Subgroups — C₂×C₁₇×#2280 #16891750

Order 4352.

7630 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₄×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₇×#117	C₂	1	2	yes	maximal, complemented
3	C₁₇×#2280	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₇×#381	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₇×#380	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₇×#379	C₂	1	2	yes	maximal
7	C₂×C₄×C₂²⋊C₄×C₁₇	C₂	1	4	yes	maximal, complemented
8	C₂⁶×C₁₇	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₁₇	—	2	16	no	—
10	C₂⁴×C₄×C₁₇	C₄	1	16	yes	complemented
11	C₂⁴×C₄×C₁₇	C₂²	1	2	yes	—
12	C₂⁴×C₄×C₁₇	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₇	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₁₇	C₂²	1	8	yes	—
15	C₂⁴×C₄×C₁₇	C₂²	1	1	yes	characteristic
16	C₂×C₁₇×#117	—	2	16	no	—
17	C₂×C₁₇×#117	C₂²	1	16	yes	complemented
18	C₂²×C₄⋊C₄×C₁₇	C₂²	1	4	yes	complemented
19	C₂²×C₂²⋊C₄×C₁₇	C₂²	1	8	yes	—
20	C₂²×C₂²⋊C₄×C₁₇	C₂²	1	4	yes	—
21	C₂²×C₄²×C₁₇	C₂²	1	4	yes	complemented
22	C₁₇×#381	C₂²	1	16	yes	complemented
23	C₁₇×#380	C₂²	1	32	yes	complemented
24	C₁₇×#379	C₂²	1	16	yes	—
25	C₄×C₂²⋊C₄×C₁₇	C₂²	1	32	yes	complemented
26	C₂×C₁₇×#95	C₂²	1	8	yes	complemented
27	C₂⁵×C₁₇	—	2	8	no	—
28	C₂⁵×C₁₇	—	2	16	no	—
29	C₂⁵×C₁₇	C₂×C₄	1	8	yes	—
30	C₂⁵×C₁₇	C₂³	1	4	yes	—
31	C₂⁵×C₁₇	C₂³	1	1	yes	characteristic
32	C₂⁵×C₁₇	C₂³	1	2	yes	—
33	C₂³×C₄×C₁₇	—	2	8	no	—
34	C₂³×C₄×C₁₇	—	2	128	no	—
35	C₂³×C₄×C₁₇	—	2	16	no	—
36	C₂³×C₄×C₁₇	—	2	16	no	—
37	C₂³×C₄×C₁₇	—	2	64	no	—
38	C₂³×C₄×C₁₇	C₂×C₄	1	8	yes	—
39	C₂³×C₄×C₁₇	C₂×C₄	1	16	yes	—
40	C₂³×C₄×C₁₇	C₂×C₄	1	16	yes	—
41	C₂³×C₄×C₁₇	C₂×C₄	1	8	yes	—
42	C₂³×C₄×C₁₇	C₂×C₄	1	64	yes	complemented
43	C₂³×C₄×C₁₇	D₄	1	16	yes	—
44	C₂³×C₄×C₁₇	C₂³	1	8	yes	—
45	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₇	C₂³	1	8	yes	—
47	C₂³×C₄×C₁₇	C₂³	1	8	yes	—
48	C₂³×C₄×C₁₇	C₂³	1	4	yes	—
49	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₇	C₂³	1	4	yes	—
51	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
52	C₁₇×#117	—	2	64	no	—
53	C₂×C₄⋊C₄×C₁₇	—	2	16	no	—
54	C₂×C₄⋊C₄×C₁₇	C₂³	1	16	yes	complemented
55	C₂×C₂²⋊C₄×C₁₇	—	2	16	no	—
56	C₂×C₂²⋊C₄×C₁₇	—	2	32	no	—
57	C₂×C₂²⋊C₄×C₁₇	C₂³	1	16	yes	—
58	C₂×C₂²⋊C₄×C₁₇	C₂³	1	32	yes	—
59	C₂×C₄²×C₁₇	—	2	16	no	—
60	C₂×C₄²×C₁₇	C₂³	1	16	yes	complemented
61	C₁₇×#95	C₂³	1	32	yes	complemented
62	C₂⁴×C₁₇	—	2	128	no	—
63	C₂⁴×C₁₇	—	2	32	no	—
64	C₂⁴×C₁₇	—	2	64	no	—
65	C₂⁴×C₁₇	—	2	16	no	—
66	C₂⁴×C₁₇	—	2	8	no	—
67	C₂⁴×C₁₇	—	2	32	no	—
68	C₂⁴×C₁₇	—	2	8	no	—
69	C₂⁴×C₁₇	—	2	8	no	—
70	C₂⁴×C₁₇	C₂²×C₄	1	16	yes	—
71	C₂⁴×C₁₇	C₂²×C₄	1	4	yes	—
72	C₂⁴×C₁₇	C₂²×C₄	1	8	yes	—
73	C₂⁴×C₁₇	C₂×D₄	1	8	yes	—
74	C₂⁴×C₁₇	#41	1	16	yes	—
75	C₂⁴×C₁₇	C₂⁴	1	2	yes	—
76	C₂⁴×C₁₇	C₂⁴	1	4	yes	—
77	C₂⁴×C₁₇	C₂⁴	1	1	yes	characteristic
78	C₂²×C₄×C₁₇	—	2	32	no	—
79	C₂²×C₄×C₁₇	—	2	16	no	—
80	C₂²×C₄×C₁₇	—	2	8	no	—
81	C₂²×C₄×C₁₇	—	2	64	no	—
82	C₂²×C₄×C₁₇	—	2	64	no	—
83	C₂²×C₄×C₁₇	—	2	256	no	—
84	C₂²×C₄×C₁₇	—	2	32	no	—
85	C₂²×C₄×C₁₇	—	2	32	no	—
86	C₂²×C₄×C₁₇	—	2	16	no	—
87	C₂²×C₄×C₁₇	—	2	32	no	—
88	C₂²×C₄×C₁₇	C₂²⋊C₄	1	64	yes	complemented
89	C₂²×C₄×C₁₇	C₂²×C₄	1	8	yes	—
90	C₂²×C₄×C₁₇	C₂²×C₄	1	16	yes	—
91	C₂²×C₄×C₁₇	C₂²×C₄	1	32	yes	—
92	C₂²×C₄×C₁₇	C₂²×C₄	1	32	yes	—
93	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	—
94	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	—
95	C₂²×C₄×C₁₇	C₂²×C₄	1	16	yes	—
96	C₂²×C₄×C₁₇	C₂×D₄	1	8	yes	—
97	C₂²×C₄×C₁₇	C₂×D₄	1	8	yes	—
98	C₂²×C₄×C₁₇	C₂×D₄	1	32	yes	—
99	C₂²×C₄×C₁₇	C₂⁴	1	16	yes	—
100	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
101	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
102	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
103	C₄⋊C₄×C₁₇	—	2	32	no	—
104	C₂²⋊C₄×C₁₇	—	2	32	no	—
105	C₂²⋊C₄×C₁₇	—	2	64	no	—
106	C₄²×C₁₇	—	2	32	no	—
107	C₂×#2280	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂³×C₁₇	—	2	128	no	—
109	C₂³×C₁₇	—	2	256	no	—
110	C₂³×C₁₇	—	2	32	no	—
111	C₂³×C₁₇	—	2	16	no	—
112	C₂³×C₁₇	—	2	16	no	—
113	C₂³×C₁₇	—	2	16	no	—
114	C₂³×C₁₇	—	2	64	no	—
115	C₂³×C₁₇	—	2	32	no	—
116	C₂³×C₁₇	—	2	64	no	—
117	C₂³×C₁₇	—	2	8	no	—
118	C₂³×C₁₇	—	2	8	no	—
119	C₂³×C₁₇	—	2	8	no	—
120	C₂³×C₁₇	C₂×C₂²⋊C₄	1	16	yes	—
121	C₂³×C₁₇	#117	1	32	yes	complemented
122	C₂³×C₁₇	C₂³×C₄	1	4	yes	—
123	C₂³×C₁₇	C₂³×C₄	1	8	yes	—
124	C₂³×C₁₇	C₂³×C₄	1	2	yes	—
125	C₂³×C₁₇	C₂²×D₄	1	8	yes	—
126	C₂³×C₁₇	C₂²×D₄	1	4	yes	—
127	C₂³×C₁₇	C₂×#41	1	16	yes	—
128	C₂³×C₁₇	C₂×#41	1	8	yes	—
129	C₂³×C₁₇	C₂⁵	1	1	yes	characteristic
130	C₂×C₄×C₁₇	—	2	32	no	—
131	C₂×C₄×C₁₇	—	2	16	no	—
132	C₂×C₄×C₁₇	—	2	8	no	—
133	C₂×C₄×C₁₇	—	2	64	no	—
134	C₂×C₄×C₁₇	—	2	64	no	—
135	C₂×C₄×C₁₇	—	2	16	no	—
136	C₂×C₄×C₁₇	—	2	32	no	—
137	C₂×C₄×C₁₇	—	4	32	no	—
138	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	16	yes	—
139	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	16	yes	—
140	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	64	yes	complemented
141	C₂×C₄×C₁₇	C₂³×C₄	1	8	yes	—
142	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
143	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
144	C₂×C₄×C₁₇	C₂²×D₄	1	8	yes	—
145	C₂×C₄×C₁₇	C₂²×D₄	1	8	yes	—
146	C₂⁵×C₄	C₂×C₁₇	1	1	yes	characteristic
147	C₂²×#117	C₂×C₁₇	1	2	yes	complemented
148	#2280	C₂×C₁₇	1	16	yes	direct product factor
149	C₂×#381	C₂×C₁₇	1	2	yes	complemented
150	C₂×#380	C₂×C₁₇	1	4	yes	complemented
151	C₂×#379	C₂×C₁₇	1	2	yes	—
152	C₂×C₄×C₂²⋊C₄	C₂×C₁₇	1	4	yes	complemented
153	C₂²×C₁₇	—	2	128	no	—
154	C₂²×C₁₇	—	2	8	no	—
155	C₂²×C₁₇	—	2	8	no	—
156	C₂²×C₁₇	—	2	8	no	—
157	C₂²×C₁₇	—	2	16	no	—
158	C₂²×C₁₇	—	2	32	no	—
159	C₂²×C₁₇	—	2	32	no	—
160	C₂²×C₁₇	—	2	64	no	—
161	C₂²×C₁₇	C₂²×C₂²⋊C₄	1	8	yes	—
162	C₂²×C₁₇	C₂²×C₂²⋊C₄	1	4	yes	—
163	C₂²×C₁₇	C₂×#117	1	8	yes	—
164	C₂²×C₁₇	C₂×#117	1	16	yes	complemented
165	C₂²×C₁₇	#525	1	16	yes	—
166	C₂²×C₁₇	C₂⁴×C₄	1	1	yes	characteristic
167	C₂²×C₁₇	C₂³×D₄	1	2	yes	—
168	C₂²×C₁₇	C₂²×#41	1	4	yes	—
169	C₄×C₁₇	—	2	8	no	—
170	C₄×C₁₇	—	4	16	no	—
171	C₄×C₁₇	C₂²×C₂²⋊C₄	1	8	yes	—
172	C₄×C₁₇	C₂²×C₂²⋊C₄	1	8	yes	—
173	C₂⁶	C₂²×C₁₇	1	1	yes	characteristic
174	C₂⁴×C₄	—	2	16	no	—
175	C₂⁴×C₄	C₄×C₁₇	1	16	yes	complemented
176	C₂⁴×C₄	C₂²×C₁₇	1	2	yes	—
177	C₂⁴×C₄	C₂²×C₁₇	1	2	yes	—
178	C₂⁴×C₄	C₂²×C₁₇	1	1	yes	characteristic
179	C₂⁴×C₄	C₂²×C₁₇	1	8	yes	—
180	C₂⁴×C₄	C₂²×C₁₇	1	1	yes	characteristic
181	C₂×#117	—	2	16	no	—
182	C₂×#117	C₂²×C₁₇	1	16	yes	complemented
183	C₂²×C₄⋊C₄	C₂²×C₁₇	1	4	yes	complemented
184	C₂²×C₂²⋊C₄	C₂²×C₁₇	1	4	yes	—
185	C₂²×C₂²⋊C₄	C₂²×C₁₇	1	8	yes	—
186	C₂²×C₄²	C₂²×C₁₇	1	4	yes	complemented
187	#381	C₂²×C₁₇	1	16	yes	complemented
188	#380	C₂²×C₁₇	1	32	yes	complemented
189	#379	C₂²×C₁₇	1	16	yes	—
190	C₄×C₂²⋊C₄	C₂²×C₁₇	1	32	yes	complemented
191	C₂×#95	C₂²×C₁₇	1	8	yes	complemented
192	C₂×C₁₇	—	2	8	no	—
193	C₂×C₁₇	—	2	16	no	—
194	C₂×C₁₇	#2280	1	8	yes	direct product factor
195	C₂×C₁₇	C₂³×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₁₇	C₂²×#117	1	2	yes	—
197	C₂×C₁₇	C₂×#525	1	4	yes	—
198	C₂⁵	—	2	8	no	—
199	C₂⁵	—	2	16	no	—
200	C₂⁵	C₂×C₄×C₁₇	1	8	yes	—
201	C₂⁵	C₂³×C₁₇	1	4	yes	—
202	C₂⁵	C₂³×C₁₇	1	1	yes	characteristic
203	C₂⁵	C₂³×C₁₇	1	2	yes	—
204	C₂³×C₄	—	2	8	no	—
205	C₂³×C₄	—	2	128	no	—
206	C₂³×C₄	—	2	16	no	—
207	C₂³×C₄	—	2	16	no	—
208	C₂³×C₄	—	2	64	no	—
209	C₂³×C₄	C₂×C₄×C₁₇	1	8	yes	—
210	C₂³×C₄	C₂×C₄×C₁₇	1	16	yes	—
211	C₂³×C₄	C₂×C₄×C₁₇	1	16	yes	—
212	C₂³×C₄	C₂×C₄×C₁₇	1	8	yes	—
213	C₂³×C₄	C₂×C₄×C₁₇	1	64	yes	complemented
214	C₂³×C₄	D₄×C₁₇	1	16	yes	—
215	C₂³×C₄	C₂³×C₁₇	1	8	yes	—
216	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
217	C₂³×C₄	C₂³×C₁₇	1	8	yes	—
218	C₂³×C₄	C₂³×C₁₇	1	8	yes	—
219	C₂³×C₄	C₂³×C₁₇	1	4	yes	—
220	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
221	C₂³×C₄	C₂³×C₁₇	1	4	yes	—
222	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
223	#117	—	2	64	no	—
224	C₂×C₄⋊C₄	—	2	16	no	—
225	C₂×C₄⋊C₄	C₂³×C₁₇	1	16	yes	complemented
226	C₂×C₂²⋊C₄	—	2	16	no	—
227	C₂×C₂²⋊C₄	—	2	32	no	—
228	C₂×C₂²⋊C₄	C₂³×C₁₇	1	16	yes	—
229	C₂×C₂²⋊C₄	C₂³×C₁₇	1	32	yes	—
230	C₂×C₄²	—	2	16	no	—
231	C₂×C₄²	C₂³×C₁₇	1	16	yes	complemented
232	#95	C₂³×C₁₇	1	32	yes	complemented
233	C₁₇	C₂×#2280	1	1	yes	characteristic, direct product factor, Sylow
234	C₂⁴	—	2	128	no	—
235	C₂⁴	—	2	16	no	—
236	C₂⁴	—	2	8	no	—
237	C₂⁴	—	2	32	no	—
238	C₂⁴	—	2	8	no	—
239	C₂⁴	—	2	8	no	—
240	C₂⁴	—	2	32	no	—
241	C₂⁴	—	2	64	no	—
242	C₂⁴	C₂²×C₄×C₁₇	1	16	yes	—
243	C₂⁴	C₂²×C₄×C₁₇	1	4	yes	—
244	C₂⁴	C₂²×C₄×C₁₇	1	8	yes	—
245	C₂⁴	C₂×D₄×C₁₇	1	8	yes	—
246	C₂⁴	#41×C₁₇	1	16	yes	—
247	C₂⁴	C₂⁴×C₁₇	1	2	yes	—
248	C₂⁴	C₂⁴×C₁₇	1	4	yes	—
249	C₂⁴	C₂⁴×C₁₇	1	1	yes	characteristic
250	C₂²×C₄	—	2	16	no	—
251	C₂²×C₄	—	2	8	no	—
252	C₂²×C₄	—	2	32	no	—
253	C₂²×C₄	—	2	32	no	—
254	C₂²×C₄	—	2	32	no	—
255	C₂²×C₄	—	2	64	no	—
256	C₂²×C₄	—	2	64	no	—
257	C₂²×C₄	—	2	256	no	—
258	C₂²×C₄	—	2	16	no	—
259	C₂²×C₄	—	2	32	no	—
260	C₂²×C₄	C₂²⋊C₄×C₁₇	1	64	yes	complemented
261	C₂²×C₄	C₂²×C₄×C₁₇	1	8	yes	—
262	C₂²×C₄	C₂²×C₄×C₁₇	1	16	yes	—
263	C₂²×C₄	C₂²×C₄×C₁₇	1	32	yes	—
264	C₂²×C₄	C₂²×C₄×C₁₇	1	32	yes	—
265	C₂²×C₄	C₂²×C₄×C₁₇	1	4	yes	—
266	C₂²×C₄	C₂²×C₄×C₁₇	1	4	yes	—
267	C₂²×C₄	C₂²×C₄×C₁₇	1	16	yes	—
268	C₂²×C₄	C₂×D₄×C₁₇	1	8	yes	—
269	C₂²×C₄	C₂×D₄×C₁₇	1	8	yes	—
270	C₂²×C₄	C₂×D₄×C₁₇	1	32	yes	—
271	C₂²×C₄	C₂⁴×C₁₇	1	16	yes	—
272	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
273	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
274	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
275	C₄⋊C₄	—	2	32	no	—
276	C₂²⋊C₄	—	2	32	no	—
277	C₂²⋊C₄	—	2	64	no	—
278	C₄²	—	2	32	no	—
279	C₂³	—	2	256	no	—
280	C₂³	—	2	128	no	—
281	C₂³	—	2	32	no	—
282	C₂³	—	2	16	no	—
283	C₂³	—	2	16	no	—
284	C₂³	—	2	16	no	—
285	C₂³	—	2	64	no	—
286	C₂³	—	2	32	no	—
287	C₂³	—	2	64	no	—
288	C₂³	—	2	8	no	—
289	C₂³	—	2	8	no	—
290	C₂³	—	2	8	no	—
291	C₂³	C₂×C₂²⋊C₄×C₁₇	1	16	yes	—
292	C₂³	C₁₇×#117	1	32	yes	complemented
293	C₂³	C₂³×C₄×C₁₇	1	4	yes	—
294	C₂³	C₂³×C₄×C₁₇	1	8	yes	—
295	C₂³	C₂³×C₄×C₁₇	1	2	yes	—
296	C₂³	C₂²×D₄×C₁₇	1	8	yes	—
297	C₂³	C₂²×D₄×C₁₇	1	4	yes	—
298	C₂³	C₂×#41×C₁₇	1	16	yes	—
299	C₂³	C₂×#41×C₁₇	1	8	yes	—
300	C₂³	C₂⁵×C₁₇	1	1	yes	characteristic
301	C₂×C₄	—	2	32	no	—
302	C₂×C₄	—	2	16	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	2	64	no	—
305	C₂×C₄	—	2	64	no	—
306	C₂×C₄	—	2	16	no	—
307	C₂×C₄	—	2	32	no	—
308	C₂×C₄	—	4	32	no	—
309	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	16	yes	—
310	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	16	yes	—
311	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	64	yes	complemented
312	C₂×C₄	C₂³×C₄×C₁₇	1	8	yes	—
313	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
314	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
315	C₂×C₄	C₂²×D₄×C₁₇	1	8	yes	—
316	C₂×C₄	C₂²×D₄×C₁₇	1	8	yes	—
317	C₂²	—	2	128	no	—
318	C₂²	—	2	32	no	—
319	C₂²	—	2	64	no	—
320	C₂²	—	2	8	no	—
321	C₂²	—	2	8	no	—
322	C₂²	—	2	8	no	—
323	C₂²	—	2	16	no	—
324	C₂²	—	2	32	no	—
325	C₂²	C₂²×C₂²⋊C₄×C₁₇	1	8	yes	—
326	C₂²	C₂²×C₂²⋊C₄×C₁₇	1	4	yes	—
327	C₂²	C₂×C₁₇×#117	1	8	yes	—
328	C₂²	C₂×C₁₇×#117	1	16	yes	complemented
329	C₂²	C₁₇×#525	1	16	yes	—
330	C₂²	C₂⁴×C₄×C₁₇	1	1	yes	characteristic
331	C₂²	C₂³×D₄×C₁₇	1	2	yes	—
332	C₂²	C₂²×#41×C₁₇	1	4	yes	—
333	C₄	—	2	8	no	—
334	C₄	—	4	16	no	—
335	C₄	C₂²×C₂²⋊C₄×C₁₇	1	8	yes	—
336	C₄	C₂²×C₂²⋊C₄×C₁₇	1	8	yes	—
337	C₂	—	2	8	no	—
338	C₂	—	2	16	no	—
339	C₂	C₁₇×#2280	1	8	yes	direct product factor
340	C₂	C₂³×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
341	C₂	C₂²×C₁₇×#117	1	2	yes	—
342	C₂	C₂×C₁₇×#525	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₇×#117	C₂	semidirect
3. C₁₇×#2280	C₂	direct (N × H)
4. C₂×C₁₇×#381	C₂	semidirect
5. C₂×C₁₇×#380	C₂	semidirect
7. C₂×C₄×C₂²⋊C₄×C₁₇	C₂	semidirect
10. C₂⁴×C₄×C₁₇	C₄	semidirect
17. C₂×C₁₇×#117	C₂²	semidirect
18. C₂²×C₄⋊C₄×C₁₇	C₂²	semidirect
21. C₂²×C₄²×C₁₇	C₂²	semidirect
22. C₁₇×#381	C₂²	semidirect
23. C₁₇×#380	C₂²	semidirect
25. C₄×C₂²⋊C₄×C₁₇	C₂²	semidirect
26. C₂×C₁₇×#95	C₂²	semidirect
42. C₂³×C₄×C₁₇	C₂×C₄	semidirect
54. C₂×C₄⋊C₄×C₁₇	C₂³	semidirect
60. C₂×C₄²×C₁₇	C₂³	semidirect
61. C₁₇×#95	C₂³	semidirect
88. C₂²×C₄×C₁₇	C₂²⋊C₄	semidirect
107. C₂×#2280	C₁₇	direct (N × H)
121. C₂³×C₁₇	#117	semidirect
140. C₂×C₄×C₁₇	C₂×C₂²⋊C₄	semidirect
147. C₂²×#117	C₂×C₁₇	semidirect
148. #2280	C₂×C₁₇	direct (N × H)
149. C₂×#381	C₂×C₁₇	semidirect
150. C₂×#380	C₂×C₁₇	semidirect
152. C₂×C₄×C₂²⋊C₄	C₂×C₁₇	semidirect
164. C₂²×C₁₇	C₂×#117	semidirect
175. C₂⁴×C₄	C₄×C₁₇	semidirect
182. C₂×#117	C₂²×C₁₇	semidirect
183. C₂²×C₄⋊C₄	C₂²×C₁₇	semidirect
186. C₂²×C₄²	C₂²×C₁₇	semidirect
187. #381	C₂²×C₁₇	semidirect
188. #380	C₂²×C₁₇	semidirect
190. C₄×C₂²⋊C₄	C₂²×C₁₇	semidirect
191. C₂×#95	C₂²×C₁₇	semidirect
194. C₂×C₁₇	#2280	direct (N × H)
213. C₂³×C₄	C₂×C₄×C₁₇	semidirect
225. C₂×C₄⋊C₄	C₂³×C₁₇	semidirect
231. C₂×C₄²	C₂³×C₁₇	semidirect
232. #95	C₂³×C₁₇	semidirect
233. C₁₇	C₂×#2280	direct (N × H)
260. C₂²×C₄	C₂²⋊C₄×C₁₇	semidirect
292. C₂³	C₁₇×#117	semidirect
311. C₂×C₄	C₂×C₂²⋊C₄×C₁₇	semidirect
328. C₂²	C₂×C₁₇×#117	semidirect
339. C₂	C₁₇×#2280	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₄×C₁₇	2
C₂²×C₁₇×#117	2
C₁₇×#2280	2
C₂×C₁₇×#381	2
C₂×C₁₇×#380	2
C₂×C₁₇×#379	2
C₂×C₄×C₂²⋊C₄×C₁₇	2
C₂×#2280	17

Subgroups — C2×C17×#2280 #16891750

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×#2280 #16891750