Subgroups — C₁₇×#2534 #14525540

Order 2176.

800 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₇×#120	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×D₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₂²⋊C₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#396	C₂	1	2	yes	maximal, complemented
6	C₁₇×#394	C₂	1	2	yes	maximal, complemented
7	C₁₇×#388	C₂	1	2	yes	maximal, complemented
8	C₁₇×#386	C₂	1	2	yes	maximal, complemented
9	C₁₇×#381	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#380	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#379	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁵×C₁₇	C₂²	1	1	yes	characteristic
13	C₂²×D₄×C₁₇	C₂²	1	2	yes	—
14	C₂²×D₄×C₁₇	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₁₇	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₁₇	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
18	C₁₇×#123	—	2	4	no	—
19	C₁₇×#120	—	2	4	no	—
20	C₄×D₄×C₁₇	—	2	4	no	—
21	C₂×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₄⋊C₄×C₁₇	C₂²	1	2	yes	complemented
23	C₂×C₄⋊C₄×C₁₇	C₂²	1	2	yes	complemented
24	C₂×C₂²⋊C₄×C₁₇	—	2	4	no	—
25	C₂×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
30	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
33	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	complemented
35	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic, complemented
36	C₁₇×#95	C₂²	1	2	yes	complemented
37	C₁₇×#95	C₂²	1	2	yes	complemented
38	C₁₇×#95	C₂²	1	2	yes	complemented
39	C₂⁴×C₁₇	—	2	2	no	—
40	C₂⁴×C₁₇	—	2	4	no	—
41	C₂⁴×C₁₇	—	2	2	no	—
42	C₂⁴×C₁₇	—	2	2	no	—
43	C₂⁴×C₁₇	—	4	2	no	—
44	C₂⁴×C₁₇	C₂³	1	1	yes	characteristic
45	C₂⁴×C₁₇	C₂³	1	2	yes	—
46	C₂⁴×C₁₇	C₂³	1	1	yes	characteristic
47	C₂×D₄×C₁₇	—	2	2	no	—
48	C₂×D₄×C₁₇	—	2	2	no	—
49	C₂×D₄×C₁₇	—	2	4	no	—
50	C₂×D₄×C₁₇	—	2	4	no	—
51	C₂×D₄×C₁₇	—	4	2	no	—
52	C₂×D₄×C₁₇	D₄	1	4	yes	—
53	C₂²×C₄×C₁₇	—	2	2	no	—
54	C₂²×C₄×C₁₇	—	2	2	no	—
55	C₂²×C₄×C₁₇	—	2	2	no	—
56	C₂²×C₄×C₁₇	—	2	2	no	—
57	C₂²×C₄×C₁₇	—	4	2	no	—
58	C₂²×C₄×C₁₇	—	4	2	no	—
59	C₂²×C₄×C₁₇	D₄	1	4	yes	complemented
60	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
61	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
63	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
65	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
68	C₄⋊C₄×C₁₇	—	2	4	no	—
69	C₄⋊C₄×C₁₇	—	2	2	no	—
70	C₄⋊C₄×C₁₇	—	4	2	no	—
71	C₂²⋊C₄×C₁₇	—	2	2	no	—
72	C₂²⋊C₄×C₁₇	—	2	4	no	—
73	C₂²⋊C₄×C₁₇	—	2	2	no	—
74	C₂²⋊C₄×C₁₇	—	2	2	no	—
75	C₂²⋊C₄×C₁₇	—	2	4	no	—
76	C₂²⋊C₄×C₁₇	—	2	4	no	—
77	C₂²⋊C₄×C₁₇	—	2	4	no	—
78	C₂²⋊C₄×C₁₇	—	2	4	no	—
79	C₂²⋊C₄×C₁₇	—	2	2	no	—
80	C₂²⋊C₄×C₁₇	—	4	2	no	—
81	C₄²×C₁₇	—	2	2	no	—
82	C₂³×C₁₇	—	2	2	no	—
83	C₂³×C₁₇	—	2	2	no	—
84	C₂³×C₁₇	—	2	8	no	—
85	C₂³×C₁₇	—	2	2	no	—
86	C₂³×C₁₇	—	2	1	no	—
87	C₂³×C₁₇	—	2	2	no	—
88	C₂³×C₁₇	—	2	1	no	—
89	C₂³×C₁₇	—	2	2	no	—
90	C₂³×C₁₇	—	2	2	no	—
91	C₂³×C₁₇	—	2	2	no	—
92	C₂³×C₁₇	—	2	2	no	—
93	C₂³×C₁₇	—	2	2	no	—
94	C₂³×C₁₇	—	2	2	no	—
95	C₂³×C₁₇	—	4	8	no	—
96	C₂³×C₁₇	—	4	8	no	—
97	C₂³×C₁₇	—	4	4	no	—
98	C₂³×C₁₇	—	4	4	no	—
99	C₂³×C₁₇	C₂×D₄	1	2	yes	—
100	C₂³×C₁₇	C₂×D₄	1	2	yes	—
101	C₂³×C₁₇	C₂×D₄	1	2	yes	—
102	C₂³×C₁₇	#41	1	4	yes	—
103	C₂³×C₁₇	#41	1	2	yes	—
104	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
105	D₄×C₁₇	—	2	8	no	—
106	D₄×C₁₇	—	4	8	no	—
107	C₂×C₄×C₁₇	—	2	1	no	—
108	C₂×C₄×C₁₇	—	2	1	no	—
109	C₂×C₄×C₁₇	—	2	2	no	—
110	C₂×C₄×C₁₇	—	2	2	no	—
111	C₂×C₄×C₁₇	—	2	1	no	—
112	C₂×C₄×C₁₇	—	2	2	no	—
113	C₂×C₄×C₁₇	—	2	2	no	—
114	C₂×C₄×C₁₇	—	2	2	no	—
115	C₂×C₄×C₁₇	—	2	2	no	—
116	C₂×C₄×C₁₇	—	2	1	no	—
117	C₂×C₄×C₁₇	—	2	2	no	—
118	C₂×C₄×C₁₇	—	2	2	no	—
119	C₂×C₄×C₁₇	—	2	2	no	—
120	C₂×C₄×C₁₇	—	2	2	no	—
121	C₂×C₄×C₁₇	—	2	2	no	—
122	C₂×C₄×C₁₇	—	2	2	no	—
123	C₂×C₄×C₁₇	—	2	2	no	—
124	C₂×C₄×C₁₇	—	4	4	no	—
125	C₂×C₄×C₁₇	—	4	4	no	—
126	C₂×C₄×C₁₇	—	4	4	no	—
127	C₂×C₄×C₁₇	C₂×D₄	1	2	yes	—
128	C₂×C₄×C₁₇	C₂×D₄	1	2	yes	—
129	C₂×C₄×C₁₇	C₂×D₄	1	2	yes	—
130	#2534	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂²×C₁₇	—	2	2	no	—
132	C₂²×C₁₇	—	2	2	no	—
133	C₂²×C₁₇	—	2	4	no	—
134	C₂²×C₁₇	—	2	4	no	—
135	C₂²×C₁₇	—	2	2	no	—
136	C₂²×C₁₇	—	2	4	no	—
137	C₂²×C₁₇	—	2	4	no	—
138	C₂²×C₁₇	—	2	4	no	—
139	C₂²×C₁₇	—	2	4	no	—
140	C₂²×C₁₇	—	4	16	no	—
141	C₂²×C₁₇	—	4	2	no	—
142	C₂²×C₁₇	—	4	1	no	—
143	C₂²×C₁₇	—	4	1	no	—
144	C₂²×C₁₇	—	4	2	no	—
145	C₂²×C₁₇	—	4	2	no	—
146	C₂²×C₁₇	—	4	2	no	—
147	C₂²×C₁₇	—	4	2	no	—
148	C₂²×C₁₇	#121	1	4	yes	—
149	C₂²×C₁₇	C₂²×D₄	1	1	yes	characteristic
150	C₂²×C₁₇	C₂²×D₄	1	1	yes	characteristic
151	C₂²×C₁₇	C₂×#41	1	1	yes	characteristic
152	C₂²×C₁₇	C₂×#41	1	2	yes	—
153	C₂²×C₁₇	H(5,𝔽₂)	1	2	yes	—
154	C₄×C₁₇	—	2	2	no	—
155	C₄×C₁₇	—	2	2	no	—
156	C₄×C₁₇	—	2	2	no	—
157	C₄×C₁₇	—	4	2	no	—
158	C₄×C₁₇	—	4	1	no	—
159	C₄×C₁₇	—	4	1	no	—
160	C₄×C₁₇	—	4	2	no	—
161	C₄×C₁₇	—	4	2	no	—
162	C₂×#123	C₂×C₁₇	1	1	yes	characteristic, complemented
163	C₂×#120	C₂×C₁₇	1	1	yes	characteristic
164	C₂×C₄×D₄	C₂×C₁₇	1	1	yes	characteristic, complemented
165	C₂²×C₂²⋊C₄	C₂×C₁₇	1	1	yes	characteristic, complemented
166	#396	C₂×C₁₇	1	2	yes	complemented
167	#394	C₂×C₁₇	1	2	yes	complemented
168	#388	C₂×C₁₇	1	2	yes	complemented
169	#386	C₂×C₁₇	1	2	yes	complemented
170	#381	C₂×C₁₇	1	1	yes	characteristic, complemented
171	#380	C₂×C₁₇	1	1	yes	characteristic, complemented
172	#379	C₂×C₁₇	1	1	yes	characteristic, complemented
173	C₂×C₁₇	—	2	4	no	—
174	C₂×C₁₇	—	4	2	no	—
175	C₂×C₁₇	—	4	4	no	—
176	C₂×C₁₇	C₂×#121	1	1	yes	characteristic
177	C₂×C₁₇	#525	1	1	yes	characteristic
178	C₂×C₁₇	#534	1	1	yes	characteristic
179	C₂×C₁₇	#546	1	2	yes	—
180	C₂×C₁₇	#551	1	2	yes	—
181	C₂⁵	C₂²×C₁₇	1	1	yes	characteristic
182	C₂²×D₄	C₂²×C₁₇	1	2	yes	—
183	C₂²×D₄	C₂²×C₁₇	1	1	yes	characteristic
184	C₂³×C₄	C₂²×C₁₇	1	1	yes	characteristic
185	C₂³×C₄	C₂²×C₁₇	1	1	yes	characteristic
186	C₂³×C₄	C₂²×C₁₇	1	1	yes	characteristic, complemented
187	#123	—	2	4	no	—
188	#120	—	2	4	no	—
189	C₄×D₄	—	2	4	no	—
190	C₂×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic, complemented
191	C₂×C₄⋊C₄	C₂²×C₁₇	1	2	yes	complemented
192	C₂×C₄⋊C₄	C₂²×C₁₇	1	2	yes	complemented
193	C₂×C₂²⋊C₄	—	2	4	no	—
194	C₂×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
195	C₂×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
196	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
197	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
198	C₂×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
199	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
200	C₂×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
201	C₂×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
202	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic, complemented
203	C₂×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	complemented
204	C₂×C₄²	C₂²×C₁₇	1	1	yes	characteristic, complemented
205	#95	C₂²×C₁₇	1	2	yes	complemented
206	#95	C₂²×C₁₇	1	2	yes	complemented
207	#95	C₂²×C₁₇	1	2	yes	complemented
208	C₁₇	#2534	1	1	yes	characteristic, direct product factor, Sylow
209	C₂⁴	—	2	2	no	—
210	C₂⁴	—	2	4	no	—
211	C₂⁴	—	2	2	no	—
212	C₂⁴	—	2	2	no	—
213	C₂⁴	—	4	2	no	—
214	C₂⁴	C₂³×C₁₇	1	1	yes	characteristic
215	C₂⁴	C₂³×C₁₇	1	2	yes	—
216	C₂⁴	C₂³×C₁₇	1	1	yes	characteristic
217	C₂×D₄	—	2	2	no	—
218	C₂×D₄	—	2	2	no	—
219	C₂×D₄	—	2	4	no	—
220	C₂×D₄	—	2	4	no	—
221	C₂×D₄	—	4	2	no	—
222	C₂×D₄	D₄×C₁₇	1	4	yes	—
223	C₂²×C₄	—	2	2	no	—
224	C₂²×C₄	—	2	2	no	—
225	C₂²×C₄	—	2	2	no	—
226	C₂²×C₄	—	2	2	no	—
227	C₂²×C₄	—	4	2	no	—
228	C₂²×C₄	—	4	2	no	—
229	C₂²×C₄	D₄×C₁₇	1	4	yes	complemented
230	C₂²×C₄	C₂³×C₁₇	1	2	yes	—
231	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
232	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
233	C₂²×C₄	C₂³×C₁₇	1	2	yes	—
234	C₂²×C₄	C₂³×C₁₇	1	2	yes	—
235	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
236	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
237	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
238	C₄⋊C₄	—	2	2	no	—
239	C₄⋊C₄	—	2	4	no	—
240	C₄⋊C₄	—	4	2	no	—
241	C₂²⋊C₄	—	2	2	no	—
242	C₂²⋊C₄	—	2	2	no	—
243	C₂²⋊C₄	—	2	2	no	—
244	C₂²⋊C₄	—	2	4	no	—
245	C₂²⋊C₄	—	2	4	no	—
246	C₂²⋊C₄	—	2	4	no	—
247	C₂²⋊C₄	—	2	4	no	—
248	C₂²⋊C₄	—	2	4	no	—
249	C₂²⋊C₄	—	2	2	no	—
250	C₂²⋊C₄	—	4	2	no	—
251	C₄²	—	2	2	no	—
252	C₂³	—	2	2	no	—
253	C₂³	—	2	2	no	—
254	C₂³	—	2	8	no	—
255	C₂³	—	2	2	no	—
256	C₂³	—	2	1	no	—
257	C₂³	—	2	2	no	—
258	C₂³	—	2	1	no	—
259	C₂³	—	2	2	no	—
260	C₂³	—	2	2	no	—
261	C₂³	—	2	2	no	—
262	C₂³	—	2	2	no	—
263	C₂³	—	2	2	no	—
264	C₂³	—	2	2	no	—
265	C₂³	—	4	8	no	—
266	C₂³	—	4	8	no	—
267	C₂³	—	4	4	no	—
268	C₂³	—	4	4	no	—
269	C₂³	C₂×D₄×C₁₇	1	2	yes	—
270	C₂³	C₂×D₄×C₁₇	1	2	yes	—
271	C₂³	C₂×D₄×C₁₇	1	2	yes	—
272	C₂³	#41×C₁₇	1	4	yes	—
273	C₂³	#41×C₁₇	1	2	yes	—
274	C₂³	C₂⁴×C₁₇	1	1	yes	characteristic
275	D₄	—	2	8	no	—
276	D₄	—	4	8	no	—
277	C₂×C₄	—	2	1	no	—
278	C₂×C₄	—	2	1	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	4	4	no	—
295	C₂×C₄	—	4	4	no	—
296	C₂×C₄	—	4	4	no	—
297	C₂×C₄	C₂×D₄×C₁₇	1	2	yes	—
298	C₂×C₄	C₂×D₄×C₁₇	1	2	yes	—
299	C₂×C₄	C₂×D₄×C₁₇	1	2	yes	—
300	C₂²	—	2	2	no	—
301	C₂²	—	2	2	no	—
302	C₂²	—	2	4	no	—
303	C₂²	—	2	4	no	—
304	C₂²	—	2	2	no	—
305	C₂²	—	2	4	no	—
306	C₂²	—	2	4	no	—
307	C₂²	—	2	4	no	—
308	C₂²	—	2	4	no	—
309	C₂²	—	4	16	no	—
310	C₂²	—	4	2	no	—
311	C₂²	—	4	1	no	—
312	C₂²	—	4	1	no	—
313	C₂²	—	4	2	no	—
314	C₂²	—	4	2	no	—
315	C₂²	—	4	2	no	—
316	C₂²	—	4	2	no	—
317	C₂²	C₁₇×#121	1	4	yes	—
318	C₂²	C₂²×D₄×C₁₇	1	1	yes	characteristic
319	C₂²	C₂²×D₄×C₁₇	1	1	yes	characteristic
320	C₂²	C₂×#41×C₁₇	1	1	yes	characteristic
321	C₂²	C₂×#41×C₁₇	1	2	yes	—
322	C₂²	C₁₇×H(5,𝔽₂)	1	2	yes	—
323	C₄	—	2	2	no	—
324	C₄	—	2	2	no	—
325	C₄	—	2	2	no	—
326	C₄	—	4	2	no	—
327	C₄	—	4	1	no	—
328	C₄	—	4	1	no	—
329	C₄	—	4	2	no	—
330	C₄	—	4	2	no	—
331	C₂	—	2	4	no	—
332	C₂	—	4	4	no	—
333	C₂	—	4	2	no	—
334	C₂	C₂×C₁₇×#121	1	1	yes	characteristic
335	C₂	C₁₇×#525	1	1	yes	characteristic
336	C₂	C₁₇×#534	1	1	yes	characteristic
337	C₂	C₁₇×#546	1	2	yes	—
338	C₂	C₁₇×#551	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₇
prime radical	C₂×C₁₇×#120	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×#123	C₂	semidirect
3. C₂×C₄×D₄×C₁₇	C₂	semidirect
4. C₂²×C₂²⋊C₄×C₁₇	C₂	semidirect
5. C₁₇×#396	C₂	semidirect
6. C₁₇×#394	C₂	semidirect
7. C₁₇×#388	C₂	semidirect
8. C₁₇×#386	C₂	semidirect
9. C₁₇×#381	C₂	semidirect
10. C₁₇×#380	C₂	semidirect
11. C₁₇×#379	C₂	semidirect
17. C₂³×C₄×C₁₇	C₂²	semidirect
21. C₂×C₄⋊C₄×C₁₇	C₂²	semidirect
22. C₂×C₄⋊C₄×C₁₇	C₂²	semidirect
23. C₂×C₄⋊C₄×C₁₇	C₂²	semidirect
33. C₂×C₂²⋊C₄×C₁₇	C₂²	semidirect
34. C₂×C₂²⋊C₄×C₁₇	C₂²	semidirect
35. C₂×C₄²×C₁₇	C₂²	semidirect
36. C₁₇×#95	C₂²	semidirect
37. C₁₇×#95	C₂²	semidirect
38. C₁₇×#95	C₂²	semidirect
59. C₂²×C₄×C₁₇	D₄	semidirect
130. #2534	C₁₇	direct (N × H)
162. C₂×#123	C₂×C₁₇	semidirect
164. C₂×C₄×D₄	C₂×C₁₇	semidirect
165. C₂²×C₂²⋊C₄	C₂×C₁₇	semidirect
166. #396	C₂×C₁₇	semidirect
167. #394	C₂×C₁₇	semidirect
168. #388	C₂×C₁₇	semidirect
169. #386	C₂×C₁₇	semidirect
170. #381	C₂×C₁₇	semidirect
171. #380	C₂×C₁₇	semidirect
172. #379	C₂×C₁₇	semidirect
186. C₂³×C₄	C₂²×C₁₇	semidirect
190. C₂×C₄⋊C₄	C₂²×C₁₇	semidirect
191. C₂×C₄⋊C₄	C₂²×C₁₇	semidirect
192. C₂×C₄⋊C₄	C₂²×C₁₇	semidirect
202. C₂×C₂²⋊C₄	C₂²×C₁₇	semidirect
203. C₂×C₂²⋊C₄	C₂²×C₁₇	semidirect
204. C₂×C₄²	C₂²×C₁₇	semidirect
205. #95	C₂²×C₁₇	semidirect
206. #95	C₂²×C₁₇	semidirect
207. #95	C₂²×C₁₇	semidirect
208. C₁₇	#2534	direct (N × H)
229. C₂²×C₄	D₄×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₇×#123	2
C₂×C₁₇×#120	2
C₂×C₄×D₄×C₁₇	2
C₂²×C₂²⋊C₄×C₁₇	2
C₁₇×#396	2
C₁₇×#394	2
C₁₇×#388	2
C₁₇×#386	2
C₁₇×#381	2
C₁₇×#380	2
C₁₇×#379	2
#2534	17

Subgroups — C17×#2534 #14525540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#2534 #14525540