Subgroups — C₄×D₁₆×D₁₇ #17187581

Order 4352.

806 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₆×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₄×D₈×D₁₇	C₂	1	2	yes	maximal, complemented
3	C₄×D₂₇₂	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₆×Dic₁₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#14530630	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#10587497	C₂	1	2	yes	maximal, complemented
7	#14530628	C₂	1	2	yes	maximal, complemented
8	D₁₇×#366	C₂	1	1	yes	maximal, characteristic, complemented
9	D₁₇×#357	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₆×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₇×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₁₇	C₂²	1	2	yes	—
13	C₄×D₄×D₁₇	—	2	2	no	—
14	C₂×D₂₇₂	C₂²	1	1	yes	characteristic
15	C₂×#10587497	C₂²	1	2	yes	—
16	D₁₆×D₁₇	C₄	1	8	yes	direct product factor
17	C₂×C₁₆×D₁₇	C₂²	1	1	yes	characteristic
18	C₂×C₁₆×D₁₇	C₂²	1	1	yes	characteristic
19	C₄×D₁₃₆	C₂²	1	2	yes	complemented
20	D₈×Dic₁₇	C₂²	1	2	yes	complemented
21	#11762891	C₂²	1	2	yes	complemented
22	C₄×#63228	—	2	2	no	—
23	#11762889	—	2	2	no	—
24	#107×D₁₇	C₂²	1	2	yes	—
25	#102×D₁₇	—	2	2	no	—
26	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
27	#11762635	C₂²	1	1	yes	characteristic, complemented
28	#11762634	C₂²	1	2	yes	complemented
29	#11762611	C₂²	1	2	yes	complemented
30	#11762610	C₂²	1	2	yes	complemented
31	#11762609	C₂²	1	2	yes	complemented
32	C₄×#63214	C₂²	1	1	yes	characteristic, complemented
33	C₁₆×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
34	C₁₆×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₁₇×D₁₆	C₂²	1	1	yes	characteristic
36	C₄×D₈×C₁₇	C₂²	1	2	yes	complemented
37	C₁₇×#366	C₂²	1	1	yes	characteristic, complemented
38	C₁₇×#357	C₂²	1	2	yes	complemented
39	C₄×C₁₆×C₁₇	C₂²	1	1	yes	characteristic, complemented
40	C₂×D₄×D₁₇	—	2	2	no	—
41	C₂²×C₄×D₁₇	—	4	2	no	—
42	C₂×D₈×C₁₇	C₂³	1	2	yes	—
43	C₄×D₄×C₁₇	—	2	2	no	—
44	D₄×Dic₁₇	—	2	2	no	—
45	C₂×#63228	—	2	2	no	—
46	C₄×C₂²⋊D₁₇	—	4	2	no	—
47	D₈×D₁₇	—	2	4	no	—
48	D₈×D₁₇	C₂×C₄	1	8	yes	complemented
49	C₂×D₁₃₆	C₂³	1	2	yes	—
50	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
51	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
52	#10587579	—	2	2	no	—
53	C₄⋊C₄×D₁₇	—	2	2	no	—
54	#10587567	—	4	2	no	—
55	C₂²⋊C₄×D₁₇	—	4	2	no	—
56	C₄×D₆₈	—	2	2	no	—
57	C₄²×D₁₇	D₄	1	1	yes	characteristic
58	C₁₇×D₁₆	C₂×C₄	1	4	yes	complemented
59	C₂×C₁₆×C₁₇	C₂³	1	1	yes	characteristic
60	C₂×C₁₆×C₁₇	C₂³	1	1	yes	characteristic
61	C₁₇×#107	C₂³	1	2	yes	—
62	C₁₇×#102	—	2	2	no	—
63	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
64	#10587503	—	2	2	no	—
65	#10587497	C₂×C₄	1	8	yes	complemented
66	#10587492	—	2	2	no	—
67	#10587489	C₂³	1	2	yes	—
68	C₈×Dic₁₇	D₄	1	1	yes	characteristic
69	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
70	C₂×#63214	C₂³	1	1	yes	characteristic
71	C₂×#63214	C₂³	1	1	yes	characteristic
72	#10587480	—	2	2	no	—
73	#10587478	—	2	2	no	—
74	C₄×#3622	D₄	1	1	yes	characteristic
75	D₂₇₂	C₂×C₄	1	4	yes	complemented
76	C₁₆×D₁₇	—	2	2	no	—
77	C₁₆×D₁₇	C₂×C₄	1	4	yes	complemented
78	C₂³×D₁₇	—	4	2	no	—
79	C₂×D₄×C₁₇	—	2	2	no	—
80	C₂²×C₄×C₁₇	—	4	2	no	—
81	C₂×C₂²⋊D₁₇	—	4	2	no	—
82	C₂²×Dic₁₇	—	4	2	no	—
83	D₄×D₁₇	—	2	8	no	—
84	D₄×D₁₇	—	4	4	no	—
85	C₂×D₆₈	—	2	2	no	—
86	C₂×C₄×D₁₇	—	4	2	no	—
87	C₂×C₄×D₁₇	—	4	2	no	—
88	C₂×C₄×D₁₇	—	4	2	no	—
89	C₂×C₄×D₁₇	—	8	8	no	—
90	C₂×C₄×D₁₇	D₈	1	1	yes	characteristic
91	C₂×C₄×D₁₇	D₈	1	1	yes	characteristic
92	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
93	D₈×C₁₇	—	2	2	no	—
94	D₈×C₁₇	C₂²×C₄	1	4	yes	complemented
95	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
96	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
97	C₄⋊C₄×C₁₇	—	2	2	no	—
98	C₂²⋊C₄×C₁₇	—	4	2	no	—
99	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
100	C₂²⋊Dic₁₇	—	4	2	no	—
101	#63228	—	2	8	no	—
102	#63227	—	4	2	no	—
103	#63227	—	4	2	no	—
104	C₄⋊Dic₁₇	—	2	2	no	—
105	#63225	—	4	2	no	—
106	C₄×Dic₁₇	D₈	1	1	yes	characteristic
107	C₄×Dic₁₇	D₈	1	1	yes	characteristic
108	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
109	C₂×#3622	C₂×D₄	1	1	yes	characteristic
110	C₂×#3622	C₂×D₄	1	1	yes	characteristic
111	D₁₃₆	—	2	2	no	—
112	D₁₃₆	C₂²×C₄	1	4	yes	complemented
113	C₈×D₁₇	—	2	2	no	—
114	C₈×D₁₇	C₂²×C₄	1	2	yes	—
115	C₈×D₁₇	#41	1	2	yes	—
116	C₁₆×C₁₇	—	2	1	no	—
117	C₁₆×C₁₇	C₂²×C₄	1	2	yes	complemented
118	#63214	—	2	1	no	—
119	#63214	C₂²×C₄	1	2	yes	complemented
120	C₂×C₄×D₁₆	—	17	1	no	maximal, Sylow
121	C₂³×C₁₇	—	4	2	no	—
122	C₂²×D₁₇	—	4	2	no	—
123	C₂²×D₁₇	—	4	8	no	—
124	C₂²×D₁₇	—	8	4	no	—
125	C₂²×D₁₇	—	8	4	no	—
126	C₂²×D₁₇	C₂×D₈	1	1	yes	characteristic
127	D₄×C₁₇	—	2	4	no	—
128	D₄×C₁₇	—	4	2	no	—
129	C₂×C₄×C₁₇	—	4	2	no	—
130	C₂×C₄×C₁₇	—	8	4	no	—
131	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
132	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
133	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
134	C₂²⋊D₁₇	—	4	8	no	—
135	C₂×Dic₁₇	—	4	2	no	—
136	C₂×Dic₁₇	—	8	4	no	—
137	C₂×Dic₁₇	C₂×D₈	1	1	yes	characteristic
138	C₂×Dic₁₇	C₂×D₈	1	1	yes	characteristic
139	C₂×Dic₁₇	C₂×D₈	1	1	yes	characteristic
140	D₆₈	—	2	4	no	—
141	D₆₈	—	4	2	no	—
142	C₄×D₁₇	—	2	2	no	—
143	C₄×D₁₇	—	8	4	no	—
144	C₄×D₁₇	—	8	4	no	—
145	C₄×D₁₇	—	8	4	no	—
146	C₄×D₁₇	D₁₆	1	4	yes	direct product factor
147	C₄×D₁₇	C₄×D₄	1	2	yes	—
148	C₄×D₁₇	#135	1	2	yes	—
149	C₈×C₁₇	—	2	1	no	—
150	C₈×C₁₇	C₂³×C₄	1	1	yes	characteristic
151	C₈×C₁₇	C₂×#41	1	1	yes	characteristic
152	#3622	—	2	1	no	—
153	#3622	C₄×D₄	1	2	yes	—
154	C₂²×D₁₆	—	17	1	no	—
155	C₂×C₄×D₈	—	17	2	no	—
156	C₄×D₁₆	—	17	1	no	—
157	C₄×D₁₆	—	17	2	no	—
158	C₄×D₁₆	—	17	1	no	—
159	C₄×D₁₆	—	17	2	no	—
160	C₄×D₁₆	—	17	1	no	—
161	C₄×D₁₆	D₁₇	1	1	yes	characteristic, direct product factor
162	C₂×#366	—	17	1	no	—
163	C₂×#357	—	17	2	no	—
164	C₂×C₄×C₁₆	—	17	1	no	—
165	C₂²×C₁₇	—	4	4	no	—
166	C₂²×C₁₇	—	8	2	no	—
167	C₂²×C₁₇	—	8	2	no	—
168	C₂²×C₁₇	C₂²×D₈	1	1	yes	characteristic
169	C₂×D₁₇	—	4	4	no	—
170	C₂×D₁₇	—	8	2	no	—
171	C₂×D₁₇	—	8	2	no	—
172	C₂×D₁₇	—	8	16	no	—
173	C₂×D₁₇	C₄×D₈	1	2	yes	—
174	C₂×D₁₇	C₂×D₁₆	1	2	yes	—
175	C₂×D₁₇	#508	1	2	yes	—
176	C₄×C₁₇	—	2	1	no	—
177	C₄×C₁₇	—	8	2	no	—
178	C₄×C₁₇	C₂×D₁₆	1	2	yes	complemented
179	C₄×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
180	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
181	Dic₁₇	—	2	1	no	—
182	Dic₁₇	—	8	2	no	—
183	Dic₁₇	C₄×D₈	1	2	yes	—
184	Dic₁₇	C₂×D₁₆	1	2	yes	complemented
185	C₂²×D₈	—	17	2	no	—
186	C₂×C₄×D₄	—	34	2	no	—
187	C₂×D₁₆	—	17	2	no	—
188	C₂×D₁₆	—	17	8	no	—
189	C₂×D₁₆	—	17	1	no	—
190	C₂×D₁₆	C₂×D₁₇	1	1	yes	characteristic
191	C₂²×C₁₆	—	17	1	no	—
192	C₂²×C₁₆	—	17	1	no	—
193	C₄×D₈	—	17	2	no	—
194	C₄×D₈	—	17	2	no	—
195	C₄×D₈	—	17	2	no	—
196	C₄×D₈	—	34	2	no	—
197	C₄×D₈	—	34	2	no	—
198	C₄×D₈	C₂×D₁₇	1	2	yes	complemented
199	C₂×#107	—	17	2	no	—
200	C₂×#102	—	34	2	no	—
201	C₂×C₄×C₈	—	17	1	no	—
202	#366	—	17	1	no	—
203	#366	—	17	2	no	—
204	#366	C₂×D₁₇	1	1	yes	characteristic, complemented
205	#357	—	17	2	no	—
206	#357	—	17	2	no	—
207	#357	—	17	2	no	—
208	#357	C₂×D₁₇	1	2	yes	complemented
209	C₄×C₁₆	—	17	1	no	—
210	C₄×C₁₆	—	17	1	no	—
211	C₄×C₁₆	—	17	1	no	—
212	C₄×C₁₆	C₂×D₁₇	1	1	yes	characteristic, complemented
213	C₂×C₁₇	—	8	4	no	—
214	C₂×C₁₇	C₂×C₄×D₈	1	1	yes	characteristic
215	C₂×C₁₇	C₂²×D₁₆	1	1	yes	characteristic
216	C₂×C₁₇	C₂×#508	1	1	yes	characteristic
217	D₁₇	—	8	4	no	—
218	D₁₇	C₄×D₁₆	1	4	yes	direct product factor
219	C₂²×D₄	—	34	2	no	—
220	C₂³×C₄	—	68	2	no	—
221	C₂×D₈	—	17	8	no	—
222	C₂×D₈	—	17	2	no	—
223	C₂×D₈	—	34	4	no	—
224	C₂×D₈	—	34	2	no	—
225	C₂×D₈	C₂²×D₁₇	1	2	yes	—
226	C₂²×C₈	—	17	1	no	—
227	C₂²×C₈	—	17	1	no	—
228	C₄×D₄	—	2	2	no	—
229	C₄×D₄	—	34	2	no	—
230	C₄×D₄	—	34	2	no	—
231	C₄×D₄	—	34	2	no	—
232	C₄×D₄	—	68	2	no	—
233	C₄×D₄	—	68	2	no	—
234	C₂×C₄⋊C₄	—	34	2	no	—
235	C₂×C₂²⋊C₄	—	68	2	no	—
236	C₂×C₄²	—	17	1	no	—
237	D₁₆	—	17	8	no	—
238	D₁₆	—	17	4	no	—
239	D₁₆	C₄×D₁₇	1	4	yes	direct product factor
240	C₂×C₁₆	—	17	1	no	—
241	C₂×C₁₆	—	17	4	no	—
242	C₂×C₁₆	—	17	1	no	—
243	C₂×C₁₆	—	34	2	no	—
244	C₂×C₁₆	C₂²×D₁₇	1	1	yes	characteristic
245	C₂×C₁₆	C₂²×D₁₇	1	1	yes	characteristic
246	#107	—	17	2	no	—
247	#107	—	34	2	no	—
248	#107	C₂²×D₁₇	1	2	yes	—
249	#102	—	2	2	no	—
250	#102	—	34	2	no	—
251	#102	—	34	2	no	—
252	#102	—	34	2	no	—
253	C₄×C₈	—	17	1	no	—
254	C₄×C₈	—	17	1	no	—
255	C₄×C₈	—	17	1	no	—
256	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
257	C₁₇	C₂×C₄×D₁₆	1	1	yes	characteristic, complemented, Sylow
258	C₂⁴	—	68	2	no	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	34	8	no	—
261	C₂×D₄	—	34	2	no	—
262	C₂×D₄	—	68	4	no	—
263	C₂×D₄	—	68	2	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	—	17	1	no	—
266	C₂²×C₄	—	17	1	no	—
267	C₂²×C₄	—	17	1	no	—
268	C₂²×C₄	—	68	2	no	—
269	C₂²×C₄	—	68	2	no	—
270	C₂²×C₄	—	68	2	no	—
271	C₂²×C₄	—	68	2	no	—
272	C₂²×C₄	—	136	8	no	—
273	D₈	—	2	2	no	—
274	D₈	—	17	4	no	—
275	D₈	—	34	8	no	—
276	D₈	—	34	2	no	—
277	D₈	C₂×C₄×D₁₇	1	4	yes	complemented
278	C₂×C₈	—	17	1	no	—
279	C₂×C₈	—	17	2	no	—
280	C₂×C₈	—	17	2	no	—
281	C₂×C₈	—	17	1	no	—
282	C₂×C₈	—	34	2	no	—
283	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
284	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	34	2	no	—
287	C₄⋊C₄	—	68	2	no	—
288	C₂²⋊C₄	—	4	2	no	—
289	C₂²⋊C₄	—	68	2	no	—
290	C₂²⋊C₄	—	68	2	no	—
291	C₂²⋊C₄	—	68	2	no	—
292	C₄²	—	17	1	no	—
293	C₄²	—	17	1	no	—
294	C₄²	—	17	1	no	—
295	C₄²	D₄×D₁₇	1	1	yes	characteristic
296	C₁₆	—	2	1	no	—
297	C₁₆	—	17	2	no	—
298	C₁₆	—	34	1	no	—
299	C₁₆	C₂×C₄×D₁₇	1	2	yes	complemented
300	C₂³	—	4	2	no	—
301	C₂³	—	17	1	no	—
302	C₂³	—	68	8	no	—
303	C₂³	—	68	2	no	—
304	C₂³	—	136	4	no	—
305	C₂³	—	136	4	no	—
306	D₄	—	2	4	no	—
307	D₄	—	4	2	no	—
308	D₄	—	34	4	no	—
309	D₄	—	68	8	no	—
310	D₄	—	68	2	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	8	4	no	—
313	C₂×C₄	—	17	1	no	—
314	C₂×C₄	—	17	1	no	—
315	C₂×C₄	—	17	4	no	—
316	C₂×C₄	—	17	2	no	—
317	C₂×C₄	—	17	2	no	—
318	C₂×C₄	—	17	1	no	—
319	C₂×C₄	—	34	2	no	—
320	C₂×C₄	—	68	2	no	—
321	C₂×C₄	—	136	4	no	—
322	C₂×C₄	—	136	4	no	—
323	C₂×C₄	—	136	4	no	—
324	C₂×C₄	—	136	4	no	—
325	C₂×C₄	D₈×D₁₇	1	1	yes	characteristic
326	C₂×C₄	D₈×D₁₇	1	1	yes	characteristic
327	C₂×C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
328	C₈	—	2	1	no	—
329	C₈	—	17	2	no	—
330	C₈	—	34	1	no	—
331	C₈	C₂²×C₄×D₁₇	1	1	yes	characteristic
332	C₈	#41×D₁₇	1	1	yes	characteristic
333	C₂²	—	4	4	no	—
334	C₂²	—	8	2	no	—
335	C₂²	—	8	2	no	—
336	C₂²	—	17	2	no	—
337	C₂²	—	17	2	no	—
338	C₂²	—	17	2	no	—
339	C₂²	—	68	4	no	—
340	C₂²	—	136	16	no	—
341	C₂²	—	136	2	no	—
342	C₂²	—	136	2	no	—
343	C₂²	C₂×D₈×D₁₇	1	1	yes	characteristic
344	C₄	—	2	1	no	—
345	C₄	—	8	2	no	—
346	C₄	—	17	2	no	—
347	C₄	—	17	2	no	—
348	C₄	—	34	1	no	—
349	C₄	—	136	2	no	—
350	C₄	D₁₆×D₁₇	1	2	yes	direct product factor
351	C₄	C₄×D₄×D₁₇	1	1	yes	characteristic
352	C₄	#135×D₁₇	1	1	yes	characteristic
353	C₂	—	8	4	no	—
354	C₂	—	17	4	no	—
355	C₂	—	136	4	no	—
356	C₂	C₄×D₈×D₁₇	1	1	yes	characteristic
357	C₂	C₂×D₁₆×D₁₇	1	1	yes	characteristic
358	C₂	D₁₇×#508	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₈×D₁₇
commutator	C₈×C₁₇	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₇
Fitting	C₄×C₁₇×D₁₆	C₂
socle	C₂²×C₁₇	C₂²×D₈
prime radical	C₂×D₁₆×D₁₇	C₂
cosocle	C₂×C₈×C₁₇	C₂⁴
hypercenter	C₄×D₁₆	D₁₇
hypocenter	C₁₇	C₂×C₄×D₁₆
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×D₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×D₈×D₁₇	C₂	semidirect
3. C₄×D₂₇₂	C₂	semidirect
4. D₁₆×Dic₁₇	C₂	semidirect
5. #14530630	C₂	semidirect
6. C₄×#10587497	C₂	semidirect
7. #14530628	C₂	semidirect
8. D₁₇×#366	C₂	semidirect
9. D₁₇×#357	C₂	semidirect
10. C₄×C₁₆×D₁₇	C₂	semidirect
11. C₄×C₁₇×D₁₆	C₂	semidirect
16. D₁₆×D₁₇	C₄	direct (N × H)
19. C₄×D₁₃₆	C₂²	semidirect
20. D₈×Dic₁₇	C₂²	semidirect
21. #11762891	C₂²	semidirect
27. #11762635	C₂²	semidirect
28. #11762634	C₂²	semidirect
29. #11762611	C₂²	semidirect
30. #11762610	C₂²	semidirect
31. #11762609	C₂²	semidirect
32. C₄×#63214	C₂²	semidirect
33. C₁₆×Dic₁₇	C₂²	semidirect
34. C₁₆×Dic₁₇	C₂²	semidirect
36. C₄×D₈×C₁₇	C₂²	semidirect
37. C₁₇×#366	C₂²	semidirect
38. C₁₇×#357	C₂²	semidirect
39. C₄×C₁₆×C₁₇	C₂²	semidirect
48. D₈×D₁₇	C₂×C₄	semidirect
58. C₁₇×D₁₆	C₂×C₄	semidirect
65. #10587497	C₂×C₄	semidirect
75. D₂₇₂	C₂×C₄	semidirect
77. C₁₆×D₁₇	C₂×C₄	semidirect
94. D₈×C₁₇	C₂²×C₄	semidirect
112. D₁₃₆	C₂²×C₄	semidirect
117. C₁₆×C₁₇	C₂²×C₄	semidirect
119. #63214	C₂²×C₄	semidirect
146. C₄×D₁₇	D₁₆	direct (N × H)
161. C₄×D₁₆	D₁₇	direct (N × H)
178. C₄×C₁₇	C₂×D₁₆	semidirect
184. Dic₁₇	C₂×D₁₆	semidirect
198. C₄×D₈	C₂×D₁₇	semidirect
204. #366	C₂×D₁₇	semidirect
208. #357	C₂×D₁₇	semidirect
212. C₄×C₁₆	C₂×D₁₇	semidirect
218. D₁₇	C₄×D₁₆	direct (N × H)
239. D₁₆	C₄×D₁₇	direct (N × H)
257. C₁₇	C₂×C₄×D₁₆	semidirect
277. D₈	C₂×C₄×D₁₇	semidirect
299. C₁₆	C₂×C₄×D₁₇	semidirect
350. C₄	D₁₆×D₁₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×D₁₆×D₁₇	2
C₄×D₈×D₁₇	2
C₄×D₂₇₂	2
D₁₆×Dic₁₇	2
#14530630	2
C₄×#10587497	2
#14530628	2
D₁₇×#366	2
D₁₇×#357	2
C₄×C₁₆×D₁₇	2
C₄×C₁₇×D₁₆	2
C₂×C₄×D₁₆	17

Subgroups — C4×D16×D17 #17187581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₁₆×D₁₇ #17187581