Subgroups — C₁₇×#22710 #16880454

Order 4352.

898 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#435	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#2354	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#2352	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#1949	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1948	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1854	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1854	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1854	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1853	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1836	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1809	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1807	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1776	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#1736	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1735	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
19	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
20	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
21	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
23	C₁₇×#435	C₄	1	8	yes	complemented
24	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
29	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
30	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
34	C₁₇×#390	—	2	1	no	—
35	C₁₇×#388	—	2	1	no	—
36	C₁₇×#388	—	2	1	no	—
37	C₁₇×#388	—	2	1	no	—
38	C₁₇×#387	—	2	1	no	—
39	C₁₇×#386	—	2	1	no	—
40	C₁₇×#384	C₂²	1	1	yes	characteristic
41	C₁₇×#382	C₂²	1	1	yes	characteristic
42	C₁₇×#380	C₂²	1	1	yes	characteristic
43	C₁₇×#380	C₂²	1	1	yes	characteristic
44	C₁₇×#380	C₂²	1	1	yes	characteristic
45	C₁₇×#380	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₁₇	—	2	1	no	—
47	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
49	C₄×C₂²⋊C₄×C₁₇	—	2	1	no	—
50	C₁₇×#340	C₂²	1	1	yes	characteristic
51	C₁₇×#340	C₂²	1	1	yes	characteristic
52	C₁₇×#340	C₂²	1	1	yes	characteristic
53	C₁₇×#340	C₂²	1	1	yes	characteristic
54	C₁₇×#340	C₂²	1	1	yes	characteristic
55	C₁₇×#340	C₂²	1	1	yes	characteristic
56	C₁₇×#340	C₂²	1	1	yes	characteristic
57	C₁₇×#340	C₂²	1	1	yes	characteristic
58	C₁₇×#340	C₂²	1	1	yes	characteristic
59	C₁₇×#340	C₂²	1	1	yes	characteristic
60	C₂²×D₄×C₁₇	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₁₇	—	2	1	no	—
62	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
64	C₂×M₁₆×C₁₇	—	4	1	no	—
65	C₂×M₁₆×C₁₇	—	4	1	no	—
66	C₂×M₁₆×C₁₇	C₂×C₄	1	4	yes	—
67	C₂²×C₈×C₁₇	—	4	1	no	—
68	C₂²×C₈×C₁₇	—	4	1	no	—
69	C₂²×C₈×C₁₇	C₂×C₄	1	4	yes	complemented
70	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
74	C₄×D₄×C₁₇	C₂×C₄	1	4	yes	—
75	C₄×D₄×C₁₇	Q₈	1	4	yes	—
76	C₁₇×#117	—	2	2	no	—
77	C₁₇×#117	—	2	2	no	—
78	C₁₇×#117	—	2	2	no	—
79	C₁₇×#117	—	4	1	no	—
80	C₁₇×#117	—	4	1	no	—
81	C₁₇×#117	—	4	1	no	—
82	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
83	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₇	—	4	1	no	—
87	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₁₇	D₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₁₇	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₁₇	—	2	1	no	—
106	C₂×C₄²×C₁₇	—	2	1	no	—
107	C₂×C₄²×C₁₇	—	2	1	no	—
108	C₂×C₄²×C₁₇	—	2	1	no	—
109	C₂×C₄²×C₁₇	—	2	1	no	—
110	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
111	C₁₇×#107	—	2	2	no	—
112	C₁₇×#107	—	4	1	no	—
113	C₁₇×#106	—	2	2	no	—
114	C₁₇×#106	—	4	1	no	—
115	C₁₇×#106	—	4	1	no	—
116	C₁₇×#106	—	4	1	no	—
117	C₁₇×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
118	C₁₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
119	C₁₇×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
120	C₁₇×#97	C₂×C₄	1	4	yes	complemented
121	C₁₇×#95	—	2	1	no	—
122	C₁₇×#95	—	2	1	no	—
123	C₁₇×#95	—	2	1	no	—
124	C₁₇×#95	—	2	1	no	—
125	C₁₇×#95	—	2	1	no	—
126	C₁₇×#95	—	2	1	no	—
127	C₁₇×#95	—	2	1	no	—
128	C₁₇×#95	—	2	1	no	—
129	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
130	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
131	C₂×D₄×C₁₇	—	4	1	no	—
132	C₂×D₄×C₁₇	—	4	1	no	—
133	C₂×D₄×C₁₇	C₄⋊C₄	1	4	yes	—
134	C₂²×C₄×C₁₇	—	2	1	no	—
135	C₂²×C₄×C₁₇	—	2	1	no	—
136	C₂²×C₄×C₁₇	—	2	1	no	—
137	C₂²×C₄×C₁₇	—	2	1	no	—
138	C₂²×C₄×C₁₇	—	2	1	no	—
139	C₂²×C₄×C₁₇	—	2	1	no	—
140	C₂²×C₄×C₁₇	—	2	1	no	—
141	C₂²×C₄×C₁₇	—	2	1	no	—
142	C₂²×C₄×C₁₇	—	2	1	no	—
143	C₂²×C₄×C₁₇	—	2	1	no	—
144	C₂²×C₄×C₁₇	—	2	1	no	—
145	C₂²×C₄×C₁₇	—	2	1	no	—
146	C₂²×C₄×C₁₇	—	2	1	no	—
147	C₂²×C₄×C₁₇	—	2	1	no	—
148	C₂²×C₄×C₁₇	—	2	1	no	—
149	C₂²×C₄×C₁₇	—	2	1	no	—
150	C₂²×C₄×C₁₇	—	4	2	no	—
151	C₂²×C₄×C₁₇	—	4	2	no	—
152	C₂²×C₄×C₁₇	—	8	1	no	—
153	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
154	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
155	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₇	C₂×Q₈	1	2	yes	—
160	C₂²×C₄×C₁₇	C₂×Q₈	1	2	yes	—
161	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
162	M₁₆×C₁₇	—	4	4	no	—
163	C₂×C₈×C₁₇	—	2	1	no	—
164	C₂×C₈×C₁₇	—	2	1	no	—
165	C₂×C₈×C₁₇	—	2	1	no	—
166	C₂×C₈×C₁₇	—	2	1	no	—
167	C₂×C₈×C₁₇	—	2	1	no	—
168	C₂×C₈×C₁₇	—	2	1	no	—
169	C₂×C₈×C₁₇	—	2	1	no	—
170	C₂×C₈×C₁₇	—	2	1	no	—
171	C₂×C₈×C₁₇	—	4	4	no	—
172	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
173	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
174	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
175	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
176	C₄⋊C₄×C₁₇	—	2	1	no	—
177	C₄⋊C₄×C₁₇	—	2	1	no	—
178	C₄⋊C₄×C₁₇	—	2	1	no	—
179	C₄⋊C₄×C₁₇	—	2	1	no	—
180	C₄⋊C₄×C₁₇	—	2	1	no	—
181	C₄⋊C₄×C₁₇	—	2	1	no	—
182	C₄⋊C₄×C₁₇	—	2	1	no	—
183	C₄⋊C₄×C₁₇	—	2	1	no	—
184	C₄⋊C₄×C₁₇	—	2	1	no	—
185	C₄⋊C₄×C₁₇	—	2	1	no	—
186	C₄⋊C₄×C₁₇	—	2	1	no	—
187	C₄⋊C₄×C₁₇	—	2	1	no	—
188	C₄⋊C₄×C₁₇	—	2	1	no	—
189	C₄⋊C₄×C₁₇	—	2	1	no	—
190	C₄⋊C₄×C₁₇	—	4	2	no	—
191	C₄⋊C₄×C₁₇	—	4	2	no	—
192	C₄⋊C₄×C₁₇	—	8	1	no	—
193	C₄⋊C₄×C₁₇	C₄⋊C₄	1	4	yes	—
194	C₄⋊C₄×C₁₇	#41	1	2	yes	—
195	C₄⋊C₄×C₁₇	#41	1	2	yes	—
196	C₂²⋊C₄×C₁₇	—	4	2	no	—
197	C₂²⋊C₄×C₁₇	—	4	2	no	—
198	C₂²⋊C₄×C₁₇	—	4	2	no	—
199	C₂²⋊C₄×C₁₇	—	4	2	no	—
200	C₂²⋊C₄×C₁₇	—	8	1	no	—
201	C₂²⋊C₄×C₁₇	—	8	1	no	—
202	C₂²⋊C₄×C₁₇	—	8	1	no	—
203	C₂²⋊C₄×C₁₇	C₄⋊C₄	1	4	yes	—
204	C₂²⋊C₄×C₁₇	C₄⋊C₄	1	4	yes	—
205	C₄²×C₁₇	—	4	2	no	—
206	C₄²×C₁₇	—	4	2	no	—
207	C₄²×C₁₇	—	4	2	no	—
208	C₄²×C₁₇	—	4	2	no	—
209	C₄²×C₁₇	—	8	1	no	—
210	C₄²×C₁₇	C₂²×C₄	1	2	yes	—
211	C₄²×C₁₇	C₂×Q₈	1	2	yes	—
212	#22710	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂³×C₁₇	—	2	1	no	—
214	C₂³×C₁₇	—	2	1	no	—
215	C₂³×C₁₇	—	2	1	no	—
216	C₂³×C₁₇	—	2	1	no	—
217	C₂³×C₁₇	—	2	1	no	—
218	C₂³×C₁₇	—	2	1	no	—
219	C₂³×C₁₇	—	2	1	no	—
220	C₂³×C₁₇	—	2	1	no	—
221	C₂³×C₁₇	—	2	1	no	—
222	C₂³×C₁₇	—	2	1	no	—
223	C₂³×C₁₇	—	2	1	no	—
224	C₂³×C₁₇	—	2	1	no	—
225	C₂³×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
226	C₂³×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
227	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
228	D₄×C₁₇	—	4	4	no	—
229	C₂×C₄×C₁₇	—	2	1	no	—
230	C₂×C₄×C₁₇	—	2	1	no	—
231	C₂×C₄×C₁₇	—	2	1	no	—
232	C₂×C₄×C₁₇	—	2	1	no	—
233	C₂×C₄×C₁₇	—	2	1	no	—
234	C₂×C₄×C₁₇	—	2	1	no	—
235	C₂×C₄×C₁₇	—	2	1	no	—
236	C₂×C₄×C₁₇	—	2	1	no	—
237	C₂×C₄×C₁₇	—	2	2	no	—
238	C₂×C₄×C₁₇	—	2	2	no	—
239	C₂×C₄×C₁₇	—	2	2	no	—
240	C₂×C₄×C₁₇	—	2	2	no	—
241	C₂×C₄×C₁₇	—	2	2	no	—
242	C₂×C₄×C₁₇	—	2	2	no	—
243	C₂×C₄×C₁₇	—	2	2	no	—
244	C₂×C₄×C₁₇	—	2	2	no	—
245	C₂×C₄×C₁₇	—	2	2	no	—
246	C₂×C₄×C₁₇	—	2	2	no	—
247	C₂×C₄×C₁₇	—	4	1	no	—
248	C₂×C₄×C₁₇	—	4	1	no	—
249	C₂×C₄×C₁₇	—	4	1	no	—
250	C₂×C₄×C₁₇	—	4	1	no	—
251	C₂×C₄×C₁₇	—	4	1	no	—
252	C₂×C₄×C₁₇	—	4	1	no	—
253	C₂×C₄×C₁₇	—	4	1	no	—
254	C₂×C₄×C₁₇	—	4	1	no	—
255	C₂×C₄×C₁₇	—	4	1	no	—
256	C₂×C₄×C₁₇	—	4	1	no	—
257	C₂×C₄×C₁₇	—	4	1	no	—
258	C₂×C₄×C₁₇	—	4	1	no	—
259	C₂×C₄×C₁₇	—	4	1	no	—
260	C₂×C₄×C₁₇	—	4	1	no	—
261	C₂×C₄×C₁₇	—	4	1	no	—
262	C₂×C₄×C₁₇	—	4	1	no	—
263	C₂×C₄×C₁₇	—	4	1	no	—
264	C₂×C₄×C₁₇	—	4	1	no	—
265	C₂×C₄×C₁₇	—	4	1	no	—
266	C₂×C₄×C₁₇	—	4	1	no	—
267	C₂×C₄×C₁₇	—	4	1	no	—
268	C₂×C₄×C₁₇	—	4	1	no	—
269	C₂×C₄×C₁₇	—	8	4	no	—
270	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
271	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
272	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
273	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
274	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
275	C₂×C₄×C₁₇	C₂²×Q₈	1	1	yes	characteristic
276	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
277	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
278	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
279	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
280	C₈×C₁₇	—	2	2	no	—
281	C₈×C₁₇	—	2	2	no	—
282	C₈×C₁₇	—	2	2	no	—
283	C₈×C₁₇	—	2	2	no	—
284	C₂×#435	C₂×C₁₇	1	1	yes	characteristic
285	#2354	C₂×C₁₇	1	1	yes	characteristic
286	#2352	C₂×C₁₇	1	1	yes	characteristic
287	#1949	C₂×C₁₇	1	1	yes	characteristic, complemented
288	#1948	C₂×C₁₇	1	1	yes	characteristic, complemented
289	#1854	C₂×C₁₇	1	1	yes	characteristic, complemented
290	#1854	C₂×C₁₇	1	1	yes	characteristic, complemented
291	#1854	C₂×C₁₇	1	1	yes	characteristic, complemented
292	#1853	C₂×C₁₇	1	1	yes	characteristic, complemented
293	#1836	C₂×C₁₇	1	1	yes	characteristic, complemented
294	#1809	C₂×C₁₇	1	1	yes	characteristic, complemented
295	#1807	C₂×C₁₇	1	1	yes	characteristic, complemented
296	#1776	C₂×C₁₇	1	1	yes	characteristic, complemented
297	#1736	C₂×C₁₇	1	1	yes	characteristic, complemented
298	#1735	C₂×C₁₇	1	1	yes	characteristic, complemented
299	C₂²×C₁₇	—	2	2	no	—
300	C₂²×C₁₇	—	2	2	no	—
301	C₂²×C₁₇	—	2	2	no	—
302	C₂²×C₁₇	—	2	2	no	—
303	C₂²×C₁₇	—	2	2	no	—
304	C₂²×C₁₇	—	2	2	no	—
305	C₂²×C₁₇	—	4	1	no	—
306	C₂²×C₁₇	—	4	1	no	—
307	C₂²×C₁₇	—	4	1	no	—
308	C₂²×C₁₇	—	4	1	no	—
309	C₂²×C₁₇	—	4	1	no	—
310	C₂²×C₁₇	—	4	1	no	—
311	C₂²×C₁₇	—	4	1	no	—
312	C₂²×C₁₇	—	4	1	no	—
313	C₂²×C₁₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
314	C₂²×C₁₇	#546	1	1	yes	characteristic
315	C₂²×C₁₇	#546	1	1	yes	characteristic
316	C₂²×C₁₇	#575	1	1	yes	characteristic
317	C₂²×C₁₇	#575	1	1	yes	characteristic
318	C₂²×C₁₇	#577	1	1	yes	characteristic
319	C₂²×C₁₇	#577	1	1	yes	characteristic
320	C₄×C₁₇	—	2	2	no	—
321	C₄×C₁₇	—	2	2	no	—
322	C₄×C₁₇	—	2	2	no	—
323	C₄×C₁₇	—	2	2	no	—
324	C₄×C₁₇	—	4	2	no	—
325	C₄×C₁₇	—	4	2	no	—
326	C₄×C₁₇	—	8	1	no	—
327	C₄×C₁₇	—	8	1	no	—
328	C₄×C₁₇	—	8	1	no	—
329	C₄×C₁₇	—	8	1	no	—
330	C₄×C₁₇	—	8	1	no	—
331	C₄×C₁₇	—	8	1	no	—
332	C₄×C₁₇	C₄×#41	1	1	yes	characteristic
333	C₄×C₁₇	#518	1	1	yes	characteristic
334	C₄×C₁₇	#554	1	1	yes	characteristic
335	C₄×C₁₇	#554	1	1	yes	characteristic
336	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
337	C₂³×C₈	C₂²×C₁₇	1	1	yes	characteristic
338	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
339	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
340	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
341	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
342	C₂²×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
343	#435	C₄×C₁₇	1	8	yes	complemented
344	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
345	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
346	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
347	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
348	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
349	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
350	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
351	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
352	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
353	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
354	#390	—	2	1	no	—
355	#388	—	2	1	no	—
356	#388	—	2	1	no	—
357	#388	—	2	1	no	—
358	#387	—	2	1	no	—
359	#386	—	2	1	no	—
360	#384	C₂²×C₁₇	1	1	yes	characteristic
361	#382	C₂²×C₁₇	1	1	yes	characteristic
362	#380	C₂²×C₁₇	1	1	yes	characteristic
363	#380	C₂²×C₁₇	1	1	yes	characteristic
364	#380	C₂²×C₁₇	1	1	yes	characteristic
365	#380	C₂²×C₁₇	1	1	yes	characteristic
366	C₄×C₄⋊C₄	—	2	1	no	—
367	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
368	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
369	C₄×C₂²⋊C₄	—	2	1	no	—
370	#340	C₂²×C₁₇	1	1	yes	characteristic
371	#340	C₂²×C₁₇	1	1	yes	characteristic
372	#340	C₂²×C₁₇	1	1	yes	characteristic
373	#340	C₂²×C₁₇	1	1	yes	characteristic
374	#340	C₂²×C₁₇	1	1	yes	characteristic
375	#340	C₂²×C₁₇	1	1	yes	characteristic
376	#340	C₂²×C₁₇	1	1	yes	characteristic
377	#340	C₂²×C₁₇	1	1	yes	characteristic
378	#340	C₂²×C₁₇	1	1	yes	characteristic
379	#340	C₂²×C₁₇	1	1	yes	characteristic
380	C₂×C₁₇	—	4	2	no	—
381	C₂×C₁₇	—	4	2	no	—
382	C₂×C₁₇	#2349	1	1	yes	characteristic
383	C₂×C₁₇	#2911	1	1	yes	characteristic
384	C₂×C₁₇	#2912	1	1	yes	characteristic
385	C₂×C₁₇	#3307	1	1	yes	characteristic
386	C₂×C₁₇	#3311	1	1	yes	characteristic
387	C₂×C₁₇	#3317	1	1	yes	characteristic
388	C₂×C₁₇	#3321	1	1	yes	characteristic
389	C₂²×D₄	D₄×C₁₇	1	1	yes	characteristic
390	C₂³×C₄	—	2	1	no	—
391	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
393	C₂×M₁₆	—	4	1	no	—
394	C₂×M₁₆	—	4	1	no	—
395	C₂×M₁₆	C₂×C₄×C₁₇	1	4	yes	—
396	C₂²×C₈	—	4	1	no	—
397	C₂²×C₈	—	4	1	no	—
398	C₂²×C₈	C₂×C₄×C₁₇	1	4	yes	complemented
399	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
400	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
401	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
402	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
403	C₄×D₄	C₂×C₄×C₁₇	1	4	yes	—
404	C₄×D₄	Q₈×C₁₇	1	4	yes	—
405	#117	—	2	2	no	—
406	#117	—	2	2	no	—
407	#117	—	2	2	no	—
408	#117	—	4	1	no	—
409	#117	—	4	1	no	—
410	#117	—	4	1	no	—
411	C₂×C₄⋊C₄	—	2	2	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	4	1	no	—
416	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	D₄×C₁₇	1	1	yes	characteristic
433	C₂×C₂²⋊C₄	D₄×C₁₇	1	1	yes	characteristic
434	C₂×C₄²	—	2	1	no	—
435	C₂×C₄²	—	2	1	no	—
436	C₂×C₄²	—	2	1	no	—
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	—	2	1	no	—
439	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
440	#107	—	2	2	no	—
441	#107	—	4	1	no	—
442	#106	—	2	2	no	—
443	#106	—	4	1	no	—
444	#106	—	4	1	no	—
445	#106	—	4	1	no	—
446	C₄⋊C₈	C₂×C₄×C₁₇	1	4	yes	complemented
447	C₂²⋊C₈	C₂×C₄×C₁₇	1	4	yes	—
448	C₂²⋊C₈	C₂×C₄×C₁₇	1	4	yes	complemented
449	#97	C₂×C₄×C₁₇	1	4	yes	complemented
450	#95	—	2	1	no	—
451	#95	—	2	1	no	—
452	#95	—	2	1	no	—
453	#95	—	2	1	no	—
454	#95	—	2	1	no	—
455	#95	—	2	1	no	—
456	#95	—	2	1	no	—
457	#95	—	2	1	no	—
458	C₁₇	#22710	1	1	yes	characteristic, direct product factor, Sylow
459	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
460	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
461	C₂×D₄	—	4	1	no	—
462	C₂×D₄	—	4	1	no	—
463	C₂×D₄	C₄⋊C₄×C₁₇	1	4	yes	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	4	2	no	—
481	C₂²×C₄	—	4	2	no	—
482	C₂²×C₄	—	8	1	no	—
483	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
484	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
485	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
487	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
488	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
489	C₂²×C₄	C₂×Q₈×C₁₇	1	2	yes	—
490	C₂²×C₄	C₂×Q₈×C₁₇	1	2	yes	—
491	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
492	M₁₆	—	4	4	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	4	4	no	—
502	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
503	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
504	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
505	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	4	2	no	—
521	C₄⋊C₄	—	4	2	no	—
522	C₄⋊C₄	—	8	1	no	—
523	C₄⋊C₄	C₄⋊C₄×C₁₇	1	4	yes	—
524	C₄⋊C₄	#41×C₁₇	1	2	yes	—
525	C₄⋊C₄	#41×C₁₇	1	2	yes	—
526	C₂²⋊C₄	—	4	2	no	—
527	C₂²⋊C₄	—	4	2	no	—
528	C₂²⋊C₄	—	4	2	no	—
529	C₂²⋊C₄	—	4	2	no	—
530	C₂²⋊C₄	—	8	1	no	—
531	C₂²⋊C₄	—	8	1	no	—
532	C₂²⋊C₄	—	8	1	no	—
533	C₂²⋊C₄	C₄⋊C₄×C₁₇	1	4	yes	—
534	C₂²⋊C₄	C₄⋊C₄×C₁₇	1	4	yes	—
535	C₄²	—	4	2	no	—
536	C₄²	—	4	2	no	—
537	C₄²	—	4	2	no	—
538	C₄²	—	4	2	no	—
539	C₄²	—	8	1	no	—
540	C₄²	C₂²×C₄×C₁₇	1	2	yes	—
541	C₄²	C₂×Q₈×C₁₇	1	2	yes	—
542	C₂³	—	2	1	no	—
543	C₂³	—	2	1	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	2	1	no	—
548	C₂³	—	2	1	no	—
549	C₂³	—	2	1	no	—
550	C₂³	—	2	1	no	—
551	C₂³	—	2	1	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	C₂×C₄⋊C₄×C₁₇	1	2	yes	—
555	C₂³	C₂×C₄⋊C₄×C₁₇	1	2	yes	—
556	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
557	D₄	—	4	4	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	8	4	no	—
599	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	2	yes	—
600	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	2	yes	—
601	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	2	yes	—
602	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	2	yes	—
603	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
604	C₂×C₄	C₂²×Q₈×C₁₇	1	1	yes	characteristic
605	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
606	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
607	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
608	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
609	C₈	—	2	2	no	—
610	C₈	—	2	2	no	—
611	C₈	—	2	2	no	—
612	C₈	—	2	2	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	1	no	—
625	C₂²	—	4	1	no	—
626	C₂²	—	4	1	no	—
627	C₂²	C₂²×C₄⋊C₄×C₁₇	1	1	yes	characteristic
628	C₂²	C₁₇×#546	1	1	yes	characteristic
629	C₂²	C₁₇×#546	1	1	yes	characteristic
630	C₂²	C₁₇×#575	1	1	yes	characteristic
631	C₂²	C₁₇×#575	1	1	yes	characteristic
632	C₂²	C₁₇×#577	1	1	yes	characteristic
633	C₂²	C₁₇×#577	1	1	yes	characteristic
634	C₄	—	2	2	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	4	2	no	—
639	C₄	—	4	2	no	—
640	C₄	—	8	1	no	—
641	C₄	—	8	1	no	—
642	C₄	—	8	1	no	—
643	C₄	—	8	1	no	—
644	C₄	—	8	1	no	—
645	C₄	—	8	1	no	—
646	C₄	C₄×#41×C₁₇	1	1	yes	characteristic
647	C₄	C₁₇×#518	1	1	yes	characteristic
648	C₄	C₁₇×#554	1	1	yes	characteristic
649	C₄	C₁₇×#554	1	1	yes	characteristic
650	C₂	—	4	2	no	—
651	C₂	—	4	2	no	—
652	C₂	C₁₇×#2349	1	1	yes	characteristic
653	C₂	C₁₇×#2911	1	1	yes	characteristic
654	C₂	C₁₇×#2912	1	1	yes	characteristic
655	C₂	C₁₇×#3307	1	1	yes	characteristic
656	C₂	C₁₇×#3311	1	1	yes	characteristic
657	C₂	C₁₇×#3317	1	1	yes	characteristic
658	C₂	C₁₇×#3321	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₁₇×#1949	C₂	semidirect
5. C₁₇×#1948	C₂	semidirect
6. C₁₇×#1854	C₂	semidirect
7. C₁₇×#1854	C₂	semidirect
8. C₁₇×#1854	C₂	semidirect
9. C₁₇×#1853	C₂	semidirect
10. C₁₇×#1836	C₂	semidirect
11. C₁₇×#1809	C₂	semidirect
12. C₁₇×#1807	C₂	semidirect
13. C₁₇×#1776	C₂	semidirect
14. C₁₇×#1736	C₂	semidirect
15. C₁₇×#1735	C₂	semidirect
23. C₁₇×#435	C₄	semidirect
69. C₂²×C₈×C₁₇	C₂×C₄	semidirect
117. C₁₇×C₄⋊C₈	C₂×C₄	semidirect
119. C₁₇×C₂²⋊C₈	C₂×C₄	semidirect
120. C₁₇×#97	C₂×C₄	semidirect
212. #22710	C₁₇	direct (N × H)
287. #1949	C₂×C₁₇	semidirect
288. #1948	C₂×C₁₇	semidirect
289. #1854	C₂×C₁₇	semidirect
290. #1854	C₂×C₁₇	semidirect
291. #1854	C₂×C₁₇	semidirect
292. #1853	C₂×C₁₇	semidirect
293. #1836	C₂×C₁₇	semidirect
294. #1809	C₂×C₁₇	semidirect
295. #1807	C₂×C₁₇	semidirect
296. #1776	C₂×C₁₇	semidirect
297. #1736	C₂×C₁₇	semidirect
298. #1735	C₂×C₁₇	semidirect
343. #435	C₄×C₁₇	semidirect
398. C₂²×C₈	C₂×C₄×C₁₇	semidirect
446. C₄⋊C₈	C₂×C₄×C₁₇	semidirect
448. C₂²⋊C₈	C₂×C₄×C₁₇	semidirect
449. #97	C₂×C₄×C₁₇	semidirect
458. C₁₇	#22710	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×#435	2
C₁₇×#2354	2
C₁₇×#2352	2
C₁₇×#1949	2
C₁₇×#1948	2
C₁₇×#1854	2
C₁₇×#1853	2
C₁₇×#1836	2
C₁₇×#1809	2
C₁₇×#1807	2
C₁₇×#1776	2
C₁₇×#1736	2
C₁₇×#1735	2
#22710	17

Subgroups — C17×#22710 #16880454

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#22710 #16880454