Subgroups — #17187746

Order 4352.

642 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₇×#508	C₂	1	1	yes	maximal, characteristic
2	#14537696	C₂	1	2	yes	maximal, complemented
3	#14530668	C₂	1	2	yes	maximal, complemented
4	#14530667	C₂	1	2	yes	maximal, complemented
5	#14530666	C₂	1	1	yes	maximal, characteristic, complemented
6	#14530665	C₂	1	1	yes	maximal, characteristic, complemented
7	#14530664	C₂	1	1	yes	maximal, characteristic, complemented
8	D₁₇×#368	C₂	1	1	yes	maximal, characteristic, complemented
9	#14530510	C₂	1	2	yes	maximal, complemented
10	#14530379	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#2178	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₁₇	C₂²	1	2	yes	—
13	#11763574	—	2	2	no	—
14	#11763242	C₄	1	1	yes	characteristic, complemented
15	#11763241	C₂²	1	1	yes	characteristic
16	#11763240	C₄	1	2	yes	complemented
17	#11763239	C₂²	1	2	yes	—
18	#11763238	C₄	1	1	yes	characteristic, complemented
19	Q₃₂×D₁₇	C₄	1	1	yes	characteristic, complemented
20	SD₃₂×D₁₇	C₄	1	2	yes	complemented
21	D₁₆×D₁₇	C₄	1	1	yes	characteristic, complemented
22	C₂×#10587469	C₂²	1	1	yes	characteristic
23	C₂×C₁₆×D₁₇	C₂²	1	1	yes	characteristic
24	#11762929	—	2	2	no	—
25	#11762928	—	2	2	no	—
26	#11762927	C₂²	1	2	yes	complemented
27	#11762926	C₂²	1	2	yes	complemented
28	#11762925	C₂²	1	2	yes	complemented
29	#108×D₁₇	C₂²	1	2	yes	—
30	#11762824	—	2	2	no	—
31	#11762763	C₂²	1	1	yes	characteristic
32	#11762639	C₂²	1	1	yes	characteristic, complemented
33	#11762638	C₂²	1	2	yes	complemented
34	#11762617	C₂²	1	2	yes	complemented
35	#11762616	C₂²	1	2	yes	complemented
36	#11762615	C₂²	1	2	yes	complemented
37	#11762585	C₂²	1	1	yes	characteristic, complemented
38	#11762584	C₂²	1	1	yes	characteristic, complemented
39	C₁₆×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
40	C₁₇×#508	C₂²	1	1	yes	characteristic
41	C₁₇×#443	C₂²	1	2	yes	complemented
42	C₁₇×#368	C₂²	1	1	yes	characteristic, complemented
43	C₁₇×#359	C₂²	1	2	yes	complemented
44	C₄×C₁₆×C₁₇	C₂²	1	1	yes	characteristic, complemented
45	#41×D₁₇	—	2	2	no	—
46	C₁₇×#135	C₂³	1	2	yes	—
47	C₁₇×#131	—	2	2	no	—
48	#10587636	—	2	2	no	—
49	#10587634	—	2	2	no	—
50	#10587605	C₂×C₄	1	2	yes	—
51	Q₁₆×D₁₇	C₂×C₄	1	2	yes	—
52	#10587602	—	2	2	no	—
53	SD₁₆×D₁₇	—	2	2	no	—
54	#10587598	C₂×C₄	1	2	yes	—
55	D₈×D₁₇	C₂×C₄	1	2	yes	—
56	#10587593	—	2	2	no	—
57	#10587593	—	4	2	no	—
58	M₁₆×D₁₇	—	2	2	no	—
59	M₁₆×D₁₇	—	4	2	no	—
60	#10587590	C₂³	1	2	yes	—
61	#10587587	—	2	2	no	—
62	#10587587	—	4	2	no	—
63	C₂×#63218	—	4	2	no	—
64	C₂×#63218	D₄	1	1	yes	characteristic
65	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
66	#10587558	D₄	1	1	yes	characteristic
67	C₁₇×Q₃₂	C₂×C₄	1	1	yes	characteristic
68	C₁₇×SD₃₂	C₂×C₄	1	2	yes	—
69	C₁₇×D₁₆	C₂×C₄	1	1	yes	characteristic
70	C₂×C₁₆×C₁₇	C₂³	1	1	yes	characteristic
71	C₂×C₁₆×C₁₇	C₂³	1	1	yes	characteristic
72	C₁₇×#108	C₂³	1	2	yes	—
73	C₁₇×#104	—	2	2	no	—
74	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
75	#10587508	—	2	2	no	—
76	#10587500	C₂×C₄	1	2	yes	—
77	#10587499	C₂×C₄	1	2	yes	—
78	#10587498	C₂×C₄	1	2	yes	—
79	#10587497	C₂×C₄	1	2	yes	—
80	#10587496	—	2	2	no	—
81	#10587493	—	2	2	no	—
82	#10587490	C₂³	1	2	yes	—
83	#10587486	D₄	1	1	yes	characteristic
84	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
85	C₂×#63214	C₂³	1	1	yes	characteristic
86	C₂×#63214	C₂³	1	1	yes	characteristic
87	#10587476	—	2	2	no	—
88	#10587474	D₄	1	1	yes	characteristic
89	Dic₁₃₆	C₂×C₄	1	1	yes	characteristic
90	#10587471	C₂×C₄	1	2	yes	—
91	D₂₇₂	C₂×C₄	1	1	yes	characteristic
92	#10587469	—	2	1	no	—
93	#10587469	—	2	1	no	—
94	C₁₆×D₁₇	C₂×C₄	1	1	yes	characteristic
95	C₁₆×D₁₇	C₂×C₄	1	1	yes	characteristic
96	C₁₆×D₁₇	C₂×C₄	1	1	yes	characteristic
97	C₁₆×D₁₇	C₂×C₄	1	1	yes	characteristic
98	#41×C₁₇	—	2	2	no	—
99	#63256	—	2	2	no	—
100	Q₈×D₁₇	—	2	2	no	—
101	#63254	—	2	2	no	—
102	#63254	—	4	2	no	—
103	D₄×D₁₇	—	2	2	no	—
104	D₄×D₁₇	—	4	2	no	—
105	#63252	—	2	2	no	—
106	#63252	—	4	2	no	—
107	C₂×C₄×D₁₇	—	4	2	no	—
108	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
109	Q₁₆×C₁₇	C₂²×C₄	1	2	yes	—
110	SD₁₆×C₁₇	—	2	2	no	—
111	D₈×C₁₇	C₂²×C₄	1	2	yes	—
112	M₁₆×C₁₇	—	2	2	no	—
113	M₁₆×C₁₇	—	4	2	no	—
114	C₂×C₈×C₁₇	—	4	2	no	—
115	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
117	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
118	#63231	—	2	2	no	—
119	#63230	—	2	2	no	—
120	#63229	—	2	2	no	—
121	#63228	—	2	2	no	—
122	#63227	—	2	1	no	—
123	#63225	—	2	1	no	—
124	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
125	#63223	—	2	2	no	—
126	#63223	—	4	2	no	—
127	C₂×#3622	—	4	2	no	—
128	C₂×#3622	C₂×D₄	1	1	yes	characteristic
129	C₂×#3622	C₂×D₄	1	1	yes	characteristic
130	Dic₆₈	C₂²×C₄	1	2	yes	—
131	D₁₃₆	C₂²×C₄	1	2	yes	—
132	#63219	—	2	2	no	—
133	#63218	—	4	2	no	—
134	#63218	—	4	2	no	—
135	#63218	—	4	2	no	—
136	#63218	D₈	1	1	yes	characteristic
137	#63218	D₈	1	1	yes	characteristic
138	#63218	D₈	1	1	yes	characteristic
139	#63218	D₈	1	1	yes	characteristic
140	C₈×D₁₇	—	4	2	no	—
141	C₈×D₁₇	—	4	2	no	—
142	C₈×D₁₇	—	4	2	no	—
143	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
144	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
145	C₈×D₁₇	#41	1	1	yes	characteristic
146	C₈×D₁₇	#41	1	1	yes	characteristic
147	C₁₆×C₁₇	—	2	1	no	—
148	C₁₆×C₁₇	C₂²×C₄	1	1	yes	characteristic
149	C₁₆×C₁₇	C₂²×C₄	1	1	yes	characteristic
150	#63214	—	2	1	no	—
151	#63214	C₂²×C₄	1	1	yes	characteristic
152	#63214	C₂²×C₄	1	1	yes	characteristic
153	#33465	—	17	1	no	maximal, Sylow
154	C₂²×D₁₇	—	4	2	no	—
155	C₂²×D₁₇	#135	1	1	yes	characteristic
156	Q₈×C₁₇	—	2	2	no	—
157	D₄×C₁₇	—	2	2	no	—
158	D₄×C₁₇	—	4	2	no	—
159	C₂×C₄×C₁₇	—	2	1	no	—
160	C₂×C₄×C₁₇	—	4	2	no	—
161	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
162	C₂²⋊D₁₇	—	4	2	no	—
163	C₂²⋊D₁₇	—	4	2	no	—
164	C₂²⋊D₁₇	—	4	2	no	—
165	C₂×Dic₁₇	—	2	1	no	—
166	C₂×Dic₁₇	—	4	2	no	—
167	C₂×Dic₁₇	#135	1	1	yes	characteristic
168	D₆₈	—	2	2	no	—
169	D₆₈	—	4	2	no	—
170	C₄×D₁₇	—	4	2	no	—
171	C₄×D₁₇	—	4	2	no	—
172	C₄×D₁₇	—	4	2	no	—
173	C₄×D₁₇	C₄×D₄	1	1	yes	characteristic
174	C₄×D₁₇	C₄×D₄	1	1	yes	characteristic
175	C₄×D₁₇	C₂×D₈	1	1	yes	characteristic
176	C₄×D₁₇	C₂×D₈	1	1	yes	characteristic
177	Dic₃₄	—	2	2	no	—
178	Dic₃₄	—	4	2	no	—
179	C₈×C₁₇	—	4	2	no	—
180	C₈×C₁₇	C₂×D₈	1	1	yes	characteristic
181	C₈×C₁₇	C₂×D₈	1	1	yes	characteristic
182	C₈×C₁₇	C₂³×C₄	1	1	yes	characteristic
183	C₈×C₁₇	C₂×#41	1	1	yes	characteristic
184	#3622	—	4	2	no	—
185	#3622	C₄×D₄	1	1	yes	characteristic
186	#3622	C₄×D₄	1	1	yes	characteristic
187	#3622	C₂×D₈	1	1	yes	characteristic
188	#3622	C₂×D₈	1	1	yes	characteristic
189	C₂×#508	—	17	1	no	—
190	#2957	—	17	2	no	—
191	#2179	—	17	2	no	—
192	#2179	—	17	2	no	—
193	#2178	—	17	1	no	—
194	#2178	—	17	1	no	—
195	#2178	—	17	1	no	—
196	#2178	D₁₇	1	1	yes	characteristic, complemented
197	C₂×#368	—	17	1	no	—
198	#2143	—	17	2	no	—
199	#2108	—	17	1	no	—
200	C₂²×C₁₇	—	4	2	no	—
201	C₂²×C₁₇	C₂×#135	1	1	yes	characteristic
202	C₂×D₁₇	—	4	1	no	—
203	C₂×D₁₇	—	4	2	no	—
204	C₂×D₁₇	—	16	2	no	—
205	C₂×D₁₇	C₄×D₈	1	1	yes	characteristic
206	C₂×D₁₇	C₄×D₈	1	1	yes	characteristic
207	C₄×C₁₇	—	4	1	no	—
208	C₄×C₁₇	—	4	2	no	—
209	C₄×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
210	C₄×C₁₇	C₂²×D₈	1	1	yes	characteristic
211	Dic₁₇	—	4	1	no	—
212	Dic₁₇	—	4	2	no	—
213	Dic₁₇	C₄×D₈	1	1	yes	characteristic
214	Dic₁₇	C₄×D₈	1	1	yes	characteristic
215	C₂×#135	—	17	2	no	—
216	#568	—	34	2	no	—
217	#508	—	17	2	no	—
218	#508	—	17	1	no	—
219	#508	—	17	2	no	—
220	#508	—	17	1	no	—
221	#508	—	17	1	no	—
222	#508	C₂×D₁₇	1	1	yes	characteristic
223	C₂×Q₃₂	—	17	1	no	—
224	C₂×SD₃₂	—	17	2	no	—
225	C₂×D₁₆	—	17	1	no	—
226	C₂×M₃₂	—	17	1	no	—
227	C₂²×C₁₆	—	17	1	no	—
228	#444	—	34	2	no	—
229	#444	—	34	2	no	—
230	#443	—	17	2	no	—
231	#443	—	17	2	no	—
232	#443	—	17	2	no	—
233	#443	C₂×D₁₇	1	2	yes	complemented
234	C₂×#108	—	17	2	no	—
235	#421	—	34	2	no	—
236	#405	—	17	1	no	—
237	#368	—	17	1	no	—
238	#368	—	17	2	no	—
239	#368	C₂×D₁₇	1	1	yes	characteristic, complemented
240	#359	—	17	2	no	—
241	#359	—	17	2	no	—
242	#359	—	17	2	no	—
243	#359	C₂×D₁₇	1	2	yes	complemented
244	#346	—	17	1	no	—
245	#346	—	17	1	no	—
246	C₄×C₁₆	—	17	1	no	—
247	C₄×C₁₆	C₂×D₁₇	1	1	yes	characteristic, complemented
248	C₂×C₁₇	—	2	1	no	—
249	C₂×C₁₇	—	8	2	no	—
250	C₂×C₁₇	C₂×C₄×D₈	1	1	yes	characteristic
251	D₁₇	—	2	1	no	—
252	D₁₇	—	2	1	no	—
253	D₁₇	—	8	2	no	—
254	C₂×#41	—	34	2	no	—
255	#135	—	17	2	no	—
256	#135	—	17	2	no	—
257	#135	—	17	2	no	—
258	#135	—	34	2	no	—
259	#135	—	34	2	no	—
260	#135	C₂²×D₁₇	1	2	yes	—
261	C₂×Q₁₆	—	17	2	no	—
262	C₂×SD₁₆	—	34	2	no	—
263	C₂×D₈	—	17	2	no	—
264	#131	—	2	2	no	—
265	#131	—	34	2	no	—
266	#131	—	34	2	no	—
267	#131	—	34	2	no	—
268	#131	—	68	2	no	—
269	#131	—	68	2	no	—
270	C₂×M₁₆	—	17	1	no	—
271	C₂×M₁₆	—	34	2	no	—
272	C₂×M₁₆	—	68	2	no	—
273	C₂×M₁₆	—	68	2	no	—
274	C₂²×C₈	—	17	1	no	—
275	#117	—	17	1	no	—
276	Q₃₂	—	17	2	no	—
277	Q₃₂	—	17	1	no	—
278	Q₃₂	C₄×D₁₇	1	1	yes	characteristic
279	SD₃₂	—	17	2	no	—
280	SD₃₂	—	17	2	no	—
281	SD₃₂	—	17	2	no	—
282	SD₃₂	C₄×D₁₇	1	2	yes	—
283	D₁₆	—	17	2	no	—
284	D₁₆	—	17	1	no	—
285	D₁₆	C₄×D₁₇	1	1	yes	characteristic
286	M₃₂	—	34	1	no	—
287	M₃₂	—	34	1	no	—
288	C₂×C₁₆	—	17	1	no	—
289	C₂×C₁₆	—	17	1	no	—
290	C₂×C₁₆	—	17	1	no	—
291	C₂×C₁₆	—	17	1	no	—
292	C₂×C₁₆	—	17	1	no	—
293	C₂×C₁₆	—	17	1	no	—
294	C₂×C₁₆	C₂²×D₁₇	1	1	yes	characteristic
295	C₂×C₁₆	C₂²×D₁₇	1	1	yes	characteristic
296	#108	—	17	2	no	—
297	#108	—	34	2	no	—
298	#108	C₂²×D₁₇	1	2	yes	—
299	#104	—	2	2	no	—
300	#104	—	34	2	no	—
301	#104	—	34	2	no	—
302	#104	—	34	2	no	—
303	#97	—	17	1	no	—
304	#97	—	17	1	no	—
305	C₄×C₈	—	17	1	no	—
306	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
307	C₁₇	#33465	1	1	yes	characteristic, complemented, Sylow
308	#41	—	2	2	no	—
309	#41	—	34	2	no	—
310	#41	—	34	2	no	—
311	#41	—	34	2	no	—
312	#41	—	68	2	no	—
313	#41	—	68	2	no	—
314	C₂×Q₈	—	34	2	no	—
315	C₂×D₄	—	34	2	no	—
316	C₂×D₄	—	68	2	no	—
317	C₂²×C₄	—	17	1	no	—
318	C₂²×C₄	—	68	2	no	—
319	Q₁₆	—	17	2	no	—
320	Q₁₆	—	34	2	no	—
321	Q₁₆	C₂×C₄×D₁₇	1	2	yes	—
322	SD₁₆	—	2	2	no	—
323	SD₁₆	—	34	2	no	—
324	SD₁₆	—	34	2	no	—
325	SD₁₆	—	34	2	no	—
326	D₈	—	17	2	no	—
327	D₈	—	34	2	no	—
328	D₈	C₂×C₄×D₁₇	1	2	yes	—
329	M₁₆	—	2	2	no	—
330	M₁₆	—	4	2	no	—
331	M₁₆	—	17	1	no	—
332	M₁₆	—	17	1	no	—
333	M₁₆	—	17	1	no	—
334	M₁₆	—	17	1	no	—
335	M₁₆	—	34	2	no	—
336	M₁₆	—	68	2	no	—
337	M₁₆	—	68	2	no	—
338	M₁₆	—	68	2	no	—
339	M₁₆	—	68	2	no	—
340	C₂×C₈	—	4	2	no	—
341	C₂×C₈	—	17	1	no	—
342	C₂×C₈	—	17	1	no	—
343	C₂×C₈	—	17	1	no	—
344	C₂×C₈	—	17	1	no	—
345	C₂×C₈	—	17	1	no	—
346	C₂×C₈	—	17	1	no	—
347	C₂×C₈	—	68	2	no	—
348	C₂×C₈	—	68	2	no	—
349	C₂×C₈	—	68	2	no	—
350	C₂×C₈	—	68	2	no	—
351	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
352	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
353	C₄⋊C₄	—	34	1	no	—
354	C₂²⋊C₄	—	34	1	no	—
355	C₄²	—	17	1	no	—
356	C₄²	D₄×D₁₇	1	1	yes	characteristic
357	C₁₆	—	2	1	no	—
358	C₁₆	—	17	1	no	—
359	C₁₆	—	17	1	no	—
360	C₁₆	—	34	1	no	—
361	C₁₆	C₂×C₄×D₁₇	1	1	yes	characteristic
362	C₁₆	C₂×C₄×D₁₇	1	1	yes	characteristic
363	C₂³	—	17	1	no	—
364	C₂³	—	68	2	no	—
365	Q₈	—	2	2	no	—
366	Q₈	—	34	2	no	—
367	Q₈	—	68	2	no	—
368	D₄	—	2	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	34	2	no	—
371	D₄	—	68	2	no	—
372	D₄	—	68	2	no	—
373	D₄	—	68	2	no	—
374	D₄	—	68	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	17	1	no	—
378	C₂×C₄	—	17	1	no	—
379	C₂×C₄	—	17	1	no	—
380	C₂×C₄	—	17	1	no	—
381	C₂×C₄	—	17	1	no	—
382	C₂×C₄	—	34	1	no	—
383	C₂×C₄	—	68	2	no	—
384	C₂×C₄	—	68	2	no	—
385	C₂×C₄	—	68	2	no	—
386	C₂×C₄	—	68	2	no	—
387	C₂×C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
388	C₈	—	4	2	no	—
389	C₈	—	17	1	no	—
390	C₈	—	17	1	no	—
391	C₈	—	17	1	no	—
392	C₈	—	17	1	no	—
393	C₈	—	68	2	no	—
394	C₈	D₈×D₁₇	1	1	yes	characteristic
395	C₈	D₈×D₁₇	1	1	yes	characteristic
396	C₈	C₂²×C₄×D₁₇	1	1	yes	characteristic
397	C₈	#41×D₁₇	1	1	yes	characteristic
398	C₂²	—	4	2	no	—
399	C₂²	—	272	2	no	—
400	C₂²	—	17	1	no	—
401	C₂²	—	17	1	no	—
402	C₂²	—	68	1	no	—
403	C₂²	—	68	2	no	—
404	C₂²	#135×D₁₇	1	1	yes	characteristic
405	C₄	—	4	1	no	—
406	C₄	—	4	2	no	—
407	C₄	—	17	1	no	—
408	C₄	—	17	1	no	—
409	C₄	—	68	1	no	—
410	C₄	—	68	2	no	—
411	C₄	C₄×D₄×D₁₇	1	1	yes	characteristic
412	C₄	C₂×D₈×D₁₇	1	1	yes	characteristic
413	C₂	—	2	1	no	—
414	C₂	—	8	2	no	—
415	C₂	—	34	1	no	—
416	C₂	—	34	1	no	—
417	C₂	—	136	2	no	—
418	C₂	C₄×D₈×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₈×D₁₇
commutator	C₈×C₁₇	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₇
Fitting	C₁₇×#2178	C₂
socle	C₂×C₁₇	C₂×C₄×D₈
prime radical	D₁₇×#508	C₂
cosocle	C₂×C₈×C₁₇	C₂⁴
hypercenter	#2178	D₁₇
hypocenter	C₁₇	#33465
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #2178

Complements

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

N	H ≅ G/N	type
2. #14537696	C₂	semidirect
3. #14530668	C₂	semidirect
4. #14530667	C₂	semidirect
5. #14530666	C₂	semidirect
6. #14530665	C₂	semidirect
7. #14530664	C₂	semidirect
8. D₁₇×#368	C₂	semidirect
9. #14530510	C₂	semidirect
10. #14530379	C₂	semidirect
11. C₁₇×#2178	C₂	semidirect
14. #11763242	C₄	semidirect
16. #11763240	C₄	semidirect
18. #11763238	C₄	semidirect
19. Q₃₂×D₁₇	C₄	semidirect
20. SD₃₂×D₁₇	C₄	semidirect
21. D₁₆×D₁₇	C₄	semidirect
26. #11762927	C₂²	semidirect
27. #11762926	C₂²	semidirect
28. #11762925	C₂²	semidirect
32. #11762639	C₂²	semidirect
33. #11762638	C₂²	semidirect
34. #11762617	C₂²	semidirect
35. #11762616	C₂²	semidirect
36. #11762615	C₂²	semidirect
37. #11762585	C₂²	semidirect
38. #11762584	C₂²	semidirect
39. C₁₆×Dic₁₇	C₂²	semidirect
41. C₁₇×#443	C₂²	semidirect
42. C₁₇×#368	C₂²	semidirect
43. C₁₇×#359	C₂²	semidirect
44. C₄×C₁₆×C₁₇	C₂²	semidirect
196. #2178	D₁₇	semidirect
233. #443	C₂×D₁₇	semidirect
239. #368	C₂×D₁₇	semidirect
243. #359	C₂×D₁₇	semidirect
247. C₄×C₁₆	C₂×D₁₇	semidirect
307. C₁₇	#33465	semidirect

Maximal subgroups

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

subgroup	index
D₁₇×#508	2
#14537696	2
#14530668	2
#14530667	2
#14530666	2
#14530665	2
#14530664	2
D₁₇×#368	2
#14530510	2
#14530379	2
C₁₇×#2178	2
#33465	17