Subgroups — C₁₇×#21426 #16879170

Order 4352.

1132 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#529	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×M₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#1998	C₂	1	2	yes	maximal, complemented
5	C₁₇×#1967	C₂	1	2	yes	maximal, complemented
6	C₁₇×#1901	C₂	1	2	yes	maximal, complemented
7	C₁₇×#1900	C₂	1	2	yes	maximal
8	C₄×C₁₇×#101	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₇×#100	C₂	1	2	yes	maximal, complemented
10	C₂²×M₁₆×C₁₇	C₂²	1	2	yes	—
11	C₁₇×#529	—	2	1	no	—
12	C₁₇×#529	—	2	1	no	—
13	C₁₇×#529	—	2	1	no	—
14	C₁₇×#529	—	2	1	no	—
15	C₁₇×#529	—	2	1	no	—
16	C₁₇×#529	—	2	1	no	—
17	C₁₇×#529	—	2	1	no	—
18	C₁₇×#529	—	2	1	no	—
19	C₂×C₁₇×#126	C₄	1	2	yes	—
20	C₂×C₁₇×#125	C₂²	1	1	yes	characteristic
21	C₂×C₁₇×#124	C₂²	1	1	yes	characteristic
22	C₂×C₁₇×#123	C₄	1	2	yes	—
23	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₇×#121	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₇	C₄	1	2	yes	—
27	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
28	C₂×C₁₇×#117	C₄	1	2	yes	—
29	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
30	C₁₇×#432	—	2	1	no	—
31	C₁₇×#432	—	2	1	no	—
32	C₁₇×#431	—	2	1	no	—
33	C₁₇×#431	—	2	1	no	—
34	C₁₇×#423	C₂²	1	2	yes	—
35	C₂×C₁₇×#101	C₂²	1	4	yes	—
36	C₂×C₁₇×#100	C₂²	1	4	yes	—
37	C₁₇×#407	C₂²	1	2	yes	—
38	C₄×M₁₆×C₁₇	—	2	1	no	—
39	C₄×M₁₆×C₁₇	—	2	1	no	—
40	C₄×M₁₆×C₁₇	C₂²	1	2	yes	—
41	C₄×M₁₆×C₁₇	C₂²	1	2	yes	—
42	C₄×M₁₆×C₁₇	C₂²	1	2	yes	—
43	C₂×C₁₇×#97	—	2	1	no	—
44	C₂×C₄×C₈×C₁₇	—	2	1	no	—
45	C₁₇×#343	C₂²	1	4	yes	—
46	C₁₇×#343	C₂²	1	4	yes	—
47	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₇	C₂×C₄	1	2	yes	—
49	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₇	C₂×C₄	1	2	yes	—
51	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
54	C₂×M₁₆×C₁₇	—	2	2	no	—
55	C₂×M₁₆×C₁₇	—	2	8	no	—
56	C₂×M₁₆×C₁₇	C₂³	1	4	yes	—
57	C₂×M₁₆×C₁₇	C₂³	1	4	yes	—
58	C₂²×C₈×C₁₇	—	2	2	no	—
59	C₁₇×#126	—	2	2	no	—
60	C₁₇×#126	—	2	2	no	—
61	C₁₇×#126	—	2	2	no	—
62	C₁₇×#126	—	2	2	no	—
63	C₁₇×#125	—	2	1	no	—
64	C₁₇×#125	—	2	1	no	—
65	C₁₇×#125	—	2	1	no	—
66	C₁₇×#125	—	2	1	no	—
67	C₁₇×#124	—	2	1	no	—
68	C₁₇×#124	—	2	1	no	—
69	C₁₇×#124	—	2	1	no	—
70	C₁₇×#124	—	2	1	no	—
71	C₁₇×#123	—	2	2	no	—
72	C₁₇×#123	—	2	2	no	—
73	C₁₇×#123	—	2	2	no	—
74	C₁₇×#123	—	2	2	no	—
75	C₁₇×C₂²⋊Q₈	—	2	1	no	—
76	C₁₇×C₂²⋊Q₈	—	2	1	no	—
77	C₁₇×C₂²⋊Q₈	—	2	1	no	—
78	C₁₇×C₂²⋊Q₈	—	2	1	no	—
79	C₁₇×#121	—	2	1	no	—
80	C₁₇×#121	—	2	1	no	—
81	C₁₇×#121	—	2	1	no	—
82	C₁₇×#121	—	2	1	no	—
83	C₄×Q₈×C₁₇	—	2	1	no	—
84	C₄×Q₈×C₁₇	—	2	1	no	—
85	C₄×Q₈×C₁₇	—	2	1	no	—
86	C₄×Q₈×C₁₇	—	2	1	no	—
87	C₄×D₄×C₁₇	—	2	2	no	—
88	C₄×D₄×C₁₇	—	2	2	no	—
89	C₄×D₄×C₁₇	—	2	2	no	—
90	C₄×D₄×C₁₇	—	2	2	no	—
91	C₄×D₄×C₁₇	—	2	1	no	—
92	C₄×D₄×C₁₇	—	2	1	no	—
93	C₄×D₄×C₁₇	—	2	1	no	—
94	C₄×D₄×C₁₇	—	2	1	no	—
95	C₁₇×#117	—	2	2	no	—
96	C₁₇×#117	—	2	2	no	—
97	C₁₇×#117	—	2	2	no	—
98	C₁₇×#117	—	2	2	no	—
99	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
100	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
101	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
102	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
103	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
106	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
107	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
108	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
109	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
110	C₂×C₄²×C₁₇	C₂×C₄	1	2	yes	—
111	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
115	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
120	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
121	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
123	C₁₇×C₄⋊C₈	—	2	2	no	—
124	C₁₇×C₄⋊C₈	—	2	2	no	—
125	C₁₇×#101	—	2	8	no	—
126	C₁₇×#100	—	2	8	no	—
127	C₁₇×C₂²⋊C₈	—	2	2	no	—
128	C₁₇×C₂²⋊C₈	—	2	2	no	—
129	C₁₇×#97	—	2	2	no	—
130	C₁₇×#97	—	2	2	no	—
131	C₁₇×#97	—	2	2	no	—
132	C₄×C₈×C₁₇	—	2	2	no	—
133	C₄×C₈×C₁₇	—	2	2	no	—
134	C₄×C₈×C₁₇	—	2	2	no	—
135	C₂⁴×C₁₇	C₂²×C₄	1	1	yes	characteristic
136	C₂⁴×C₁₇	C₂²×C₄	1	2	yes	—
137	C₂×Q₈×C₁₇	—	2	1	no	—
138	C₂×Q₈×C₁₇	—	2	1	no	—
139	C₂×Q₈×C₁₇	—	2	4	no	—
140	C₂×D₄×C₁₇	—	2	2	no	—
141	C₂×D₄×C₁₇	—	2	2	no	—
142	C₂×D₄×C₁₇	—	2	1	no	—
143	C₂×D₄×C₁₇	—	2	1	no	—
144	C₂×D₄×C₁₇	—	2	4	no	—
145	C₂×D₄×C₁₇	—	4	4	no	—
146	C₂²×C₄×C₁₇	—	2	4	no	—
147	C₂²×C₄×C₁₇	—	2	2	no	—
148	C₂²×C₄×C₁₇	—	2	2	no	—
149	C₂²×C₄×C₁₇	—	4	2	no	—
150	C₂²×C₄×C₁₇	—	4	2	no	—
151	C₂²×C₄×C₁₇	—	4	4	no	—
152	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
161	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
164	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
165	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
173	M₁₆×C₁₇	—	2	8	no	—
174	M₁₆×C₁₇	—	2	4	no	—
175	M₁₆×C₁₇	—	2	4	no	—
176	M₁₆×C₁₇	—	2	4	no	—
177	M₁₆×C₁₇	#41	1	8	yes	—
178	C₂×C₈×C₁₇	—	2	8	no	—
179	C₂×C₈×C₁₇	—	2	4	no	—
180	C₂×C₈×C₁₇	—	2	4	no	—
181	C₄⋊C₄×C₁₇	—	2	2	no	—
182	C₄⋊C₄×C₁₇	—	2	2	no	—
183	C₄⋊C₄×C₁₇	—	2	2	no	—
184	C₄⋊C₄×C₁₇	—	2	2	no	—
185	C₄⋊C₄×C₁₇	—	2	2	no	—
186	C₄⋊C₄×C₁₇	—	2	2	no	—
187	C₄⋊C₄×C₁₇	—	2	2	no	—
188	C₄⋊C₄×C₁₇	—	2	2	no	—
189	C₄⋊C₄×C₁₇	—	2	1	no	—
190	C₄⋊C₄×C₁₇	—	2	1	no	—
191	C₄⋊C₄×C₁₇	—	2	1	no	—
192	C₄⋊C₄×C₁₇	—	2	1	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	—	2	2	no	—
197	C₂²⋊C₄×C₁₇	—	2	2	no	—
198	C₂²⋊C₄×C₁₇	—	2	2	no	—
199	C₂²⋊C₄×C₁₇	—	2	2	no	—
200	C₂²⋊C₄×C₁₇	—	2	2	no	—
201	C₂²⋊C₄×C₁₇	—	2	2	no	—
202	C₂²⋊C₄×C₁₇	—	2	2	no	—
203	C₄²×C₁₇	—	2	2	no	—
204	C₄²×C₁₇	—	2	2	no	—
205	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
206	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
207	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
208	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
209	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
210	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
211	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
212	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
213	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
217	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
218	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
220	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
221	#21426	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂³×C₁₇	—	2	2	no	—
223	C₂³×C₁₇	—	2	2	no	—
224	C₂³×C₁₇	—	2	2	no	—
225	C₂³×C₁₇	—	2	4	no	—
226	C₂³×C₁₇	—	4	1	no	—
227	C₂³×C₁₇	—	4	2	no	—
228	C₂³×C₁₇	—	4	2	no	—
229	C₂³×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂³×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂³×C₁₇	C₂³×C₄	1	1	yes	characteristic
232	Q₈×C₁₇	—	4	2	no	—
233	Q₈×C₁₇	—	4	2	no	—
234	D₄×C₁₇	—	4	4	no	—
235	D₄×C₁₇	—	4	4	no	—
236	D₄×C₁₇	—	4	2	no	—
237	D₄×C₁₇	—	4	2	no	—
238	C₂×C₄×C₁₇	—	2	2	no	—
239	C₂×C₄×C₁₇	—	2	2	no	—
240	C₂×C₄×C₁₇	—	2	2	no	—
241	C₂×C₄×C₁₇	—	2	2	no	—
242	C₂×C₄×C₁₇	—	2	2	no	—
243	C₂×C₄×C₁₇	—	2	2	no	—
244	C₂×C₄×C₁₇	—	2	2	no	—
245	C₂×C₄×C₁₇	—	2	2	no	—
246	C₂×C₄×C₁₇	—	2	2	no	—
247	C₂×C₄×C₁₇	—	2	2	no	—
248	C₂×C₄×C₁₇	—	2	2	no	—
249	C₂×C₄×C₁₇	—	2	2	no	—
250	C₂×C₄×C₁₇	—	2	2	no	—
251	C₂×C₄×C₁₇	—	2	4	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	4	no	—
260	C₂×C₄×C₁₇	—	4	4	no	—
261	C₂×C₄×C₁₇	—	4	2	no	—
262	C₂×C₄×C₁₇	—	4	2	no	—
263	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₁₇	C₂×#41	1	4	yes	—
276	C₈×C₁₇	—	2	8	no	—
277	C₈×C₁₇	—	4	4	no	—
278	C₂×#529	C₂×C₁₇	1	1	yes	characteristic
279	#2920	C₂×C₁₇	1	1	yes	characteristic, complemented
280	C₂×C₄×M₁₆	C₂×C₁₇	1	1	yes	characteristic, complemented
281	#1998	C₂×C₁₇	1	2	yes	complemented
282	#1967	C₂×C₁₇	1	2	yes	complemented
283	#1901	C₂×C₁₇	1	2	yes	complemented
284	#1900	C₂×C₁₇	1	2	yes	—
285	C₄×#101	C₂×C₁₇	1	2	yes	complemented
286	C₄×#100	C₂×C₁₇	1	2	yes	complemented
287	C₂²×C₁₇	—	2	1	no	—
288	C₂²×C₁₇	—	2	1	no	—
289	C₂²×C₁₇	—	2	1	no	—
290	C₂²×C₁₇	—	2	1	no	—
291	C₂²×C₁₇	—	2	1	no	—
292	C₂²×C₁₇	—	2	1	no	—
293	C₂²×C₁₇	—	2	1	no	—
294	C₂²×C₁₇	—	4	4	no	—
295	C₂²×C₁₇	—	4	2	no	—
296	C₂²×C₁₇	—	4	2	no	—
297	C₂²×C₁₇	—	4	2	no	—
298	C₂²×C₁₇	—	8	4	no	—
299	C₂²×C₁₇	#413	1	2	yes	—
300	C₂²×C₁₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
301	C₂²×C₁₇	C₄×#41	1	2	yes	—
302	C₄×C₁₇	—	2	1	no	—
303	C₄×C₁₇	—	2	1	no	—
304	C₄×C₁₇	—	2	1	no	—
305	C₄×C₁₇	—	2	1	no	—
306	C₄×C₁₇	—	2	1	no	—
307	C₄×C₁₇	—	2	1	no	—
308	C₄×C₁₇	—	2	1	no	—
309	C₄×C₁₇	—	2	1	no	—
310	C₄×C₁₇	—	2	1	no	—
311	C₄×C₁₇	—	4	2	no	—
312	C₄×C₁₇	—	4	2	no	—
313	C₄×C₁₇	—	4	2	no	—
314	C₄×C₁₇	#413	1	2	yes	—
315	C₄×C₁₇	#525	1	2	yes	—
316	C₄×C₁₇	#532	1	2	yes	—
317	C₂²×M₁₆	C₂²×C₁₇	1	2	yes	—
318	#529	—	2	1	no	—
319	#529	—	2	1	no	—
320	#529	—	2	1	no	—
321	#529	—	2	1	no	—
322	#529	—	2	1	no	—
323	#529	—	2	1	no	—
324	#529	—	2	1	no	—
325	#529	—	2	1	no	—
326	C₂×#126	C₄×C₁₇	1	2	yes	—
327	C₂×#125	C₂²×C₁₇	1	1	yes	characteristic
328	C₂×#124	C₂²×C₁₇	1	1	yes	characteristic
329	C₂×#123	C₄×C₁₇	1	2	yes	—
330	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
331	C₂×#121	C₂²×C₁₇	1	1	yes	characteristic
332	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
333	C₂×C₄×D₄	C₄×C₁₇	1	2	yes	—
334	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
335	C₂×#117	C₄×C₁₇	1	2	yes	—
336	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic
337	#432	—	2	1	no	—
338	#432	—	2	1	no	—
339	#431	—	2	1	no	—
340	#431	—	2	1	no	—
341	#423	C₂²×C₁₇	1	2	yes	—
342	C₂×#101	C₂²×C₁₇	1	4	yes	—
343	C₂×#100	C₂²×C₁₇	1	4	yes	—
344	#407	C₂²×C₁₇	1	2	yes	—
345	C₄×M₁₆	—	2	1	no	—
346	C₄×M₁₆	—	2	1	no	—
347	C₄×M₁₆	C₂²×C₁₇	1	2	yes	—
348	C₄×M₁₆	C₂²×C₁₇	1	2	yes	—
349	C₄×M₁₆	C₂²×C₁₇	1	2	yes	—
350	C₂×#97	—	2	1	no	—
351	C₂×C₄×C₈	—	2	1	no	—
352	#343	C₂²×C₁₇	1	4	yes	—
353	#343	C₂²×C₁₇	1	4	yes	—
354	C₂×C₁₇	—	2	2	no	—
355	C₂×C₁₇	—	2	2	no	—
356	C₂×C₁₇	—	4	1	no	—
357	C₂×C₁₇	—	8	2	no	—
358	C₂×C₁₇	#2297	1	1	yes	characteristic
359	C₂×C₁₇	C₂×#413	1	1	yes	characteristic
360	C₂×C₁₇	C₂×#413	1	1	yes	characteristic
361	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
362	C₂²×D₄	C₂×C₄×C₁₇	1	2	yes	—
363	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
364	C₂³×C₄	C₂×C₄×C₁₇	1	2	yes	—
365	C₂³×C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
366	C₂³×C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
367	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
368	C₂×M₁₆	—	2	2	no	—
369	C₂×M₁₆	—	2	8	no	—
370	C₂×M₁₆	C₂³×C₁₇	1	4	yes	—
371	C₂×M₁₆	C₂³×C₁₇	1	4	yes	—
372	C₂²×C₈	—	2	2	no	—
373	#126	—	2	2	no	—
374	#126	—	2	2	no	—
375	#126	—	2	2	no	—
376	#126	—	2	2	no	—
377	#125	—	2	1	no	—
378	#125	—	2	1	no	—
379	#125	—	2	1	no	—
380	#125	—	2	1	no	—
381	#124	—	2	1	no	—
382	#124	—	2	1	no	—
383	#124	—	2	1	no	—
384	#124	—	2	1	no	—
385	#123	—	2	2	no	—
386	#123	—	2	2	no	—
387	#123	—	2	2	no	—
388	#123	—	2	2	no	—
389	C₂²⋊Q₈	—	2	1	no	—
390	C₂²⋊Q₈	—	2	1	no	—
391	C₂²⋊Q₈	—	2	1	no	—
392	C₂²⋊Q₈	—	2	1	no	—
393	#121	—	2	1	no	—
394	#121	—	2	1	no	—
395	#121	—	2	1	no	—
396	#121	—	2	1	no	—
397	C₄×Q₈	—	2	1	no	—
398	C₄×Q₈	—	2	1	no	—
399	C₄×Q₈	—	2	1	no	—
400	C₄×Q₈	—	2	1	no	—
401	C₄×D₄	—	2	2	no	—
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	—	2	1	no	—
409	#117	—	2	2	no	—
410	#117	—	2	2	no	—
411	#117	—	2	2	no	—
412	#117	—	2	2	no	—
413	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
414	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
415	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
416	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
417	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
419	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
420	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
421	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
422	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
423	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
424	C₂×C₄²	C₂×C₄×C₁₇	1	2	yes	—
425	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
426	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
427	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
428	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
429	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
430	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
431	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
432	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
433	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
434	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
436	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
437	C₄⋊C₈	—	2	2	no	—
438	C₄⋊C₈	—	2	2	no	—
439	#101	—	2	8	no	—
440	#100	—	2	8	no	—
441	C₂²⋊C₈	—	2	2	no	—
442	C₂²⋊C₈	—	2	2	no	—
443	#97	—	2	2	no	—
444	#97	—	2	2	no	—
445	#97	—	2	2	no	—
446	C₄×C₈	—	2	2	no	—
447	C₄×C₈	—	2	2	no	—
448	C₄×C₈	—	2	2	no	—
449	C₁₇	#21426	1	1	yes	characteristic, direct product factor, Sylow
450	C₂⁴	C₂²×C₄×C₁₇	1	1	yes	characteristic
451	C₂⁴	C₂²×C₄×C₁₇	1	2	yes	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	4	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	4	no	—
460	C₂×D₄	—	4	4	no	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	4	2	no	—
465	C₂²×C₄	—	4	2	no	—
466	C₂²×C₄	—	4	4	no	—
467	C₂²×C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
468	C₂²×C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
469	C₂²×C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
470	C₂²×C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
471	C₂²×C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
472	C₂²×C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
473	C₂²×C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
474	C₂²×C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
475	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
476	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
477	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
478	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
479	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
480	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
481	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
482	C₂²×C₄	C₂²×C₄×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	M₁₆	—	2	8	no	—
489	M₁₆	—	2	4	no	—
490	M₁₆	—	2	4	no	—
491	M₁₆	—	2	4	no	—
492	M₁₆	#41×C₁₇	1	8	yes	—
493	C₂×C₈	—	2	8	no	—
494	C₂×C₈	—	2	4	no	—
495	C₂×C₈	—	2	4	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₄²	—	2	2	no	—
519	C₄²	—	2	2	no	—
520	C₄²	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
521	C₄²	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
522	C₄²	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
523	C₄²	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
524	C₄²	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
525	C₄²	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
526	C₄²	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
527	C₄²	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
528	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
529	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
530	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
531	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
532	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
533	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
534	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
535	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
536	C₂³	—	2	2	no	—
537	C₂³	—	2	2	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	2	4	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	4	2	no	—
542	C₂³	—	4	2	no	—
543	C₂³	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
544	C₂³	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
545	C₂³	C₂³×C₄×C₁₇	1	1	yes	characteristic
546	Q₈	—	4	2	no	—
547	Q₈	—	4	2	no	—
548	D₄	—	4	4	no	—
549	D₄	—	4	4	no	—
550	D₄	—	4	2	no	—
551	D₄	—	4	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	4	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	—	4	1	no	—
573	C₂×C₄	—	4	4	no	—
574	C₂×C₄	—	4	4	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
578	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
579	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
580	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
581	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
582	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
583	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
584	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
585	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
586	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
587	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
588	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
589	C₂×C₄	C₂×#41×C₁₇	1	4	yes	—
590	C₈	—	2	8	no	—
591	C₈	—	4	4	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	2	1	no	—
598	C₂²	—	2	1	no	—
599	C₂²	—	4	4	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	2	no	—
602	C₂²	—	4	2	no	—
603	C₂²	—	8	4	no	—
604	C₂²	C₁₇×#413	1	2	yes	—
605	C₂²	C₂²×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
606	C₂²	C₄×#41×C₁₇	1	2	yes	—
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	2	1	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	4	2	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	2	no	—
619	C₄	C₁₇×#413	1	2	yes	—
620	C₄	C₁₇×#525	1	2	yes	—
621	C₄	C₁₇×#532	1	2	yes	—
622	C₂	—	2	2	no	—
623	C₂	—	2	2	no	—
624	C₂	—	4	1	no	—
625	C₂	—	8	2	no	—
626	C₂	C₁₇×#2297	1	1	yes	characteristic
627	C₂	C₂×C₁₇×#413	1	1	yes	characteristic
628	C₂	C₂×C₁₇×#413	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
socle	C₂²×C₁₇	C₂²×C₂²⋊C₄
prime radical	C₂×C₁₇×#121	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄²×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₇×#2920	C₂	semidirect
3. C₂×C₄×M₁₆×C₁₇	C₂	semidirect
4. C₁₇×#1998	C₂	semidirect
5. C₁₇×#1967	C₂	semidirect
6. C₁₇×#1901	C₂	semidirect
8. C₄×C₁₇×#101	C₂	semidirect
9. C₄×C₁₇×#100	C₂	semidirect
221. #21426	C₁₇	direct (N × H)
279. #2920	C₂×C₁₇	semidirect
280. C₂×C₄×M₁₆	C₂×C₁₇	semidirect
281. #1998	C₂×C₁₇	semidirect
282. #1967	C₂×C₁₇	semidirect
283. #1901	C₂×C₁₇	semidirect
285. C₄×#101	C₂×C₁₇	semidirect
286. C₄×#100	C₂×C₁₇	semidirect
449. C₁₇	#21426	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×#529	2
C₁₇×#2920	2
C₂×C₄×M₁₆×C₁₇	2
C₁₇×#1998	2
C₁₇×#1967	2
C₁₇×#1901	2
C₁₇×#1900	2
C₄×C₁₇×#101	2
C₄×C₁₇×#100	2
#21426	17

Subgroups — C17×#21426 #16879170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#21426 #16879170