Subgroups — C₁₇×#8148 #16865892

Order 4352.

578 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#431	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₇×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₇×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₇×#322	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₈²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1273	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1273	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
9	C₁₇×#431	—	2	2	no	—
10	C₁₇×#431	—	2	2	no	—
11	C₂×C₁₇×C₄⋊C₈	C₄	1	2	yes	—
12	C₂×C₁₇×C₂²⋊C₈	C₄	1	2	yes	—
13	C₂×C₁₇×C₂²⋊C₈	C₄	1	2	yes	—
14	C₂×C₁₇×C₂²⋊C₈	C₄	1	2	yes	—
15	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
21	C₁₇×#336	C₄	1	2	yes	—
22	C₁₇×#336	C₄	1	2	yes	—
23	C₁₇×#322	—	2	2	no	—
24	C₈²×C₁₇	—	2	2	no	—
25	C₂³×C₄×C₁₇	C₂×C₄	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	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
29	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
30	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
31	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
33	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
34	C₂×C₄²×C₁₇	—	2	1	no	—
35	C₂×C₄²×C₁₇	—	2	1	no	—
36	C₂×C₄²×C₁₇	—	2	1	no	—
37	C₂×C₄²×C₁₇	—	2	1	no	—
38	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
42	C₁₇×C₄⋊C₈	—	2	4	no	—
43	C₁₇×C₂²⋊C₈	—	2	4	no	—
44	C₁₇×C₂²⋊C₈	—	2	4	no	—
45	C₁₇×C₂²⋊C₈	C₈	1	8	yes	complemented
46	C₄×C₈×C₁₇	—	2	1	no	—
47	C₄×C₈×C₁₇	—	2	1	no	—
48	C₄×C₈×C₁₇	—	2	1	no	—
49	C₄×C₈×C₁₇	—	2	1	no	—
50	C₄×C₈×C₁₇	—	2	1	no	—
51	C₄×C₈×C₁₇	—	2	1	no	—
52	C₄×C₈×C₁₇	—	2	1	no	—
53	C₄×C₈×C₁₇	—	2	1	no	—
54	C₄×C₈×C₁₇	—	2	1	no	—
55	C₄×C₈×C₁₇	—	2	1	no	—
56	C₄×C₈×C₁₇	D₄	1	2	yes	—
57	C₄×C₈×C₁₇	D₄	1	2	yes	—
58	C₂⁴×C₁₇	C₄²	1	1	yes	characteristic
59	C₂²×C₄×C₁₇	—	2	1	no	—
60	C₂²×C₄×C₁₇	—	2	1	no	—
61	C₂²×C₄×C₁₇	—	2	2	no	—
62	C₂²×C₄×C₁₇	—	2	1	no	—
63	C₂²×C₄×C₁₇	—	2	1	no	—
64	C₂²×C₄×C₁₇	—	2	1	no	—
65	C₂²×C₄×C₁₇	—	2	1	no	—
66	C₂²×C₄×C₁₇	—	2	2	no	—
67	C₂²×C₄×C₁₇	—	2	2	no	—
68	C₂²×C₄×C₁₇	—	2	2	no	—
69	C₂²×C₄×C₁₇	—	2	2	no	—
70	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
73	C₂²×C₄×C₁₇	C₂×C₈	1	4	yes	—
74	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₈×C₁₇	—	2	2	no	—
78	C₂×C₈×C₁₇	—	2	2	no	—
79	C₂×C₈×C₁₇	—	2	2	no	—
80	C₂×C₈×C₁₇	—	2	2	no	—
81	C₂×C₈×C₁₇	—	2	2	no	—
82	C₂×C₈×C₁₇	—	2	2	no	—
83	C₂×C₈×C₁₇	—	2	2	no	—
84	C₂×C₈×C₁₇	—	2	2	no	—
85	C₂×C₈×C₁₇	—	2	2	no	—
86	C₂×C₈×C₁₇	—	2	2	no	—
87	C₂×C₈×C₁₇	—	2	2	no	—
88	C₂×C₈×C₁₇	—	2	2	no	—
89	C₂×C₈×C₁₇	—	2	2	no	—
90	C₂×C₈×C₁₇	—	2	2	no	—
91	C₂×C₈×C₁₇	C₂²⋊C₄	1	4	yes	—
92	C₂×C₈×C₁₇	C₂×C₈	1	4	yes	—
93	C₂×C₈×C₁₇	C₂×C₈	1	4	yes	—
94	C₂×C₈×C₁₇	M₁₆	1	4	yes	—
95	C₄²×C₁₇	—	2	1	no	—
96	C₄²×C₁₇	—	2	1	no	—
97	C₄²×C₁₇	—	2	1	no	—
98	C₄²×C₁₇	—	2	1	no	—
99	C₄²×C₁₇	—	2	1	no	—
100	C₄²×C₁₇	—	2	1	no	—
101	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₁₇	#41	1	1	yes	characteristic
104	C₄²×C₁₇	#41	1	1	yes	characteristic
105	#8148	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂³×C₁₇	—	2	1	no	—
107	C₂³×C₁₇	—	2	1	no	—
108	C₂³×C₁₇	—	2	1	no	—
109	C₂³×C₁₇	—	2	1	no	—
110	C₂³×C₁₇	—	2	1	no	—
111	C₂³×C₁₇	—	2	1	no	—
112	C₂³×C₁₇	C₄×C₈	1	2	yes	—
113	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
114	C₂×C₄×C₁₇	—	2	1	no	—
115	C₂×C₄×C₁₇	—	2	1	no	—
116	C₂×C₄×C₁₇	—	2	4	no	—
117	C₂×C₄×C₁₇	—	2	4	no	—
118	C₂×C₄×C₁₇	—	2	1	no	—
119	C₂×C₄×C₁₇	—	2	1	no	—
120	C₂×C₄×C₁₇	—	2	1	no	—
121	C₂×C₄×C₁₇	—	2	1	no	—
122	C₂×C₄×C₁₇	—	2	1	no	—
123	C₂×C₄×C₁₇	—	2	1	no	—
124	C₂×C₄×C₁₇	—	4	2	no	—
125	C₂×C₄×C₁₇	—	4	2	no	—
126	C₂×C₄×C₁₇	—	4	2	no	—
127	C₂×C₄×C₁₇	—	4	2	no	—
128	C₂×C₄×C₁₇	C₄×C₈	1	2	yes	—
129	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
131	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
132	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
133	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
134	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
135	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
136	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
137	C₂×C₄×C₁₇	#131	1	2	yes	—
138	C₂×C₄×C₁₇	#131	1	2	yes	—
139	C₂×C₄×C₁₇	#131	1	2	yes	—
140	C₂×C₄×C₁₇	#131	1	2	yes	—
141	C₈×C₁₇	—	2	4	no	—
142	C₈×C₁₇	—	2	4	no	—
143	C₈×C₁₇	—	2	4	no	—
144	C₈×C₁₇	—	2	4	no	—
145	C₈×C₁₇	—	4	2	no	—
146	C₈×C₁₇	—	4	2	no	—
147	C₂×#431	C₂×C₁₇	1	1	yes	characteristic
148	C₄×C₂²⋊C₈	C₂×C₁₇	1	1	yes	characteristic
149	C₄×C₂²⋊C₈	C₂×C₁₇	1	1	yes	characteristic
150	C₂×#322	C₂×C₁₇	1	1	yes	characteristic, complemented
151	C₂×C₈²	C₂×C₁₇	1	1	yes	characteristic, complemented
152	#1273	C₂×C₁₇	1	1	yes	characteristic, complemented
153	#1273	C₂×C₁₇	1	1	yes	characteristic, complemented
154	C₂²×C₁₇	—	2	2	no	—
155	C₂²×C₁₇	—	2	2	no	—
156	C₂²×C₁₇	—	2	2	no	—
157	C₂²×C₁₇	—	4	1	no	—
158	C₂²×C₁₇	—	4	1	no	—
159	C₂²×C₁₇	—	4	1	no	—
160	C₂²×C₁₇	—	4	1	no	—
161	C₂²×C₁₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
162	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
163	C₂²×C₁₇	C₄×M₁₆	1	1	yes	characteristic
164	C₂²×C₁₇	#405	1	1	yes	characteristic
165	C₂²×C₁₇	#405	1	1	yes	characteristic
166	C₂²×C₁₇	#405	1	1	yes	characteristic
167	C₂²×C₁₇	#405	1	1	yes	characteristic
168	C₄×C₁₇	—	2	2	no	—
169	C₄×C₁₇	—	4	1	no	—
170	C₄×C₁₇	—	4	1	no	—
171	C₄×C₁₇	#408	1	2	yes	—
172	C₄×C₁₇	#433	1	2	yes	—
173	C₄×C₁₇	C₈×D₄	1	2	yes	—
174	C₄×C₁₇	C₈×D₄	1	2	yes	—
175	C₄×C₁₇	#435	1	2	yes	—
176	C₄×C₁₇	#436	1	2	yes	—
177	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic
178	#431	—	2	2	no	—
179	#431	—	2	2	no	—
180	C₂×C₄⋊C₈	C₄×C₁₇	1	2	yes	—
181	C₂×C₂²⋊C₈	C₄×C₁₇	1	2	yes	—
182	C₂×C₂²⋊C₈	C₄×C₁₇	1	2	yes	—
183	C₂×C₂²⋊C₈	C₄×C₁₇	1	2	yes	—
184	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
185	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
186	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
187	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
188	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
189	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
190	#336	C₄×C₁₇	1	2	yes	—
191	#336	C₄×C₁₇	1	2	yes	—
192	#322	—	2	2	no	—
193	C₈²	—	2	2	no	—
194	C₂×C₁₇	—	4	2	no	—
195	C₂×C₁₇	C₈×M₁₆	1	1	yes	characteristic
196	C₂×C₁₇	#1450	1	1	yes	characteristic
197	C₂×C₁₇	#1453	1	1	yes	characteristic
198	C₂×C₁₇	#1454	1	1	yes	characteristic
199	C₂×C₁₇	#1750	1	1	yes	characteristic
200	C₂×C₁₇	C₈×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₁₇	#1753	1	1	yes	characteristic
202	C₂³×C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
203	C₂³×C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
204	C₂³×C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
205	C₂²×C₈	C₂×C₄×C₁₇	1	2	yes	—
206	C₂²×C₈	C₂×C₄×C₁₇	1	2	yes	—
207	C₂²×C₈	C₂×C₄×C₁₇	1	2	yes	—
208	C₂²×C₈	C₂×C₄×C₁₇	1	2	yes	—
209	C₂²×C₈	C₂×C₄×C₁₇	1	2	yes	—
210	C₂²×C₈	C₂×C₄×C₁₇	1	2	yes	—
211	C₂×C₄²	—	2	1	no	—
212	C₂×C₄²	—	2	1	no	—
213	C₂×C₄²	—	2	1	no	—
214	C₂×C₄²	—	2	1	no	—
215	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
216	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
217	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
218	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
219	C₄⋊C₈	—	2	4	no	—
220	C₂²⋊C₈	—	2	4	no	—
221	C₂²⋊C₈	—	2	4	no	—
222	C₂²⋊C₈	C₈×C₁₇	1	8	yes	complemented
223	C₄×C₈	—	2	1	no	—
224	C₄×C₈	—	2	1	no	—
225	C₄×C₈	—	2	1	no	—
226	C₄×C₈	—	2	1	no	—
227	C₄×C₈	—	2	1	no	—
228	C₄×C₈	—	2	1	no	—
229	C₄×C₈	—	2	1	no	—
230	C₄×C₈	—	2	1	no	—
231	C₄×C₈	—	2	1	no	—
232	C₄×C₈	—	2	1	no	—
233	C₄×C₈	D₄×C₁₇	1	2	yes	—
234	C₄×C₈	D₄×C₁₇	1	2	yes	—
235	C₁₇	#8148	1	1	yes	characteristic, direct product factor, Sylow
236	C₂⁴	C₄²×C₁₇	1	1	yes	characteristic
237	C₂²×C₄	—	2	2	no	—
238	C₂²×C₄	—	2	1	no	—
239	C₂²×C₄	—	2	1	no	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	—	2	2	no	—
244	C₂²×C₄	—	2	1	no	—
245	C₂²×C₄	—	2	1	no	—
246	C₂²×C₄	—	2	1	no	—
247	C₂²×C₄	—	2	1	no	—
248	C₂²×C₄	C₄²×C₁₇	1	1	yes	characteristic
249	C₂²×C₄	C₄²×C₁₇	1	1	yes	characteristic
250	C₂²×C₄	C₄²×C₁₇	1	1	yes	characteristic
251	C₂²×C₄	C₂×C₈×C₁₇	1	4	yes	—
252	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
253	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
254	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	C₂²⋊C₄×C₁₇	1	4	yes	—
270	C₂×C₈	C₂×C₈×C₁₇	1	4	yes	—
271	C₂×C₈	C₂×C₈×C₁₇	1	4	yes	—
272	C₂×C₈	M₁₆×C₁₇	1	4	yes	—
273	C₄²	—	2	1	no	—
274	C₄²	—	2	1	no	—
275	C₄²	—	2	1	no	—
276	C₄²	—	2	1	no	—
277	C₄²	—	2	1	no	—
278	C₄²	—	2	1	no	—
279	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
280	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
281	C₄²	#41×C₁₇	1	1	yes	characteristic
282	C₄²	#41×C₁₇	1	1	yes	characteristic
283	C₂³	—	2	1	no	—
284	C₂³	—	2	1	no	—
285	C₂³	—	2	1	no	—
286	C₂³	—	2	1	no	—
287	C₂³	—	2	1	no	—
288	C₂³	—	2	1	no	—
289	C₂³	C₄×C₈×C₁₇	1	2	yes	—
290	C₂³	C₂×C₄²×C₁₇	1	1	yes	characteristic
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	4	2	no	—
302	C₂×C₄	—	4	2	no	—
303	C₂×C₄	—	4	2	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	C₄×C₈×C₁₇	1	2	yes	—
306	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
307	C₂×C₄	C₁₇×#117	1	1	yes	characteristic
308	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
309	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
310	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
311	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
312	C₂×C₄	C₂²×C₈×C₁₇	1	2	yes	—
313	C₂×C₄	C₂×M₁₆×C₁₇	1	2	yes	—
314	C₂×C₄	C₁₇×#131	1	2	yes	—
315	C₂×C₄	C₁₇×#131	1	2	yes	—
316	C₂×C₄	C₁₇×#131	1	2	yes	—
317	C₂×C₄	C₁₇×#131	1	2	yes	—
318	C₈	—	2	4	no	—
319	C₈	—	2	4	no	—
320	C₈	—	2	4	no	—
321	C₈	—	2	4	no	—
322	C₈	—	4	2	no	—
323	C₈	—	4	2	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	2	2	no	—
326	C₂²	—	2	2	no	—
327	C₂²	—	4	1	no	—
328	C₂²	—	4	1	no	—
329	C₂²	—	4	1	no	—
330	C₂²	—	4	1	no	—
331	C₂²	C₄×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
332	C₂²	C₂×C₄×C₈×C₁₇	1	1	yes	characteristic
333	C₂²	C₄×M₁₆×C₁₇	1	1	yes	characteristic
334	C₂²	C₁₇×#405	1	1	yes	characteristic
335	C₂²	C₁₇×#405	1	1	yes	characteristic
336	C₂²	C₁₇×#405	1	1	yes	characteristic
337	C₂²	C₁₇×#405	1	1	yes	characteristic
338	C₄	—	2	2	no	—
339	C₄	—	4	1	no	—
340	C₄	—	4	1	no	—
341	C₄	C₁₇×#408	1	2	yes	—
342	C₄	C₁₇×#433	1	2	yes	—
343	C₄	C₈×D₄×C₁₇	1	2	yes	—
344	C₄	C₈×D₄×C₁₇	1	2	yes	—
345	C₄	C₁₇×#435	1	2	yes	—
346	C₄	C₁₇×#436	1	2	yes	—
347	C₂	—	4	2	no	—
348	C₂	C₈×M₁₆×C₁₇	1	1	yes	characteristic
349	C₂	C₁₇×#1450	1	1	yes	characteristic
350	C₂	C₁₇×#1453	1	1	yes	characteristic
351	C₂	C₁₇×#1454	1	1	yes	characteristic
352	C₂	C₁₇×#1750	1	1	yes	characteristic
353	C₂	C₈×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
354	C₂	C₁₇×#1753	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²×C₁₇	C₂³
commutator	C₂²	C₂×C₄×C₈×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
socle	C₂³×C₁₇	C₂×C₄²
prime radical	C₂⁴×C₁₇	C₄²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₁₇×#322	C₂	semidirect
5. C₂×C₈²×C₁₇	C₂	semidirect
6. C₁₇×#1273	C₂	semidirect
7. C₁₇×#1273	C₂	semidirect
45. C₁₇×C₂²⋊C₈	C₈	semidirect
105. #8148	C₁₇	direct (N × H)
150. C₂×#322	C₂×C₁₇	semidirect
151. C₂×C₈²	C₂×C₁₇	semidirect
152. #1273	C₂×C₁₇	semidirect
153. #1273	C₂×C₁₇	semidirect
222. C₂²⋊C₈	C₈×C₁₇	semidirect
235. C₁₇	#8148	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×C₁₇×#431	2
C₄×C₁₇×C₂²⋊C₈	2
C₂×C₁₇×#322	2
C₂×C₈²×C₁₇	2
C₁₇×#1273	2
#8148	17

Subgroups — C17×#8148 #16865892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#8148 #16865892