Subgroups — C₁₇×#21591 #16879335

Order 4352.

844 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#485	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#2323	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#2274	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#1927	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1927	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1921	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1919	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1872	C₂	1	1	yes	maximal, characteristic
9	C₁₇×#1853	C₂	1	1	yes	maximal, characteristic
10	C₁₇×#1825	C₂	1	1	yes	maximal, characteristic
11	C₁₇×#1776	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₇×#106	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1763	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₇×#103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1750	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
18	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
19	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
21	C₁₇×#485	C₄	1	8	yes	complemented
22	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
34	C₁₇×#391	C₂²	1	1	yes	characteristic
35	C₁₇×#389	—	2	1	no	—
36	C₁₇×#389	C₂²	1	1	yes	characteristic
37	C₁₇×#388	—	2	1	no	—
38	C₁₇×#388	—	2	1	no	—
39	C₁₇×#387	—	2	1	no	—
40	C₁₇×#380	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₁₇	—	2	1	no	—
42	C₄×C₄⋊C₄×C₁₇	—	2	1	no	—
43	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
48	C₄×C₂²⋊C₄×C₁₇	—	2	1	no	—
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×#336	C₂²	1	1	yes	characteristic
59	C₁₇×#336	C₂²	1	1	yes	characteristic
60	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₇	—	2	1	no	—
62	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
67	C₁₇×C₂²⋊Q₈	—	2	2	no	—
68	C₁₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
69	C₄×Q₈×C₁₇	—	2	2	no	—
70	C₄×Q₈×C₁₇	—	2	2	no	—
71	C₁₇×#117	—	2	2	no	—
72	C₁₇×#117	—	2	2	no	—
73	C₁₇×#117	—	2	2	no	—
74	C₁₇×#117	C₂×C₄	1	4	yes	—
75	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
79	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₇	C₂³	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×C₂²⋊C₄×C₁₇	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₇	D₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₁₇	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₁₇	—	2	1	no	—
96	C₂×C₄²×C₁₇	—	2	1	no	—
97	C₂×C₄²×C₁₇	—	2	1	no	—
98	C₂×C₄²×C₁₇	—	2	1	no	—
99	C₂×C₄²×C₁₇	—	2	1	no	—
100	C₂×C₄²×C₁₇	—	2	1	no	—
101	C₂×C₄²×C₁₇	—	2	1	no	—
102	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
104	C₁₇×#107	C₂×C₄	1	4	yes	complemented
105	C₁₇×#106	—	2	2	no	—
106	C₁₇×#106	—	2	2	no	—
107	C₁₇×#106	C₂×C₄	1	4	yes	complemented
108	C₁₇×#103	—	2	2	no	—
109	C₁₇×#103	—	2	2	no	—
110	C₁₇×#103	C₂×C₄	1	4	yes	complemented
111	C₁₇×#103	C₂×C₄	1	4	yes	complemented
112	C₁₇×C₂²⋊C₈	—	2	2	no	—
113	C₁₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
114	C₁₇×#97	—	2	2	no	—
115	C₄×C₈×C₁₇	—	2	2	no	—
116	C₁₇×#95	—	2	1	no	—
117	C₁₇×#95	—	2	1	no	—
118	C₁₇×#95	—	2	1	no	—
119	C₁₇×#95	—	2	1	no	—
120	C₁₇×#95	—	2	1	no	—
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	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
126	C₂×Q₈×C₁₇	—	2	1	no	—
127	C₂×Q₈×C₁₇	—	2	1	no	—
128	C₂×Q₈×C₁₇	—	2	1	no	—
129	C₂×Q₈×C₁₇	—	2	1	no	—
130	C₂×Q₈×C₁₇	—	2	1	no	—
131	C₂×Q₈×C₁₇	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₁₇	—	2	1	no	—
133	C₂²×C₄×C₁₇	—	2	1	no	—
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	4	no	—
143	C₂²×C₄×C₁₇	—	2	1	no	—
144	C₂²×C₄×C₁₇	—	2	1	no	—
145	C₂²×C₄×C₁₇	—	8	1	no	—
146	C₂²×C₄×C₁₇	—	8	1	no	—
147	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
148	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₇	#41	1	2	yes	—
154	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
155	C₂×C₈×C₁₇	—	2	1	no	—
156	C₂×C₈×C₁₇	—	2	1	no	—
157	C₂×C₈×C₁₇	—	2	1	no	—
158	C₂×C₈×C₁₇	—	2	1	no	—
159	C₂×C₈×C₁₇	—	2	1	no	—
160	C₂×C₈×C₁₇	—	2	1	no	—
161	C₂×C₈×C₁₇	—	2	1	no	—
162	C₂×C₈×C₁₇	—	2	1	no	—
163	C₂×C₈×C₁₇	—	2	1	no	—
164	C₂×C₈×C₁₇	—	2	1	no	—
165	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
166	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
167	C₄⋊C₄×C₁₇	—	2	4	no	—
168	C₄⋊C₄×C₁₇	—	2	4	no	—
169	C₄⋊C₄×C₁₇	—	2	2	no	—
170	C₄⋊C₄×C₁₇	—	2	2	no	—
171	C₄⋊C₄×C₁₇	—	2	1	no	—
172	C₄⋊C₄×C₁₇	—	2	1	no	—
173	C₄⋊C₄×C₁₇	—	2	1	no	—
174	C₄⋊C₄×C₁₇	—	2	1	no	—
175	C₄⋊C₄×C₁₇	—	2	1	no	—
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	—	4	2	no	—
181	C₄⋊C₄×C₁₇	—	8	1	no	—
182	C₄⋊C₄×C₁₇	C₂²×C₄	1	2	yes	—
183	C₄⋊C₄×C₁₇	C₂²×C₄	1	2	yes	—
184	C₄⋊C₄×C₁₇	C₂²×C₄	1	2	yes	—
185	C₄⋊C₄×C₁₇	#41	1	2	yes	—
186	C₄⋊C₄×C₁₇	#41	1	2	yes	—
187	C₂²⋊C₄×C₁₇	—	2	4	no	—
188	C₂²⋊C₄×C₁₇	—	2	4	no	—
189	C₂²⋊C₄×C₁₇	—	2	2	no	—
190	C₂²⋊C₄×C₁₇	—	2	2	no	—
191	C₂²⋊C₄×C₁₇	—	8	1	no	—
192	C₄²×C₁₇	—	2	4	no	—
193	C₄²×C₁₇	—	2	1	no	—
194	C₄²×C₁₇	—	2	1	no	—
195	C₄²×C₁₇	—	4	2	no	—
196	C₄²×C₁₇	—	8	1	no	—
197	C₄²×C₁₇	—	8	1	no	—
198	C₄²×C₁₇	—	8	1	no	—
199	C₄²×C₁₇	—	8	1	no	—
200	C₄²×C₁₇	—	8	1	no	—
201	C₄²×C₁₇	#41	1	2	yes	—
202	C₄²×C₁₇	#41	1	2	yes	—
203	#21591	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂³×C₁₇	—	2	1	no	—
205	C₂³×C₁₇	—	2	1	no	—
206	C₂³×C₁₇	—	2	1	no	—
207	C₂³×C₁₇	—	2	1	no	—
208	C₂³×C₁₇	—	2	1	no	—
209	C₂³×C₁₇	—	2	1	no	—
210	C₂³×C₁₇	C₄×D₄	1	2	yes	—
211	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
212	Q₈×C₁₇	—	2	2	no	—
213	Q₈×C₁₇	—	2	2	no	—
214	Q₈×C₁₇	—	4	1	no	—
215	Q₈×C₁₇	—	4	1	no	—
216	C₂×C₄×C₁₇	—	2	1	no	—
217	C₂×C₄×C₁₇	—	2	1	no	—
218	C₂×C₄×C₁₇	—	2	1	no	—
219	C₂×C₄×C₁₇	—	2	1	no	—
220	C₂×C₄×C₁₇	—	2	1	no	—
221	C₂×C₄×C₁₇	—	2	1	no	—
222	C₂×C₄×C₁₇	—	2	2	no	—
223	C₂×C₄×C₁₇	—	2	2	no	—
224	C₂×C₄×C₁₇	—	2	2	no	—
225	C₂×C₄×C₁₇	—	2	2	no	—
226	C₂×C₄×C₁₇	—	2	2	no	—
227	C₂×C₄×C₁₇	—	2	2	no	—
228	C₂×C₄×C₁₇	—	2	2	no	—
229	C₂×C₄×C₁₇	—	2	2	no	—
230	C₂×C₄×C₁₇	—	2	1	no	—
231	C₂×C₄×C₁₇	—	2	1	no	—
232	C₂×C₄×C₁₇	—	2	2	no	—
233	C₂×C₄×C₁₇	—	2	2	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	1	no	—
238	C₂×C₄×C₁₇	—	4	1	no	—
239	C₂×C₄×C₁₇	—	4	1	no	—
240	C₂×C₄×C₁₇	—	4	1	no	—
241	C₂×C₄×C₁₇	—	4	1	no	—
242	C₂×C₄×C₁₇	—	4	1	no	—
243	C₂×C₄×C₁₇	—	4	1	no	—
244	C₂×C₄×C₁₇	—	4	1	no	—
245	C₂×C₄×C₁₇	—	4	1	no	—
246	C₂×C₄×C₁₇	—	4	1	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	—	8	4	no	—
257	C₂×C₄×C₁₇	C₄×D₄	1	2	yes	—
258	C₂×C₄×C₁₇	#123	1	2	yes	—
259	C₂×C₄×C₁₇	#123	1	2	yes	—
260	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
261	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
262	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
263	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
266	C₈×C₁₇	—	2	2	no	—
267	C₈×C₁₇	—	2	2	no	—
268	C₈×C₁₇	—	4	1	no	—
269	C₈×C₁₇	—	4	1	no	—
270	C₂×#485	C₂×C₁₇	1	1	yes	characteristic
271	#2323	C₂×C₁₇	1	1	yes	characteristic
272	#2274	C₂×C₁₇	1	1	yes	characteristic
273	#1927	C₂×C₁₇	1	1	yes	characteristic, complemented
274	#1927	C₂×C₁₇	1	1	yes	characteristic, complemented
275	#1921	C₂×C₁₇	1	1	yes	characteristic, complemented
276	#1919	C₂×C₁₇	1	1	yes	characteristic, complemented
277	#1872	C₂×C₁₇	1	1	yes	characteristic
278	#1853	C₂×C₁₇	1	1	yes	characteristic
279	#1825	C₂×C₁₇	1	1	yes	characteristic
280	#1776	C₂×C₁₇	1	1	yes	characteristic, complemented
281	C₄×#106	C₂×C₁₇	1	1	yes	characteristic, complemented
282	#1763	C₂×C₁₇	1	1	yes	characteristic, complemented
283	C₄×#103	C₂×C₁₇	1	1	yes	characteristic, complemented
284	#1750	C₂×C₁₇	1	1	yes	characteristic
285	C₂²×C₁₇	—	2	2	no	—
286	C₂²×C₁₇	—	2	2	no	—
287	C₂²×C₁₇	—	2	2	no	—
288	C₂²×C₁₇	—	4	1	no	—
289	C₂²×C₁₇	—	4	1	no	—
290	C₂²×C₁₇	—	4	1	no	—
291	C₂²×C₁₇	—	4	1	no	—
292	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
293	C₂²×C₁₇	C₂×#123	1	1	yes	characteristic
294	C₂²×C₁₇	#525	1	1	yes	characteristic
295	C₂²×C₁₇	#577	1	1	yes	characteristic
296	C₂²×C₁₇	#577	1	1	yes	characteristic
297	C₂²×C₁₇	#577	1	1	yes	characteristic
298	C₂²×C₁₇	#578	1	1	yes	characteristic
299	C₄×C₁₇	—	2	2	no	—
300	C₄×C₁₇	—	2	2	no	—
301	C₄×C₁₇	—	2	2	no	—
302	C₄×C₁₇	—	4	1	no	—
303	C₄×C₁₇	—	4	1	no	—
304	C₄×C₁₇	—	4	2	no	—
305	C₄×C₁₇	—	4	2	no	—
306	C₄×C₁₇	—	4	2	no	—
307	C₄×C₁₇	—	4	2	no	—
308	C₄×C₁₇	—	4	2	no	—
309	C₄×C₁₇	—	4	2	no	—
310	C₄×C₁₇	—	8	1	no	—
311	C₄×C₁₇	—	8	1	no	—
312	C₄×C₁₇	C₄×#41	1	1	yes	characteristic
313	C₄×C₁₇	C₄×#41	1	1	yes	characteristic
314	C₄×C₁₇	#529	1	1	yes	characteristic
315	C₄×C₁₇	#529	1	1	yes	characteristic
316	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
317	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
318	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
319	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
320	C₂²×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
321	#485	C₄×C₁₇	1	8	yes	complemented
322	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
323	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
324	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
325	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
326	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
327	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
328	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
329	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
330	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
331	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
332	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
333	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
334	#391	C₂²×C₁₇	1	1	yes	characteristic
335	#389	—	2	1	no	—
336	#389	C₂²×C₁₇	1	1	yes	characteristic
337	#388	—	2	1	no	—
338	#388	—	2	1	no	—
339	#387	—	2	1	no	—
340	#380	C₂²×C₁₇	1	1	yes	characteristic
341	C₄×C₄⋊C₄	—	2	1	no	—
342	C₄×C₄⋊C₄	—	2	1	no	—
343	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
344	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
345	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
346	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
347	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
348	C₄×C₂²⋊C₄	—	2	1	no	—
349	C₄×C₂²⋊C₄	—	2	1	no	—
350	#340	C₂²×C₁₇	1	1	yes	characteristic
351	#340	C₂²×C₁₇	1	1	yes	characteristic
352	#340	C₂²×C₁₇	1	1	yes	characteristic
353	#340	C₂²×C₁₇	1	1	yes	characteristic
354	#340	C₂²×C₁₇	1	1	yes	characteristic
355	#340	C₂²×C₁₇	1	1	yes	characteristic
356	#340	C₂²×C₁₇	1	1	yes	characteristic
357	#340	C₂²×C₁₇	1	1	yes	characteristic
358	#336	C₂²×C₁₇	1	1	yes	characteristic
359	#336	C₂²×C₁₇	1	1	yes	characteristic
360	C₂×C₁₇	—	4	2	no	—
361	C₂×C₁₇	C₄×#123	1	1	yes	characteristic
362	C₂×C₁₇	#2947	1	1	yes	characteristic
363	C₂×C₁₇	#2952	1	1	yes	characteristic
364	C₂×C₁₇	#3097	1	1	yes	characteristic
365	C₂×C₁₇	#3099	1	1	yes	characteristic
366	C₂×C₁₇	#3121	1	1	yes	characteristic
367	C₂×C₁₇	#3123	1	1	yes	characteristic
368	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
369	C₂³×C₄	—	2	1	no	—
370	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
373	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
374	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
375	C₂²⋊Q₈	—	2	2	no	—
376	C₂²⋊Q₈	C₂×C₄×C₁₇	1	4	yes	—
377	C₄×Q₈	—	2	2	no	—
378	C₄×Q₈	—	2	2	no	—
379	#117	—	2	2	no	—
380	#117	—	2	2	no	—
381	#117	—	2	2	no	—
382	#117	C₂×C₄×C₁₇	1	4	yes	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	2	no	—
386	C₂×C₄⋊C₄	—	2	2	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
390	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₂²⋊C₄	—	2	1	no	—
400	C₂×C₂²⋊C₄	—	2	1	no	—
401	C₂×C₂²⋊C₄	D₄×C₁₇	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	D₄×C₁₇	1	1	yes	characteristic
403	C₂×C₄²	—	2	1	no	—
404	C₂×C₄²	—	2	1	no	—
405	C₂×C₄²	—	2	1	no	—
406	C₂×C₄²	—	2	1	no	—
407	C₂×C₄²	—	2	1	no	—
408	C₂×C₄²	—	2	1	no	—
409	C₂×C₄²	—	2	1	no	—
410	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
411	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
412	#107	C₂×C₄×C₁₇	1	4	yes	complemented
413	#106	—	2	2	no	—
414	#106	—	2	2	no	—
415	#106	C₂×C₄×C₁₇	1	4	yes	complemented
416	#103	—	2	2	no	—
417	#103	—	2	2	no	—
418	#103	C₂×C₄×C₁₇	1	4	yes	complemented
419	#103	C₂×C₄×C₁₇	1	4	yes	complemented
420	C₂²⋊C₈	—	2	2	no	—
421	C₂²⋊C₈	C₂×C₄×C₁₇	1	4	yes	—
422	#97	—	2	2	no	—
423	C₄×C₈	—	2	2	no	—
424	#95	—	2	1	no	—
425	#95	—	2	1	no	—
426	#95	—	2	1	no	—
427	#95	—	2	1	no	—
428	#95	—	2	1	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	#95	—	2	1	no	—
432	#95	—	2	1	no	—
433	C₁₇	#21591	1	1	yes	characteristic, direct product factor, Sylow
434	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	C₂²×C₄×C₁₇	1	2	yes	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	8	1	no	—
455	C₂²×C₄	—	8	1	no	—
456	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
457	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
462	C₂²×C₄	#41×C₁₇	1	2	yes	—
463	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
475	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
476	C₄⋊C₄	—	2	4	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	4	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	4	2	no	—
490	C₄⋊C₄	—	8	1	no	—
491	C₄⋊C₄	C₂²×C₄×C₁₇	1	2	yes	—
492	C₄⋊C₄	C₂²×C₄×C₁₇	1	2	yes	—
493	C₄⋊C₄	C₂²×C₄×C₁₇	1	2	yes	—
494	C₄⋊C₄	#41×C₁₇	1	2	yes	—
495	C₄⋊C₄	#41×C₁₇	1	2	yes	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₂²⋊C₄	—	2	4	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	8	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	4	no	—
504	C₄²	—	4	2	no	—
505	C₄²	—	8	1	no	—
506	C₄²	—	8	1	no	—
507	C₄²	—	8	1	no	—
508	C₄²	—	8	1	no	—
509	C₄²	—	8	1	no	—
510	C₄²	#41×C₁₇	1	2	yes	—
511	C₄²	#41×C₁₇	1	2	yes	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	C₄×D₄×C₁₇	1	2	yes	—
519	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
520	Q₈	—	2	2	no	—
521	Q₈	—	2	2	no	—
522	Q₈	—	4	1	no	—
523	Q₈	—	4	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	8	4	no	—
565	C₂×C₄	C₄×D₄×C₁₇	1	2	yes	—
566	C₂×C₄	C₁₇×#123	1	2	yes	—
567	C₂×C₄	C₁₇×#123	1	2	yes	—
568	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
569	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
570	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
571	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
572	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
573	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
574	C₈	—	2	2	no	—
575	C₈	—	2	2	no	—
576	C₈	—	4	1	no	—
577	C₈	—	4	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	C₂×C₄×D₄×C₁₇	1	1	yes	characteristic
586	C₂²	C₂×C₁₇×#123	1	1	yes	characteristic
587	C₂²	C₁₇×#525	1	1	yes	characteristic
588	C₂²	C₁₇×#577	1	1	yes	characteristic
589	C₂²	C₁₇×#577	1	1	yes	characteristic
590	C₂²	C₁₇×#577	1	1	yes	characteristic
591	C₂²	C₁₇×#578	1	1	yes	characteristic
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	2	2	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	2	no	—
597	C₄	—	4	2	no	—
598	C₄	—	4	2	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	2	no	—
603	C₄	—	8	1	no	—
604	C₄	—	8	1	no	—
605	C₄	C₄×#41×C₁₇	1	1	yes	characteristic
606	C₄	C₄×#41×C₁₇	1	1	yes	characteristic
607	C₄	C₁₇×#529	1	1	yes	characteristic
608	C₄	C₁₇×#529	1	1	yes	characteristic
609	C₂	—	4	2	no	—
610	C₂	C₄×C₁₇×#123	1	1	yes	characteristic
611	C₂	C₁₇×#2947	1	1	yes	characteristic
612	C₂	C₁₇×#2952	1	1	yes	characteristic
613	C₂	C₁₇×#3097	1	1	yes	characteristic
614	C₂	C₁₇×#3099	1	1	yes	characteristic
615	C₂	C₁₇×#3121	1	1	yes	characteristic
616	C₂	C₁₇×#3123	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	C₂⁴×C₁₇	C₂×D₄
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
4. C₁₇×#1927	C₂	semidirect
5. C₁₇×#1927	C₂	semidirect
6. C₁₇×#1921	C₂	semidirect
7. C₁₇×#1919	C₂	semidirect
11. C₁₇×#1776	C₂	semidirect
12. C₄×C₁₇×#106	C₂	semidirect
13. C₁₇×#1763	C₂	semidirect
14. C₄×C₁₇×#103	C₂	semidirect
21. C₁₇×#485	C₄	semidirect
104. C₁₇×#107	C₂×C₄	semidirect
107. C₁₇×#106	C₂×C₄	semidirect
110. C₁₇×#103	C₂×C₄	semidirect
111. C₁₇×#103	C₂×C₄	semidirect
203. #21591	C₁₇	direct (N × H)
273. #1927	C₂×C₁₇	semidirect
274. #1927	C₂×C₁₇	semidirect
275. #1921	C₂×C₁₇	semidirect
276. #1919	C₂×C₁₇	semidirect
280. #1776	C₂×C₁₇	semidirect
281. C₄×#106	C₂×C₁₇	semidirect
282. #1763	C₂×C₁₇	semidirect
283. C₄×#103	C₂×C₁₇	semidirect
321. #485	C₄×C₁₇	semidirect
412. #107	C₂×C₄×C₁₇	semidirect
415. #106	C₂×C₄×C₁₇	semidirect
418. #103	C₂×C₄×C₁₇	semidirect
419. #103	C₂×C₄×C₁₇	semidirect
433. C₁₇	#21591	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×#485	2
C₁₇×#2323	2
C₁₇×#2274	2
C₁₇×#1927	2
C₁₇×#1921	2
C₁₇×#1919	2
C₁₇×#1872	2
C₁₇×#1853	2
C₁₇×#1825	2
C₁₇×#1776	2
C₄×C₁₇×#106	2
C₁₇×#1763	2
C₄×C₁₇×#103	2
C₁₇×#1750	2
#21591	17

Subgroups — C17×#21591 #16879335

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#21591 #16879335