Subgroups — C₁₇×#22669 #16880413

Order 4352.

862 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×M₁₆×C₁₇	C₂	1	2	yes	maximal
2	C₂×C₁₇×#436	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₇×#430	C₂	1	2	yes	maximal, complemented
4	C₁₇×#1950	C₂	1	2	yes	maximal, complemented
5	C₁₇×#1855	C₂	1	4	yes	maximal, complemented
6	C₁₇×#1848	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1811	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₇×#108	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×M₁₆×C₁₇	C₂²	1	4	yes	—
10	C₂²×M₁₆×C₁₇	C₂²	1	2	yes	—
11	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
12	C₁₇×#436	—	2	2	no	—
13	C₁₇×#436	C₄	1	4	yes	—
14	C₁₇×#436	C₄	1	4	yes	—
15	C₁₇×#435	—	2	4	no	—
16	C₈×D₄×C₁₇	—	2	2	no	—
17	C₁₇×#430	—	2	8	no	—
18	C₂×C₁₇×#108	C₂²	1	4	yes	—
19	C₂×C₁₇×#108	C₂²	1	1	yes	characteristic
20	C₂×C₁₇×#108	C₂²	1	2	yes	—
21	C₂×C₁₇×#108	C₂²	1	2	yes	—
22	C₂×C₁₇×#108	C₂²	1	1	yes	characteristic
23	C₁₇×#423	C₂²	1	2	yes	—
24	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₁₇×#407	C₂²	1	4	yes	—
26	C₂×C₁₇×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₄×M₁₆×C₁₇	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
29	C₁₇×#341	C₂²	1	4	yes	—
30	C₁₇×#341	C₂²	1	2	yes	—
31	C₂²×D₄×C₁₇	Q₈	1	1	yes	characteristic
32	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
33	C₂×M₁₆×C₁₇	—	2	4	no	—
34	C₂×M₁₆×C₁₇	—	2	4	no	—
35	C₂×M₁₆×C₁₇	—	2	4	no	—
36	C₂×M₁₆×C₁₇	—	2	8	no	—
37	C₂×M₁₆×C₁₇	—	4	4	no	—
38	C₂×M₁₆×C₁₇	C₂×C₄	1	8	yes	—
39	C₂×M₁₆×C₁₇	C₂³	1	4	yes	—
40	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
41	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₇	—	2	4	no	—
43	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
46	C₄×D₄×C₁₇	C₂×C₄	1	2	yes	—
47	C₄×D₄×C₁₇	C₂×C₄	1	2	yes	—
48	C₄×D₄×C₁₇	D₄	1	2	yes	—
49	C₄×D₄×C₁₇	D₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₁₇	Q₈	1	1	yes	characteristic
51	C₂×C₂²⋊C₄×C₁₇	Q₈	1	2	yes	—
52	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
53	C₁₇×#108	—	2	8	no	—
54	C₁₇×#108	—	2	4	no	—
55	C₁₇×#108	—	2	2	no	—
56	C₁₇×#108	—	4	2	no	—
57	C₁₇×#108	D₄	1	4	yes	complemented
58	C₁₇×C₄⋊C₈	—	2	2	no	—
59	C₁₇×C₄⋊C₈	—	2	2	no	—
60	C₁₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
61	C₁₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
62	C₁₇×C₂²⋊C₈	—	2	4	no	—
63	C₁₇×C₂²⋊C₈	—	2	4	no	—
64	C₁₇×C₂²⋊C₈	C₂×C₄	1	8	yes	—
65	C₁₇×#97	—	2	2	no	—
66	C₄×C₈×C₁₇	—	2	2	no	—
67	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	—
68	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	—
69	C₂⁴×C₁₇	C₂×Q₈	1	2	yes	—
70	C₂×D₄×C₁₇	—	4	2	no	—
71	C₂×D₄×C₁₇	C₄⋊C₄	1	2	yes	—
72	C₂×D₄×C₁₇	C₄⋊C₄	1	2	yes	—
73	C₂²×C₄×C₁₇	—	2	2	no	—
74	C₂²×C₄×C₁₇	—	2	2	no	—
75	C₂²×C₄×C₁₇	—	2	2	no	—
76	C₂²×C₄×C₁₇	—	2	2	no	—
77	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	—
78	C₂²×C₄×C₁₇	C₂×D₄	1	4	yes	—
79	C₂²×C₄×C₁₇	C₂×Q₈	1	2	yes	—
80	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
81	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
82	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
83	M₁₆×C₁₇	—	2	2	no	—
84	M₁₆×C₁₇	—	2	16	no	—
85	M₁₆×C₁₇	—	2	4	no	—
86	M₁₆×C₁₇	—	2	2	no	—
87	M₁₆×C₁₇	—	2	4	no	—
88	M₁₆×C₁₇	—	2	2	no	—
89	M₁₆×C₁₇	—	4	8	no	—
90	M₁₆×C₁₇	C₂×D₄	1	4	yes	—
91	C₂×C₈×C₁₇	—	2	2	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	4	no	—
97	C₂×C₈×C₁₇	—	2	2	no	—
98	C₂×C₈×C₁₇	—	4	8	no	—
99	C₂×C₈×C₁₇	C₂²×C₄	1	4	yes	—
100	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
102	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
103	C₂×C₈×C₁₇	#41	1	2	yes	—
104	C₄⋊C₄×C₁₇	C₄⋊C₄	1	2	yes	—
105	C₄⋊C₄×C₁₇	C₄⋊C₄	1	2	yes	—
106	C₂²⋊C₄×C₁₇	C₄⋊C₄	1	4	yes	—
107	C₂²⋊C₄×C₁₇	C₄⋊C₄	1	4	yes	—
108	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
112	#22669	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂³×C₁₇	—	2	2	no	—
114	C₂³×C₁₇	—	2	2	no	—
115	C₂³×C₁₇	—	4	2	no	—
116	C₂³×C₁₇	—	4	2	no	—
117	C₂³×C₁₇	C₂×C₄⋊C₄	1	4	yes	—
118	C₂³×C₁₇	C₂²×Q₈	1	1	yes	characteristic
119	D₄×C₁₇	—	2	4	no	—
120	D₄×C₁₇	—	4	2	no	—
121	C₂×C₄×C₁₇	—	2	2	no	—
122	C₂×C₄×C₁₇	—	2	2	no	—
123	C₂×C₄×C₁₇	—	2	4	no	—
124	C₂×C₄×C₁₇	—	2	4	no	—
125	C₂×C₄×C₁₇	—	2	4	no	—
126	C₂×C₄×C₁₇	—	2	4	no	—
127	C₂×C₄×C₁₇	—	2	2	no	—
128	C₂×C₄×C₁₇	—	4	1	no	—
129	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	4	yes	—
133	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
136	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
137	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
138	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
139	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
140	C₈×C₁₇	—	2	4	no	—
141	C₈×C₁₇	—	2	2	no	—
142	C₈×C₁₇	—	2	4	no	—
143	C₈×C₁₇	—	4	4	no	—
144	C₈×C₁₇	—	4	2	no	—
145	C₈×C₁₇	C₄×D₄	1	4	yes	—
146	D₄×M₁₆	C₂×C₁₇	1	2	yes	—
147	C₂×#436	C₂×C₁₇	1	1	yes	characteristic
148	C₂×#430	C₂×C₁₇	1	2	yes	complemented
149	#1950	C₂×C₁₇	1	2	yes	complemented
150	#1855	C₂×C₁₇	1	4	yes	complemented
151	#1848	C₂×C₁₇	1	1	yes	characteristic, complemented
152	#1811	C₂×C₁₇	1	2	yes	complemented
153	C₄×#108	C₂×C₁₇	1	1	yes	characteristic, complemented
154	C₂²×C₁₇	—	2	1	no	—
155	C₂²×C₁₇	—	2	1	no	—
156	C₂²×C₁₇	—	2	4	no	—
157	C₂²×C₁₇	—	2	4	no	—
158	C₂²×C₁₇	—	2	4	no	—
159	C₂²×C₁₇	—	8	2	no	—
160	C₂²×C₁₇	—	8	2	no	—
161	C₂²×C₁₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
162	C₂²×C₁₇	D₄×Q₈	1	1	yes	characteristic
163	C₂²×C₁₇	#554	1	1	yes	characteristic
164	C₄×C₁₇	—	2	4	no	—
165	C₄×C₁₇	—	2	1	no	—
166	C₄×C₁₇	—	2	1	no	—
167	C₄×C₁₇	—	2	1	no	—
168	C₄×C₁₇	#430	1	2	yes	complemented
169	C₄×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
170	C₄×C₁₇	#520	1	1	yes	characteristic
171	C₄×C₁₇	D₄²	1	1	yes	characteristic
172	C₄×C₁₇	#547	1	1	yes	characteristic
173	C₂²×M₁₆	C₂²×C₁₇	1	4	yes	—
174	C₂²×M₁₆	C₂²×C₁₇	1	2	yes	—
175	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
176	#436	—	2	2	no	—
177	#436	C₄×C₁₇	1	4	yes	—
178	#436	C₄×C₁₇	1	4	yes	—
179	#435	—	2	4	no	—
180	C₈×D₄	—	2	2	no	—
181	#430	—	2	8	no	—
182	C₂×#108	C₂²×C₁₇	1	1	yes	characteristic
183	C₂×#108	C₂²×C₁₇	1	2	yes	—
184	C₂×#108	C₂²×C₁₇	1	4	yes	—
185	C₂×#108	C₂²×C₁₇	1	2	yes	—
186	C₂×#108	C₂²×C₁₇	1	1	yes	characteristic
187	#423	C₂²×C₁₇	1	2	yes	—
188	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
189	#407	C₂²×C₁₇	1	4	yes	—
190	C₂×C₂²⋊C₈	C₂²×C₁₇	1	2	yes	—
191	C₄×M₁₆	C₂²×C₁₇	1	2	yes	—
192	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
193	#341	C₂²×C₁₇	1	4	yes	—
194	#341	C₂²×C₁₇	1	2	yes	—
195	C₂×C₁₇	—	2	1	no	—
196	C₂×C₁₇	—	2	1	no	—
197	C₂×C₁₇	—	4	4	no	—
198	C₂×C₁₇	D₄×C₄⋊C₄	1	1	yes	characteristic
199	C₂×C₁₇	C₂×#430	1	1	yes	characteristic
200	C₂×C₁₇	#2916	1	1	yes	characteristic
201	C₂²×D₄	Q₈×C₁₇	1	1	yes	characteristic
202	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
203	C₂×M₁₆	—	2	4	no	—
204	C₂×M₁₆	—	2	4	no	—
205	C₂×M₁₆	—	2	4	no	—
206	C₂×M₁₆	—	2	8	no	—
207	C₂×M₁₆	—	4	4	no	—
208	C₂×M₁₆	C₂×C₄×C₁₇	1	8	yes	—
209	C₂×M₁₆	C₂³×C₁₇	1	4	yes	—
210	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
211	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
212	C₂²×C₈	—	2	4	no	—
213	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
214	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
215	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
216	C₄×D₄	C₂×C₄×C₁₇	1	2	yes	—
217	C₄×D₄	C₂×C₄×C₁₇	1	2	yes	—
218	C₄×D₄	D₄×C₁₇	1	2	yes	—
219	C₄×D₄	D₄×C₁₇	1	2	yes	—
220	C₂×C₄⋊C₄	Q₈×C₁₇	1	1	yes	characteristic
221	C₂×C₂²⋊C₄	Q₈×C₁₇	1	2	yes	—
222	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
223	#108	—	2	8	no	—
224	#108	—	2	4	no	—
225	#108	—	2	2	no	—
226	#108	—	4	2	no	—
227	#108	D₄×C₁₇	1	4	yes	complemented
228	C₄⋊C₈	—	2	2	no	—
229	C₄⋊C₈	—	2	2	no	—
230	C₄⋊C₈	C₂×C₄×C₁₇	1	2	yes	—
231	C₄⋊C₈	C₂×C₄×C₁₇	1	2	yes	—
232	C₂²⋊C₈	—	2	4	no	—
233	C₂²⋊C₈	—	2	4	no	—
234	C₂²⋊C₈	C₂×C₄×C₁₇	1	8	yes	—
235	#97	—	2	2	no	—
236	C₄×C₈	—	2	2	no	—
237	C₄×C₈	C₂×C₄×C₁₇	1	2	yes	—
238	C₄×C₈	C₂×C₄×C₁₇	1	2	yes	—
239	C₁₇	#22669	1	1	yes	characteristic, direct product factor, Sylow
240	C₂⁴	C₂×Q₈×C₁₇	1	2	yes	—
241	C₂×D₄	—	4	2	no	—
242	C₂×D₄	C₄⋊C₄×C₁₇	1	2	yes	—
243	C₂×D₄	C₄⋊C₄×C₁₇	1	2	yes	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	C₂²×C₄×C₁₇	1	4	yes	—
249	C₂²×C₄	C₂×D₄×C₁₇	1	4	yes	—
250	C₂²×C₄	C₂×Q₈×C₁₇	1	1	yes	characteristic
251	C₂²×C₄	C₂×Q₈×C₁₇	1	2	yes	—
252	C₂²×C₄	C₂×Q₈×C₁₇	1	1	yes	characteristic
253	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
254	M₁₆	—	2	2	no	—
255	M₁₆	—	2	16	no	—
256	M₁₆	—	2	4	no	—
257	M₁₆	—	2	2	no	—
258	M₁₆	—	2	4	no	—
259	M₁₆	—	2	2	no	—
260	M₁₆	—	4	8	no	—
261	M₁₆	C₂×D₄×C₁₇	1	4	yes	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	1	no	—
266	C₂×C₈	—	2	1	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	4	no	—
269	C₂×C₈	—	4	8	no	—
270	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
271	C₂×C₈	C₂²×C₄×C₁₇	1	4	yes	—
272	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
273	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
274	C₂×C₈	#41×C₁₇	1	2	yes	—
275	C₄⋊C₄	C₄⋊C₄×C₁₇	1	2	yes	—
276	C₄⋊C₄	C₄⋊C₄×C₁₇	1	2	yes	—
277	C₂²⋊C₄	C₄⋊C₄×C₁₇	1	4	yes	—
278	C₂²⋊C₄	C₄⋊C₄×C₁₇	1	4	yes	—
279	C₄²	C₂²×C₄×C₁₇	1	1	yes	characteristic
280	C₄²	C₂²×C₄×C₁₇	1	1	yes	characteristic
281	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
282	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
283	C₂³	—	2	2	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	4	2	no	—
286	C₂³	—	4	2	no	—
287	C₂³	C₂×C₄⋊C₄×C₁₇	1	4	yes	—
288	C₂³	C₂²×Q₈×C₁₇	1	1	yes	characteristic
289	D₄	—	2	4	no	—
290	D₄	—	4	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	4	1	no	—
299	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
300	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
301	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
302	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	4	yes	—
303	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
304	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
305	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
306	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
307	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
308	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
309	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
310	C₈	—	2	4	no	—
311	C₈	—	2	2	no	—
312	C₈	—	2	4	no	—
313	C₈	—	4	4	no	—
314	C₈	—	4	2	no	—
315	C₈	C₄×D₄×C₁₇	1	4	yes	—
316	C₂²	—	2	1	no	—
317	C₂²	—	2	1	no	—
318	C₂²	—	2	4	no	—
319	C₂²	—	2	4	no	—
320	C₂²	—	2	4	no	—
321	C₂²	—	8	2	no	—
322	C₂²	—	8	2	no	—
323	C₂²	C₂²×C₄⋊C₄×C₁₇	1	1	yes	characteristic
324	C₂²	D₄×Q₈×C₁₇	1	1	yes	characteristic
325	C₂²	C₁₇×#554	1	1	yes	characteristic
326	C₄	—	2	4	no	—
327	C₄	—	2	1	no	—
328	C₄	—	2	1	no	—
329	C₄	—	2	1	no	—
330	C₄	C₁₇×#430	1	2	yes	complemented
331	C₄	C₂×C₄×D₄×C₁₇	1	1	yes	characteristic
332	C₄	C₁₇×#520	1	1	yes	characteristic
333	C₄	D₄²×C₁₇	1	1	yes	characteristic
334	C₄	C₁₇×#547	1	1	yes	characteristic
335	C₂	—	2	1	no	—
336	C₂	—	2	1	no	—
337	C₂	—	4	4	no	—
338	C₂	D₄×C₄⋊C₄×C₁₇	1	1	yes	characteristic
339	C₂	C₂×C₁₇×#430	1	1	yes	characteristic
340	C₂	C₁₇×#2916	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
socle	C₂²×C₁₇	C₂²×C₄⋊C₄
prime radical	C₂²×D₄×C₁₇	Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₄×D₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₇×#430	C₂	semidirect
4. C₁₇×#1950	C₂	semidirect
5. C₁₇×#1855	C₂	semidirect
6. C₁₇×#1848	C₂	semidirect
7. C₁₇×#1811	C₂	semidirect
8. C₄×C₁₇×#108	C₂	semidirect
57. C₁₇×#108	D₄	semidirect
112. #22669	C₁₇	direct (N × H)
148. C₂×#430	C₂×C₁₇	semidirect
149. #1950	C₂×C₁₇	semidirect
150. #1855	C₂×C₁₇	semidirect
151. #1848	C₂×C₁₇	semidirect
152. #1811	C₂×C₁₇	semidirect
153. C₄×#108	C₂×C₁₇	semidirect
168. C₄×C₁₇	#430	semidirect
227. #108	D₄×C₁₇	semidirect
239. C₁₇	#22669	direct (N × H)
330. C₄	C₁₇×#430	semidirect

Maximal subgroups

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

subgroup	index
D₄×M₁₆×C₁₇	2
C₂×C₁₇×#436	2
C₂×C₁₇×#430	2
C₁₇×#1950	2
C₁₇×#1855	2
C₁₇×#1848	2
C₁₇×#1811	2
C₄×C₁₇×#108	2
#22669	17

Subgroups — C17×#22669 #16880413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#22669 #16880413