Subgroups — C₁₇×#22083 #16879827

Order 4352.

812 conjugacy classes of subgroups.

The subgroup lattice has 624 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	C₄×C₁₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#2296	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#1944	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1943	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1935	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1935	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1921	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1919	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1873	C₂	1	1	yes	maximal, characteristic
11	C₁₇×#1865	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1863	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1854	C₂	1	1	yes	maximal, characteristic
14	C₁₇×#1825	C₂	1	1	yes	maximal, characteristic
15	C₁₇×#1749	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×C₄²×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×#107	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×C₁₇×#97	C₂²	1	1	yes	characteristic
34	C₁₇×#391	C₂²	1	1	yes	characteristic
35	C₁₇×#389	C₂²	1	1	yes	characteristic
36	C₁₇×#389	C₂²	1	1	yes	characteristic
37	C₁₇×#389	C₂²	1	1	yes	characteristic
38	C₁₇×#389	C₂²	1	1	yes	characteristic
39	C₁₇×#389	C₂²	1	1	yes	characteristic
40	C₁₇×#387	—	2	1	no	—
41	C₁₇×#385	—	2	1	no	—
42	C₁₇×#385	—	2	1	no	—
43	C₁₇×#385	—	2	1	no	—
44	C₁₇×#380	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊C₄×C₁₇	—	2	1	no	—
46	C₄×C₄⋊C₄×C₁₇	—	2	1	no	—
47	C₄×C₄⋊C₄×C₁₇	—	2	1	no	—
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×#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	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₇	D₄	1	1	yes	characteristic
63	C₂³×C₄×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	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
68	C₁₇×C₂²⋊Q₈	—	2	2	no	—
69	C₁₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
70	C₄×Q₈×C₁₇	—	4	1	no	—
71	C₄×Q₈×C₁₇	—	4	1	no	—
72	C₁₇×#117	—	2	2	no	—
73	C₁₇×#117	—	4	1	no	—
74	C₁₇×#117	—	4	1	no	—
75	C₁₇×#117	C₂×C₄	1	4	yes	—
76	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
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	—	2	1	no	—
94	C₂×C₄²×C₁₇	—	2	1	no	—
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	—	4	1	no	—
99	C₂×C₄²×C₁₇	—	4	1	no	—
100	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
104	C₁₇×#107	—	4	1	no	—
105	C₁₇×#107	C₂×C₄	1	4	yes	complemented
106	C₁₇×#106	—	4	1	no	—
107	C₁₇×#106	C₂×C₄	1	4	yes	complemented
108	C₁₇×#103	—	4	1	no	—
109	C₁₇×#103	—	4	1	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	—	4	1	no	—
115	C₁₇×#97	—	4	1	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	2	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	—	4	1	no	—
146	C₂²×C₄×C₁₇	—	4	1	no	—
147	C₂²×C₄×C₁₇	—	4	1	no	—
148	C₂²×C₄×C₁₇	—	4	1	no	—
149	C₂²×C₄×C₁₇	—	4	1	no	—
150	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
151	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₇	#41	1	2	yes	—
157	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
166	C₂×C₈×C₁₇	—	2	1	no	—
167	C₂×C₈×C₁₇	—	2	1	no	—
168	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
169	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
170	C₄⋊C₄×C₁₇	—	2	4	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	—	2	1	no	—
181	C₄⋊C₄×C₁₇	—	2	1	no	—
182	C₄⋊C₄×C₁₇	—	4	2	no	—
183	C₄⋊C₄×C₁₇	—	4	2	no	—
184	C₄⋊C₄×C₁₇	—	4	2	no	—
185	C₄⋊C₄×C₁₇	—	4	2	no	—
186	C₄⋊C₄×C₁₇	—	4	2	no	—
187	C₄⋊C₄×C₁₇	—	4	2	no	—
188	C₄⋊C₄×C₁₇	C₂²×C₄	1	2	yes	—
189	C₄⋊C₄×C₁₇	C₂²×C₄	1	2	yes	—
190	C₄⋊C₄×C₁₇	C₂²×C₄	1	2	yes	—
191	C₂²⋊C₄×C₁₇	—	2	4	no	—
192	C₂²⋊C₄×C₁₇	—	2	4	no	—
193	C₂²⋊C₄×C₁₇	—	4	2	no	—
194	C₂²⋊C₄×C₁₇	—	4	2	no	—
195	C₄²×C₁₇	—	2	4	no	—
196	C₄²×C₁₇	—	2	1	no	—
197	C₄²×C₁₇	—	2	1	no	—
198	C₄²×C₁₇	—	2	1	no	—
199	C₄²×C₁₇	—	2	1	no	—
200	C₄²×C₁₇	—	4	1	no	—
201	C₄²×C₁₇	—	4	1	no	—
202	C₄²×C₁₇	—	4	2	no	—
203	C₄²×C₁₇	—	4	2	no	—
204	C₄²×C₁₇	—	4	2	no	—
205	#22083	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	2	1	no	—
211	C₂³×C₁₇	—	2	1	no	—
212	C₂³×C₁₇	C₄×D₄	1	2	yes	—
213	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
214	Q₈×C₁₇	—	2	2	no	—
215	Q₈×C₁₇	—	2	2	no	—
216	Q₈×C₁₇	—	4	1	no	—
217	Q₈×C₁₇	—	4	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	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	1	no	—
238	C₂×C₄×C₁₇	—	2	1	no	—
239	C₂×C₄×C₁₇	—	4	4	no	—
240	C₂×C₄×C₁₇	—	4	4	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	—	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	C₄×D₄	1	2	yes	—
262	C₂×C₄×C₁₇	#137	1	2	yes	—
263	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
264	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
266	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
267	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
268	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
269	C₈×C₁₇	—	2	2	no	—
270	C₈×C₁₇	—	2	2	no	—
271	C₈×C₁₇	—	4	1	no	—
272	C₈×C₁₇	—	4	1	no	—
273	C₂×#485	C₂×C₁₇	1	1	yes	characteristic
274	C₄×C₂²⋊Q₈	C₂×C₁₇	1	1	yes	characteristic
275	#2296	C₂×C₁₇	1	1	yes	characteristic
276	#1944	C₂×C₁₇	1	1	yes	characteristic, complemented
277	#1943	C₂×C₁₇	1	1	yes	characteristic, complemented
278	#1935	C₂×C₁₇	1	1	yes	characteristic, complemented
279	#1935	C₂×C₁₇	1	1	yes	characteristic, complemented
280	#1921	C₂×C₁₇	1	1	yes	characteristic, complemented
281	#1919	C₂×C₁₇	1	1	yes	characteristic, complemented
282	#1873	C₂×C₁₇	1	1	yes	characteristic
283	#1865	C₂×C₁₇	1	1	yes	characteristic, complemented
284	#1863	C₂×C₁₇	1	1	yes	characteristic, complemented
285	#1854	C₂×C₁₇	1	1	yes	characteristic
286	#1825	C₂×C₁₇	1	1	yes	characteristic
287	#1749	C₂×C₁₇	1	1	yes	characteristic
288	C₂²×C₁₇	—	2	2	no	—
289	C₂²×C₁₇	—	2	2	no	—
290	C₂²×C₁₇	—	2	2	no	—
291	C₂²×C₁₇	—	4	1	no	—
292	C₂²×C₁₇	—	4	1	no	—
293	C₂²×C₁₇	—	4	1	no	—
294	C₂²×C₁₇	—	4	1	no	—
295	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
296	C₂²×C₁₇	#534	1	1	yes	characteristic
297	C₂²×C₁₇	#536	1	1	yes	characteristic
298	C₂²×C₁₇	C₂×#137	1	1	yes	characteristic
299	C₂²×C₁₇	#575	1	1	yes	characteristic
300	C₂²×C₁₇	#575	1	1	yes	characteristic
301	C₂²×C₁₇	#575	1	1	yes	characteristic
302	C₄×C₁₇	—	2	2	no	—
303	C₄×C₁₇	—	2	2	no	—
304	C₄×C₁₇	—	4	2	no	—
305	C₄×C₁₇	—	4	1	no	—
306	C₄×C₁₇	—	4	1	no	—
307	C₄×C₁₇	—	4	1	no	—
308	C₄×C₁₇	—	4	2	no	—
309	C₄×C₁₇	—	4	2	no	—
310	C₄×C₁₇	—	4	2	no	—
311	C₄×C₁₇	—	8	1	no	—
312	C₄×C₁₇	—	8	1	no	—
313	C₄×C₁₇	—	8	1	no	—
314	C₄×C₁₇	—	8	1	no	—
315	C₄×C₁₇	#520	1	1	yes	characteristic
316	C₄×C₁₇	#520	1	1	yes	characteristic
317	C₄×C₁₇	#539	1	1	yes	characteristic
318	C₄×C₁₇	#539	1	1	yes	characteristic
319	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
320	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
321	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
322	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
323	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic
324	#485	C₄×C₁₇	1	8	yes	complemented
325	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
326	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
327	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
328	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
329	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
330	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
331	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
332	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
333	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
334	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
335	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
336	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
337	#391	C₂²×C₁₇	1	1	yes	characteristic
338	#389	C₂²×C₁₇	1	1	yes	characteristic
339	#389	C₂²×C₁₇	1	1	yes	characteristic
340	#389	C₂²×C₁₇	1	1	yes	characteristic
341	#389	C₂²×C₁₇	1	1	yes	characteristic
342	#389	C₂²×C₁₇	1	1	yes	characteristic
343	#387	—	2	1	no	—
344	#385	—	2	1	no	—
345	#385	—	2	1	no	—
346	#385	—	2	1	no	—
347	#380	C₂²×C₁₇	1	1	yes	characteristic
348	C₄×C₄⋊C₄	—	2	1	no	—
349	C₄×C₄⋊C₄	—	2	1	no	—
350	C₄×C₄⋊C₄	—	2	1	no	—
351	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
352	C₄×C₂²⋊C₄	—	2	1	no	—
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	#340	C₂²×C₁₇	1	1	yes	characteristic
359	#340	C₂²×C₁₇	1	1	yes	characteristic
360	#340	C₂²×C₁₇	1	1	yes	characteristic
361	#336	C₂²×C₁₇	1	1	yes	characteristic
362	#336	C₂²×C₁₇	1	1	yes	characteristic
363	C₂×C₁₇	—	4	2	no	—
364	C₂×C₁₇	#2322	1	1	yes	characteristic
365	C₂×C₁₇	#2943	1	1	yes	characteristic
366	C₂×C₁₇	C₄×#137	1	1	yes	characteristic
367	C₂×C₁₇	#3196	1	1	yes	characteristic
368	C₂×C₁₇	#3197	1	1	yes	characteristic
369	C₂×C₁₇	#3237	1	1	yes	characteristic
370	C₂×C₁₇	#3240	1	1	yes	characteristic
371	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
372	C₂³×C₄	D₄×C₁₇	1	1	yes	characteristic
373	C₂³×C₄	D₄×C₁₇	1	1	yes	characteristic
374	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
375	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
376	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
377	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
378	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
379	C₂²⋊Q₈	—	2	2	no	—
380	C₂²⋊Q₈	C₂×C₄×C₁₇	1	4	yes	—
381	C₄×Q₈	—	4	1	no	—
382	C₄×Q₈	—	4	1	no	—
383	#117	—	2	2	no	—
384	#117	—	4	1	no	—
385	#117	—	4	1	no	—
386	#117	C₂×C₄×C₁₇	1	4	yes	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
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×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	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	—	4	1	no	—
410	C₂×C₄²	—	4	1	no	—
411	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
412	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
413	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
414	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
415	#107	—	4	1	no	—
416	#107	C₂×C₄×C₁₇	1	4	yes	complemented
417	#106	—	4	1	no	—
418	#106	C₂×C₄×C₁₇	1	4	yes	complemented
419	#103	—	4	1	no	—
420	#103	—	4	1	no	—
421	#103	C₂×C₄×C₁₇	1	4	yes	complemented
422	#103	C₂×C₄×C₁₇	1	4	yes	complemented
423	C₂²⋊C₈	—	2	2	no	—
424	C₂²⋊C₈	C₂×C₄×C₁₇	1	4	yes	—
425	#97	—	4	1	no	—
426	#97	—	4	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	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	#95	—	2	1	no	—
436	C₁₇	#22083	1	1	yes	characteristic, direct product factor, Sylow
437	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	C₂²×C₄×C₁₇	1	2	yes	—
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	1	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	4	1	no	—
458	C₂²×C₄	—	4	1	no	—
459	C₂²×C₄	—	4	1	no	—
460	C₂²×C₄	—	4	1	no	—
461	C₂²×C₄	—	4	1	no	—
462	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
463	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
468	C₂²×C₄	#41×C₁₇	1	2	yes	—
469	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
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	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
481	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	4	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	4	2	no	—
495	C₄⋊C₄	—	4	2	no	—
496	C₄⋊C₄	—	4	2	no	—
497	C₄⋊C₄	—	4	2	no	—
498	C₄⋊C₄	—	4	2	no	—
499	C₄⋊C₄	—	4	2	no	—
500	C₄⋊C₄	C₂²×C₄×C₁₇	1	2	yes	—
501	C₄⋊C₄	C₂²×C₄×C₁₇	1	2	yes	—
502	C₄⋊C₄	C₂²×C₄×C₁₇	1	2	yes	—
503	C₂²⋊C₄	—	2	4	no	—
504	C₂²⋊C₄	—	2	4	no	—
505	C₂²⋊C₄	—	4	2	no	—
506	C₂²⋊C₄	—	4	2	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	4	no	—
512	C₄²	—	4	1	no	—
513	C₄²	—	4	1	no	—
514	C₄²	—	4	2	no	—
515	C₄²	—	4	2	no	—
516	C₄²	—	4	2	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	—	2	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	—	2	1	no	—
523	C₂³	C₄×D₄×C₁₇	1	2	yes	—
524	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
525	Q₈	—	2	2	no	—
526	Q₈	—	2	2	no	—
527	Q₈	—	4	1	no	—
528	Q₈	—	4	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	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	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	1	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	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	4	4	no	—
551	C₂×C₄	—	4	4	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	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	C₄×D₄×C₁₇	1	2	yes	—
573	C₂×C₄	C₁₇×#137	1	2	yes	—
574	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
575	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
576	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
577	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
578	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
579	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
580	C₈	—	2	2	no	—
581	C₈	—	2	2	no	—
582	C₈	—	4	1	no	—
583	C₈	—	4	1	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	C₂×C₄×D₄×C₁₇	1	1	yes	characteristic
592	C₂²	C₁₇×#534	1	1	yes	characteristic
593	C₂²	C₁₇×#536	1	1	yes	characteristic
594	C₂²	C₂×C₁₇×#137	1	1	yes	characteristic
595	C₂²	C₁₇×#575	1	1	yes	characteristic
596	C₂²	C₁₇×#575	1	1	yes	characteristic
597	C₂²	C₁₇×#575	1	1	yes	characteristic
598	C₄	—	2	2	no	—
599	C₄	—	2	2	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	2	no	—
605	C₄	—	4	2	no	—
606	C₄	—	4	2	no	—
607	C₄	—	8	1	no	—
608	C₄	—	8	1	no	—
609	C₄	—	8	1	no	—
610	C₄	—	8	1	no	—
611	C₄	C₁₇×#520	1	1	yes	characteristic
612	C₄	C₁₇×#520	1	1	yes	characteristic
613	C₄	C₁₇×#539	1	1	yes	characteristic
614	C₄	C₁₇×#539	1	1	yes	characteristic
615	C₂	—	4	2	no	—
616	C₂	C₁₇×#2322	1	1	yes	characteristic
617	C₂	C₁₇×#2943	1	1	yes	characteristic
618	C₂	C₄×C₁₇×#137	1	1	yes	characteristic
619	C₂	C₁₇×#3196	1	1	yes	characteristic
620	C₂	C₁₇×#3197	1	1	yes	characteristic
621	C₂	C₁₇×#3237	1	1	yes	characteristic
622	C₂	C₁₇×#3240	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 ◁ C₂²×C₄²×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₇×#1944	C₂	semidirect
5. C₁₇×#1943	C₂	semidirect
6. C₁₇×#1935	C₂	semidirect
7. C₁₇×#1935	C₂	semidirect
8. C₁₇×#1921	C₂	semidirect
9. C₁₇×#1919	C₂	semidirect
11. C₁₇×#1865	C₂	semidirect
12. C₁₇×#1863	C₂	semidirect
21. C₁₇×#485	C₄	semidirect
105. C₁₇×#107	C₂×C₄	semidirect
107. C₁₇×#106	C₂×C₄	semidirect
110. C₁₇×#103	C₂×C₄	semidirect
111. C₁₇×#103	C₂×C₄	semidirect
205. #22083	C₁₇	direct (N × H)
276. #1944	C₂×C₁₇	semidirect
277. #1943	C₂×C₁₇	semidirect
278. #1935	C₂×C₁₇	semidirect
279. #1935	C₂×C₁₇	semidirect
280. #1921	C₂×C₁₇	semidirect
281. #1919	C₂×C₁₇	semidirect
283. #1865	C₂×C₁₇	semidirect
284. #1863	C₂×C₁₇	semidirect
324. #485	C₄×C₁₇	semidirect
416. #107	C₂×C₄×C₁₇	semidirect
418. #106	C₂×C₄×C₁₇	semidirect
421. #103	C₂×C₄×C₁₇	semidirect
422. #103	C₂×C₄×C₁₇	semidirect
436. C₁₇	#22083	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
C₄×C₁₇×C₂²⋊Q₈	2
C₁₇×#2296	2
C₁₇×#1944	2
C₁₇×#1943	2
C₁₇×#1935	2
C₁₇×#1921	2
C₁₇×#1919	2
C₁₇×#1873	2
C₁₇×#1865	2
C₁₇×#1863	2
C₁₇×#1854	2
C₁₇×#1825	2
C₁₇×#1749	2
#22083	17

Subgroups — C17×#22083 #16879827

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#22083 #16879827