Subgroups — C₁₇×#21653 #16879397

Order 4352.

770 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#491	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#2330	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#2327	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#1991	C₂	1	1	yes	maximal, characteristic
5	C₁₇×#1956	C₂	1	1	yes	maximal, characteristic
6	C₁₇×#1935	C₂	1	2	yes	maximal
7	C₁₇×#1933	C₂	1	2	yes	maximal
8	C₁₇×#1836	C₂	1	1	yes	maximal, characteristic
9	C₁₇×#1763	C₂	1	2	yes	maximal
10	C₄×C₁₇×#103	C₂	1	2	yes	maximal
11	C₁₇×#1726	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₇×#125	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₇	C₂²	1	2	yes	—
15	C₁₇×#491	C₄	1	8	yes	complemented
16	C₂×C₁₇×#103	C₂²	1	2	yes	—
17	C₂×C₁₇×#103	C₂²	1	2	yes	—
18	C₂×C₁₇×#103	C₂²	1	2	yes	—
19	C₂×C₁₇×#103	C₂²	1	2	yes	—
20	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
21	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
22	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
26	C₁₇×#391	C₂²	1	2	yes	—
27	C₁₇×#389	—	2	2	no	—
28	C₁₇×#389	C₂²	1	2	yes	—
29	C₁₇×#387	—	2	2	no	—
30	C₁₇×#387	—	2	2	no	—
31	C₁₇×#387	—	2	2	no	—
32	C₁₇×#384	C₂²	1	1	yes	characteristic
33	C₁₇×#382	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₁₇	C₂²	1	2	yes	—
35	C₁₇×#376	C₂²	1	1	yes	characteristic
36	C₁₇×#340	C₂²	1	2	yes	—
37	C₁₇×#340	C₂²	1	2	yes	—
38	C₁₇×#340	C₂²	1	2	yes	—
39	C₁₇×#340	C₂²	1	2	yes	—
40	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
45	C₁₇×C₄⋊Q₈	—	2	2	no	—
46	C₁₇×C₄⋊Q₈	C₂×C₄	1	4	yes	—
47	C₁₇×#125	—	2	2	no	—
48	C₁₇×#125	C₂×C₄	1	4	yes	—
49	C₄×Q₈×C₁₇	—	2	4	no	—
50	C₄×Q₈×C₁₇	—	2	4	no	—
51	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
59	C₂×C₄²×C₁₇	—	2	2	no	—
60	C₂×C₄²×C₁₇	—	2	2	no	—
61	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
64	C₁₇×#103	—	2	4	no	—
65	C₁₇×#103	—	2	4	no	—
66	C₁₇×#103	C₂×C₄	1	8	yes	—
67	C₁₇×#103	C₂×C₄	1	8	yes	—
68	C₁₇×#97	—	2	2	no	—
69	C₁₇×#97	—	2	2	no	—
70	C₁₇×#97	C₂×C₄	1	4	yes	—
71	C₄×C₈×C₁₇	—	2	2	no	—
72	C₄×C₈×C₁₇	—	2	2	no	—
73	C₄×C₈×C₁₇	—	2	2	no	—
74	C₁₇×#95	—	2	2	no	—
75	C₁₇×#95	—	2	2	no	—
76	C₁₇×#95	—	2	2	no	—
77	C₁₇×#95	—	2	2	no	—
78	C₁₇×#95	—	2	2	no	—
79	C₁₇×#95	D₄	1	2	yes	—
80	C₁₇×#95	D₄	1	2	yes	—
81	C₂×Q₈×C₁₇	—	2	2	no	—
82	C₂×Q₈×C₁₇	—	2	2	no	—
83	C₂×Q₈×C₁₇	—	2	2	no	—
84	C₂×Q₈×C₁₇	—	2	2	no	—
85	C₂×Q₈×C₁₇	—	2	2	no	—
86	C₂×Q₈×C₁₇	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₁₇	—	2	2	no	—
88	C₂²×C₄×C₁₇	—	2	2	no	—
89	C₂²×C₄×C₁₇	—	2	2	no	—
90	C₂²×C₄×C₁₇	—	2	2	no	—
91	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
96	C₂×C₈×C₁₇	—	2	1	no	—
97	C₂×C₈×C₁₇	—	2	1	no	—
98	C₂×C₈×C₁₇	—	2	1	no	—
99	C₂×C₈×C₁₇	—	2	1	no	—
100	C₂×C₈×C₁₇	—	2	1	no	—
101	C₂×C₈×C₁₇	—	2	1	no	—
102	C₂×C₈×C₁₇	—	2	1	no	—
103	C₂×C₈×C₁₇	—	2	1	no	—
104	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
106	C₂×C₈×C₁₇	#41	1	2	yes	—
107	C₂×C₈×C₁₇	#41	1	2	yes	—
108	C₄⋊C₄×C₁₇	—	2	8	no	—
109	C₄⋊C₄×C₁₇	—	2	8	no	—
110	C₄⋊C₄×C₁₇	—	2	2	no	—
111	C₄⋊C₄×C₁₇	—	2	2	no	—
112	C₄⋊C₄×C₁₇	—	2	2	no	—
113	C₄⋊C₄×C₁₇	—	2	2	no	—
114	C₄⋊C₄×C₁₇	—	2	2	no	—
115	C₄⋊C₄×C₁₇	—	4	4	no	—
116	C₄⋊C₄×C₁₇	—	8	2	no	—
117	C₄⋊C₄×C₁₇	—	8	2	no	—
118	C₄⋊C₄×C₁₇	C₂²×C₄	1	4	yes	—
119	C₄²×C₁₇	—	2	1	no	—
120	C₄²×C₁₇	—	2	1	no	—
121	C₄²×C₁₇	—	4	4	no	—
122	C₄²×C₁₇	—	8	2	no	—
123	C₄²×C₁₇	C₂²×C₄	1	2	yes	—
124	C₄²×C₁₇	#41	1	2	yes	—
125	C₄²×C₁₇	#41	1	2	yes	—
126	C₄²×C₁₇	#41	1	2	yes	—
127	#21653	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
129	Q₈×C₁₇	—	2	4	no	—
130	Q₈×C₁₇	—	2	4	no	—
131	Q₈×C₁₇	—	4	2	no	—
132	Q₈×C₁₇	—	4	2	no	—
133	C₂×C₄×C₁₇	—	2	2	no	—
134	C₂×C₄×C₁₇	—	2	2	no	—
135	C₂×C₄×C₁₇	—	2	2	no	—
136	C₂×C₄×C₁₇	—	2	2	no	—
137	C₂×C₄×C₁₇	—	2	4	no	—
138	C₂×C₄×C₁₇	—	2	4	no	—
139	C₂×C₄×C₁₇	—	2	1	no	—
140	C₂×C₄×C₁₇	—	2	1	no	—
141	C₂×C₄×C₁₇	—	2	2	no	—
142	C₂×C₄×C₁₇	—	2	2	no	—
143	C₂×C₄×C₁₇	—	4	2	no	—
144	C₂×C₄×C₁₇	—	4	2	no	—
145	C₂×C₄×C₁₇	—	4	2	no	—
146	C₂×C₄×C₁₇	—	4	2	no	—
147	C₂×C₄×C₁₇	—	4	2	no	—
148	C₂×C₄×C₁₇	—	4	2	no	—
149	C₂×C₄×C₁₇	—	4	2	no	—
150	C₂×C₄×C₁₇	—	4	2	no	—
151	C₂×C₄×C₁₇	—	4	2	no	—
152	C₂×C₄×C₁₇	—	4	2	no	—
153	C₂×C₄×C₁₇	C₄×D₄	1	4	yes	—
154	C₂×C₄×C₁₇	#124	1	4	yes	—
155	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
161	C₈×C₁₇	—	2	2	no	—
162	C₈×C₁₇	—	2	2	no	—
163	C₈×C₁₇	—	2	2	no	—
164	C₈×C₁₇	—	2	2	no	—
165	C₂×#491	C₂×C₁₇	1	1	yes	characteristic
166	#2330	C₂×C₁₇	1	1	yes	characteristic
167	#2327	C₂×C₁₇	1	1	yes	characteristic
168	#1991	C₂×C₁₇	1	1	yes	characteristic
169	#1956	C₂×C₁₇	1	1	yes	characteristic
170	#1935	C₂×C₁₇	1	2	yes	—
171	#1933	C₂×C₁₇	1	2	yes	—
172	#1836	C₂×C₁₇	1	1	yes	characteristic
173	#1763	C₂×C₁₇	1	2	yes	—
174	C₄×#103	C₂×C₁₇	1	2	yes	—
175	#1726	C₂×C₁₇	1	1	yes	characteristic
176	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
177	C₂²×C₁₇	C₂×#124	1	1	yes	characteristic
178	C₂²×C₁₇	#532	1	1	yes	characteristic
179	C₂²×C₁₇	#577	1	2	yes	—
180	C₂²×C₁₇	#578	1	2	yes	—
181	C₄×C₁₇	—	2	4	no	—
182	C₄×C₁₇	—	2	4	no	—
183	C₄×C₁₇	—	4	1	no	—
184	C₄×C₁₇	—	4	1	no	—
185	C₄×C₁₇	—	4	4	no	—
186	C₄×C₁₇	—	4	4	no	—
187	C₄×C₁₇	—	8	2	no	—
188	C₄×C₁₇	—	8	2	no	—
189	C₄×C₁₇	C₄×#41	1	1	yes	characteristic
190	C₄×C₁₇	C₄×#41	1	1	yes	characteristic
191	C₄×C₁₇	#529	1	1	yes	characteristic
192	C₄×C₁₇	#529	1	1	yes	characteristic
193	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
194	C₂×#125	C₂²×C₁₇	1	1	yes	characteristic
195	C₂×C₄×Q₈	C₂²×C₁₇	1	2	yes	—
196	#491	C₄×C₁₇	1	8	yes	complemented
197	C₂×#103	C₂²×C₁₇	1	2	yes	—
198	C₂×#103	C₂²×C₁₇	1	2	yes	—
199	C₂×#103	C₂²×C₁₇	1	2	yes	—
200	C₂×#103	C₂²×C₁₇	1	2	yes	—
201	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
202	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
203	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
204	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
205	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
206	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
207	#391	C₂²×C₁₇	1	2	yes	—
208	#389	—	2	2	no	—
209	#389	C₂²×C₁₇	1	2	yes	—
210	#387	—	2	2	no	—
211	#387	—	2	2	no	—
212	#387	—	2	2	no	—
213	#384	C₂²×C₁₇	1	1	yes	characteristic
214	#382	C₂²×C₁₇	1	1	yes	characteristic
215	C₄×C₄⋊C₄	C₂²×C₁₇	1	2	yes	—
216	#376	C₂²×C₁₇	1	1	yes	characteristic
217	#340	C₂²×C₁₇	1	2	yes	—
218	#340	C₂²×C₁₇	1	2	yes	—
219	#340	C₂²×C₁₇	1	2	yes	—
220	#340	C₂²×C₁₇	1	2	yes	—
221	C₂×C₁₇	C₄×#124	1	1	yes	characteristic
222	C₂×C₁₇	#2947	1	2	yes	—
223	C₂×C₁₇	#3137	1	2	yes	—
224	C₂×C₁₇	#3174	1	1	yes	characteristic
225	C₂×C₁₇	#3177	1	1	yes	characteristic
226	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
227	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
228	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
229	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
230	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
231	C₄⋊Q₈	—	2	2	no	—
232	C₄⋊Q₈	C₂×C₄×C₁₇	1	4	yes	—
233	#125	—	2	2	no	—
234	#125	C₂×C₄×C₁₇	1	4	yes	—
235	C₄×Q₈	—	2	4	no	—
236	C₄×Q₈	—	2	4	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
243	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
244	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
245	C₂×C₄²	—	2	2	no	—
246	C₂×C₄²	—	2	2	no	—
247	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
248	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
250	#103	—	2	4	no	—
251	#103	—	2	4	no	—
252	#103	C₂×C₄×C₁₇	1	8	yes	—
253	#103	C₂×C₄×C₁₇	1	8	yes	—
254	#97	—	2	2	no	—
255	#97	—	2	2	no	—
256	#97	C₂×C₄×C₁₇	1	4	yes	—
257	C₄×C₈	—	2	2	no	—
258	C₄×C₈	—	2	2	no	—
259	C₄×C₈	—	2	2	no	—
260	#95	—	2	2	no	—
261	#95	—	2	2	no	—
262	#95	—	2	2	no	—
263	#95	—	2	2	no	—
264	#95	—	2	2	no	—
265	#95	D₄×C₁₇	1	2	yes	—
266	#95	D₄×C₁₇	1	2	yes	—
267	C₁₇	#21653	1	1	yes	characteristic, direct product factor, Sylow
268	C₂×Q₈	—	2	2	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	C₂²×C₄×C₁₇	1	4	yes	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
279	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
282	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
283	C₂×C₈	—	2	1	no	—
284	C₂×C₈	—	2	1	no	—
285	C₂×C₈	—	2	1	no	—
286	C₂×C₈	—	2	1	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
292	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
293	C₂×C₈	#41×C₁₇	1	2	yes	—
294	C₂×C₈	#41×C₁₇	1	2	yes	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	8	no	—
297	C₄⋊C₄	—	2	8	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	4	4	no	—
303	C₄⋊C₄	—	8	2	no	—
304	C₄⋊C₄	—	8	2	no	—
305	C₄⋊C₄	C₂²×C₄×C₁₇	1	4	yes	—
306	C₄²	—	2	1	no	—
307	C₄²	—	2	1	no	—
308	C₄²	—	4	4	no	—
309	C₄²	—	8	2	no	—
310	C₄²	C₂²×C₄×C₁₇	1	2	yes	—
311	C₄²	#41×C₁₇	1	2	yes	—
312	C₄²	#41×C₁₇	1	2	yes	—
313	C₄²	#41×C₁₇	1	2	yes	—
314	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
315	Q₈	—	2	4	no	—
316	Q₈	—	2	4	no	—
317	Q₈	—	4	2	no	—
318	Q₈	—	4	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	C₄×D₄×C₁₇	1	4	yes	—
340	C₂×C₄	C₁₇×#124	1	4	yes	—
341	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
342	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
343	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
344	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
345	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
346	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
347	C₈	—	2	2	no	—
348	C₈	—	2	2	no	—
349	C₈	—	2	2	no	—
350	C₈	—	2	2	no	—
351	C₂²	C₂×C₄×D₄×C₁₇	1	1	yes	characteristic
352	C₂²	C₂×C₁₇×#124	1	1	yes	characteristic
353	C₂²	C₁₇×#532	1	1	yes	characteristic
354	C₂²	C₁₇×#577	1	2	yes	—
355	C₂²	C₁₇×#578	1	2	yes	—
356	C₄	—	2	4	no	—
357	C₄	—	2	4	no	—
358	C₄	—	4	4	no	—
359	C₄	—	4	4	no	—
360	C₄	—	4	1	no	—
361	C₄	—	4	1	no	—
362	C₄	—	8	2	no	—
363	C₄	—	8	2	no	—
364	C₄	C₄×#41×C₁₇	1	1	yes	characteristic
365	C₄	C₄×#41×C₁₇	1	1	yes	characteristic
366	C₄	C₁₇×#529	1	1	yes	characteristic
367	C₄	C₁₇×#529	1	1	yes	characteristic
368	C₂	C₄×C₁₇×#124	1	1	yes	characteristic
369	C₂	C₁₇×#2947	1	2	yes	—
370	C₂	C₁₇×#3137	1	2	yes	—
371	C₂	C₁₇×#3174	1	1	yes	characteristic
372	C₂	C₁₇×#3177	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₁₇×#376 ◁ G

Complements

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

N	H ≅ G/N	type
15. C₁₇×#491	C₄	semidirect
127. #21653	C₁₇	direct (N × H)
196. #491	C₄×C₁₇	semidirect
267. C₁₇	#21653	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×#491	2
C₁₇×#2330	2
C₁₇×#2327	2
C₁₇×#1991	2
C₁₇×#1956	2
C₁₇×#1935	2
C₁₇×#1933	2
C₁₇×#1836	2
C₁₇×#1763	2
C₄×C₁₇×#103	2
C₁₇×#1726	2
#21653	17

Subgroups — C17×#21653 #16879397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#21653 #16879397