Subgroups — C₁₇×#60865 #16918609

Order 4352.

1756 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₇×#533	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#3237	C₂	1	4	yes	maximal, complemented
4	C₁₇×#3236	C₂	1	4	yes	maximal, complemented
5	C₁₇×#3231	C₂	1	4	yes	maximal, complemented
6	C₁₇×#3230	C₂	1	2	yes	maximal, complemented
7	C₁₇×#3229	C₂	1	2	yes	maximal, complemented
8	C₁₇×#3165	C₂	1	2	yes	maximal, complemented
9	C₁₇×#3139	C₂	1	2	yes	maximal, complemented
10	C₁₇×#3095	C₂	1	4	yes	maximal
11	C₁₇×#3078	C₂	1	4	yes	maximal, complemented
12	C₁₇×#2920	C₂	1	1	yes	maximal, characteristic
13	C₁₇×#533	—	2	1	no	—
14	C₁₇×#533	—	2	1	no	—
15	C₁₇×#533	—	2	1	no	—
16	C₁₇×#533	—	2	1	no	—
17	C₁₇×#533	—	2	1	no	—
18	C₁₇×#533	—	2	1	no	—
19	C₁₇×#533	—	2	1	no	—
20	C₁₇×#533	—	2	1	no	—
21	C₁₇×#533	C₂²	1	2	yes	—
22	C₁₇×#533	C₂²	1	2	yes	—
23	C₁₇×#533	C₂²	1	2	yes	—
24	C₁₇×#533	C₂²	1	2	yes	—
25	C₁₇×#533	C₂²	1	2	yes	—
26	C₁₇×#533	C₂²	1	2	yes	—
27	C₁₇×#533	C₂²	1	2	yes	—
28	C₁₇×#533	C₂²	1	2	yes	—
29	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₇×#125	—	2	1	no	—
34	C₂×C₁₇×#125	C₂²	1	2	yes	—
35	C₂×C₁₇×C₂²⋊Q₈	—	2	1	no	—
36	C₂×C₁₇×C₂²⋊Q₈	—	2	1	no	—
37	C₂×C₁₇×C₂²⋊Q₈	—	2	1	no	—
38	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	2	yes	—
39	C₂×C₄×Q₈×C₁₇	—	2	1	no	—
40	C₂×C₄×Q₈×C₁₇	—	2	1	no	—
41	C₂×C₄×Q₈×C₁₇	—	2	1	no	—
42	C₂×C₄×Q₈×C₁₇	C₂²	1	2	yes	—
43	C₂×C₁₇×#117	—	2	1	no	—
44	C₂×C₁₇×#117	C₂²	1	2	yes	—
45	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
46	C₁₇×#501	C₂²	1	8	yes	complemented
47	C₁₇×#500	C₂²	1	4	yes	complemented
48	C₁₇×#498	C₂²	1	4	yes	complemented
49	C₁₇×#491	C₂²	1	8	yes	complemented
50	C₁₇×#487	C₂²	1	4	yes	complemented
51	C₁₇×#487	C₂²	1	4	yes	complemented
52	C₁₇×#485	C₂²	1	16	yes	—
53	C₁₇×#484	C₂²	1	8	yes	—
54	C₁₇×#483	C₂²	1	8	yes	—
55	C₁₇×#479	C₂²	1	16	yes	complemented
56	C₁₇×#477	C₂²	1	8	yes	complemented
57	C₁₇×#475	C₂²	1	8	yes	complemented
58	C₁₇×#432	C₂²	1	2	yes	—
59	C₁₇×#432	C₂²	1	2	yes	—
60	C₁₇×#431	C₂²	1	2	yes	—
61	C₁₇×#431	C₂²	1	2	yes	—
62	C₁₇×#428	C₂²	1	8	yes	—
63	C₁₇×#423	C₂²	1	2	yes	—
64	C₁₇×#419	C₂²	1	8	yes	—
65	C₁₇×#407	C₂²	1	2	yes	—
66	C₄×M₁₆×C₁₇	C₂²	1	2	yes	—
67	C₂²×Q₈×C₁₇	—	2	1	no	—
68	C₂²×Q₈×C₁₇	—	2	1	no	—
69	C₂²×Q₈×C₁₇	—	2	1	no	—
70	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
71	C₂³×C₄×C₁₇	D₄	1	1	yes	characteristic
72	C₂³×C₄×C₁₇	D₄	1	1	yes	characteristic
73	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
74	C₂×M₁₆×C₁₇	C₂³	1	4	yes	—
75	C₁₇×C₄⋊Q₈	—	2	1	no	—
76	C₁₇×C₄⋊Q₈	—	2	1	no	—
77	C₁₇×C₄⋊Q₈	—	2	1	no	—
78	C₁₇×C₄⋊Q₈	—	2	1	no	—
79	C₁₇×C₄⋊Q₈	—	2	1	no	—
80	C₁₇×C₄⋊Q₈	—	2	1	no	—
81	C₁₇×C₄⋊Q₈	—	2	1	no	—
82	C₁₇×C₄⋊Q₈	—	2	1	no	—
83	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
84	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
85	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
86	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
87	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
88	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
89	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
90	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
91	C₁₇×#125	—	2	2	no	—
92	C₁₇×#125	—	2	2	no	—
93	C₁₇×#125	—	2	2	no	—
94	C₁₇×#125	—	2	2	no	—
95	C₁₇×#125	—	2	2	no	—
96	C₁₇×#125	—	2	2	no	—
97	C₁₇×#125	C₂³	1	4	yes	—
98	C₁₇×#125	C₂³	1	4	yes	—
99	C₁₇×C₂²⋊Q₈	—	2	2	no	—
100	C₁₇×C₂²⋊Q₈	—	2	2	no	—
101	C₁₇×C₂²⋊Q₈	—	2	2	no	—
102	C₁₇×C₂²⋊Q₈	—	2	2	no	—
103	C₁₇×C₂²⋊Q₈	—	2	2	no	—
104	C₁₇×C₂²⋊Q₈	—	2	2	no	—
105	C₁₇×C₂²⋊Q₈	—	2	2	no	—
106	C₁₇×C₂²⋊Q₈	—	2	2	no	—
107	C₁₇×C₂²⋊Q₈	—	2	2	no	—
108	C₁₇×C₂²⋊Q₈	—	2	2	no	—
109	C₁₇×C₂²⋊Q₈	—	2	2	no	—
110	C₁₇×C₂²⋊Q₈	—	2	2	no	—
111	C₁₇×C₂²⋊Q₈	—	2	2	no	—
112	C₁₇×C₂²⋊Q₈	—	2	2	no	—
113	C₁₇×C₂²⋊Q₈	C₂³	1	4	yes	—
114	C₁₇×C₂²⋊Q₈	C₂³	1	4	yes	—
115	C₄×Q₈×C₁₇	—	2	2	no	—
116	C₄×Q₈×C₁₇	—	2	2	no	—
117	C₄×Q₈×C₁₇	—	2	2	no	—
118	C₄×Q₈×C₁₇	—	2	2	no	—
119	C₄×Q₈×C₁₇	—	2	2	no	—
120	C₄×Q₈×C₁₇	—	2	2	no	—
121	C₄×Q₈×C₁₇	—	2	2	no	—
122	C₄×Q₈×C₁₇	—	2	2	no	—
123	C₄×Q₈×C₁₇	—	2	2	no	—
124	C₄×Q₈×C₁₇	—	2	2	no	—
125	C₄×Q₈×C₁₇	—	2	2	no	—
126	C₄×Q₈×C₁₇	—	2	2	no	—
127	C₄×Q₈×C₁₇	—	2	2	no	—
128	C₄×Q₈×C₁₇	—	2	2	no	—
129	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
130	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
131	C₁₇×#117	—	2	2	no	—
132	C₁₇×#117	—	2	2	no	—
133	C₁₇×#117	—	2	2	no	—
134	C₁₇×#117	—	2	2	no	—
135	C₁₇×#117	—	2	2	no	—
136	C₁₇×#117	—	2	2	no	—
137	C₁₇×#117	C₂³	1	4	yes	—
138	C₁₇×#117	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
140	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
141	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
142	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
143	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
144	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
145	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
146	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
147	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
148	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
152	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
153	C₂×C₄²×C₁₇	—	2	2	no	—
154	C₂×C₄²×C₁₇	—	2	2	no	—
155	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
156	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
157	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
158	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
159	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
160	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
161	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
167	C₁₇×#107	C₂³	1	16	yes	—
168	C₁₇×#106	C₂³	1	16	yes	—
169	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
170	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
171	C₁₇×#103	C₂³	1	16	yes	—
172	C₁₇×#103	C₂³	1	16	yes	—
173	C₁₇×C₂²⋊C₈	C₂³	1	4	yes	—
174	C₁₇×C₂²⋊C₈	C₂³	1	4	yes	—
175	C₁₇×#97	C₂³	1	4	yes	—
176	C₄×C₈×C₁₇	C₂³	1	4	yes	—
177	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
178	C₂×Q₈×C₁₇	—	2	2	no	—
179	C₂×Q₈×C₁₇	—	2	2	no	—
180	C₂×Q₈×C₁₇	—	2	2	no	—
181	C₂×Q₈×C₁₇	—	2	2	no	—
182	C₂×Q₈×C₁₇	—	2	2	no	—
183	C₂×Q₈×C₁₇	—	2	2	no	—
184	C₂×Q₈×C₁₇	—	2	2	no	—
185	C₂×Q₈×C₁₇	—	2	8	no	—
186	C₂×Q₈×C₁₇	—	4	4	no	—
187	C₂×Q₈×C₁₇	—	4	4	no	—
188	C₂×Q₈×C₁₇	—	4	4	no	—
189	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₁₇	—	2	4	no	—
191	C₂²×C₄×C₁₇	—	2	4	no	—
192	C₂²×C₄×C₁₇	—	2	2	no	—
193	C₂²×C₄×C₁₇	—	2	2	no	—
194	C₂²×C₄×C₁₇	—	2	2	no	—
195	C₂²×C₄×C₁₇	—	2	2	no	—
196	C₂²×C₄×C₁₇	—	4	2	no	—
197	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
215	M₁₆×C₁₇	—	2	8	no	—
216	C₂×C₈×C₁₇	C₂⁴	1	8	yes	—
217	C₄⋊C₄×C₁₇	—	2	4	no	—
218	C₄⋊C₄×C₁₇	—	2	4	no	—
219	C₄⋊C₄×C₁₇	—	2	4	no	—
220	C₄⋊C₄×C₁₇	—	2	4	no	—
221	C₄⋊C₄×C₁₇	—	2	4	no	—
222	C₄⋊C₄×C₁₇	—	2	4	no	—
223	C₄⋊C₄×C₁₇	—	2	2	no	—
224	C₄⋊C₄×C₁₇	—	2	2	no	—
225	C₄⋊C₄×C₁₇	—	2	2	no	—
226	C₄⋊C₄×C₁₇	—	2	2	no	—
227	C₄⋊C₄×C₁₇	—	2	2	no	—
228	C₄⋊C₄×C₁₇	—	2	2	no	—
229	C₄⋊C₄×C₁₇	—	2	2	no	—
230	C₄⋊C₄×C₁₇	—	2	4	no	—
231	C₄⋊C₄×C₁₇	—	2	4	no	—
232	C₄⋊C₄×C₁₇	—	2	2	no	—
233	C₄⋊C₄×C₁₇	—	2	2	no	—
234	C₄⋊C₄×C₁₇	—	2	2	no	—
235	C₄⋊C₄×C₁₇	—	2	2	no	—
236	C₄⋊C₄×C₁₇	—	2	2	no	—
237	C₄⋊C₄×C₁₇	—	2	2	no	—
238	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
239	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
240	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
241	C₂²⋊C₄×C₁₇	—	2	4	no	—
242	C₂²⋊C₄×C₁₇	—	2	4	no	—
243	C₂²⋊C₄×C₁₇	—	2	4	no	—
244	C₂²⋊C₄×C₁₇	—	2	4	no	—
245	C₄²×C₁₇	—	2	4	no	—
246	C₄²×C₁₇	—	2	4	no	—
247	C₄²×C₁₇	—	2	4	no	—
248	C₄²×C₁₇	—	2	4	no	—
249	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
250	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
251	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
252	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
253	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
254	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
255	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
256	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
257	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
258	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
259	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
260	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
261	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
262	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
263	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
264	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
265	#60865	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
266	C₂³×C₁₇	—	2	2	no	—
267	C₂³×C₁₇	—	2	2	no	—
268	C₂³×C₁₇	—	4	1	no	—
269	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
270	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
271	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
272	Q₈×C₁₇	—	2	8	no	—
273	Q₈×C₁₇	—	4	4	no	—
274	Q₈×C₁₇	—	4	4	no	—
275	Q₈×C₁₇	—	4	4	no	—
276	Q₈×C₁₇	—	4	4	no	—
277	Q₈×C₁₇	—	4	4	no	—
278	Q₈×C₁₇	—	4	4	no	—
279	Q₈×C₁₇	—	4	4	no	—
280	C₂×C₄×C₁₇	—	2	2	no	—
281	C₂×C₄×C₁₇	—	2	2	no	—
282	C₂×C₄×C₁₇	—	2	2	no	—
283	C₂×C₄×C₁₇	—	2	2	no	—
284	C₂×C₄×C₁₇	—	2	2	no	—
285	C₂×C₄×C₁₇	—	2	2	no	—
286	C₂×C₄×C₁₇	—	2	2	no	—
287	C₂×C₄×C₁₇	—	2	2	no	—
288	C₂×C₄×C₁₇	—	2	2	no	—
289	C₂×C₄×C₁₇	—	2	2	no	—
290	C₂×C₄×C₁₇	—	2	2	no	—
291	C₂×C₄×C₁₇	—	2	2	no	—
292	C₂×C₄×C₁₇	—	2	2	no	—
293	C₂×C₄×C₁₇	—	2	4	no	—
294	C₂×C₄×C₁₇	—	2	4	no	—
295	C₂×C₄×C₁₇	—	2	4	no	—
296	C₂×C₄×C₁₇	—	2	4	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	4	no	—
301	C₂×C₄×C₁₇	—	4	4	no	—
302	C₂×C₄×C₁₇	—	4	4	no	—
303	C₂×C₄×C₁₇	—	4	4	no	—
304	C₂×C₄×C₁₇	#137	1	4	yes	—
305	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
309	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
310	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₁₇	2₋¹⁺⁴	1	4	yes	—
317	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
318	C₈×C₁₇	—	2	8	no	—
319	C₂×#533	C₂×C₁₇	1	1	yes	characteristic
320	C₂×#533	C₂×C₁₇	1	1	yes	characteristic
321	#3237	C₂×C₁₇	1	4	yes	complemented
322	#3236	C₂×C₁₇	1	4	yes	complemented
323	#3231	C₂×C₁₇	1	4	yes	complemented
324	#3230	C₂×C₁₇	1	2	yes	complemented
325	#3229	C₂×C₁₇	1	2	yes	complemented
326	#3165	C₂×C₁₇	1	2	yes	complemented
327	#3139	C₂×C₁₇	1	2	yes	complemented
328	#3095	C₂×C₁₇	1	4	yes	—
329	#3078	C₂×C₁₇	1	4	yes	complemented
330	#2920	C₂×C₁₇	1	1	yes	characteristic
331	C₂²×C₁₇	—	2	1	no	—
332	C₂²×C₁₇	—	2	1	no	—
333	C₂²×C₁₇	—	2	1	no	—
334	C₂²×C₁₇	—	2	1	no	—
335	C₂²×C₁₇	—	2	1	no	—
336	C₂²×C₁₇	—	2	1	no	—
337	C₂²×C₁₇	—	2	1	no	—
338	C₂²×C₁₇	—	4	4	no	—
339	C₂²×C₁₇	#536	1	2	yes	—
340	C₂²×C₁₇	C₂×#137	1	2	yes	—
341	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
342	C₄×C₁₇	—	2	1	no	—
343	C₄×C₁₇	—	2	1	no	—
344	C₄×C₁₇	—	2	1	no	—
345	C₄×C₁₇	—	2	1	no	—
346	C₄×C₁₇	—	2	1	no	—
347	C₄×C₁₇	—	2	1	no	—
348	C₄×C₁₇	—	2	1	no	—
349	C₄×C₁₇	—	4	4	no	—
350	C₄×C₁₇	—	4	4	no	—
351	C₄×C₁₇	—	4	4	no	—
352	C₄×C₁₇	—	4	4	no	—
353	C₄×C₁₇	#536	1	2	yes	—
354	C₄×C₁₇	C₂×#137	1	2	yes	—
355	C₄×C₁₇	C₂×#137	1	2	yes	—
356	C₄×C₁₇	#575	1	2	yes	—
357	C₄×C₁₇	C₂×2₋¹⁺⁴	1	2	yes	—
358	#533	—	2	1	no	—
359	#533	—	2	1	no	—
360	#533	—	2	1	no	—
361	#533	—	2	1	no	—
362	#533	—	2	1	no	—
363	#533	—	2	1	no	—
364	#533	—	2	1	no	—
365	#533	—	2	1	no	—
366	#533	C₂²×C₁₇	1	2	yes	—
367	#533	C₂²×C₁₇	1	2	yes	—
368	#533	C₂²×C₁₇	1	2	yes	—
369	#533	C₂²×C₁₇	1	2	yes	—
370	#533	C₂²×C₁₇	1	2	yes	—
371	#533	C₂²×C₁₇	1	2	yes	—
372	#533	C₂²×C₁₇	1	2	yes	—
373	#533	C₂²×C₁₇	1	2	yes	—
374	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
375	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
376	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
377	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
378	C₂×#125	—	2	1	no	—
379	C₂×#125	C₂²×C₁₇	1	2	yes	—
380	C₂×C₂²⋊Q₈	—	2	1	no	—
381	C₂×C₂²⋊Q₈	—	2	1	no	—
382	C₂×C₂²⋊Q₈	—	2	1	no	—
383	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	2	yes	—
384	C₂×C₄×Q₈	—	2	1	no	—
385	C₂×C₄×Q₈	—	2	1	no	—
386	C₂×C₄×Q₈	—	2	1	no	—
387	C₂×C₄×Q₈	C₂²×C₁₇	1	2	yes	—
388	C₂×#117	—	2	1	no	—
389	C₂×#117	C₂²×C₁₇	1	2	yes	—
390	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic
391	#501	C₂²×C₁₇	1	8	yes	complemented
392	#500	C₂²×C₁₇	1	4	yes	complemented
393	#498	C₂²×C₁₇	1	4	yes	complemented
394	#491	C₂²×C₁₇	1	8	yes	complemented
395	#487	C₂²×C₁₇	1	4	yes	complemented
396	#487	C₂²×C₁₇	1	4	yes	complemented
397	#485	C₂²×C₁₇	1	16	yes	—
398	#484	C₂²×C₁₇	1	8	yes	—
399	#483	C₂²×C₁₇	1	8	yes	—
400	#479	C₂²×C₁₇	1	16	yes	complemented
401	#477	C₂²×C₁₇	1	8	yes	complemented
402	#475	C₂²×C₁₇	1	8	yes	complemented
403	#432	C₂²×C₁₇	1	2	yes	—
404	#432	C₂²×C₁₇	1	2	yes	—
405	#431	C₂²×C₁₇	1	2	yes	—
406	#431	C₂²×C₁₇	1	2	yes	—
407	#428	C₂²×C₁₇	1	8	yes	—
408	#423	C₂²×C₁₇	1	2	yes	—
409	#419	C₂²×C₁₇	1	8	yes	—
410	#407	C₂²×C₁₇	1	2	yes	—
411	C₄×M₁₆	C₂²×C₁₇	1	2	yes	—
412	C₂×C₁₇	—	2	2	no	—
413	C₂×C₁₇	—	2	2	no	—
414	C₂×C₁₇	—	4	1	no	—
415	C₂×C₁₇	C₂×#536	1	1	yes	characteristic
416	C₂×C₁₇	C₂²×#137	1	1	yes	characteristic
417	C₂×C₁₇	C₂×#575	1	1	yes	characteristic
418	C₂²×Q₈	—	2	1	no	—
419	C₂²×Q₈	—	2	1	no	—
420	C₂²×Q₈	—	2	1	no	—
421	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
422	C₂³×C₄	D₄×C₁₇	1	1	yes	characteristic
423	C₂³×C₄	D₄×C₁₇	1	1	yes	characteristic
424	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
425	C₂×M₁₆	C₂³×C₁₇	1	4	yes	—
426	C₄⋊Q₈	—	2	1	no	—
427	C₄⋊Q₈	—	2	1	no	—
428	C₄⋊Q₈	—	2	1	no	—
429	C₄⋊Q₈	—	2	1	no	—
430	C₄⋊Q₈	—	2	1	no	—
431	C₄⋊Q₈	—	2	1	no	—
432	C₄⋊Q₈	—	2	1	no	—
433	C₄⋊Q₈	—	2	1	no	—
434	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
435	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
436	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
437	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
438	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
439	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
440	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
441	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
442	#125	—	2	2	no	—
443	#125	—	2	2	no	—
444	#125	—	2	2	no	—
445	#125	—	2	2	no	—
446	#125	—	2	2	no	—
447	#125	—	2	2	no	—
448	#125	C₂³×C₁₇	1	4	yes	—
449	#125	C₂³×C₁₇	1	4	yes	—
450	C₂²⋊Q₈	—	2	2	no	—
451	C₂²⋊Q₈	—	2	2	no	—
452	C₂²⋊Q₈	—	2	2	no	—
453	C₂²⋊Q₈	—	2	2	no	—
454	C₂²⋊Q₈	—	2	2	no	—
455	C₂²⋊Q₈	—	2	2	no	—
456	C₂²⋊Q₈	—	2	2	no	—
457	C₂²⋊Q₈	—	2	2	no	—
458	C₂²⋊Q₈	—	2	2	no	—
459	C₂²⋊Q₈	—	2	2	no	—
460	C₂²⋊Q₈	—	2	2	no	—
461	C₂²⋊Q₈	—	2	2	no	—
462	C₂²⋊Q₈	—	2	2	no	—
463	C₂²⋊Q₈	—	2	2	no	—
464	C₂²⋊Q₈	C₂³×C₁₇	1	4	yes	—
465	C₂²⋊Q₈	C₂³×C₁₇	1	4	yes	—
466	C₄×Q₈	—	2	2	no	—
467	C₄×Q₈	—	2	2	no	—
468	C₄×Q₈	—	2	2	no	—
469	C₄×Q₈	—	2	2	no	—
470	C₄×Q₈	—	2	2	no	—
471	C₄×Q₈	—	2	2	no	—
472	C₄×Q₈	—	2	2	no	—
473	C₄×Q₈	—	2	2	no	—
474	C₄×Q₈	—	2	2	no	—
475	C₄×Q₈	—	2	2	no	—
476	C₄×Q₈	—	2	2	no	—
477	C₄×Q₈	—	2	2	no	—
478	C₄×Q₈	—	2	2	no	—
479	C₄×Q₈	—	2	2	no	—
480	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
481	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
482	#117	—	2	2	no	—
483	#117	—	2	2	no	—
484	#117	—	2	2	no	—
485	#117	—	2	2	no	—
486	#117	—	2	2	no	—
487	#117	—	2	2	no	—
488	#117	C₂³×C₁₇	1	4	yes	—
489	#117	C₂³×C₁₇	1	4	yes	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	—	2	1	no	—
492	C₂×C₄⋊C₄	—	2	2	no	—
493	C₂×C₄⋊C₄	—	2	2	no	—
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	2	no	—
498	C₂×C₄⋊C₄	—	2	2	no	—
499	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
502	C₂×C₂²⋊C₄	—	2	2	no	—
503	C₂×C₂²⋊C₄	—	2	2	no	—
504	C₂×C₄²	—	2	2	no	—
505	C₂×C₄²	—	2	2	no	—
506	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
507	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
508	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
509	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
510	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
511	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
512	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
513	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
514	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
515	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
516	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
517	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
518	#107	C₂³×C₁₇	1	16	yes	—
519	#106	C₂³×C₁₇	1	16	yes	—
520	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
521	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
522	#103	C₂³×C₁₇	1	16	yes	—
523	#103	C₂³×C₁₇	1	16	yes	—
524	C₂²⋊C₈	C₂³×C₁₇	1	4	yes	—
525	C₂²⋊C₈	C₂³×C₁₇	1	4	yes	—
526	#97	C₂³×C₁₇	1	4	yes	—
527	C₄×C₈	C₂³×C₁₇	1	4	yes	—
528	C₁₇	#60865	1	1	yes	characteristic, direct product factor, Sylow
529	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
530	C₂×Q₈	—	2	2	no	—
531	C₂×Q₈	—	2	2	no	—
532	C₂×Q₈	—	2	2	no	—
533	C₂×Q₈	—	2	2	no	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	2	2	no	—
536	C₂×Q₈	—	2	2	no	—
537	C₂×Q₈	—	2	8	no	—
538	C₂×Q₈	—	4	4	no	—
539	C₂×Q₈	—	4	4	no	—
540	C₂×Q₈	—	4	4	no	—
541	C₂×Q₈	C₂⁴×C₁₇	1	4	yes	—
542	C₂²×C₄	—	2	4	no	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	4	2	no	—
549	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
550	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
551	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
552	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
553	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
554	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
555	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
556	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
557	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
558	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
559	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
560	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
561	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
562	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
564	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
566	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
567	M₁₆	—	2	8	no	—
568	C₂×C₈	C₂⁴×C₁₇	1	8	yes	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	—	2	2	no	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	2	2	no	—
588	C₄⋊C₄	—	2	2	no	—
589	C₄⋊C₄	—	2	2	no	—
590	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
591	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
592	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
593	C₂²⋊C₄	—	2	4	no	—
594	C₂²⋊C₄	—	2	4	no	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	—	2	4	no	—
597	C₄²	—	2	4	no	—
598	C₄²	—	2	4	no	—
599	C₄²	—	2	4	no	—
600	C₄²	—	2	4	no	—
601	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
602	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
603	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
604	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
605	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
606	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
607	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
608	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
609	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
610	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
611	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
612	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
613	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
614	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
615	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
616	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
617	C₂³	—	2	2	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	4	1	no	—
620	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
621	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
622	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
623	Q₈	—	2	8	no	—
624	Q₈	—	4	4	no	—
625	Q₈	—	4	4	no	—
626	Q₈	—	4	4	no	—
627	Q₈	—	4	4	no	—
628	Q₈	—	4	4	no	—
629	Q₈	—	4	4	no	—
630	Q₈	—	4	4	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	4	no	—
652	C₂×C₄	—	4	4	no	—
653	C₂×C₄	—	4	4	no	—
654	C₂×C₄	—	4	4	no	—
655	C₂×C₄	C₁₇×#137	1	4	yes	—
656	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
657	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
658	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
659	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
660	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
661	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
662	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
663	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
664	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
665	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
666	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
667	C₂×C₄	C₁₇×2₋¹⁺⁴	1	4	yes	—
668	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
669	C₈	—	2	8	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	4	4	no	—
678	C₂²	C₁₇×#536	1	2	yes	—
679	C₂²	C₂×C₁₇×#137	1	2	yes	—
680	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	1	no	—
688	C₄	—	4	4	no	—
689	C₄	—	4	4	no	—
690	C₄	—	4	4	no	—
691	C₄	—	4	4	no	—
692	C₄	C₁₇×#536	1	2	yes	—
693	C₄	C₂×C₁₇×#137	1	2	yes	—
694	C₄	C₂×C₁₇×#137	1	2	yes	—
695	C₄	C₁₇×#575	1	2	yes	—
696	C₄	C₂×C₁₇×2₋¹⁺⁴	1	2	yes	—
697	C₂	—	2	2	no	—
698	C₂	—	2	2	no	—
699	C₂	—	4	1	no	—
700	C₂	C₂×C₁₇×#536	1	1	yes	characteristic
701	C₂	C₂²×C₁₇×#137	1	1	yes	characteristic
702	C₂	C₂×C₁₇×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
prime radical	C₂⁴×C₁₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄²×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₇×#3237	C₂	semidirect
4. C₁₇×#3236	C₂	semidirect
5. C₁₇×#3231	C₂	semidirect
6. C₁₇×#3230	C₂	semidirect
7. C₁₇×#3229	C₂	semidirect
8. C₁₇×#3165	C₂	semidirect
9. C₁₇×#3139	C₂	semidirect
11. C₁₇×#3078	C₂	semidirect
46. C₁₇×#501	C₂²	semidirect
47. C₁₇×#500	C₂²	semidirect
48. C₁₇×#498	C₂²	semidirect
49. C₁₇×#491	C₂²	semidirect
50. C₁₇×#487	C₂²	semidirect
51. C₁₇×#487	C₂²	semidirect
55. C₁₇×#479	C₂²	semidirect
56. C₁₇×#477	C₂²	semidirect
57. C₁₇×#475	C₂²	semidirect
265. #60865	C₁₇	direct (N × H)
321. #3237	C₂×C₁₇	semidirect
322. #3236	C₂×C₁₇	semidirect
323. #3231	C₂×C₁₇	semidirect
324. #3230	C₂×C₁₇	semidirect
325. #3229	C₂×C₁₇	semidirect
326. #3165	C₂×C₁₇	semidirect
327. #3139	C₂×C₁₇	semidirect
329. #3078	C₂×C₁₇	semidirect
391. #501	C₂²×C₁₇	semidirect
392. #500	C₂²×C₁₇	semidirect
393. #498	C₂²×C₁₇	semidirect
394. #491	C₂²×C₁₇	semidirect
395. #487	C₂²×C₁₇	semidirect
396. #487	C₂²×C₁₇	semidirect
400. #479	C₂²×C₁₇	semidirect
401. #477	C₂²×C₁₇	semidirect
402. #475	C₂²×C₁₇	semidirect
528. C₁₇	#60865	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×#533	2
C₁₇×#3237	2
C₁₇×#3236	2
C₁₇×#3231	2
C₁₇×#3230	2
C₁₇×#3229	2
C₁₇×#3165	2
C₁₇×#3139	2
C₁₇×#3095	2
C₁₇×#3078	2
C₁₇×#2920	2
#60865	17

Subgroups — C17×#60865 #16918609

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#60865 #16918609