Subgroups — C₁₇×#22059 #16879803

Order 4352.

968 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#452	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#2323	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#2311	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#1971	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1968	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1936	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1933	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1927	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1926	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1880	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1872	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1853	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#1788	C₂	1	1	yes	maximal, characteristic
15	C₁₇×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₇	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
19	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₇	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×#452	C₄	1	8	yes	complemented
24	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
25	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
28	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
38	C₁₇×#391	C₂²	1	1	yes	characteristic
39	C₁₇×#391	C₂²	1	1	yes	characteristic
40	C₁₇×#391	C₂²	1	1	yes	characteristic
41	C₁₇×#390	C₂²	1	1	yes	characteristic
42	C₁₇×#390	C₂²	1	1	yes	characteristic
43	C₁₇×#389	—	2	1	no	—
44	C₁₇×#389	C₂²	1	1	yes	characteristic
45	C₁₇×#388	—	2	1	no	—
46	C₁₇×#388	—	2	1	no	—
47	C₁₇×#387	—	2	1	no	—
48	C₁₇×#386	—	2	1	no	—
49	C₁₇×#386	—	2	1	no	—
50	C₁₇×#380	—	2	1	no	—
51	C₁₇×#380	—	2	1	no	—
52	C₁₇×#380	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₁₇	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×#336	C₂²	1	1	yes	characteristic
59	C₁₇×#336	C₂²	1	1	yes	characteristic
60	C₂×#41×C₁₇	—	2	2	no	—
61	C₂×#41×C₁₇	—	4	1	no	—
62	C₂×#41×C₁₇	—	4	1	no	—
63	C₂×#41×C₁₇	—	4	1	no	—
64	C₂×#41×C₁₇	—	4	1	no	—
65	C₂×#41×C₁₇	C₂×C₄	1	4	yes	—
66	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
67	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₇	—	2	1	no	—
69	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₇	—	2	1	no	—
71	C₂³×C₄×C₁₇	—	2	1	no	—
72	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
73	C₂×Q₁₆×C₁₇	—	4	1	no	—
74	C₂×Q₁₆×C₁₇	—	4	1	no	—
75	C₂×Q₁₆×C₁₇	C₂×C₄	1	4	yes	complemented
76	C₂×SD₁₆×C₁₇	—	4	1	no	—
77	C₂×SD₁₆×C₁₇	—	4	1	no	—
78	C₂×SD₁₆×C₁₇	C₂×C₄	1	4	yes	complemented
79	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
83	C₁₇×C₂²⋊Q₈	—	2	2	no	—
84	C₁₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
85	C₄×Q₈×C₁₇	—	4	1	no	—
86	C₄×Q₈×C₁₇	—	4	1	no	—
87	C₁₇×#117	—	4	1	no	—
88	C₁₇×#117	—	4	1	no	—
89	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
90	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
91	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₇	—	4	1	no	—
94	C₂×C₄⋊C₄×C₁₇	—	4	1	no	—
95	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₁₇	D₄	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₁₇	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₁₇	—	2	1	no	—
111	C₂×C₄²×C₁₇	—	2	1	no	—
112	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
114	C₁₇×#106	—	4	1	no	—
115	C₁₇×#106	—	4	1	no	—
116	C₁₇×#103	—	4	1	no	—
117	C₁₇×#103	—	4	1	no	—
118	C₁₇×#103	—	4	1	no	—
119	C₁₇×#103	—	4	1	no	—
120	C₁₇×#103	C₂×C₄	1	4	yes	complemented
121	C₁₇×#102	—	4	1	no	—
122	C₁₇×#102	—	4	1	no	—
123	C₁₇×#102	C₂×C₄	1	4	yes	complemented
124	C₁₇×C₂²⋊C₈	—	2	2	no	—
125	C₁₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
126	C₁₇×#97	—	4	1	no	—
127	C₄×C₈×C₁₇	—	4	1	no	—
128	C₁₇×#95	—	2	1	no	—
129	C₁₇×#95	—	2	1	no	—
130	C₁₇×#95	—	2	1	no	—
131	C₁₇×#95	—	2	1	no	—
132	C₁₇×#95	—	2	1	no	—
133	C₁₇×#95	—	2	1	no	—
134	C₁₇×#95	—	2	1	no	—
135	C₁₇×#95	—	2	1	no	—
136	C₁₇×#95	—	2	1	no	—
137	C₂⁴×C₁₇	—	2	1	no	—
138	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
139	#41×C₁₇	—	4	4	no	—
140	#41×C₁₇	—	4	4	no	—
141	#41×C₁₇	—	4	4	no	—
142	#41×C₁₇	—	4	4	no	—
143	C₂×Q₈×C₁₇	—	2	1	no	—
144	C₂×Q₈×C₁₇	—	2	1	no	—
145	C₂×Q₈×C₁₇	—	2	1	no	—
146	C₂×Q₈×C₁₇	—	2	1	no	—
147	C₂×Q₈×C₁₇	—	2	1	no	—
148	C₂×Q₈×C₁₇	—	2	1	no	—
149	C₂×Q₈×C₁₇	—	2	1	no	—
150	C₂×Q₈×C₁₇	—	2	1	no	—
151	C₂×Q₈×C₁₇	—	2	1	no	—
152	C₂×Q₈×C₁₇	—	2	1	no	—
153	C₂×Q₈×C₁₇	C₂²×C₄	1	2	yes	—
154	C₂×Q₈×C₁₇	C₂²×C₄	1	2	yes	—
155	C₂×D₄×C₁₇	—	2	4	no	—
156	C₂×D₄×C₁₇	—	2	1	no	—
157	C₂×D₄×C₁₇	—	2	1	no	—
158	C₂×D₄×C₁₇	—	2	1	no	—
159	C₂×D₄×C₁₇	—	2	1	no	—
160	C₂×D₄×C₁₇	—	2	1	no	—
161	C₂×D₄×C₁₇	—	4	2	no	—
162	C₂×D₄×C₁₇	—	4	2	no	—
163	C₂×D₄×C₁₇	C₂²×C₄	1	2	yes	—
164	C₂²×C₄×C₁₇	—	2	1	no	—
165	C₂²×C₄×C₁₇	—	2	1	no	—
166	C₂²×C₄×C₁₇	—	2	1	no	—
167	C₂²×C₄×C₁₇	—	2	1	no	—
168	C₂²×C₄×C₁₇	—	2	1	no	—
169	C₂²×C₄×C₁₇	—	2	1	no	—
170	C₂²×C₄×C₁₇	—	2	1	no	—
171	C₂²×C₄×C₁₇	—	2	4	no	—
172	C₂²×C₄×C₁₇	—	2	1	no	—
173	C₂²×C₄×C₁₇	—	2	1	no	—
174	C₂²×C₄×C₁₇	—	2	1	no	—
175	C₂²×C₄×C₁₇	—	2	1	no	—
176	C₂²×C₄×C₁₇	—	4	2	no	—
177	C₂²×C₄×C₁₇	—	4	2	no	—
178	C₂²×C₄×C₁₇	—	4	2	no	—
179	C₂²×C₄×C₁₇	—	8	1	no	—
180	C₂²×C₄×C₁₇	—	8	1	no	—
181	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
182	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₇	#41	1	2	yes	—
188	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
189	Q₁₆×C₁₇	—	4	4	no	—
190	SD₁₆×C₁₇	—	4	4	no	—
191	C₂×C₈×C₁₇	—	2	1	no	—
192	C₂×C₈×C₁₇	—	2	1	no	—
193	C₂×C₈×C₁₇	—	2	1	no	—
194	C₂×C₈×C₁₇	—	2	1	no	—
195	C₂×C₈×C₁₇	—	2	1	no	—
196	C₂×C₈×C₁₇	—	2	1	no	—
197	C₂×C₈×C₁₇	—	2	1	no	—
198	C₂×C₈×C₁₇	—	2	1	no	—
199	C₂×C₈×C₁₇	—	2	1	no	—
200	C₂×C₈×C₁₇	—	2	1	no	—
201	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
202	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
203	C₄⋊C₄×C₁₇	—	2	4	no	—
204	C₄⋊C₄×C₁₇	—	2	1	no	—
205	C₄⋊C₄×C₁₇	—	2	1	no	—
206	C₄⋊C₄×C₁₇	—	2	1	no	—
207	C₄⋊C₄×C₁₇	—	2	1	no	—
208	C₄⋊C₄×C₁₇	—	2	1	no	—
209	C₄⋊C₄×C₁₇	—	2	1	no	—
210	C₄⋊C₄×C₁₇	—	2	1	no	—
211	C₄⋊C₄×C₁₇	—	2	1	no	—
212	C₄⋊C₄×C₁₇	—	2	1	no	—
213	C₄⋊C₄×C₁₇	—	4	1	no	—
214	C₄⋊C₄×C₁₇	—	4	1	no	—
215	C₄⋊C₄×C₁₇	—	4	2	no	—
216	C₄⋊C₄×C₁₇	—	4	2	no	—
217	C₄⋊C₄×C₁₇	—	8	1	no	—
218	C₄⋊C₄×C₁₇	C₂²×C₄	1	2	yes	—
219	C₂²⋊C₄×C₁₇	—	2	4	no	—
220	C₂²⋊C₄×C₁₇	—	4	1	no	—
221	C₂²⋊C₄×C₁₇	—	4	1	no	—
222	C₂²⋊C₄×C₁₇	—	8	1	no	—
223	C₂²⋊C₄×C₁₇	—	8	1	no	—
224	C₂²⋊C₄×C₁₇	—	8	1	no	—
225	C₂²⋊C₄×C₁₇	—	8	1	no	—
226	C₂²⋊C₄×C₁₇	—	8	1	no	—
227	C₄²×C₁₇	—	2	1	no	—
228	C₄²×C₁₇	—	2	1	no	—
229	C₄²×C₁₇	—	2	1	no	—
230	C₄²×C₁₇	—	2	1	no	—
231	C₄²×C₁₇	—	4	2	no	—
232	C₄²×C₁₇	—	8	1	no	—
233	#22059	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂³×C₁₇	—	2	1	no	—
235	C₂³×C₁₇	—	2	1	no	—
236	C₂³×C₁₇	—	2	1	no	—
237	C₂³×C₁₇	—	2	1	no	—
238	C₂³×C₁₇	—	2	1	no	—
239	C₂³×C₁₇	—	2	1	no	—
240	C₂³×C₁₇	—	2	2	no	—
241	C₂³×C₁₇	—	4	1	no	—
242	C₂³×C₁₇	—	4	1	no	—
243	C₂³×C₁₇	—	4	1	no	—
244	C₂³×C₁₇	—	4	1	no	—
245	C₂³×C₁₇	—	4	1	no	—
246	C₂³×C₁₇	—	4	1	no	—
247	C₂³×C₁₇	C₄×D₄	1	2	yes	—
248	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
249	Q₈×C₁₇	—	2	2	no	—
250	Q₈×C₁₇	—	2	2	no	—
251	Q₈×C₁₇	—	2	2	no	—
252	Q₈×C₁₇	—	2	2	no	—
253	Q₈×C₁₇	—	4	1	no	—
254	Q₈×C₁₇	—	4	1	no	—
255	Q₈×C₁₇	—	4	1	no	—
256	Q₈×C₁₇	—	4	1	no	—
257	D₄×C₁₇	—	2	2	no	—
258	D₄×C₁₇	—	2	2	no	—
259	D₄×C₁₇	—	4	8	no	—
260	D₄×C₁₇	—	4	1	no	—
261	D₄×C₁₇	—	4	1	no	—
262	C₂×C₄×C₁₇	—	2	1	no	—
263	C₂×C₄×C₁₇	—	2	1	no	—
264	C₂×C₄×C₁₇	—	2	2	no	—
265	C₂×C₄×C₁₇	—	2	2	no	—
266	C₂×C₄×C₁₇	—	2	2	no	—
267	C₂×C₄×C₁₇	—	2	2	no	—
268	C₂×C₄×C₁₇	—	2	2	no	—
269	C₂×C₄×C₁₇	—	2	2	no	—
270	C₂×C₄×C₁₇	—	2	2	no	—
271	C₂×C₄×C₁₇	—	2	1	no	—
272	C₂×C₄×C₁₇	—	2	1	no	—
273	C₂×C₄×C₁₇	—	2	1	no	—
274	C₂×C₄×C₁₇	—	2	1	no	—
275	C₂×C₄×C₁₇	—	2	1	no	—
276	C₂×C₄×C₁₇	—	2	1	no	—
277	C₂×C₄×C₁₇	—	2	1	no	—
278	C₂×C₄×C₁₇	—	2	1	no	—
279	C₂×C₄×C₁₇	—	2	1	no	—
280	C₂×C₄×C₁₇	—	2	1	no	—
281	C₂×C₄×C₁₇	—	2	1	no	—
282	C₂×C₄×C₁₇	—	2	1	no	—
283	C₂×C₄×C₁₇	—	4	8	no	—
284	C₂×C₄×C₁₇	—	4	1	no	—
285	C₂×C₄×C₁₇	—	4	1	no	—
286	C₂×C₄×C₁₇	—	4	1	no	—
287	C₂×C₄×C₁₇	—	4	1	no	—
288	C₂×C₄×C₁₇	—	4	1	no	—
289	C₂×C₄×C₁₇	—	4	1	no	—
290	C₂×C₄×C₁₇	—	4	1	no	—
291	C₂×C₄×C₁₇	—	4	1	no	—
292	C₂×C₄×C₁₇	—	4	1	no	—
293	C₂×C₄×C₁₇	—	4	1	no	—
294	C₂×C₄×C₁₇	—	4	1	no	—
295	C₂×C₄×C₁₇	—	4	1	no	—
296	C₂×C₄×C₁₇	—	4	1	no	—
297	C₂×C₄×C₁₇	—	4	1	no	—
298	C₂×C₄×C₁₇	—	4	1	no	—
299	C₂×C₄×C₁₇	—	4	1	no	—
300	C₂×C₄×C₁₇	—	4	1	no	—
301	C₂×C₄×C₁₇	—	4	1	no	—
302	C₂×C₄×C₁₇	—	8	4	no	—
303	C₂×C₄×C₁₇	C₄×D₄	1	2	yes	—
304	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
305	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
306	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
307	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
308	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
309	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
310	C₈×C₁₇	—	2	2	no	—
311	C₈×C₁₇	—	2	2	no	—
312	C₈×C₁₇	—	4	1	no	—
313	C₈×C₁₇	—	4	1	no	—
314	C₂×#452	C₂×C₁₇	1	1	yes	characteristic
315	#2323	C₂×C₁₇	1	1	yes	characteristic, complemented
316	#2311	C₂×C₁₇	1	1	yes	characteristic
317	#1971	C₂×C₁₇	1	1	yes	characteristic, complemented
318	#1968	C₂×C₁₇	1	1	yes	characteristic, complemented
319	#1936	C₂×C₁₇	1	1	yes	characteristic, complemented
320	#1933	C₂×C₁₇	1	1	yes	characteristic, complemented
321	#1927	C₂×C₁₇	1	1	yes	characteristic, complemented
322	#1926	C₂×C₁₇	1	1	yes	characteristic, complemented
323	#1880	C₂×C₁₇	1	1	yes	characteristic, complemented
324	#1878	C₂×C₁₇	1	1	yes	characteristic, complemented
325	#1872	C₂×C₁₇	1	1	yes	characteristic, complemented
326	#1853	C₂×C₁₇	1	1	yes	characteristic, complemented
327	#1788	C₂×C₁₇	1	1	yes	characteristic
328	#1750	C₂×C₁₇	1	1	yes	characteristic, complemented
329	C₂²×C₁₇	—	2	2	no	—
330	C₂²×C₁₇	—	2	2	no	—
331	C₂²×C₁₇	—	2	2	no	—
332	C₂²×C₁₇	—	4	1	no	—
333	C₂²×C₁₇	—	4	1	no	—
334	C₂²×C₁₇	—	4	1	no	—
335	C₂²×C₁₇	—	4	1	no	—
336	C₂²×C₁₇	—	4	2	no	—
337	C₂²×C₁₇	—	4	2	no	—
338	C₂²×C₁₇	—	4	2	no	—
339	C₂²×C₁₇	—	8	1	no	—
340	C₂²×C₁₇	—	8	1	no	—
341	C₂²×C₁₇	—	8	1	no	—
342	C₂²×C₁₇	—	8	1	no	—
343	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
344	C₂²×C₁₇	#534	1	1	yes	characteristic
345	C₂²×C₁₇	#535	1	1	yes	characteristic
346	C₂²×C₁₇	#577	1	1	yes	characteristic
347	C₂²×C₁₇	#577	1	1	yes	characteristic
348	C₂²×C₁₇	#577	1	1	yes	characteristic
349	C₂²×C₁₇	#578	1	1	yes	characteristic
350	C₄×C₁₇	—	2	2	no	—
351	C₄×C₁₇	—	4	2	no	—
352	C₄×C₁₇	—	4	2	no	—
353	C₄×C₁₇	—	4	1	no	—
354	C₄×C₁₇	—	4	1	no	—
355	C₄×C₁₇	—	4	1	no	—
356	C₄×C₁₇	—	4	1	no	—
357	C₄×C₁₇	—	4	2	no	—
358	C₄×C₁₇	—	8	1	no	—
359	C₄×C₁₇	—	8	1	no	—
360	C₄×C₁₇	—	8	1	no	—
361	C₄×C₁₇	—	8	1	no	—
362	C₄×C₁₇	#518	1	1	yes	characteristic
363	C₄×C₁₇	#518	1	1	yes	characteristic
364	C₄×C₁₇	#538	1	1	yes	characteristic
365	C₄×C₁₇	#538	1	1	yes	characteristic
366	C₂²×#41	C₂²×C₁₇	1	1	yes	characteristic
367	C₂²×Q₁₆	C₂²×C₁₇	1	1	yes	characteristic
368	C₂²×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
369	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
370	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
371	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
372	C₂²×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
373	#452	C₄×C₁₇	1	8	yes	complemented
374	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
375	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
376	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
377	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
378	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
379	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
380	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
381	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
382	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
383	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
384	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
385	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
386	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
387	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
388	#391	C₂²×C₁₇	1	1	yes	characteristic
389	#391	C₂²×C₁₇	1	1	yes	characteristic
390	#391	C₂²×C₁₇	1	1	yes	characteristic
391	#390	C₂²×C₁₇	1	1	yes	characteristic
392	#390	C₂²×C₁₇	1	1	yes	characteristic
393	#389	—	2	1	no	—
394	#389	C₂²×C₁₇	1	1	yes	characteristic
395	#388	—	2	1	no	—
396	#388	—	2	1	no	—
397	#387	—	2	1	no	—
398	#386	—	2	1	no	—
399	#386	—	2	1	no	—
400	#380	—	2	1	no	—
401	#380	—	2	1	no	—
402	#380	C₂²×C₁₇	1	1	yes	characteristic
403	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
404	#340	C₂²×C₁₇	1	1	yes	characteristic
405	#340	C₂²×C₁₇	1	1	yes	characteristic
406	#340	C₂²×C₁₇	1	1	yes	characteristic
407	#340	C₂²×C₁₇	1	1	yes	characteristic
408	#336	C₂²×C₁₇	1	1	yes	characteristic
409	#336	C₂²×C₁₇	1	1	yes	characteristic
410	C₂×C₁₇	—	4	2	no	—
411	C₂×C₁₇	—	8	2	no	—
412	C₂×C₁₇	#2321	1	1	yes	characteristic
413	C₂×C₁₇	#2947	1	1	yes	characteristic
414	C₂×C₁₇	#2952	1	1	yes	characteristic
415	C₂×C₁₇	#3201	1	1	yes	characteristic
416	C₂×C₁₇	#3204	1	1	yes	characteristic
417	C₂×C₁₇	#3222	1	1	yes	characteristic
418	C₂×C₁₇	#3225	1	1	yes	characteristic
419	C₂×#41	—	2	2	no	—
420	C₂×#41	—	4	1	no	—
421	C₂×#41	—	4	1	no	—
422	C₂×#41	—	4	1	no	—
423	C₂×#41	—	4	1	no	—
424	C₂×#41	C₂×C₄×C₁₇	1	4	yes	—
425	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
426	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
427	C₂²×D₄	—	2	1	no	—
428	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
429	C₂³×C₄	—	2	1	no	—
430	C₂³×C₄	—	2	1	no	—
431	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
432	C₂×Q₁₆	—	4	1	no	—
433	C₂×Q₁₆	—	4	1	no	—
434	C₂×Q₁₆	C₂×C₄×C₁₇	1	4	yes	complemented
435	C₂×SD₁₆	—	4	1	no	—
436	C₂×SD₁₆	—	4	1	no	—
437	C₂×SD₁₆	C₂×C₄×C₁₇	1	4	yes	complemented
438	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
439	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
440	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
441	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
442	C₂²⋊Q₈	—	2	2	no	—
443	C₂²⋊Q₈	C₂×C₄×C₁₇	1	4	yes	—
444	C₄×Q₈	—	4	1	no	—
445	C₄×Q₈	—	4	1	no	—
446	#117	—	4	1	no	—
447	#117	—	4	1	no	—
448	C₂×C₄⋊C₄	—	2	1	no	—
449	C₂×C₄⋊C₄	—	2	1	no	—
450	C₂×C₄⋊C₄	—	2	1	no	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	—	4	1	no	—
453	C₂×C₄⋊C₄	—	4	1	no	—
454	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
455	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
461	C₂×C₂²⋊C₄	—	2	1	no	—
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₂²⋊C₄	—	2	1	no	—
467	C₂×C₂²⋊C₄	D₄×C₁₇	1	1	yes	characteristic
468	C₂×C₂²⋊C₄	D₄×C₁₇	1	1	yes	characteristic
469	C₂×C₄²	—	2	1	no	—
470	C₂×C₄²	—	2	1	no	—
471	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
472	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
473	#106	—	4	1	no	—
474	#106	—	4	1	no	—
475	#103	—	4	1	no	—
476	#103	—	4	1	no	—
477	#103	—	4	1	no	—
478	#103	—	4	1	no	—
479	#103	C₂×C₄×C₁₇	1	4	yes	complemented
480	#102	—	4	1	no	—
481	#102	—	4	1	no	—
482	#102	C₂×C₄×C₁₇	1	4	yes	complemented
483	C₂²⋊C₈	—	2	2	no	—
484	C₂²⋊C₈	C₂×C₄×C₁₇	1	4	yes	—
485	#97	—	4	1	no	—
486	C₄×C₈	—	4	1	no	—
487	#95	—	2	1	no	—
488	#95	—	2	1	no	—
489	#95	—	2	1	no	—
490	#95	—	2	1	no	—
491	#95	—	2	1	no	—
492	#95	—	2	1	no	—
493	#95	—	2	1	no	—
494	#95	—	2	1	no	—
495	#95	—	2	1	no	—
496	C₁₇	#22059	1	1	yes	characteristic, direct product factor, Sylow
497	C₂⁴	—	2	1	no	—
498	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
499	#41	—	4	4	no	—
500	#41	—	4	4	no	—
501	#41	—	4	4	no	—
502	#41	—	4	4	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	C₂²×C₄×C₁₇	1	2	yes	—
514	C₂×Q₈	C₂²×C₄×C₁₇	1	2	yes	—
515	C₂×D₄	—	2	4	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	4	2	no	—
522	C₂×D₄	—	4	2	no	—
523	C₂×D₄	C₂²×C₄×C₁₇	1	2	yes	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	4	2	no	—
537	C₂²×C₄	—	4	2	no	—
538	C₂²×C₄	—	4	2	no	—
539	C₂²×C₄	—	8	1	no	—
540	C₂²×C₄	—	8	1	no	—
541	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
542	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
543	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
544	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
545	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
546	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
547	C₂²×C₄	#41×C₁₇	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
549	Q₁₆	—	4	4	no	—
550	SD₁₆	—	4	4	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
562	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	4	1	no	—
574	C₄⋊C₄	—	4	1	no	—
575	C₄⋊C₄	—	4	2	no	—
576	C₄⋊C₄	—	4	2	no	—
577	C₄⋊C₄	—	8	1	no	—
578	C₄⋊C₄	C₂²×C₄×C₁₇	1	2	yes	—
579	C₂²⋊C₄	—	2	4	no	—
580	C₂²⋊C₄	—	4	1	no	—
581	C₂²⋊C₄	—	4	1	no	—
582	C₂²⋊C₄	—	8	1	no	—
583	C₂²⋊C₄	—	8	1	no	—
584	C₂²⋊C₄	—	8	1	no	—
585	C₂²⋊C₄	—	8	1	no	—
586	C₂²⋊C₄	—	8	1	no	—
587	C₄²	—	2	1	no	—
588	C₄²	—	2	1	no	—
589	C₄²	—	2	1	no	—
590	C₄²	—	2	1	no	—
591	C₄²	—	4	2	no	—
592	C₄²	—	8	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	4	1	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	C₄×D₄×C₁₇	1	2	yes	—
607	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
608	Q₈	—	2	2	no	—
609	Q₈	—	2	2	no	—
610	Q₈	—	2	2	no	—
611	Q₈	—	2	2	no	—
612	Q₈	—	4	1	no	—
613	Q₈	—	4	1	no	—
614	Q₈	—	4	1	no	—
615	Q₈	—	4	1	no	—
616	D₄	—	2	2	no	—
617	D₄	—	2	2	no	—
618	D₄	—	4	8	no	—
619	D₄	—	4	1	no	—
620	D₄	—	4	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	4	8	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	8	4	no	—
662	C₂×C₄	C₄×D₄×C₁₇	1	2	yes	—
663	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
664	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
665	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
666	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
667	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
668	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
669	C₈	—	2	2	no	—
670	C₈	—	2	2	no	—
671	C₈	—	4	1	no	—
672	C₈	—	4	1	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	4	1	no	—
677	C₂²	—	4	1	no	—
678	C₂²	—	4	1	no	—
679	C₂²	—	4	1	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	4	2	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	8	1	no	—
684	C₂²	—	8	1	no	—
685	C₂²	—	8	1	no	—
686	C₂²	—	8	1	no	—
687	C₂²	C₂×C₄×D₄×C₁₇	1	1	yes	characteristic
688	C₂²	C₁₇×#534	1	1	yes	characteristic
689	C₂²	C₁₇×#535	1	1	yes	characteristic
690	C₂²	C₁₇×#577	1	1	yes	characteristic
691	C₂²	C₁₇×#577	1	1	yes	characteristic
692	C₂²	C₁₇×#577	1	1	yes	characteristic
693	C₂²	C₁₇×#578	1	1	yes	characteristic
694	C₄	—	2	2	no	—
695	C₄	—	4	1	no	—
696	C₄	—	4	1	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	2	no	—
699	C₄	—	4	2	no	—
700	C₄	—	4	1	no	—
701	C₄	—	4	1	no	—
702	C₄	—	8	1	no	—
703	C₄	—	8	1	no	—
704	C₄	—	8	1	no	—
705	C₄	—	8	1	no	—
706	C₄	C₁₇×#518	1	1	yes	characteristic
707	C₄	C₁₇×#518	1	1	yes	characteristic
708	C₄	C₁₇×#538	1	1	yes	characteristic
709	C₄	C₁₇×#538	1	1	yes	characteristic
710	C₂	—	4	2	no	—
711	C₂	—	8	2	no	—
712	C₂	C₁₇×#2321	1	1	yes	characteristic
713	C₂	C₁₇×#2947	1	1	yes	characteristic
714	C₂	C₁₇×#2952	1	1	yes	characteristic
715	C₂	C₁₇×#3201	1	1	yes	characteristic
716	C₂	C₁₇×#3204	1	1	yes	characteristic
717	C₂	C₁₇×#3222	1	1	yes	characteristic
718	C₂	C₁₇×#3225	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×#41×C₁₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₁₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₇×#2323	C₂	semidirect
4. C₁₇×#1971	C₂	semidirect
5. C₁₇×#1968	C₂	semidirect
6. C₁₇×#1936	C₂	semidirect
7. C₁₇×#1933	C₂	semidirect
8. C₁₇×#1927	C₂	semidirect
9. C₁₇×#1926	C₂	semidirect
10. C₁₇×#1880	C₂	semidirect
11. C₁₇×#1878	C₂	semidirect
12. C₁₇×#1872	C₂	semidirect
13. C₁₇×#1853	C₂	semidirect
15. C₁₇×#1750	C₂	semidirect
23. C₁₇×#452	C₄	semidirect
75. C₂×Q₁₆×C₁₇	C₂×C₄	semidirect
78. C₂×SD₁₆×C₁₇	C₂×C₄	semidirect
120. C₁₇×#103	C₂×C₄	semidirect
123. C₁₇×#102	C₂×C₄	semidirect
233. #22059	C₁₇	direct (N × H)
315. #2323	C₂×C₁₇	semidirect
317. #1971	C₂×C₁₇	semidirect
318. #1968	C₂×C₁₇	semidirect
319. #1936	C₂×C₁₇	semidirect
320. #1933	C₂×C₁₇	semidirect
321. #1927	C₂×C₁₇	semidirect
322. #1926	C₂×C₁₇	semidirect
323. #1880	C₂×C₁₇	semidirect
324. #1878	C₂×C₁₇	semidirect
325. #1872	C₂×C₁₇	semidirect
326. #1853	C₂×C₁₇	semidirect
328. #1750	C₂×C₁₇	semidirect
373. #452	C₄×C₁₇	semidirect
434. C₂×Q₁₆	C₂×C₄×C₁₇	semidirect
437. C₂×SD₁₆	C₂×C₄×C₁₇	semidirect
479. #103	C₂×C₄×C₁₇	semidirect
482. #102	C₂×C₄×C₁₇	semidirect
496. C₁₇	#22059	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×#452	2
C₁₇×#2323	2
C₁₇×#2311	2
C₁₇×#1971	2
C₁₇×#1968	2
C₁₇×#1936	2
C₁₇×#1933	2
C₁₇×#1927	2
C₁₇×#1926	2
C₁₇×#1880	2
C₁₇×#1878	2
C₁₇×#1872	2
C₁₇×#1853	2
C₁₇×#1788	2
C₁₇×#1750	2
#22059	17

Subgroups — C17×#22059 #16879803

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#22059 #16879803