Subgroups — D₁₇×#2108 #17186956

Order 4352.

854 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₆×D₁₇	C₂	1	1	yes	maximal, characteristic
3	D₁₇×#405	C₂	1	1	yes	maximal, characteristic
4	#14530383	C₂	1	1	yes	maximal, characteristic, complemented
5	#14530382	C₂	1	2	yes	maximal, complemented
6	#14530381	C₂	1	1	yes	maximal, characteristic, complemented
7	#14530380	C₂	1	1	yes	maximal, characteristic, complemented
8	#14530379	C₂	1	2	yes	maximal, complemented
9	D₁₇×#346	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₆×D₁₇	C₂	1	2	yes	maximal, complemented
11	C₁₇×#2108	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₁₇	C₄	1	1	yes	characteristic
13	C₂²×C₈×D₁₇	C₂²	1	1	yes	characteristic
14	#117×D₁₇	C₄	1	1	yes	characteristic
15	C₂×#10587483	C₂²	1	1	yes	characteristic
16	C₂×#10587469	C₂²	1	2	yes	—
17	M₃₂×D₁₇	C₄	1	8	yes	complemented
18	C₂²×#63214	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×D₁₇	C₄	1	8	yes	complemented
20	C₂×C₁₆×D₁₇	C₂²	1	1	yes	characteristic
21	C₂×C₁₆×D₁₇	C₂²	1	1	yes	characteristic
22	C₂×C₁₆×D₁₇	C₂²	1	2	yes	—
23	C₂×C₁₆×D₁₇	C₂²	1	1	yes	characteristic
24	C₂×C₁₆×D₁₇	C₂²	1	1	yes	characteristic
25	#11762767	C₄	1	1	yes	characteristic
26	#11762766	C₄	1	2	yes	—
27	#11762765	C₄	1	1	yes	characteristic
28	#11762764	C₂²	1	1	yes	characteristic
29	#11762763	C₂²	1	2	yes	—
30	#97×D₁₇	C₄	1	2	yes	—
31	C₄×C₈×D₁₇	C₂²	1	2	yes	—
32	#11762585	C₂²	1	2	yes	complemented
33	#11762584	C₂²	1	2	yes	complemented
34	#11762584	C₂²	1	2	yes	complemented
35	C₄×#63214	C₂²	1	2	yes	complemented
36	C₁₆×Dic₁₇	C₂²	1	2	yes	complemented
37	C₁₆×Dic₁₇	C₂²	1	2	yes	complemented
38	C₂×C₁₇×M₃₂	C₂²	1	1	yes	characteristic
39	C₂²×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
40	C₁₇×#405	C₂²	1	1	yes	characteristic
41	C₁₇×#346	C₂²	1	2	yes	complemented
42	C₄×C₁₆×C₁₇	C₂²	1	2	yes	complemented
43	C₂²×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
44	C₂×M₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
46	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
47	#10587612	C₂×C₄	1	1	yes	characteristic
48	C₂×#63223	C₂×C₄	1	1	yes	characteristic
49	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
50	M₁₆×D₁₇	C₈	1	8	yes	—
51	C₂×#63218	C₂×C₄	1	2	yes	—
52	C₂×C₈×D₁₇	C₂×C₄	1	4	yes	—
53	C₂×C₈×D₁₇	C₂×C₄	1	4	yes	—
54	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
57	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
58	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
59	#10587578	C₈	1	2	yes	—
60	C₄⋊C₄×D₁₇	C₈	1	2	yes	—
61	C₂²⋊C₄×D₁₇	C₈	1	2	yes	—
62	#10587563	C₈	1	2	yes	—
63	#10587558	C₂×C₄	1	2	yes	—
64	C₄²×D₁₇	C₂×C₄	1	2	yes	—
65	C₁₇×M₃₂	C₂×C₄	1	4	yes	complemented
66	C₂×C₁₆×C₁₇	C₂×C₄	1	4	yes	complemented
67	C₂×C₁₆×C₁₇	C₂³	1	1	yes	characteristic
68	C₂×C₁₆×C₁₇	C₂³	1	2	yes	—
69	C₂×C₁₆×C₁₇	C₂³	1	1	yes	characteristic
70	C₁₇×#97	C₂×C₄	1	2	yes	—
71	C₄×C₈×C₁₇	C₂³	1	2	yes	—
72	#10587486	C₂×C₄	1	2	yes	—
73	#10587486	C₂×C₄	1	2	yes	—
74	C₈×Dic₁₇	C₂×C₄	1	2	yes	—
75	C₈×Dic₁₇	C₂³	1	2	yes	—
76	#10587483	C₂×C₄	1	4	yes	complemented
77	C₂×#63214	C₂×C₄	1	4	yes	complemented
78	C₂×#63214	C₂³	1	1	yes	characteristic
79	C₂×#63214	C₂³	1	1	yes	characteristic
80	C₂×#63214	C₂³	1	2	yes	—
81	#10587474	C₂×C₄	1	2	yes	—
82	C₄×#3622	C₂×C₄	1	2	yes	—
83	#10587469	C₂×C₄	1	8	yes	complemented
84	C₁₆×D₁₇	C₂×C₄	1	4	yes	—
85	C₁₆×D₁₇	C₂×C₄	1	4	yes	—
86	C₁₆×D₁₇	C₂×C₄	1	8	yes	—
87	C₁₆×D₁₇	C₂×C₄	1	4	yes	complemented
88	C₁₆×D₁₇	C₂×C₄	1	4	yes	complemented
89	C₂³×D₁₇	C₂×C₈	1	1	yes	characteristic
90	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×Dic₁₇	C₂×C₈	1	1	yes	characteristic
92	C₂×C₄×D₁₇	C₄²	1	4	yes	—
93	C₂×C₄×D₁₇	C₂×C₈	1	4	yes	—
94	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
95	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
96	C₂×C₄×D₁₇	C₂×C₈	1	4	yes	—
97	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
99	M₁₆×C₁₇	C₂×C₈	1	4	yes	—
100	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
102	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
103	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
104	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
105	C₄⋊C₄×C₁₇	C₂×C₈	1	2	yes	—
106	C₂²⋊C₄×C₁₇	C₂×C₈	1	2	yes	—
107	C₄²×C₁₇	C₂²×C₄	1	2	yes	—
108	C₂²⋊Dic₁₇	C₂×C₈	1	2	yes	—
109	#63227	C₂×C₈	1	4	yes	—
110	C₄⋊Dic₁₇	C₂×C₈	1	2	yes	—
111	#63225	C₂×C₈	1	4	yes	—
112	C₄×Dic₁₇	C₂×C₈	1	4	yes	—
113	C₄×Dic₁₇	C₂²×C₄	1	2	yes	—
114	#63223	C₂×C₈	1	4	yes	—
115	C₂×#3622	C₄²	1	4	yes	—
116	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
117	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
118	C₂×#3622	C₂²×C₄	1	2	yes	—
119	#63218	C₂×C₈	1	8	yes	—
120	C₈×D₁₇	C₄²	1	4	yes	—
121	C₈×D₁₇	C₄²	1	4	yes	—
122	C₈×D₁₇	C₂×C₈	1	8	yes	—
123	C₈×D₁₇	C₂²×C₄	1	2	yes	—
124	C₈×D₁₇	C₂²×C₄	1	2	yes	—
125	C₈×D₁₇	C₂²×C₄	1	2	yes	—
126	C₈×D₁₇	C₂²×C₄	1	2	yes	—
127	C₁₆×C₁₇	C₂²×C₄	1	2	yes	—
128	C₁₆×C₁₇	C₂²×C₄	1	2	yes	—
129	C₁₆×C₁₇	C₂²×C₄	1	4	yes	—
130	#63214	C₂²×C₄	1	2	yes	—
131	#63214	C₂²×C₄	1	2	yes	—
132	#63214	C₂²×C₄	1	4	yes	—
133	C₂×#2108	—	17	1	no	maximal, Sylow
134	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
135	C₂²×D₁₇	—	2	4	no	—
136	C₂²×D₁₇	C₄×C₈	1	4	yes	—
137	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
138	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
139	C₂×C₄×C₁₇	C₂×C₄²	1	2	yes	—
140	C₂×C₄×C₁₇	C₂²×C₈	1	4	yes	—
141	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
142	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
143	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
144	C₂×Dic₁₇	C₄×C₈	1	4	yes	—
145	C₂×Dic₁₇	C₂²×C₈	1	4	yes	—
146	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
147	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
148	C₄×D₁₇	—	2	8	no	—
149	C₄×D₁₇	C₄×C₈	1	4	yes	—
150	C₄×D₁₇	C₄×C₈	1	4	yes	—
151	C₄×D₁₇	C₂×C₄²	1	2	yes	—
152	C₄×D₁₇	C₂×C₄²	1	2	yes	—
153	C₄×D₁₇	C₂²×C₈	1	2	yes	—
154	C₄×D₁₇	C₂²×C₈	1	2	yes	—
155	C₈×C₁₇	C₂×C₄²	1	2	yes	—
156	C₈×C₁₇	C₂²×C₈	1	4	yes	—
157	C₈×C₁₇	C₂³×C₄	1	1	yes	characteristic
158	C₈×C₁₇	C₂³×C₄	1	1	yes	characteristic
159	#3622	C₂×C₄²	1	2	yes	—
160	#3622	C₂×C₄²	1	2	yes	—
161	#3622	C₂²×C₈	1	4	yes	—
162	C₂²×M₃₂	—	17	1	no	—
163	C₂³×C₁₆	—	17	1	no	—
164	C₂×#405	—	17	1	no	—
165	#2108	—	17	1	no	—
166	#2108	—	17	1	no	—
167	#2108	—	17	1	no	—
168	#2108	—	17	2	no	—
169	#2108	—	17	2	no	—
170	#2108	D₁₇	1	1	yes	characteristic, direct product factor
171	C₂×#346	—	17	2	no	—
172	C₂×C₄×C₁₆	—	17	2	no	—
173	C₂²×C₁₇	—	2	2	no	—
174	C₂²×C₁₇	C₂×C₄×C₈	1	2	yes	—
175	C₂²×C₁₇	C₂³×C₈	1	1	yes	characteristic
176	C₂×D₁₇	—	2	2	no	—
177	C₂×D₁₇	—	2	8	no	—
178	C₂×D₁₇	C₂×C₄×C₈	1	2	yes	—
179	C₂×D₁₇	C₂×C₄×C₈	1	2	yes	—
180	C₂×D₁₇	#504	1	4	yes	—
181	C₄×C₁₇	—	2	4	no	—
182	C₄×C₁₇	C₂×C₄×C₈	1	2	yes	—
183	C₄×C₁₇	C₂²×C₄²	1	1	yes	characteristic
184	C₄×C₁₇	C₂³×C₈	1	1	yes	characteristic
185	Dic₁₇	—	2	4	no	—
186	Dic₁₇	C₂×C₄×C₈	1	2	yes	—
187	Dic₁₇	C₂×C₄×C₈	1	2	yes	—
188	C₂²×M₁₆	—	17	1	no	—
189	C₂³×C₈	—	17	1	no	—
190	C₂×#117	—	17	1	no	—
191	C₂×M₃₂	—	17	1	no	—
192	C₂×M₃₂	—	17	8	no	—
193	C₂×M₃₂	—	17	2	no	—
194	C₂×M₃₂	C₂×D₁₇	1	1	yes	characteristic
195	C₂²×C₁₆	—	17	1	no	—
196	C₂²×C₁₆	—	17	8	no	—
197	C₂²×C₁₆	—	17	2	no	—
198	C₂²×C₁₆	—	17	1	no	—
199	C₂²×C₁₆	—	17	1	no	—
200	C₂²×C₁₆	—	17	1	no	—
201	C₂²×C₁₆	—	17	1	no	—
202	C₂²×C₁₆	C₂×D₁₇	1	1	yes	characteristic
203	#405	—	17	1	no	—
204	#405	—	17	1	no	—
205	#405	—	17	1	no	—
206	#405	—	17	2	no	—
207	#405	—	17	2	no	—
208	#405	C₂×D₁₇	1	1	yes	characteristic
209	C₂×#97	—	17	2	no	—
210	C₂×C₄×C₈	—	17	2	no	—
211	#346	—	17	2	no	—
212	#346	—	17	2	no	—
213	#346	—	17	2	no	—
214	#346	C₂×D₁₇	1	2	yes	complemented
215	C₄×C₁₆	—	17	2	no	—
216	C₄×C₁₆	—	17	2	no	—
217	C₄×C₁₆	—	17	2	no	—
218	C₄×C₁₆	C₂×D₁₇	1	2	yes	complemented
219	C₂×C₁₇	—	2	2	no	—
220	C₂×C₁₇	C₂²×C₄×C₈	1	1	yes	characteristic
221	C₂×C₁₇	C₂×#504	1	2	yes	—
222	D₁₇	—	2	2	no	—
223	D₁₇	#2108	1	4	yes	direct product factor
224	C₂³×C₄	—	17	1	no	—
225	C₂×M₁₆	—	17	1	no	—
226	C₂×M₁₆	—	17	8	no	—
227	C₂×M₁₆	—	17	2	no	—
228	C₂×M₁₆	C₄×D₁₇	1	1	yes	characteristic
229	C₂²×C₈	—	17	1	no	—
230	C₂²×C₈	—	17	1	no	—
231	C₂²×C₈	—	17	1	no	—
232	C₂²×C₈	—	17	4	no	—
233	C₂²×C₈	—	17	4	no	—
234	C₂²×C₈	—	17	2	no	—
235	C₂²×C₈	—	17	1	no	—
236	C₂²×C₈	—	17	1	no	—
237	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
238	#117	—	17	1	no	—
239	#117	—	17	2	no	—
240	#117	—	17	2	no	—
241	#117	—	17	2	no	—
242	#117	C₄×D₁₇	1	1	yes	characteristic
243	C₂×C₄⋊C₄	—	17	2	no	—
244	C₂×C₂²⋊C₄	—	17	2	no	—
245	C₂×C₄²	—	17	2	no	—
246	M₃₂	—	17	4	no	—
247	M₃₂	—	17	8	no	—
248	M₃₂	C₄×D₁₇	1	4	yes	complemented
249	C₂×C₁₆	—	17	4	no	—
250	C₂×C₁₆	—	17	1	no	—
251	C₂×C₁₆	—	17	2	no	—
252	C₂×C₁₆	—	17	1	no	—
253	C₂×C₁₆	—	17	4	no	—
254	C₂×C₁₆	—	17	4	no	—
255	C₂×C₁₆	—	17	8	no	—
256	C₂×C₁₆	—	17	4	no	—
257	C₂×C₁₆	—	17	4	no	—
258	C₂×C₁₆	C₄×D₁₇	1	4	yes	complemented
259	C₂×C₁₆	C₂²×D₁₇	1	2	yes	—
260	C₂×C₁₆	C₂²×D₁₇	1	1	yes	characteristic
261	C₂×C₁₆	C₂²×D₁₇	1	1	yes	characteristic
262	#97	—	17	2	no	—
263	#97	—	17	2	no	—
264	#97	—	17	2	no	—
265	#97	C₄×D₁₇	1	2	yes	—
266	C₄×C₈	—	17	2	no	—
267	C₄×C₈	—	17	2	no	—
268	C₄×C₈	—	17	2	no	—
269	C₄×C₈	C₂²×D₁₇	1	2	yes	—
270	C₁₇	C₂×#2108	1	1	yes	characteristic, complemented, Sylow
271	C₂⁴	—	17	1	no	—
272	C₂²×C₄	—	17	1	no	—
273	C₂²×C₄	—	17	1	no	—
274	C₂²×C₄	—	17	1	no	—
275	C₂²×C₄	—	17	4	no	—
276	C₂²×C₄	—	17	1	no	—
277	C₂²×C₄	—	17	1	no	—
278	C₂²×C₄	—	17	4	no	—
279	C₂²×C₄	—	17	4	no	—
280	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
281	M₁₆	—	17	4	no	—
282	M₁₆	—	17	8	no	—
283	M₁₆	C₈×D₁₇	1	4	yes	—
284	C₂×C₈	—	17	1	no	—
285	C₂×C₈	—	17	2	no	—
286	C₂×C₈	—	17	1	no	—
287	C₂×C₈	—	17	4	no	—
288	C₂×C₈	—	17	2	no	—
289	C₂×C₈	—	17	2	no	—
290	C₂×C₈	—	17	2	no	—
291	C₂×C₈	—	17	2	no	—
292	C₂×C₈	—	17	4	no	—
293	C₂×C₈	—	17	4	no	—
294	C₂×C₈	—	17	8	no	—
295	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
296	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
297	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
298	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
299	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
300	C₄⋊C₄	—	17	4	no	—
301	C₄⋊C₄	—	17	2	no	—
302	C₄⋊C₄	C₈×D₁₇	1	2	yes	—
303	C₂²⋊C₄	—	17	2	no	—
304	C₂²⋊C₄	—	17	4	no	—
305	C₂²⋊C₄	C₈×D₁₇	1	2	yes	—
306	C₄²	—	17	2	no	—
307	C₄²	—	17	4	no	—
308	C₄²	C₂×C₄×D₁₇	1	2	yes	—
309	C₁₆	—	17	2	no	—
310	C₁₆	—	17	2	no	—
311	C₁₆	—	17	4	no	—
312	C₁₆	C₂×C₄×D₁₇	1	2	yes	—
313	C₁₆	C₂×C₄×D₁₇	1	2	yes	—
314	C₁₆	C₂×C₄×D₁₇	1	4	yes	—
315	C₂³	—	17	1	no	—
316	C₂³	—	17	4	no	—
317	C₂³	—	17	1	no	—
318	C₂³	—	34	4	no	—
319	C₂³	C₂×C₈×D₁₇	1	1	yes	characteristic
320	C₂×C₄	—	17	4	no	—
321	C₂×C₄	—	17	1	no	—
322	C₂×C₄	—	17	1	no	—
323	C₂×C₄	—	17	2	no	—
324	C₂×C₄	—	17	2	no	—
325	C₂×C₄	—	17	4	no	—
326	C₂×C₄	—	17	4	no	—
327	C₂×C₄	—	17	2	no	—
328	C₂×C₄	—	17	2	no	—
329	C₂×C₄	—	17	4	no	—
330	C₂×C₄	—	34	8	no	—
331	C₂×C₄	C₄²×D₁₇	1	2	yes	—
332	C₂×C₄	C₂×C₈×D₁₇	1	4	yes	—
333	C₂×C₄	C₂×C₈×D₁₇	1	1	yes	characteristic
334	C₂×C₄	C₂×C₈×D₁₇	1	2	yes	—
335	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
336	C₈	—	17	2	no	—
337	C₈	—	17	2	no	—
338	C₈	—	17	4	no	—
339	C₈	C₄²×D₁₇	1	2	yes	—
340	C₈	C₂×C₈×D₁₇	1	4	yes	—
341	C₈	C₂²×C₄×D₁₇	1	1	yes	characteristic
342	C₈	C₂²×C₄×D₁₇	1	1	yes	characteristic
343	C₂²	—	2	2	no	—
344	C₂²	—	17	4	no	—
345	C₂²	—	17	2	no	—
346	C₂²	—	17	2	no	—
347	C₂²	—	34	8	no	—
348	C₂²	—	34	2	no	—
349	C₂²	C₄×C₈×D₁₇	1	2	yes	—
350	C₂²	C₂²×C₈×D₁₇	1	1	yes	characteristic
351	C₄	—	2	4	no	—
352	C₄	—	17	2	no	—
353	C₄	—	17	2	no	—
354	C₄	—	34	4	no	—
355	C₄	C₄×C₈×D₁₇	1	2	yes	—
356	C₄	C₂×C₄²×D₁₇	1	1	yes	characteristic
357	C₄	C₂²×C₈×D₁₇	1	1	yes	characteristic
358	C₂	—	2	2	no	—
359	C₂	—	17	4	no	—
360	C₂	—	34	2	no	—
361	C₂	C₂×C₄×C₈×D₁₇	1	1	yes	characteristic
362	C₂	D₁₇×#504	1	2	yes	—

	subgroup	G/H
center	C₂×C₁₆	C₂²×D₁₇
commutator	C₂×C₁₇	C₂²×C₄×C₈
Frattini	C₂×C₈	C₂³×D₁₇
Fitting	C₁₇×#2108	C₂
socle	C₂²×C₁₇	C₂³×C₈
prime radical	C₂³×D₁₇	C₂×C₈
cosocle	C₂×C₈×C₁₇	C₂⁴
hypercenter	#2108	D₁₇
hypocenter	C₁₇	C₂×#2108
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₁₆ ◁ #2108

Complements

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

N	H ≅ G/N	type
4. #14530383	C₂	semidirect
5. #14530382	C₂	semidirect
6. #14530381	C₂	semidirect
7. #14530380	C₂	semidirect
8. #14530379	C₂	semidirect
9. D₁₇×#346	C₂	semidirect
10. C₄×C₁₆×D₁₇	C₂	semidirect
11. C₁₇×#2108	C₂	semidirect
17. M₃₂×D₁₇	C₄	semidirect
19. C₂×C₁₆×D₁₇	C₄	semidirect
32. #11762585	C₂²	semidirect
33. #11762584	C₂²	semidirect
34. #11762584	C₂²	semidirect
35. C₄×#63214	C₂²	semidirect
36. C₁₆×Dic₁₇	C₂²	semidirect
37. C₁₆×Dic₁₇	C₂²	semidirect
41. C₁₇×#346	C₂²	semidirect
42. C₄×C₁₆×C₁₇	C₂²	semidirect
65. C₁₇×M₃₂	C₂×C₄	semidirect
66. C₂×C₁₆×C₁₇	C₂×C₄	semidirect
76. #10587483	C₂×C₄	semidirect
77. C₂×#63214	C₂×C₄	semidirect
83. #10587469	C₂×C₄	semidirect
87. C₁₆×D₁₇	C₂×C₄	semidirect
88. C₁₆×D₁₇	C₂×C₄	semidirect
170. #2108	D₁₇	direct (N × H)
214. #346	C₂×D₁₇	semidirect
218. C₄×C₁₆	C₂×D₁₇	semidirect
223. D₁₇	#2108	direct (N × H)
248. M₃₂	C₄×D₁₇	semidirect
258. C₂×C₁₆	C₄×D₁₇	semidirect
270. C₁₇	C₂×#2108	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₃₂×D₁₇	2
C₂²×C₁₆×D₁₇	2
D₁₇×#405	2
#14530383	2
#14530382	2
#14530381	2
#14530380	2
#14530379	2
D₁₇×#346	2
C₄×C₁₆×D₁₇	2
C₁₇×#2108	2
C₂×#2108	17

Subgroups — D17×#2108 #17186956

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₇×#2108 #17186956