Subgroups — C₁₇×#34176 #16891920

Order 4352.

4110 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂²⋊C₄×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#2342	C₂	1	16	yes	maximal, complemented
3	C₁₇×#2315	C₂	1	2	yes	maximal, complemented
4	C₁₇×#2312	C₂	1	4	yes	maximal, complemented
5	C₁₇×#2280	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₇×#379	C₂	1	2	yes	maximal
7	C₁₇×#2273	C₂	1	2	yes	maximal, complemented
8	C₂⁶×C₁₇	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₁₇	C₂²	1	2	yes	—
10	C₂×C₁₇×#117	C₂²	1	8	yes	complemented
11	C₂²×C₂²⋊C₄×C₁₇	C₄	1	16	yes	complemented
12	C₂²×C₂²⋊C₄×C₁₇	C₂²	1	4	yes	—
13	C₂²×C₂²⋊C₄×C₁₇	C₂²	1	8	yes	—
14	C₂²×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
15	C₂²×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₁₇	C₂²	1	8	yes	—
18	C₁₇×#388	C₂²	1	32	yes	complemented
19	C₁₇×#385	C₂²	1	16	yes	complemented
20	C₁₇×#381	C₂²	1	8	yes	complemented
21	C₁₇×#380	C₂²	1	8	yes	complemented
22	C₁₇×#380	C₂²	1	8	yes	complemented
23	C₁₇×#379	C₂²	1	4	yes	—
24	C₁₇×#379	C₂²	1	4	yes	—
25	C₁₇×#379	C₂²	1	8	yes	—
26	C₄×C₂²⋊C₄×C₁₇	C₂²	1	8	yes	complemented
27	C₄×C₂²⋊C₄×C₁₇	C₂²	1	16	yes	complemented
28	C₄×C₂²⋊C₄×C₁₇	C₂²	1	8	yes	complemented
29	C₂⁵×C₁₇	—	2	8	no	—
30	C₂⁵×C₁₇	—	4	8	no	—
31	C₂⁵×C₁₇	C₂×C₄	1	8	yes	—
32	C₂⁵×C₁₇	C₂³	1	1	yes	characteristic
33	C₂⁵×C₁₇	C₂³	1	4	yes	—
34	C₂⁵×C₁₇	C₂³	1	1	yes	characteristic
35	C₂⁵×C₁₇	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₁₇	—	4	8	no	—
37	C₂³×C₄×C₁₇	C₂×C₄	1	16	yes	complemented
38	C₂³×C₄×C₁₇	C₂³	1	4	yes	—
39	C₂³×C₄×C₁₇	C₂³	1	8	yes	—
40	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₇	C₂³	1	4	yes	—
42	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
43	C₁₇×#117	—	4	16	no	—
44	C₂×C₄⋊C₄×C₁₇	C₂³	1	16	yes	complemented
45	C₂×C₂²⋊C₄×C₁₇	—	2	16	no	—
46	C₂×C₂²⋊C₄×C₁₇	—	4	16	no	—
47	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	8	yes	—
48	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	8	yes	—
49	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	64	yes	complemented
50	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	16	yes	complemented
51	C₂×C₂²⋊C₄×C₁₇	C₂³	1	16	yes	—
52	C₂×C₂²⋊C₄×C₁₇	C₂³	1	8	yes	—
53	C₂×C₂²⋊C₄×C₁₇	C₂³	1	8	yes	—
54	C₂×C₂²⋊C₄×C₁₇	C₂³	1	16	yes	—
55	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
56	C₂×C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
57	C₂×C₂²⋊C₄×C₁₇	C₂³	1	8	yes	—
58	C₂×C₄²×C₁₇	C₂³	1	16	yes	complemented
59	C₁₇×#95	C₂³	1	16	yes	complemented
60	C₁₇×#95	C₂³	1	16	yes	complemented
61	C₂⁴×C₁₇	—	2	4	no	—
62	C₂⁴×C₁₇	—	2	8	no	—
63	C₂⁴×C₁₇	—	2	32	no	—
64	C₂⁴×C₁₇	—	2	16	no	—
65	C₂⁴×C₁₇	—	2	4	no	—
66	C₂⁴×C₁₇	—	2	16	no	—
67	C₂⁴×C₁₇	—	4	32	no	—
68	C₂⁴×C₁₇	—	4	4	no	—
69	C₂⁴×C₁₇	—	4	8	no	—
70	C₂⁴×C₁₇	—	4	4	no	—
71	C₂⁴×C₁₇	—	4	64	no	—
72	C₂⁴×C₁₇	C₂²×C₄	1	4	yes	—
73	C₂⁴×C₁₇	C₂²×C₄	1	16	yes	—
74	C₂⁴×C₁₇	C₂²×C₄	1	4	yes	—
75	C₂⁴×C₁₇	C₂²×C₄	1	4	yes	—
76	C₂⁴×C₁₇	#41	1	8	yes	—
77	C₂⁴×C₁₇	C₂⁴	1	2	yes	—
78	C₂⁴×C₁₇	C₂⁴	1	2	yes	—
79	C₂⁴×C₁₇	C₂⁴	1	1	yes	characteristic
80	C₂⁴×C₁₇	C₂⁴	1	2	yes	—
81	C₂²×C₄×C₁₇	—	2	16	no	—
82	C₂²×C₄×C₁₇	—	2	16	no	—
83	C₂²×C₄×C₁₇	—	4	32	no	—
84	C₂²×C₄×C₁₇	—	4	4	no	—
85	C₂²×C₄×C₁₇	—	4	8	no	—
86	C₂²×C₄×C₁₇	—	4	4	no	—
87	C₂²×C₄×C₁₇	—	4	16	no	—
88	C₂²×C₄×C₁₇	C₂²×C₄	1	16	yes	—
89	C₂²×C₄×C₁₇	C₂²×C₄	1	8	yes	—
90	C₂²×C₄×C₁₇	C₂²×C₄	1	8	yes	—
91	C₂²×C₄×C₁₇	C₂²×C₄	1	16	yes	—
92	C₂²×C₄×C₁₇	C₂⁴	1	16	yes	—
93	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
94	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
95	C₄⋊C₄×C₁₇	—	4	16	no	—
96	C₂²⋊C₄×C₁₇	—	2	16	no	—
97	C₂²⋊C₄×C₁₇	—	2	16	no	—
98	C₂²⋊C₄×C₁₇	—	2	32	no	—
99	C₂²⋊C₄×C₁₇	—	4	16	no	—
100	C₂²⋊C₄×C₁₇	C₂²×C₄	1	16	yes	—
101	C₂²⋊C₄×C₁₇	C₂²×C₄	1	16	yes	—
102	C₂²⋊C₄×C₁₇	C₂²×C₄	1	32	yes	—
103	C₄²×C₁₇	—	4	16	no	—
104	#34176	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂³×C₁₇	—	2	32	no	—
106	C₂³×C₁₇	—	2	8	no	—
107	C₂³×C₁₇	—	2	16	no	—
108	C₂³×C₁₇	—	2	4	no	—
109	C₂³×C₁₇	—	2	4	no	—
110	C₂³×C₁₇	—	2	4	no	—
111	C₂³×C₁₇	—	2	8	no	—
112	C₂³×C₁₇	—	2	32	no	—
113	C₂³×C₁₇	—	2	8	no	—
114	C₂³×C₁₇	—	2	32	no	—
115	C₂³×C₁₇	—	2	4	no	—
116	C₂³×C₁₇	—	2	8	no	—
117	C₂³×C₁₇	—	4	8	no	—
118	C₂³×C₁₇	—	4	16	no	—
119	C₂³×C₁₇	—	4	8	no	—
120	C₂³×C₁₇	—	4	16	no	—
121	C₂³×C₁₇	—	4	64	no	—
122	C₂³×C₁₇	—	4	128	no	—
123	C₂³×C₁₇	—	4	16	no	—
124	C₂³×C₁₇	#117	1	16	yes	complemented
125	C₂³×C₁₇	C₂³×C₄	1	4	yes	—
126	C₂³×C₁₇	C₂³×C₄	1	4	yes	—
127	C₂³×C₁₇	C₂³×C₄	1	2	yes	—
128	C₂³×C₁₇	C₂³×C₄	1	4	yes	—
129	C₂³×C₁₇	C₂×#41	1	4	yes	—
130	C₂³×C₁₇	C₂×#41	1	8	yes	—
131	C₂³×C₁₇	H(5,𝔽₂)	1	8	yes	—
132	C₂³×C₁₇	C₂⁵	1	1	yes	characteristic
133	C₂×C₄×C₁₇	—	2	32	no	—
134	C₂×C₄×C₁₇	—	2	8	no	—
135	C₂×C₄×C₁₇	—	2	8	no	—
136	C₂×C₄×C₁₇	—	2	16	no	—
137	C₂×C₄×C₁₇	—	2	32	no	—
138	C₂×C₄×C₁₇	—	4	8	no	—
139	C₂×C₄×C₁₇	—	4	8	no	—
140	C₂×C₄×C₁₇	—	4	16	no	—
141	C₂×C₄×C₁₇	—	8	16	no	—
142	C₂×C₄×C₁₇	C₂³×C₄	1	8	yes	—
143	C₂×C₄×C₁₇	C₂³×C₄	1	8	yes	—
144	C₂³×C₂²⋊C₄	C₂×C₁₇	1	1	yes	characteristic
145	#2342	C₂×C₁₇	1	16	yes	complemented
146	#2315	C₂×C₁₇	1	2	yes	complemented
147	#2312	C₂×C₁₇	1	4	yes	complemented
148	#2280	C₂×C₁₇	1	4	yes	complemented
149	C₂×#379	C₂×C₁₇	1	2	yes	—
150	#2273	C₂×C₁₇	1	2	yes	complemented
151	C₂²×C₁₇	—	2	32	no	—
152	C₂²×C₁₇	—	2	4	no	—
153	C₂²×C₁₇	—	2	4	no	—
154	C₂²×C₁₇	—	2	4	no	—
155	C₂²×C₁₇	—	2	8	no	—
156	C₂²×C₁₇	—	2	16	no	—
157	C₂²×C₁₇	—	2	8	no	—
158	C₂²×C₁₇	—	2	16	no	—
159	C₂²×C₁₇	—	2	4	no	—
160	C₂²×C₁₇	—	2	8	no	—
161	C₂²×C₁₇	—	4	16	no	—
162	C₂²×C₁₇	—	4	64	no	—
163	C₂²×C₁₇	—	4	16	no	—
164	C₂²×C₁₇	—	4	8	no	—
165	C₂²×C₁₇	C₂×#117	1	4	yes	—
166	C₂²×C₁₇	C₂×#117	1	8	yes	—
167	C₂²×C₁₇	#518	1	8	yes	—
168	C₂²×C₁₇	C₂⁴×C₄	1	1	yes	characteristic
169	C₂²×C₁₇	C₂²×#41	1	2	yes	—
170	C₂²×C₁₇	C₂×H(5,𝔽₂)	1	4	yes	—
171	C₄×C₁₇	—	2	8	no	—
172	C₄×C₁₇	—	2	8	no	—
173	C₄×C₁₇	—	4	16	no	—
174	C₂⁶	C₂²×C₁₇	1	1	yes	characteristic
175	C₂⁴×C₄	C₂²×C₁₇	1	2	yes	—
176	C₂×#117	C₂²×C₁₇	1	8	yes	complemented
177	C₂²×C₂²⋊C₄	C₄×C₁₇	1	16	yes	complemented
178	C₂²×C₂²⋊C₄	C₂²×C₁₇	1	4	yes	—
179	C₂²×C₂²⋊C₄	C₂²×C₁₇	1	8	yes	—
180	C₂²×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
181	C₂²×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
182	C₂²×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
183	C₂²×C₂²⋊C₄	C₂²×C₁₇	1	8	yes	—
184	#388	C₂²×C₁₇	1	32	yes	complemented
185	#385	C₂²×C₁₇	1	16	yes	complemented
186	#381	C₂²×C₁₇	1	8	yes	complemented
187	#380	C₂²×C₁₇	1	8	yes	complemented
188	#380	C₂²×C₁₇	1	8	yes	complemented
189	#379	C₂²×C₁₇	1	4	yes	—
190	#379	C₂²×C₁₇	1	8	yes	—
191	#379	C₂²×C₁₇	1	4	yes	—
192	C₄×C₂²⋊C₄	C₂²×C₁₇	1	8	yes	complemented
193	C₄×C₂²⋊C₄	C₂²×C₁₇	1	16	yes	complemented
194	C₄×C₂²⋊C₄	C₂²×C₁₇	1	8	yes	complemented
195	C₂×C₁₇	—	2	4	no	—
196	C₂×C₁₇	—	2	8	no	—
197	C₂×C₁₇	—	2	8	no	—
198	C₂×C₁₇	—	4	4	no	—
199	C₂×C₁₇	C₂²×#117	1	1	yes	characteristic
200	C₂×C₁₇	C₂×#518	1	2	yes	—
201	C₂×C₁₇	#3490	1	4	yes	—
202	C₂⁵	—	2	8	no	—
203	C₂⁵	—	4	8	no	—
204	C₂⁵	C₂×C₄×C₁₇	1	8	yes	—
205	C₂⁵	C₂³×C₁₇	1	1	yes	characteristic
206	C₂⁵	C₂³×C₁₇	1	4	yes	—
207	C₂⁵	C₂³×C₁₇	1	1	yes	characteristic
208	C₂⁵	C₂³×C₁₇	1	1	yes	characteristic
209	C₂³×C₄	—	4	8	no	—
210	C₂³×C₄	C₂×C₄×C₁₇	1	16	yes	complemented
211	C₂³×C₄	C₂³×C₁₇	1	4	yes	—
212	C₂³×C₄	C₂³×C₁₇	1	8	yes	—
213	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
214	C₂³×C₄	C₂³×C₁₇	1	4	yes	—
215	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
216	#117	—	4	16	no	—
217	C₂×C₄⋊C₄	C₂³×C₁₇	1	16	yes	complemented
218	C₂×C₂²⋊C₄	—	2	16	no	—
219	C₂×C₂²⋊C₄	—	4	16	no	—
220	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	8	yes	—
221	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	8	yes	—
222	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	64	yes	complemented
223	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	16	yes	complemented
224	C₂×C₂²⋊C₄	C₂³×C₁₇	1	16	yes	—
225	C₂×C₂²⋊C₄	C₂³×C₁₇	1	8	yes	—
226	C₂×C₂²⋊C₄	C₂³×C₁₇	1	8	yes	—
227	C₂×C₂²⋊C₄	C₂³×C₁₇	1	16	yes	—
228	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
229	C₂×C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
230	C₂×C₂²⋊C₄	C₂³×C₁₇	1	8	yes	—
231	C₂×C₄²	C₂³×C₁₇	1	16	yes	complemented
232	#95	C₂³×C₁₇	1	16	yes	complemented
233	#95	C₂³×C₁₇	1	16	yes	complemented
234	C₁₇	#34176	1	1	yes	characteristic, direct product factor, Sylow
235	C₂⁴	—	2	4	no	—
236	C₂⁴	—	2	8	no	—
237	C₂⁴	—	2	16	no	—
238	C₂⁴	—	2	4	no	—
239	C₂⁴	—	2	16	no	—
240	C₂⁴	—	2	32	no	—
241	C₂⁴	—	4	32	no	—
242	C₂⁴	—	4	4	no	—
243	C₂⁴	—	4	8	no	—
244	C₂⁴	—	4	4	no	—
245	C₂⁴	—	4	64	no	—
246	C₂⁴	C₂²×C₄×C₁₇	1	4	yes	—
247	C₂⁴	C₂²×C₄×C₁₇	1	16	yes	—
248	C₂⁴	C₂²×C₄×C₁₇	1	4	yes	—
249	C₂⁴	C₂²×C₄×C₁₇	1	4	yes	—
250	C₂⁴	#41×C₁₇	1	8	yes	—
251	C₂⁴	C₂⁴×C₁₇	1	2	yes	—
252	C₂⁴	C₂⁴×C₁₇	1	2	yes	—
253	C₂⁴	C₂⁴×C₁₇	1	1	yes	characteristic
254	C₂⁴	C₂⁴×C₁₇	1	2	yes	—
255	C₂²×C₄	—	2	16	no	—
256	C₂²×C₄	—	2	16	no	—
257	C₂²×C₄	—	4	32	no	—
258	C₂²×C₄	—	4	4	no	—
259	C₂²×C₄	—	4	8	no	—
260	C₂²×C₄	—	4	4	no	—
261	C₂²×C₄	—	4	16	no	—
262	C₂²×C₄	C₂²×C₄×C₁₇	1	16	yes	—
263	C₂²×C₄	C₂²×C₄×C₁₇	1	8	yes	—
264	C₂²×C₄	C₂²×C₄×C₁₇	1	8	yes	—
265	C₂²×C₄	C₂²×C₄×C₁₇	1	16	yes	—
266	C₂²×C₄	C₂⁴×C₁₇	1	16	yes	—
267	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
268	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
269	C₄⋊C₄	—	4	16	no	—
270	C₂²⋊C₄	—	2	16	no	—
271	C₂²⋊C₄	—	2	16	no	—
272	C₂²⋊C₄	—	2	32	no	—
273	C₂²⋊C₄	—	4	16	no	—
274	C₂²⋊C₄	C₂²×C₄×C₁₇	1	16	yes	—
275	C₂²⋊C₄	C₂²×C₄×C₁₇	1	16	yes	—
276	C₂²⋊C₄	C₂²×C₄×C₁₇	1	32	yes	—
277	C₄²	—	4	16	no	—
278	C₂³	—	2	32	no	—
279	C₂³	—	2	8	no	—
280	C₂³	—	2	16	no	—
281	C₂³	—	2	4	no	—
282	C₂³	—	2	8	no	—
283	C₂³	—	2	4	no	—
284	C₂³	—	2	4	no	—
285	C₂³	—	2	32	no	—
286	C₂³	—	2	8	no	—
287	C₂³	—	2	32	no	—
288	C₂³	—	2	4	no	—
289	C₂³	—	2	8	no	—
290	C₂³	—	4	8	no	—
291	C₂³	—	4	16	no	—
292	C₂³	—	4	8	no	—
293	C₂³	—	4	16	no	—
294	C₂³	—	4	64	no	—
295	C₂³	—	4	128	no	—
296	C₂³	—	4	16	no	—
297	C₂³	C₁₇×#117	1	16	yes	complemented
298	C₂³	C₂³×C₄×C₁₇	1	4	yes	—
299	C₂³	C₂³×C₄×C₁₇	1	4	yes	—
300	C₂³	C₂³×C₄×C₁₇	1	2	yes	—
301	C₂³	C₂³×C₄×C₁₇	1	4	yes	—
302	C₂³	C₂×#41×C₁₇	1	4	yes	—
303	C₂³	C₂×#41×C₁₇	1	8	yes	—
304	C₂³	C₁₇×H(5,𝔽₂)	1	8	yes	—
305	C₂³	C₂⁵×C₁₇	1	1	yes	characteristic
306	C₂×C₄	—	2	32	no	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	2	16	no	—
310	C₂×C₄	—	2	32	no	—
311	C₂×C₄	—	4	8	no	—
312	C₂×C₄	—	4	8	no	—
313	C₂×C₄	—	4	16	no	—
314	C₂×C₄	—	8	16	no	—
315	C₂×C₄	C₂³×C₄×C₁₇	1	8	yes	—
316	C₂×C₄	C₂³×C₄×C₁₇	1	8	yes	—
317	C₂²	—	2	32	no	—
318	C₂²	—	2	16	no	—
319	C₂²	—	2	8	no	—
320	C₂²	—	2	16	no	—
321	C₂²	—	2	4	no	—
322	C₂²	—	2	4	no	—
323	C₂²	—	2	4	no	—
324	C₂²	—	2	8	no	—
325	C₂²	—	2	4	no	—
326	C₂²	—	2	8	no	—
327	C₂²	—	4	16	no	—
328	C₂²	—	4	64	no	—
329	C₂²	—	4	16	no	—
330	C₂²	—	4	8	no	—
331	C₂²	C₂×C₁₇×#117	1	4	yes	—
332	C₂²	C₂×C₁₇×#117	1	8	yes	—
333	C₂²	C₁₇×#518	1	8	yes	—
334	C₂²	C₂⁴×C₄×C₁₇	1	1	yes	characteristic
335	C₂²	C₂²×#41×C₁₇	1	2	yes	—
336	C₂²	C₂×C₁₇×H(5,𝔽₂)	1	4	yes	—
337	C₄	—	2	8	no	—
338	C₄	—	2	8	no	—
339	C₄	—	4	16	no	—
340	C₂	—	2	4	no	—
341	C₂	—	2	8	no	—
342	C₂	—	2	8	no	—
343	C₂	—	4	4	no	—
344	C₂	C₂²×C₁₇×#117	1	1	yes	characteristic
345	C₂	C₂×C₁₇×#518	1	2	yes	—
346	C₂	C₁₇×#3490	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₇
Frattini, cosocle	C₂³	C₂⁵×C₁₇
prime radical	C₂⁶×C₁₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₇×#2342	C₂	semidirect
3. C₁₇×#2315	C₂	semidirect
4. C₁₇×#2312	C₂	semidirect
5. C₁₇×#2280	C₂	semidirect
7. C₁₇×#2273	C₂	semidirect
10. C₂×C₁₇×#117	C₂²	semidirect
11. C₂²×C₂²⋊C₄×C₁₇	C₄	semidirect
18. C₁₇×#388	C₂²	semidirect
19. C₁₇×#385	C₂²	semidirect
20. C₁₇×#381	C₂²	semidirect
21. C₁₇×#380	C₂²	semidirect
22. C₁₇×#380	C₂²	semidirect
26. C₄×C₂²⋊C₄×C₁₇	C₂²	semidirect
27. C₄×C₂²⋊C₄×C₁₇	C₂²	semidirect
28. C₄×C₂²⋊C₄×C₁₇	C₂²	semidirect
37. C₂³×C₄×C₁₇	C₂×C₄	semidirect
44. C₂×C₄⋊C₄×C₁₇	C₂³	semidirect
49. C₂×C₂²⋊C₄×C₁₇	C₂×C₄	semidirect
50. C₂×C₂²⋊C₄×C₁₇	C₂×C₄	semidirect
58. C₂×C₄²×C₁₇	C₂³	semidirect
59. C₁₇×#95	C₂³	semidirect
60. C₁₇×#95	C₂³	semidirect
104. #34176	C₁₇	direct (N × H)
124. C₂³×C₁₇	#117	semidirect
145. #2342	C₂×C₁₇	semidirect
146. #2315	C₂×C₁₇	semidirect
147. #2312	C₂×C₁₇	semidirect
148. #2280	C₂×C₁₇	semidirect
150. #2273	C₂×C₁₇	semidirect
176. C₂×#117	C₂²×C₁₇	semidirect
177. C₂²×C₂²⋊C₄	C₄×C₁₇	semidirect
184. #388	C₂²×C₁₇	semidirect
185. #385	C₂²×C₁₇	semidirect
186. #381	C₂²×C₁₇	semidirect
187. #380	C₂²×C₁₇	semidirect
188. #380	C₂²×C₁₇	semidirect
192. C₄×C₂²⋊C₄	C₂²×C₁₇	semidirect
193. C₄×C₂²⋊C₄	C₂²×C₁₇	semidirect
194. C₄×C₂²⋊C₄	C₂²×C₁₇	semidirect
210. C₂³×C₄	C₂×C₄×C₁₇	semidirect
217. C₂×C₄⋊C₄	C₂³×C₁₇	semidirect
222. C₂×C₂²⋊C₄	C₂×C₄×C₁₇	semidirect
223. C₂×C₂²⋊C₄	C₂×C₄×C₁₇	semidirect
231. C₂×C₄²	C₂³×C₁₇	semidirect
232. #95	C₂³×C₁₇	semidirect
233. #95	C₂³×C₁₇	semidirect
234. C₁₇	#34176	direct (N × H)
297. C₂³	C₁₇×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₂²⋊C₄×C₁₇	2
C₁₇×#2342	2
C₁₇×#2315	2
C₁₇×#2312	2
C₁₇×#2280	2
C₂×C₁₇×#379	2
C₁₇×#2273	2
#34176	17

Subgroups — C17×#34176 #16891920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#34176 #16891920