
259	C₂²×C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
260	C₂²×C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
261	C₂²×C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
262	C₂²×C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
263	C₂²×C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
264	C₂²×C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
265	C₂²×C₄	C₄⋊C₄×C₁₇	1	1	yes	characteristic
266	C₂²×C₄	C₄⋊C₄×C₁₇	1	1	yes	characteristic
267	C₂²×C₄	C₄⋊C₄×C₁₇	1	1	yes	characteristic
268	C₂²×C₄	C₄⋊C₄×C₁₇	1	1	yes	characteristic
269	C₂²×C₄	C₄⋊C₄×C₁₇	1	1	yes	characteristic
270	C₂²×C₄	C₄⋊C₄×C₁₇	1	1	yes	characteristic
271	C₂²×C₄	C₄⋊C₄×C₁₇	1	1	yes	characteristic
272	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
274	C₂²×C₄	C₂×Q₈×C₁₇	1	1	yes	characteristic
275	M₁₆	—	2	8	no	—
276	M₁₆	—	2	8	no	—
277	M₁₆	—	4	4	no	—
278	M₁₆	—	4	4	no	—
279	M₁₆	—	4	4	no	—
280	C₂×C₈	—	2	8	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	4	4	no	—
285	C₄²	C₄²×C₁₇	1	1	yes	characteristic
286	C₄²	C₄²×C₁₇	1	1	yes	characteristic
287	C₄²	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
288	C₄²	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
289	C₄²	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
290	C₄²	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
291	C₄²	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
292	C₄²	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
293	C₄²	C₄⋊C₄×C₁₇	1	1	yes	characteristic
294	C₄²	C₄⋊C₄×C₁₇	1	1	yes	characteristic
295	C₄²	C₄⋊C₄×C₁₇	1	1	yes	characteristic
296	C₄²	C₄⋊C₄×C₁₇	1	1	yes	characteristic
297	C₄²	C₂²×C₄×C₁₇	1	1	yes	characteristic
298	C₄²	C₂²×C₄×C₁₇	1	1	yes	characteristic
299	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
300	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
301	C₂³	—	2	2	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	4	1	no	—
304	C₂³	C₁₇×#95	1	1	yes	characteristic
305	C₂³	C₁₇×#95	1	1	yes	characteristic
306	C₂³	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	C₁₇×#95	1	1	yes	characteristic
326	C₂×C₄	C₁₇×#95	1	1	yes	characteristic
327	C₂×C₄	C₁₇×#95	1	1	yes	characteristic
328	C₂×C₄	C₁₇×#95	1	1	yes	characteristic
329	C₂×C₄	C₁₇×#95	1	1	yes	characteristic
330	C₂×C₄	C₁₇×#95	1	1	yes	characteristic
331	C₂×C₄	C₁₇×#100	1	2	yes	—
332	C₂×C₄	C₁₇×#101	1	2	yes	—
333	C₂×C₄	C₁₇×#104	1	4	yes	—
334	C₂×C₄	C₂×C₄²×C₁₇	1	1	yes	characteristic
335	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
336	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
337	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
338	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
339	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
340	C₈	—	2	8	no	—
341	C₈	—	4	4	no	—
342	C₈	—	4	4	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	4	4	no	—
351	C₂²	C₁₇×#339	1	2	yes	—
352	C₂²	C₁₇×#343	1	2	yes	—
353	C₂²	C₂×C₁₇×#95	1	1	yes	characteristic
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	C₁₇×#339	1	2	yes	—
362	C₄	C₁₇×#343	1	2	yes	—
363	C₄	C₂×C₁₇×#100	1	1	yes	characteristic
364	C₄	C₂×C₁₇×#101	1	1	yes	characteristic
365	C₄	C₂×C₁₇×#104	1	2	yes	—
366	C₄	C₁₇×#430	1	2	yes	—
367	C₂	—	2	2	no	—
368	C₂	—	2	2	no	—
369	C₂	—	4	1	no	—
370	C₂	C₂×C₁₇×#339	1	1	yes	characteristic
371	C₂	C₁₇×#1738	1	1	yes	characteristic
372	C₂	C₂×C₁₇×#343	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
socle	C₂²×C₁₇	C₂×#95
prime radical	C₂⁴×C₁₇	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄²×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₇×#1299	C₂	semidirect
114. #8063	C₁₇	direct (N × H)
160. #1299	C₂×C₁₇	semidirect
251. C₁₇	#8063	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×#2920	2
C₂×C₁₇×#423	2
C₂×C₄×M₁₆×C₁₇	2
C₁₇×#1299	2
#8063	17

Subgroups — C17×#8063 #16865807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#8063 #16865807