Subgroups — C₁₇×#12985 #16870729

Order 4352.

510 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₇×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₇×#435	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₇×#349	C₂	1	2	yes	maximal, complemented
4	C₁₇×#2112	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1377	C₂	1	2	yes	maximal, complemented
6	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₇	C₂²	1	1	yes	characteristic
8	C₂×C₄×D₄×C₁₇	C₄	1	1	yes	characteristic
9	C₂×C₁₇×M₃₂	—	2	4	no	—
10	C₂×C₁₇×M₃₂	—	2	1	no	—
11	C₂×C₁₇×M₃₂	C₂²	1	2	yes	—
12	C₂×C₁₇×M₃₂	C₂²	1	2	yes	—
13	C₂²×C₁₆×C₁₇	—	2	1	no	—
14	C₁₇×#435	—	2	1	no	—
15	C₁₇×#435	—	2	1	no	—
16	C₁₇×#435	—	2	1	no	—
17	C₁₇×#435	—	2	1	no	—
18	C₂×C₁₇×C₄⋊C₈	C₄	1	1	yes	characteristic
19	C₂×C₁₇×C₂²⋊C₈	C₄	1	1	yes	characteristic
20	C₂×C₁₇×C₂²⋊C₈	C₄	1	1	yes	characteristic
21	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
22	C₁₇×#349	—	2	4	no	—
23	C₁₇×C₂²⋊C₁₆	—	2	1	no	—
24	C₁₇×C₂²⋊C₁₆	—	2	1	no	—
25	C₂²×D₄×C₁₇	C₈	1	1	yes	characteristic
26	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
28	C₂×M₁₆×C₁₇	—	2	2	no	—
29	C₂×M₁₆×C₁₇	—	2	1	no	—
30	C₂×M₁₆×C₁₇	—	2	1	no	—
31	C₂×M₁₆×C₁₇	—	2	2	no	—
32	C₂²×C₈×C₁₇	—	2	2	no	—
33	C₂²×C₈×C₁₇	—	2	2	no	—
34	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
42	C₄×D₄×C₁₇	—	2	1	no	—
43	C₄×D₄×C₁₇	—	2	1	no	—
44	C₄×D₄×C₁₇	—	2	1	no	—
45	C₄×D₄×C₁₇	—	2	1	no	—
46	C₂×C₄⋊C₄×C₁₇	C₈	1	1	yes	characteristic
47	C₂×C₂²⋊C₄×C₁₇	C₈	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×C₁₇	C₈	1	1	yes	characteristic
49	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
50	C₁₇×M₃₂	—	2	4	no	—
51	C₁₇×M₃₂	—	2	2	no	—
52	C₁₇×M₃₂	—	2	2	no	—
53	C₁₇×M₃₂	—	2	2	no	—
54	C₁₇×M₃₂	D₄	1	4	yes	complemented
55	C₂×C₁₆×C₁₇	—	2	4	no	—
56	C₂×C₁₆×C₁₇	—	2	2	no	—
57	C₂×C₁₆×C₁₇	—	2	2	no	—
58	C₁₇×C₄⋊C₈	—	2	1	no	—
59	C₁₇×C₄⋊C₈	—	2	1	no	—
60	C₁₇×C₂²⋊C₈	—	2	1	no	—
61	C₁₇×C₂²⋊C₈	—	2	1	no	—
62	C₁₇×C₂²⋊C₈	—	2	1	no	—
63	C₁₇×C₂²⋊C₈	—	2	1	no	—
64	C₁₇×#97	—	2	1	no	—
65	C₁₇×#97	—	2	1	no	—
66	C₂⁴×C₁₇	C₂×C₈	1	1	yes	characteristic
67	C₂⁴×C₁₇	C₂×C₈	1	1	yes	characteristic
68	C₂×D₄×C₁₇	—	2	1	no	—
69	C₂×D₄×C₁₇	—	2	1	no	—
70	C₂×D₄×C₁₇	—	4	2	no	—
71	C₂²×C₄×C₁₇	—	2	2	no	—
72	C₂²×C₄×C₁₇	—	2	2	no	—
73	C₂²×C₄×C₁₇	—	2	1	no	—
74	C₂²×C₄×C₁₇	—	2	2	no	—
75	C₂²×C₄×C₁₇	—	2	1	no	—
76	C₂²×C₄×C₁₇	—	2	2	no	—
77	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
80	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
81	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
82	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
83	C₂²×C₄×C₁₇	M₁₆	1	1	yes	characteristic
84	C₂²×C₄×C₁₇	M₁₆	1	1	yes	characteristic
85	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
86	M₁₆×C₁₇	—	4	1	no	—
87	M₁₆×C₁₇	—	4	2	no	—
88	M₁₆×C₁₇	—	4	1	no	—
89	C₂×C₈×C₁₇	—	2	2	no	—
90	C₂×C₈×C₁₇	—	2	1	no	—
91	C₂×C₈×C₁₇	—	2	1	no	—
92	C₂×C₈×C₁₇	—	2	2	no	—
93	C₂×C₈×C₁₇	—	2	2	no	—
94	C₂×C₈×C₁₇	—	2	1	no	—
95	C₂×C₈×C₁₇	—	2	1	no	—
96	C₂×C₈×C₁₇	—	2	1	no	—
97	C₂×C₈×C₁₇	—	2	1	no	—
98	C₂×C₈×C₁₇	—	2	2	no	—
99	C₂×C₈×C₁₇	—	2	2	no	—
100	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
103	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
104	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
105	C₂×C₈×C₁₇	#41	1	2	yes	—
106	C₄⋊C₄×C₁₇	—	2	1	no	—
107	C₄⋊C₄×C₁₇	—	2	1	no	—
108	C₂²⋊C₄×C₁₇	—	2	1	no	—
109	C₂²⋊C₄×C₁₇	—	2	1	no	—
110	C₂²⋊C₄×C₁₇	—	2	1	no	—
111	C₂²⋊C₄×C₁₇	—	2	1	no	—
112	C₄²×C₁₇	—	2	1	no	—
113	C₄²×C₁₇	—	2	1	no	—
114	C₁₆×C₁₇	—	2	4	no	—
115	C₁₆×C₁₇	—	4	2	no	—
116	#12985	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂³×C₁₇	—	2	2	no	—
118	C₂³×C₁₇	—	2	2	no	—
119	C₂³×C₁₇	—	2	1	no	—
120	C₂³×C₁₇	—	2	2	no	—
121	C₂³×C₁₇	—	4	1	no	—
122	C₂³×C₁₇	—	4	1	no	—
123	C₂³×C₁₇	—	4	1	no	—
124	C₂³×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
125	C₂³×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
126	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
127	D₄×C₁₇	—	4	2	no	—
128	D₄×C₁₇	—	4	2	no	—
129	C₂×C₄×C₁₇	—	2	2	no	—
130	C₂×C₄×C₁₇	—	2	1	no	—
131	C₂×C₄×C₁₇	—	2	1	no	—
132	C₂×C₄×C₁₇	—	2	1	no	—
133	C₂×C₄×C₁₇	—	2	1	no	—
134	C₂×C₄×C₁₇	—	2	2	no	—
135	C₂×C₄×C₁₇	—	2	2	no	—
136	C₂×C₄×C₁₇	—	2	1	no	—
137	C₂×C₄×C₁₇	—	2	1	no	—
138	C₂×C₄×C₁₇	—	2	1	no	—
139	C₂×C₄×C₁₇	—	2	2	no	—
140	C₂×C₄×C₁₇	—	4	1	no	—
141	C₂×C₄×C₁₇	—	4	1	no	—
142	C₂×C₄×C₁₇	—	4	2	no	—
143	C₂×C₄×C₁₇	—	4	1	no	—
144	C₂×C₄×C₁₇	—	4	1	no	—
145	C₂×C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
146	C₂×C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
147	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₇	C₄×D₄	1	2	yes	—
149	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
150	C₂×C₄×C₁₇	#131	1	2	yes	—
151	C₈×C₁₇	—	2	1	no	—
152	C₈×C₁₇	—	2	1	no	—
153	C₈×C₁₇	—	4	1	no	—
154	C₈×C₁₇	—	4	1	no	—
155	C₈×C₁₇	#120	1	1	yes	characteristic
156	C₈×C₁₇	#121	1	2	yes	—
157	C₈×C₁₇	#123	1	1	yes	characteristic
158	C₂²×M₃₂	C₂×C₁₇	1	1	yes	characteristic, complemented
159	C₂×#435	C₂×C₁₇	1	1	yes	characteristic
160	C₂×#349	C₂×C₁₇	1	2	yes	complemented
161	#2112	C₂×C₁₇	1	1	yes	characteristic, complemented
162	#1377	C₂×C₁₇	1	2	yes	complemented
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	—	2	1	no	—
169	C₂²×C₁₇	—	2	1	no	—
170	C₂²×C₁₇	—	4	4	no	—
171	C₂²×C₁₇	—	4	1	no	—
172	C₂²×C₁₇	—	4	1	no	—
173	C₂²×C₁₇	—	4	1	no	—
174	C₂²×C₁₇	—	8	2	no	—
175	C₂²×C₁₇	#349	1	2	yes	complemented
176	C₂²×C₁₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
177	C₂²×C₁₇	C₈×D₄	1	2	yes	—
178	C₄×C₁₇	—	2	1	no	—
179	C₄×C₁₇	—	2	1	no	—
180	C₄×C₁₇	—	4	1	no	—
181	C₄×C₁₇	—	4	1	no	—
182	C₄×C₁₇	—	4	1	no	—
183	C₄×C₁₇	#386	1	1	yes	characteristic
184	C₄×C₁₇	#408	1	1	yes	characteristic
185	C₄×C₁₇	#435	1	2	yes	—
186	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
187	C₂³×C₈	C₂²×C₁₇	1	1	yes	characteristic
188	C₂×C₄×D₄	C₄×C₁₇	1	1	yes	characteristic
189	C₂×M₃₂	—	2	1	no	—
190	C₂×M₃₂	—	2	4	no	—
191	C₂×M₃₂	C₂²×C₁₇	1	2	yes	—
192	C₂×M₃₂	C₂²×C₁₇	1	2	yes	—
193	C₂²×C₁₆	—	2	1	no	—
194	#435	—	2	1	no	—
195	#435	—	2	1	no	—
196	#435	—	2	1	no	—
197	#435	—	2	1	no	—
198	C₂×C₄⋊C₈	C₄×C₁₇	1	1	yes	characteristic
199	C₂×C₂²⋊C₈	C₄×C₁₇	1	1	yes	characteristic
200	C₂×C₂²⋊C₈	C₄×C₁₇	1	1	yes	characteristic
201	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
202	#349	—	2	4	no	—
203	C₂²⋊C₁₆	—	2	1	no	—
204	C₂²⋊C₁₆	—	2	1	no	—
205	C₂×C₁₇	—	2	2	no	—
206	C₂×C₁₇	—	2	2	no	—
207	C₂×C₁₇	—	4	1	no	—
208	C₂×C₁₇	—	8	1	no	—
209	C₂×C₁₇	#1869	1	1	yes	characteristic
210	C₂×C₁₇	C₂×#349	1	1	yes	characteristic
211	C₂×C₁₇	#2115	1	1	yes	characteristic
212	C₂²×D₄	C₈×C₁₇	1	1	yes	characteristic
213	C₂³×C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
214	C₂³×C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
215	C₂×M₁₆	—	2	2	no	—
216	C₂×M₁₆	—	2	1	no	—
217	C₂×M₁₆	—	2	1	no	—
218	C₂×M₁₆	—	2	2	no	—
219	C₂²×C₈	—	2	2	no	—
220	C₂²×C₈	—	2	2	no	—
221	C₂²×C₈	C₂×C₄×C₁₇	1	1	yes	characteristic
222	C₂²×C₈	C₂×C₄×C₁₇	1	1	yes	characteristic
223	C₂²×C₈	C₂×C₄×C₁₇	1	1	yes	characteristic
224	C₂²×C₈	D₄×C₁₇	1	1	yes	characteristic
225	C₂²×C₈	D₄×C₁₇	1	1	yes	characteristic
226	C₂²×C₈	D₄×C₁₇	1	1	yes	characteristic
227	C₂²×C₈	D₄×C₁₇	1	1	yes	characteristic
228	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
229	C₄×D₄	—	2	1	no	—
230	C₄×D₄	—	2	1	no	—
231	C₄×D₄	—	2	1	no	—
232	C₄×D₄	—	2	1	no	—
233	C₂×C₄⋊C₄	C₈×C₁₇	1	1	yes	characteristic
234	C₂×C₂²⋊C₄	C₈×C₁₇	1	1	yes	characteristic
235	C₂×C₂²⋊C₄	C₈×C₁₇	1	1	yes	characteristic
236	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
237	M₃₂	—	2	4	no	—
238	M₃₂	—	2	2	no	—
239	M₃₂	—	2	2	no	—
240	M₃₂	—	2	2	no	—
241	M₃₂	D₄×C₁₇	1	4	yes	complemented
242	C₂×C₁₆	—	2	4	no	—
243	C₂×C₁₆	—	2	2	no	—
244	C₂×C₁₆	—	2	2	no	—
245	C₄⋊C₈	—	2	1	no	—
246	C₄⋊C₈	—	2	1	no	—
247	C₂²⋊C₈	—	2	1	no	—
248	C₂²⋊C₈	—	2	1	no	—
249	C₂²⋊C₈	—	2	1	no	—
250	C₂²⋊C₈	—	2	1	no	—
251	#97	—	2	1	no	—
252	#97	—	2	1	no	—
253	C₁₇	#12985	1	1	yes	characteristic, direct product factor, Sylow
254	C₂⁴	C₂×C₈×C₁₇	1	1	yes	characteristic
255	C₂⁴	C₂×C₈×C₁₇	1	1	yes	characteristic
256	C₂×D₄	—	2	1	no	—
257	C₂×D₄	—	2	1	no	—
258	C₂×D₄	—	4	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
266	C₂²×C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₈×C₁₇	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₈×C₁₇	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₈×C₁₇	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₈×C₁₇	1	1	yes	characteristic
271	C₂²×C₄	M₁₆×C₁₇	1	1	yes	characteristic
272	C₂²×C₄	M₁₆×C₁₇	1	1	yes	characteristic
273	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
274	M₁₆	—	4	1	no	—
275	M₁₆	—	4	1	no	—
276	M₁₆	—	4	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	1	no	—
279	C₂×C₈	—	2	1	no	—
280	C₂×C₈	—	2	1	no	—
281	C₂×C₈	—	2	1	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	1	no	—
286	C₂×C₈	—	2	1	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
289	C₂×C₈	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
290	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
291	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
292	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
293	C₂×C₈	#41×C₁₇	1	2	yes	—
294	C₄⋊C₄	—	2	1	no	—
295	C₄⋊C₄	—	2	1	no	—
296	C₂²⋊C₄	—	2	1	no	—
297	C₂²⋊C₄	—	2	1	no	—
298	C₂²⋊C₄	—	2	1	no	—
299	C₂²⋊C₄	—	2	1	no	—
300	C₄²	—	2	1	no	—
301	C₄²	—	2	1	no	—
302	C₁₆	—	2	4	no	—
303	C₁₆	—	4	2	no	—
304	C₂³	—	2	2	no	—
305	C₂³	—	2	2	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	2	2	no	—
308	C₂³	—	4	1	no	—
309	C₂³	—	4	1	no	—
310	C₂³	—	4	1	no	—
311	C₂³	C₁₇×C₂²⋊C₈	1	1	yes	characteristic
312	C₂³	C₁₇×C₂²⋊C₈	1	1	yes	characteristic
313	C₂³	C₂²×C₈×C₁₇	1	1	yes	characteristic
314	D₄	—	4	2	no	—
315	D₄	—	4	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	C₁₇×C₂²⋊C₈	1	1	yes	characteristic
333	C₂×C₄	C₁₇×C₂²⋊C₈	1	1	yes	characteristic
334	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
335	C₂×C₄	C₄×D₄×C₁₇	1	2	yes	—
336	C₂×C₄	C₂×M₁₆×C₁₇	1	1	yes	characteristic
337	C₂×C₄	C₁₇×#131	1	2	yes	—
338	C₈	—	2	1	no	—
339	C₈	—	2	1	no	—
340	C₈	—	4	1	no	—
341	C₈	—	4	1	no	—
342	C₈	C₁₇×#120	1	1	yes	characteristic
343	C₈	C₁₇×#121	1	2	yes	—
344	C₈	C₁₇×#123	1	1	yes	characteristic
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	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	4	4	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	8	2	no	—
357	C₂²	C₁₇×#349	1	2	yes	complemented
358	C₂²	C₂×C₁₇×C₂²⋊C₈	1	1	yes	characteristic
359	C₂²	C₈×D₄×C₁₇	1	2	yes	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	4	1	no	—
363	C₄	—	4	1	no	—
364	C₄	—	4	1	no	—
365	C₄	C₁₇×#386	1	1	yes	characteristic
366	C₄	C₁₇×#408	1	1	yes	characteristic
367	C₄	C₁₇×#435	1	2	yes	—
368	C₂	—	2	2	no	—
369	C₂	—	2	2	no	—
370	C₂	—	4	1	no	—
371	C₂	—	8	1	no	—
372	C₂	C₁₇×#1869	1	1	yes	characteristic
373	C₂	C₂×C₁₇×#349	1	1	yes	characteristic
374	C₂	C₁₇×#2115	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₈×C₁₇
Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
socle	C₂²×C₁₇	C₂×C₂²⋊C₈
prime radical	C₂²×D₄×C₁₇	C₈
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂³×C₈×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₇×M₃₂	C₂	semidirect
3. C₂×C₁₇×#349	C₂	semidirect
4. C₁₇×#2112	C₂	semidirect
5. C₁₇×#1377	C₂	semidirect
54. C₁₇×M₃₂	D₄	semidirect
116. #12985	C₁₇	direct (N × H)
158. C₂²×M₃₂	C₂×C₁₇	semidirect
160. C₂×#349	C₂×C₁₇	semidirect
161. #2112	C₂×C₁₇	semidirect
162. #1377	C₂×C₁₇	semidirect
175. C₂²×C₁₇	#349	semidirect
241. M₃₂	D₄×C₁₇	semidirect
253. C₁₇	#12985	direct (N × H)
357. C₂²	C₁₇×#349	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₇×M₃₂	2
C₂×C₁₇×#435	2
C₂×C₁₇×#349	2
C₁₇×#2112	2
C₁₇×#1377	2
#12985	17

Subgroups — C17×#12985 #16870729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#12985 #16870729