Subgroups — C₁₇×#22163 #16879907

Order 4352.

816 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#464	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#2326	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#2320	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#1983	C₂	1	1	yes	maximal, characteristic
5	C₁₇×#1973	C₂	1	1	yes	maximal, characteristic
6	C₁₇×#1969	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1947	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1935	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1934	C₂	1	1	yes	maximal, characteristic
10	C₁₇×#1878	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1877	C₂	1	1	yes	maximal, characteristic
12	C₁₇×#1863	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1862	C₂	1	1	yes	maximal, characteristic
14	C₁₇×#1803	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
18	C₂×C₁₇×#124	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
22	C₁₇×#464	C₄	1	8	yes	complemented
23	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₇×C₄⋊C₈	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×#103	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×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
37	C₁₇×#391	C₂²	1	1	yes	characteristic
38	C₁₇×#391	C₂²	1	1	yes	characteristic
39	C₁₇×#391	C₂²	1	1	yes	characteristic
40	C₁₇×#390	C₂²	1	1	yes	characteristic
41	C₁₇×#389	C₂²	1	1	yes	characteristic
42	C₁₇×#389	C₂²	1	1	yes	characteristic
43	C₁₇×#388	—	2	1	no	—
44	C₁₇×#388	—	2	1	no	—
45	C₁₇×#387	—	2	1	no	—
46	C₁₇×#387	—	2	1	no	—
47	C₁₇×#385	—	2	1	no	—
48	C₁₇×#385	—	2	1	no	—
49	C₁₇×#384	C₂²	1	1	yes	characteristic
50	C₁₇×#383	—	2	1	no	—
51	C₁₇×#382	—	2	1	no	—
52	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
53	C₁₇×#376	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	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₇	—	2	1	no	—
64	C₂×Q₁₆×C₁₇	—	4	1	no	—
65	C₂×Q₁₆×C₁₇	—	4	1	no	—
66	C₂×Q₁₆×C₁₇	C₂×C₄	1	4	yes	complemented
67	C₂×SD₁₆×C₁₇	—	4	1	no	—
68	C₂×SD₁₆×C₁₇	—	4	1	no	—
69	C₂×SD₁₆×C₁₇	C₂×C₄	1	4	yes	—
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	C₁₇×#124	—	2	2	no	—
75	C₁₇×#124	C₂×C₄	1	4	yes	—
76	C₄×Q₈×C₁₇	—	2	2	no	—
77	C₄×Q₈×C₁₇	—	4	1	no	—
78	C₄×Q₈×C₁₇	—	4	1	no	—
79	C₄×Q₈×C₁₇	C₂×C₄	1	4	yes	complemented
80	C₄×D₄×C₁₇	—	4	1	no	—
81	C₄×D₄×C₁₇	—	4	1	no	—
82	C₂×C₄⋊C₄×C₁₇	—	2	1	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	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
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×C₂²⋊C₄×C₁₇	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
97	C₂×C₂²⋊C₄×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	C₂³	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	—	4	1	no	—
106	C₁₇×C₄⋊C₈	—	2	2	no	—
107	C₁₇×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
108	C₁₇×#103	—	4	1	no	—
109	C₁₇×#103	—	4	1	no	—
110	C₁₇×#103	—	4	1	no	—
111	C₁₇×#103	—	4	1	no	—
112	C₁₇×#103	C₂×C₄	1	4	yes	complemented
113	C₁₇×#102	—	4	1	no	—
114	C₁₇×#102	—	4	1	no	—
115	C₁₇×#102	C₂×C₄	1	4	yes	—
116	C₁₇×#97	—	4	1	no	—
117	C₄×C₈×C₁₇	—	4	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	C₁₇×#95	—	2	1	no	—
126	C₁₇×#95	—	2	1	no	—
127	C₁₇×#95	D₄	1	1	yes	characteristic
128	C₁₇×#95	D₄	1	1	yes	characteristic
129	C₁₇×#95	D₄	1	1	yes	characteristic
130	C₁₇×#95	D₄	1	1	yes	characteristic
131	C₂⁴×C₁₇	—	2	1	no	—
132	C₂×Q₈×C₁₇	—	2	1	no	—
133	C₂×Q₈×C₁₇	—	2	1	no	—
134	C₂×Q₈×C₁₇	—	2	1	no	—
135	C₂×Q₈×C₁₇	—	2	1	no	—
136	C₂×Q₈×C₁₇	—	2	1	no	—
137	C₂×Q₈×C₁₇	—	2	1	no	—
138	C₂×Q₈×C₁₇	—	2	1	no	—
139	C₂×Q₈×C₁₇	—	2	1	no	—
140	C₂×Q₈×C₁₇	—	2	1	no	—
141	C₂×Q₈×C₁₇	—	2	1	no	—
142	C₂×Q₈×C₁₇	C₂²×C₄	1	2	yes	—
143	C₂×Q₈×C₁₇	C₂²×C₄	1	2	yes	—
144	C₂×D₄×C₁₇	—	2	1	no	—
145	C₂×D₄×C₁₇	—	2	1	no	—
146	C₂×D₄×C₁₇	—	2	1	no	—
147	C₂×D₄×C₁₇	—	2	1	no	—
148	C₂×D₄×C₁₇	—	2	1	no	—
149	C₂×D₄×C₁₇	C₂²×C₄	1	2	yes	—
150	C₂²×C₄×C₁₇	—	2	1	no	—
151	C₂²×C₄×C₁₇	—	2	1	no	—
152	C₂²×C₄×C₁₇	—	2	1	no	—
153	C₂²×C₄×C₁₇	—	2	1	no	—
154	C₂²×C₄×C₁₇	—	2	1	no	—
155	C₂²×C₄×C₁₇	—	2	1	no	—
156	C₂²×C₄×C₁₇	—	2	1	no	—
157	C₂²×C₄×C₁₇	—	4	2	no	—
158	C₂²×C₄×C₁₇	—	8	1	no	—
159	C₂²×C₄×C₁₇	—	8	1	no	—
160	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
167	Q₁₆×C₁₇	—	4	4	no	—
168	SD₁₆×C₁₇	—	4	4	no	—
169	C₂×C₈×C₁₇	—	2	1	no	—
170	C₂×C₈×C₁₇	—	2	1	no	—
171	C₂×C₈×C₁₇	—	2	1	no	—
172	C₂×C₈×C₁₇	—	2	1	no	—
173	C₂×C₈×C₁₇	—	2	1	no	—
174	C₂×C₈×C₁₇	—	2	1	no	—
175	C₂×C₈×C₁₇	—	2	1	no	—
176	C₂×C₈×C₁₇	—	2	1	no	—
177	C₂×C₈×C₁₇	—	2	1	no	—
178	C₂×C₈×C₁₇	—	2	1	no	—
179	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
180	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
181	C₄⋊C₄×C₁₇	—	2	4	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	—	2	1	no	—
191	C₄⋊C₄×C₁₇	—	4	2	no	—
192	C₄⋊C₄×C₁₇	—	8	1	no	—
193	C₄⋊C₄×C₁₇	—	8	1	no	—
194	C₄⋊C₄×C₁₇	—	8	1	no	—
195	C₄⋊C₄×C₁₇	—	8	1	no	—
196	C₄⋊C₄×C₁₇	C₂²×C₄	1	2	yes	—
197	C₂²⋊C₄×C₁₇	—	2	4	no	—
198	C₂²⋊C₄×C₁₇	—	2	4	no	—
199	C₂²⋊C₄×C₁₇	—	4	2	no	—
200	C₂²⋊C₄×C₁₇	—	8	1	no	—
201	C₂²⋊C₄×C₁₇	—	8	1	no	—
202	C₄²×C₁₇	—	2	4	no	—
203	C₄²×C₁₇	—	2	1	no	—
204	C₄²×C₁₇	—	2	1	no	—
205	C₄²×C₁₇	—	2	1	no	—
206	C₄²×C₁₇	—	2	1	no	—
207	C₄²×C₁₇	—	4	2	no	—
208	C₄²×C₁₇	—	8	1	no	—
209	C₄²×C₁₇	C₂²×C₄	1	2	yes	—
210	C₄²×C₁₇	#41	1	2	yes	—
211	#22163	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂³×C₁₇	—	2	2	no	—
213	C₂³×C₁₇	—	4	1	no	—
214	C₂³×C₁₇	—	4	1	no	—
215	C₂³×C₁₇	—	4	1	no	—
216	C₂³×C₁₇	—	4	1	no	—
217	C₂³×C₁₇	—	4	1	no	—
218	C₂³×C₁₇	—	4	1	no	—
219	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
220	Q₈×C₁₇	—	2	2	no	—
221	Q₈×C₁₇	—	2	2	no	—
222	Q₈×C₁₇	—	2	2	no	—
223	Q₈×C₁₇	—	2	2	no	—
224	Q₈×C₁₇	—	4	1	no	—
225	Q₈×C₁₇	—	4	1	no	—
226	Q₈×C₁₇	—	4	1	no	—
227	Q₈×C₁₇	—	4	1	no	—
228	D₄×C₁₇	—	2	2	no	—
229	D₄×C₁₇	—	2	2	no	—
230	D₄×C₁₇	—	4	1	no	—
231	D₄×C₁₇	—	4	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	2	no	—
237	C₂×C₄×C₁₇	—	2	2	no	—
238	C₂×C₄×C₁₇	—	2	2	no	—
239	C₂×C₄×C₁₇	—	2	1	no	—
240	C₂×C₄×C₁₇	—	2	1	no	—
241	C₂×C₄×C₁₇	—	2	1	no	—
242	C₂×C₄×C₁₇	—	2	1	no	—
243	C₂×C₄×C₁₇	—	2	1	no	—
244	C₂×C₄×C₁₇	—	2	1	no	—
245	C₂×C₄×C₁₇	—	2	1	no	—
246	C₂×C₄×C₁₇	—	2	1	no	—
247	C₂×C₄×C₁₇	—	2	1	no	—
248	C₂×C₄×C₁₇	—	2	1	no	—
249	C₂×C₄×C₁₇	—	2	1	no	—
250	C₂×C₄×C₁₇	—	2	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	C₄×D₄	1	2	yes	—
271	C₂×C₄×C₁₇	C₄×D₄	1	2	yes	—
272	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
273	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
274	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
275	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
276	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
277	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
278	C₈×C₁₇	—	2	2	no	—
279	C₈×C₁₇	—	2	2	no	—
280	C₈×C₁₇	—	4	1	no	—
281	C₈×C₁₇	—	4	1	no	—
282	C₂×#464	C₂×C₁₇	1	1	yes	characteristic
283	#2326	C₂×C₁₇	1	1	yes	characteristic
284	#2320	C₂×C₁₇	1	1	yes	characteristic, complemented
285	#1983	C₂×C₁₇	1	1	yes	characteristic
286	#1973	C₂×C₁₇	1	1	yes	characteristic
287	#1969	C₂×C₁₇	1	1	yes	characteristic, complemented
288	#1947	C₂×C₁₇	1	1	yes	characteristic, complemented
289	#1935	C₂×C₁₇	1	1	yes	characteristic, complemented
290	#1934	C₂×C₁₇	1	1	yes	characteristic
291	#1878	C₂×C₁₇	1	1	yes	characteristic, complemented
292	#1877	C₂×C₁₇	1	1	yes	characteristic
293	#1863	C₂×C₁₇	1	1	yes	characteristic, complemented
294	#1862	C₂×C₁₇	1	1	yes	characteristic
295	#1803	C₂×C₁₇	1	1	yes	characteristic, complemented
296	#1768	C₂×C₁₇	1	1	yes	characteristic, complemented
297	C₂²×C₁₇	—	4	2	no	—
298	C₂²×C₁₇	—	4	2	no	—
299	C₂²×C₁₇	—	4	2	no	—
300	C₂²×C₁₇	—	8	1	no	—
301	C₂²×C₁₇	—	8	1	no	—
302	C₂²×C₁₇	—	8	1	no	—
303	C₂²×C₁₇	—	8	1	no	—
304	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
305	C₂²×C₁₇	#535	1	1	yes	characteristic
306	C₂²×C₁₇	#537	1	1	yes	characteristic
307	C₂²×C₁₇	#576	1	1	yes	characteristic
308	C₂²×C₁₇	#577	1	1	yes	characteristic
309	C₂²×C₁₇	#578	1	1	yes	characteristic
310	C₂²×C₁₇	#578	1	1	yes	characteristic
311	C₄×C₁₇	—	2	2	no	—
312	C₄×C₁₇	—	2	2	no	—
313	C₄×C₁₇	—	4	2	no	—
314	C₄×C₁₇	—	4	2	no	—
315	C₄×C₁₇	—	4	2	no	—
316	C₄×C₁₇	—	4	1	no	—
317	C₄×C₁₇	—	4	1	no	—
318	C₄×C₁₇	—	4	1	no	—
319	C₄×C₁₇	—	4	1	no	—
320	C₄×C₁₇	—	8	1	no	—
321	C₄×C₁₇	—	8	1	no	—
322	C₄×C₁₇	—	8	1	no	—
323	C₄×C₁₇	—	8	1	no	—
324	C₄×C₁₇	#518	1	1	yes	characteristic
325	C₄×C₁₇	#520	1	1	yes	characteristic
326	C₄×C₁₇	#540	1	1	yes	characteristic
327	C₄×C₁₇	#542	1	1	yes	characteristic
328	C₂²×Q₁₆	C₂²×C₁₇	1	1	yes	characteristic
329	C₂²×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
330	C₂×#124	C₂²×C₁₇	1	1	yes	characteristic
331	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
332	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
333	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
334	#464	C₄×C₁₇	1	8	yes	complemented
335	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
336	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
337	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
338	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
339	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
340	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
341	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
342	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
343	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
344	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
345	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
346	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
347	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
348	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
349	#391	C₂²×C₁₇	1	1	yes	characteristic
350	#391	C₂²×C₁₇	1	1	yes	characteristic
351	#391	C₂²×C₁₇	1	1	yes	characteristic
352	#390	C₂²×C₁₇	1	1	yes	characteristic
353	#389	C₂²×C₁₇	1	1	yes	characteristic
354	#389	C₂²×C₁₇	1	1	yes	characteristic
355	#388	—	2	1	no	—
356	#388	—	2	1	no	—
357	#387	—	2	1	no	—
358	#387	—	2	1	no	—
359	#385	—	2	1	no	—
360	#385	—	2	1	no	—
361	#384	C₂²×C₁₇	1	1	yes	characteristic
362	#383	—	2	1	no	—
363	#382	—	2	1	no	—
364	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
365	#376	C₂²×C₁₇	1	1	yes	characteristic
366	#340	C₂²×C₁₇	1	1	yes	characteristic
367	#340	C₂²×C₁₇	1	1	yes	characteristic
368	#340	C₂²×C₁₇	1	1	yes	characteristic
369	#340	C₂²×C₁₇	1	1	yes	characteristic
370	#336	C₂²×C₁₇	1	1	yes	characteristic
371	#336	C₂²×C₁₇	1	1	yes	characteristic
372	C₂×C₁₇	—	8	2	no	—
373	C₂×C₁₇	#2324	1	1	yes	characteristic
374	C₂×C₁₇	#2947	1	1	yes	characteristic
375	C₂×C₁₇	#2951	1	1	yes	characteristic
376	C₂×C₁₇	#3223	1	1	yes	characteristic
377	C₂×C₁₇	#3224	1	1	yes	characteristic
378	C₂×C₁₇	#3258	1	1	yes	characteristic
379	C₂×C₁₇	#3262	1	1	yes	characteristic
380	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
381	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
382	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
383	C₂³×C₄	—	2	1	no	—
384	C₂×Q₁₆	—	4	1	no	—
385	C₂×Q₁₆	—	4	1	no	—
386	C₂×Q₁₆	C₂×C₄×C₁₇	1	4	yes	complemented
387	C₂×SD₁₆	—	4	1	no	—
388	C₂×SD₁₆	—	4	1	no	—
389	C₂×SD₁₆	C₂×C₄×C₁₇	1	4	yes	—
390	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
391	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
392	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
393	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
394	#124	—	2	2	no	—
395	#124	C₂×C₄×C₁₇	1	4	yes	—
396	C₄×Q₈	—	2	2	no	—
397	C₄×Q₈	—	4	1	no	—
398	C₄×Q₈	—	4	1	no	—
399	C₄×Q₈	C₂×C₄×C₁₇	1	4	yes	complemented
400	C₄×D₄	—	4	1	no	—
401	C₄×D₄	—	4	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	—	2	1	no	—
420	C₂×C₄²	—	2	1	no	—
421	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
424	#107	—	4	1	no	—
425	#107	—	4	1	no	—
426	C₄⋊C₈	—	2	2	no	—
427	C₄⋊C₈	C₂×C₄×C₁₇	1	4	yes	complemented
428	#103	—	4	1	no	—
429	#103	—	4	1	no	—
430	#103	—	4	1	no	—
431	#103	—	4	1	no	—
432	#103	C₂×C₄×C₁₇	1	4	yes	complemented
433	#102	—	4	1	no	—
434	#102	—	4	1	no	—
435	#102	C₂×C₄×C₁₇	1	4	yes	—
436	#97	—	4	1	no	—
437	C₄×C₈	—	4	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	#95	D₄×C₁₇	1	1	yes	characteristic
448	#95	D₄×C₁₇	1	1	yes	characteristic
449	#95	D₄×C₁₇	1	1	yes	characteristic
450	#95	D₄×C₁₇	1	1	yes	characteristic
451	C₁₇	#22163	1	1	yes	characteristic, direct product factor, Sylow
452	C₂⁴	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	C₂²×C₄×C₁₇	1	2	yes	—
464	C₂×Q₈	C₂²×C₄×C₁₇	1	2	yes	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	C₂²×C₄×C₁₇	1	2	yes	—
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	—	4	2	no	—
479	C₂²×C₄	—	8	1	no	—
480	C₂²×C₄	—	8	1	no	—
481	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
487	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
488	Q₁₆	—	4	4	no	—
489	SD₁₆	—	4	4	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	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	C₂²×C₄×C₁₇	1	2	yes	—
501	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	4	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
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	—	4	2	no	—
513	C₄⋊C₄	—	8	1	no	—
514	C₄⋊C₄	—	8	1	no	—
515	C₄⋊C₄	—	8	1	no	—
516	C₄⋊C₄	—	8	1	no	—
517	C₄⋊C₄	C₂²×C₄×C₁₇	1	2	yes	—
518	C₂²⋊C₄	—	2	4	no	—
519	C₂²⋊C₄	—	2	4	no	—
520	C₂²⋊C₄	—	4	2	no	—
521	C₂²⋊C₄	—	8	1	no	—
522	C₂²⋊C₄	—	8	1	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	2	4	no	—
528	C₄²	—	4	2	no	—
529	C₄²	—	8	1	no	—
530	C₄²	C₂²×C₄×C₁₇	1	2	yes	—
531	C₄²	#41×C₁₇	1	2	yes	—
532	C₂³	—	2	2	no	—
533	C₂³	—	4	1	no	—
534	C₂³	—	4	1	no	—
535	C₂³	—	4	1	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	4	1	no	—
538	C₂³	—	4	1	no	—
539	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
540	Q₈	—	2	2	no	—
541	Q₈	—	2	2	no	—
542	Q₈	—	2	2	no	—
543	Q₈	—	2	2	no	—
544	Q₈	—	4	1	no	—
545	Q₈	—	4	1	no	—
546	Q₈	—	4	1	no	—
547	Q₈	—	4	1	no	—
548	D₄	—	2	2	no	—
549	D₄	—	2	2	no	—
550	D₄	—	4	1	no	—
551	D₄	—	4	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	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	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	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	—	8	4	no	—
590	C₂×C₄	C₄×D₄×C₁₇	1	2	yes	—
591	C₂×C₄	C₄×D₄×C₁₇	1	2	yes	—
592	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
593	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
594	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
595	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
596	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
597	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
598	C₈	—	2	2	no	—
599	C₈	—	2	2	no	—
600	C₈	—	4	1	no	—
601	C₈	—	4	1	no	—
602	C₂²	—	4	2	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	8	1	no	—
606	C₂²	—	8	1	no	—
607	C₂²	—	8	1	no	—
608	C₂²	—	8	1	no	—
609	C₂²	C₂×C₄×D₄×C₁₇	1	1	yes	characteristic
610	C₂²	C₁₇×#535	1	1	yes	characteristic
611	C₂²	C₁₇×#537	1	1	yes	characteristic
612	C₂²	C₁₇×#576	1	1	yes	characteristic
613	C₂²	C₁₇×#577	1	1	yes	characteristic
614	C₂²	C₁₇×#578	1	1	yes	characteristic
615	C₂²	C₁₇×#578	1	1	yes	characteristic
616	C₄	—	2	2	no	—
617	C₄	—	2	2	no	—
618	C₄	—	4	2	no	—
619	C₄	—	4	1	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	2	no	—
624	C₄	—	4	2	no	—
625	C₄	—	8	1	no	—
626	C₄	—	8	1	no	—
627	C₄	—	8	1	no	—
628	C₄	—	8	1	no	—
629	C₄	C₁₇×#518	1	1	yes	characteristic
630	C₄	C₁₇×#520	1	1	yes	characteristic
631	C₄	C₁₇×#540	1	1	yes	characteristic
632	C₄	C₁₇×#542	1	1	yes	characteristic
633	C₂	—	8	2	no	—
634	C₂	C₁₇×#2324	1	1	yes	characteristic
635	C₂	C₁₇×#2947	1	1	yes	characteristic
636	C₂	C₁₇×#2951	1	1	yes	characteristic
637	C₂	C₁₇×#3223	1	1	yes	characteristic
638	C₂	C₁₇×#3224	1	1	yes	characteristic
639	C₂	C₁₇×#3258	1	1	yes	characteristic
640	C₂	C₁₇×#3262	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	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₁₇×#376 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₇×#2320	C₂	semidirect
6. C₁₇×#1969	C₂	semidirect
7. C₁₇×#1947	C₂	semidirect
8. C₁₇×#1935	C₂	semidirect
10. C₁₇×#1878	C₂	semidirect
12. C₁₇×#1863	C₂	semidirect
14. C₁₇×#1803	C₂	semidirect
15. C₁₇×#1768	C₂	semidirect
22. C₁₇×#464	C₄	semidirect
66. C₂×Q₁₆×C₁₇	C₂×C₄	semidirect
79. C₄×Q₈×C₁₇	C₂×C₄	semidirect
107. C₁₇×C₄⋊C₈	C₂×C₄	semidirect
112. C₁₇×#103	C₂×C₄	semidirect
211. #22163	C₁₇	direct (N × H)
284. #2320	C₂×C₁₇	semidirect
287. #1969	C₂×C₁₇	semidirect
288. #1947	C₂×C₁₇	semidirect
289. #1935	C₂×C₁₇	semidirect
291. #1878	C₂×C₁₇	semidirect
293. #1863	C₂×C₁₇	semidirect
295. #1803	C₂×C₁₇	semidirect
296. #1768	C₂×C₁₇	semidirect
334. #464	C₄×C₁₇	semidirect
386. C₂×Q₁₆	C₂×C₄×C₁₇	semidirect
399. C₄×Q₈	C₂×C₄×C₁₇	semidirect
427. C₄⋊C₈	C₂×C₄×C₁₇	semidirect
432. #103	C₂×C₄×C₁₇	semidirect
451. C₁₇	#22163	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×#464	2
C₁₇×#2326	2
C₁₇×#2320	2
C₁₇×#1983	2
C₁₇×#1973	2
C₁₇×#1969	2
C₁₇×#1947	2
C₁₇×#1935	2
C₁₇×#1934	2
C₁₇×#1878	2
C₁₇×#1877	2
C₁₇×#1863	2
C₁₇×#1862	2
C₁₇×#1803	2
C₁₇×#1768	2
#22163	17

Subgroups — C17×#22163 #16879907

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#22163 #16879907