Subgroups — C₁₇×#60142 #16917886

Order 4352.

2714 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₇×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3449	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#2935	C₂	1	8	yes	maximal, complemented
5	C₁₇×#2933	C₂	1	8	yes	maximal, complemented
6	C₁₇×#2930	C₂	1	4	yes	maximal, complemented
7	C₁₇×#2929	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₇×#424	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#2879	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₇×#408	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#2873	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₇	C₂²	1	1	yes	characteristic
13	C₂²×#41×C₁₇	C₂²	1	1	yes	characteristic
14	C₁₇×#568	—	2	8	no	—
15	C₂×C₁₇×#131	—	2	8	no	—
16	C₂×C₁₇×#131	C₂²	1	4	yes	—
17	C₂×C₁₇×#131	C₂²	1	4	yes	—
18	C₂×C₁₇×#131	C₂²	1	4	yes	complemented
19	C₂×C₁₇×#131	C₂²	1	4	yes	complemented
20	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
22	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
23	C₂²×M₁₆×C₁₇	C₂²	1	2	yes	complemented
24	C₂²×M₁₆×C₁₇	C₂²	1	4	yes	complemented
25	C₂³×C₈×C₁₇	C₂²	1	1	yes	characteristic
26	C₂³×C₈×C₁₇	C₂²	1	2	yes	complemented
27	C₁₇×#537	C₄	1	4	yes	—
28	C₁₇×#536	C₄	1	2	yes	—
29	C₁₇×#536	C₄	1	2	yes	—
30	C₁₇×#535	C₄	1	2	yes	—
31	C₁₇×#535	C₄	1	2	yes	—
32	C₁₇×#534	C₄	1	4	yes	—
33	C₁₇×#532	C₂²	1	4	yes	—
34	C₁₇×#525	C₂²	1	4	yes	—
35	C₁₇×#525	C₂²	1	4	yes	—
36	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
37	C₁₇×#436	C₂²	1	16	yes	complemented
38	C₁₇×#435	C₂²	1	16	yes	complemented
39	C₁₇×#435	C₂²	1	16	yes	complemented
40	C₈×D₄×C₁₇	C₂²	1	16	yes	complemented
41	C₁₇×#424	C₂²	1	2	yes	complemented
42	C₁₇×#424	C₂²	1	2	yes	complemented
43	C₁₇×#424	C₂²	1	4	yes	complemented
44	C₂×C₁₇×C₄⋊C₈	C₂²	1	4	yes	complemented
45	C₁₇×#408	C₂²	1	2	yes	—
46	C₁₇×#408	C₂²	1	2	yes	—
47	C₁₇×#408	C₂²	1	4	yes	—
48	C₁₇×#408	C₂²	1	4	yes	complemented
49	C₁₇×#408	C₂²	1	4	yes	complemented
50	C₁₇×#407	C₂²	1	4	yes	complemented
51	C₂×C₁₇×C₂²⋊C₈	C₂²	1	4	yes	complemented
52	C₁₇×#405	C₂²	1	4	yes	complemented
53	C₁₇×#405	C₂²	1	4	yes	complemented
54	C₄×M₁₆×C₁₇	C₂²	1	4	yes	complemented
55	C₂×#41×C₁₇	—	2	4	no	—
56	C₂×#41×C₁₇	—	2	4	no	—
57	C₂×#41×C₁₇	—	2	4	no	—
58	C₂×#41×C₁₇	—	2	4	no	—
59	C₂×#41×C₁₇	C₂×C₄	1	2	yes	—
60	C₂×#41×C₁₇	C₂×C₄	1	2	yes	—
61	C₂×#41×C₁₇	C₂×C₄	1	2	yes	—
62	C₂×#41×C₁₇	C₂×C₄	1	2	yes	—
63	C₂×#41×C₁₇	C₂³	1	2	yes	—
64	C₂×#41×C₁₇	C₂³	1	2	yes	—
65	C₂×#41×C₁₇	C₂³	1	2	yes	—
66	C₂×#41×C₁₇	C₂³	1	2	yes	—
67	C₂²×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
68	C₂²×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
69	C₂²×D₄×C₁₇	C₂×C₄	1	2	yes	—
70	C₂²×D₄×C₁₇	C₂×C₄	1	2	yes	—
71	C₂²×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
72	C₂²×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
73	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
74	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
76	C₁₇×#131	—	2	16	no	—
77	C₁₇×#131	—	2	16	no	—
78	C₁₇×#131	—	2	16	no	—
79	C₁₇×#131	—	2	16	no	—
80	C₂×M₁₆×C₁₇	—	2	4	no	—
81	C₂×M₁₆×C₁₇	—	2	4	no	—
82	C₂×M₁₆×C₁₇	—	2	16	no	—
83	C₂×M₁₆×C₁₇	—	2	8	no	—
84	C₂×M₁₆×C₁₇	D₄	1	8	yes	complemented
85	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
86	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
87	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
88	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
89	C₂×M₁₆×C₁₇	C₂³	1	8	yes	—
90	C₂×M₁₆×C₁₇	C₂³	1	8	yes	—
91	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
92	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
93	C₂²×C₈×C₁₇	—	2	4	no	—
94	C₂²×C₈×C₁₇	—	2	8	no	—
95	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
98	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
99	C₂²×C₈×C₁₇	C₂³	1	8	yes	—
100	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
101	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
102	C₂²×C₈×C₁₇	C₂³	1	8	yes	—
103	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
104	C₁₇×C₄⋊Q₈	C₂×C₄	1	4	yes	—
105	C₁₇×#127	C₂×C₄	1	4	yes	—
106	C₁₇×#124	C₂×C₄	1	4	yes	—
107	C₁₇×#124	C₂×C₄	1	4	yes	—
108	C₁₇×#123	C₂×C₄	1	8	yes	—
109	C₁₇×#123	C₂×C₄	1	8	yes	—
110	C₁₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
111	C₁₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
112	C₁₇×#121	C₂×C₄	1	8	yes	—
113	C₁₇×#121	C₂×C₄	1	8	yes	—
114	C₁₇×#121	C₂×C₄	1	16	yes	—
115	C₁₇×#120	C₂×C₄	1	8	yes	—
116	C₁₇×#120	C₂×C₄	1	8	yes	—
117	C₄×D₄×C₁₇	C₂³	1	16	yes	—
118	C₁₇×#117	C₂×C₄	1	2	yes	—
119	C₁₇×#117	C₂×C₄	1	2	yes	—
120	C₁₇×#117	C₂³	1	2	yes	—
121	C₁₇×#117	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
123	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
124	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
125	C₁₇×C₄⋊C₈	C₂³	1	8	yes	—
126	C₁₇×C₄⋊C₈	C₂³	1	8	yes	—
127	C₁₇×C₂²⋊C₈	C₂³	1	8	yes	—
128	C₁₇×C₂²⋊C₈	C₂³	1	8	yes	—
129	C₁₇×C₂²⋊C₈	C₂³	1	16	yes	—
130	C₁₇×#97	C₂³	1	8	yes	—
131	C₄×C₈×C₁₇	C₂³	1	8	yes	—
132	C₂⁴×C₁₇	C₂²×C₄	1	2	yes	—
133	C₂⁴×C₁₇	C₂²×C₄	1	2	yes	—
134	C₂⁴×C₁₇	C₂²×C₄	1	1	yes	characteristic
135	#41×C₁₇	—	2	8	no	—
136	#41×C₁₇	—	2	8	no	—
137	#41×C₁₇	—	2	8	no	—
138	#41×C₁₇	—	2	8	no	—
139	#41×C₁₇	—	2	4	no	—
140	#41×C₁₇	—	2	4	no	—
141	#41×C₁₇	—	2	4	no	—
142	#41×C₁₇	—	2	4	no	—
143	#41×C₁₇	—	2	4	no	—
144	#41×C₁₇	—	2	4	no	—
145	#41×C₁₇	—	2	4	no	—
146	#41×C₁₇	—	2	4	no	—
147	C₂×Q₈×C₁₇	—	2	4	no	—
148	C₂×Q₈×C₁₇	—	2	4	no	—
149	C₂×Q₈×C₁₇	C₂²×C₄	1	2	yes	—
150	C₂×Q₈×C₁₇	C₂²×C₄	1	2	yes	—
151	C₂×Q₈×C₁₇	C₂²×C₄	1	2	yes	—
152	C₂×Q₈×C₁₇	C₂²×C₄	1	2	yes	—
153	C₂×D₄×C₁₇	—	2	8	no	—
154	C₂×D₄×C₁₇	—	2	8	no	—
155	C₂×D₄×C₁₇	—	2	4	no	—
156	C₂×D₄×C₁₇	—	2	4	no	—
157	C₂×D₄×C₁₇	C₂²×C₄	1	4	yes	—
158	C₂×D₄×C₁₇	C₂²×C₄	1	4	yes	—
159	C₂×D₄×C₁₇	C₂²×C₄	1	2	yes	—
160	C₂×D₄×C₁₇	C₂²×C₄	1	2	yes	—
161	C₂×D₄×C₁₇	C₂²×C₄	1	4	yes	—
162	C₂×D₄×C₁₇	C₂²×C₄	1	4	yes	—
163	C₂×D₄×C₁₇	C₂²×C₄	1	2	yes	—
164	C₂×D₄×C₁₇	C₂²×C₄	1	2	yes	—
165	C₂×D₄×C₁₇	C₂²×C₄	1	16	yes	—
166	C₂²×C₄×C₁₇	—	2	4	no	—
167	C₂²×C₄×C₁₇	—	2	4	no	—
168	C₂²×C₄×C₁₇	—	2	4	no	—
169	C₂²×C₄×C₁₇	—	2	4	no	—
170	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	—
171	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	—
172	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
173	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
174	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	—
175	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₇	C₂×D₄	1	4	yes	—
179	C₂²×C₄×C₁₇	#41	1	4	yes	—
180	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
185	M₁₆×C₁₇	—	2	4	no	—
186	M₁₆×C₁₇	—	2	4	no	—
187	M₁₆×C₁₇	—	2	4	no	—
188	M₁₆×C₁₇	—	2	4	no	—
189	M₁₆×C₁₇	—	2	16	no	—
190	M₁₆×C₁₇	—	2	16	no	—
191	M₁₆×C₁₇	C₂×D₄	1	8	yes	—
192	M₁₆×C₁₇	C₂×D₄	1	8	yes	—
193	C₂×C₈×C₁₇	—	2	2	no	—
194	C₂×C₈×C₁₇	—	2	2	no	—
195	C₂×C₈×C₁₇	—	2	4	no	—
196	C₂×C₈×C₁₇	—	2	4	no	—
197	C₂×C₈×C₁₇	—	2	4	no	—
198	C₂×C₈×C₁₇	—	2	4	no	—
199	C₂×C₈×C₁₇	—	2	16	no	—
200	C₂×C₈×C₁₇	—	2	16	no	—
201	C₂×C₈×C₁₇	C₂×D₄	1	8	yes	—
202	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
203	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
204	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
205	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
206	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
207	C₄⋊C₄×C₁₇	C₂²×C₄	1	16	yes	—
208	C₄⋊C₄×C₁₇	C₂²×C₄	1	4	yes	—
209	C₄⋊C₄×C₁₇	C₂²×C₄	1	4	yes	—
210	C₂²⋊C₄×C₁₇	C₂²×C₄	1	16	yes	—
211	C₂²⋊C₄×C₁₇	C₂²×C₄	1	16	yes	—
212	C₂²⋊C₄×C₁₇	C₂²×C₄	1	4	yes	—
213	C₂²⋊C₄×C₁₇	C₂²×C₄	1	4	yes	—
214	C₄²×C₁₇	C₂²×C₄	1	4	yes	—
215	C₄²×C₁₇	C₂⁴	1	4	yes	—
216	#60142	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂³×C₁₇	—	2	4	no	—
218	C₂³×C₁₇	—	2	4	no	—
219	C₂³×C₁₇	—	4	2	no	—
220	C₂³×C₁₇	—	4	4	no	—
221	C₂³×C₁₇	—	4	4	no	—
222	C₂³×C₁₇	C₄×D₄	1	4	yes	—
223	C₂³×C₁₇	C₂³×C₄	1	4	yes	—
224	C₂³×C₁₇	C₂³×C₄	1	4	yes	—
225	C₂³×C₁₇	C₂³×C₄	1	1	yes	characteristic
226	C₂³×C₁₇	C₂³×C₄	1	1	yes	characteristic
227	C₂³×C₁₇	C₂³×C₄	1	1	yes	characteristic
228	Q₈×C₁₇	—	2	4	no	—
229	Q₈×C₁₇	—	2	4	no	—
230	Q₈×C₁₇	—	2	4	no	—
231	Q₈×C₁₇	—	2	4	no	—
232	D₄×C₁₇	—	2	8	no	—
233	D₄×C₁₇	—	2	8	no	—
234	D₄×C₁₇	—	2	8	no	—
235	D₄×C₁₇	—	2	8	no	—
236	D₄×C₁₇	—	2	4	no	—
237	D₄×C₁₇	—	2	4	no	—
238	D₄×C₁₇	—	2	4	no	—
239	D₄×C₁₇	—	2	4	no	—
240	D₄×C₁₇	—	4	16	no	—
241	C₂×C₄×C₁₇	—	2	4	no	—
242	C₂×C₄×C₁₇	—	2	4	no	—
243	C₂×C₄×C₁₇	—	2	8	no	—
244	C₂×C₄×C₁₇	—	2	8	no	—
245	C₂×C₄×C₁₇	—	2	4	no	—
246	C₂×C₄×C₁₇	—	2	4	no	—
247	C₂×C₄×C₁₇	—	2	4	no	—
248	C₂×C₄×C₁₇	—	2	4	no	—
249	C₂×C₄×C₁₇	—	4	4	no	—
250	C₂×C₄×C₁₇	C₄×D₄	1	4	yes	—
251	C₂×C₄×C₁₇	C₄×D₄	1	4	yes	—
252	C₂×C₄×C₁₇	C₄×D₄	1	4	yes	—
253	C₂×C₄×C₁₇	C₂³×C₄	1	8	yes	—
254	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
255	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
256	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
257	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
258	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
259	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
260	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
261	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
263	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
264	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
265	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
266	C₈×C₁₇	—	2	2	no	—
267	C₈×C₁₇	—	2	2	no	—
268	C₈×C₁₇	—	2	4	no	—
269	C₈×C₁₇	—	2	4	no	—
270	C₈×C₁₇	C₂²×D₄	1	8	yes	—
271	C₂×#568	C₂×C₁₇	1	1	yes	characteristic, complemented
272	C₂²×#131	C₂×C₁₇	1	1	yes	characteristic, complemented
273	#3449	C₂×C₁₇	1	1	yes	characteristic
274	#2935	C₂×C₁₇	1	8	yes	complemented
275	#2933	C₂×C₁₇	1	8	yes	complemented
276	#2930	C₂×C₁₇	1	4	yes	complemented
277	#2929	C₂×C₁₇	1	4	yes	complemented
278	C₂×#424	C₂×C₁₇	1	1	yes	characteristic, complemented
279	#2879	C₂×C₁₇	1	1	yes	characteristic, complemented
280	C₂×#408	C₂×C₁₇	1	1	yes	characteristic, complemented
281	#2873	C₂×C₁₇	1	1	yes	characteristic, complemented
282	C₂²×C₁₇	—	2	2	no	—
283	C₂²×C₁₇	—	2	2	no	—
284	C₂²×C₁₇	—	2	2	no	—
285	C₂²×C₁₇	—	2	4	no	—
286	C₂²×C₁₇	—	2	4	no	—
287	C₂²×C₁₇	—	2	8	no	—
288	C₂²×C₁₇	—	2	8	no	—
289	C₂²×C₁₇	—	4	4	no	—
290	C₂²×C₁₇	—	4	8	no	—
291	C₂²×C₁₇	—	8	4	no	—
292	C₂²×C₁₇	C₂×C₄×D₄	1	2	yes	—
293	C₂²×C₁₇	C₂×C₄×D₄	1	2	yes	—
294	C₂²×C₁₇	C₂×C₄×D₄	1	2	yes	—
295	C₂²×C₁₇	C₂⁴×C₄	1	1	yes	characteristic
296	C₄×C₁₇	—	2	4	no	—
297	C₄×C₁₇	—	2	4	no	—
298	C₄×C₁₇	—	2	8	no	—
299	C₄×C₁₇	C₂×C₄×D₄	1	2	yes	—
300	C₄×C₁₇	C₂×C₄×D₄	1	2	yes	—
301	C₄×C₁₇	C₂×C₄×D₄	1	2	yes	—
302	C₄×C₁₇	C₂³×D₄	1	1	yes	characteristic
303	C₄×C₁₇	C₂²×#41	1	1	yes	characteristic
304	C₂²×#41	C₂²×C₁₇	1	1	yes	characteristic
305	C₂²×#41	C₂²×C₁₇	1	1	yes	characteristic
306	#568	—	2	8	no	—
307	C₂×#131	—	2	8	no	—
308	C₂×#131	C₂²×C₁₇	1	4	yes	—
309	C₂×#131	C₂²×C₁₇	1	4	yes	—
310	C₂×#131	C₂²×C₁₇	1	4	yes	complemented
311	C₂×#131	C₂²×C₁₇	1	4	yes	complemented
312	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
313	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
314	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
315	C₂²×M₁₆	C₂²×C₁₇	1	2	yes	complemented
316	C₂²×M₁₆	C₂²×C₁₇	1	4	yes	complemented
317	C₂³×C₈	C₂²×C₁₇	1	1	yes	characteristic
318	C₂³×C₈	C₂²×C₁₇	1	2	yes	complemented
319	#537	C₄×C₁₇	1	4	yes	—
320	#536	C₄×C₁₇	1	2	yes	—
321	#536	C₄×C₁₇	1	2	yes	—
322	#535	C₄×C₁₇	1	2	yes	—
323	#535	C₄×C₁₇	1	2	yes	—
324	#534	C₄×C₁₇	1	4	yes	—
325	#532	C₂²×C₁₇	1	4	yes	—
326	#525	C₂²×C₁₇	1	4	yes	—
327	#525	C₂²×C₁₇	1	4	yes	—
328	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
329	#436	C₂²×C₁₇	1	16	yes	complemented
330	#435	C₂²×C₁₇	1	16	yes	complemented
331	#435	C₂²×C₁₇	1	16	yes	complemented
332	C₈×D₄	C₂²×C₁₇	1	16	yes	complemented
333	#424	C₂²×C₁₇	1	2	yes	complemented
334	#424	C₂²×C₁₇	1	2	yes	complemented
335	#424	C₂²×C₁₇	1	4	yes	complemented
336	C₂×C₄⋊C₈	C₂²×C₁₇	1	4	yes	complemented
337	#408	C₂²×C₁₇	1	2	yes	—
338	#408	C₂²×C₁₇	1	2	yes	—
339	#408	C₂²×C₁₇	1	4	yes	—
340	#408	C₂²×C₁₇	1	4	yes	complemented
341	#408	C₂²×C₁₇	1	4	yes	complemented
342	#407	C₂²×C₁₇	1	4	yes	complemented
343	C₂×C₂²⋊C₈	C₂²×C₁₇	1	4	yes	complemented
344	#405	C₂²×C₁₇	1	4	yes	complemented
345	#405	C₂²×C₁₇	1	4	yes	complemented
346	C₄×M₁₆	C₂²×C₁₇	1	4	yes	complemented
347	C₂×C₁₇	—	2	2	no	—
348	C₂×C₁₇	—	2	2	no	—
349	C₂×C₁₇	—	2	2	no	—
350	C₂×C₁₇	—	4	4	no	—
351	C₂×C₁₇	—	4	4	no	—
352	C₂×C₁₇	C₂²×C₄×D₄	1	1	yes	characteristic
353	C₂×C₁₇	#3573	1	2	yes	—
354	C₂×#41	—	2	4	no	—
355	C₂×#41	—	2	4	no	—
356	C₂×#41	—	2	4	no	—
357	C₂×#41	—	2	4	no	—
358	C₂×#41	C₂×C₄×C₁₇	1	2	yes	—
359	C₂×#41	C₂×C₄×C₁₇	1	2	yes	—
360	C₂×#41	C₂×C₄×C₁₇	1	2	yes	—
361	C₂×#41	C₂×C₄×C₁₇	1	2	yes	—
362	C₂×#41	C₂³×C₁₇	1	2	yes	—
363	C₂×#41	C₂³×C₁₇	1	2	yes	—
364	C₂×#41	C₂³×C₁₇	1	2	yes	—
365	C₂×#41	C₂³×C₁₇	1	2	yes	—
366	C₂²×Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
367	C₂²×Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
368	C₂²×D₄	C₂×C₄×C₁₇	1	2	yes	—
369	C₂²×D₄	C₂×C₄×C₁₇	1	2	yes	—
370	C₂²×D₄	C₂×C₄×C₁₇	1	1	yes	characteristic
371	C₂²×D₄	C₂×C₄×C₁₇	1	1	yes	characteristic
372	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
373	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
374	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
375	#131	—	2	16	no	—
376	#131	—	2	16	no	—
377	#131	—	2	16	no	—
378	#131	—	2	16	no	—
379	C₂×M₁₆	—	2	4	no	—
380	C₂×M₁₆	—	2	4	no	—
381	C₂×M₁₆	—	2	16	no	—
382	C₂×M₁₆	—	2	8	no	—
383	C₂×M₁₆	D₄×C₁₇	1	8	yes	complemented
384	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
385	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
386	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
387	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
388	C₂×M₁₆	C₂³×C₁₇	1	8	yes	—
389	C₂×M₁₆	C₂³×C₁₇	1	8	yes	—
390	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
391	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
392	C₂²×C₈	—	2	4	no	—
393	C₂²×C₈	—	2	8	no	—
394	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
395	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
396	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
397	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
398	C₂²×C₈	C₂³×C₁₇	1	8	yes	—
399	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
400	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
401	C₂²×C₈	C₂³×C₁₇	1	8	yes	—
402	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
403	C₄⋊Q₈	C₂×C₄×C₁₇	1	4	yes	—
404	#127	C₂×C₄×C₁₇	1	4	yes	—
405	#124	C₂×C₄×C₁₇	1	4	yes	—
406	#124	C₂×C₄×C₁₇	1	4	yes	—
407	#123	C₂×C₄×C₁₇	1	8	yes	—
408	#123	C₂×C₄×C₁₇	1	8	yes	—
409	C₂²⋊Q₈	C₂×C₄×C₁₇	1	8	yes	—
410	C₂²⋊Q₈	C₂×C₄×C₁₇	1	8	yes	—
411	#121	C₂×C₄×C₁₇	1	8	yes	—
412	#121	C₂×C₄×C₁₇	1	8	yes	—
413	#121	C₂×C₄×C₁₇	1	16	yes	—
414	#120	C₂×C₄×C₁₇	1	8	yes	—
415	#120	C₂×C₄×C₁₇	1	8	yes	—
416	C₄×D₄	C₂³×C₁₇	1	16	yes	—
417	#117	C₂×C₄×C₁₇	1	2	yes	—
418	#117	C₂×C₄×C₁₇	1	2	yes	—
419	#117	C₂³×C₁₇	1	2	yes	—
420	#117	C₂³×C₁₇	1	2	yes	—
421	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
422	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
423	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
424	C₄⋊C₈	C₂³×C₁₇	1	8	yes	—
425	C₄⋊C₈	C₂³×C₁₇	1	8	yes	—
426	C₂²⋊C₈	C₂³×C₁₇	1	8	yes	—
427	C₂²⋊C₈	C₂³×C₁₇	1	8	yes	—
428	C₂²⋊C₈	C₂³×C₁₇	1	16	yes	—
429	#97	C₂³×C₁₇	1	8	yes	—
430	C₄×C₈	C₂³×C₁₇	1	8	yes	—
431	C₁₇	#60142	1	1	yes	characteristic, direct product factor, Sylow
432	C₂⁴	C₂²×C₄×C₁₇	1	2	yes	—
433	C₂⁴	C₂²×C₄×C₁₇	1	2	yes	—
434	C₂⁴	C₂²×C₄×C₁₇	1	1	yes	characteristic
435	#41	—	2	4	no	—
436	#41	—	2	4	no	—
437	#41	—	2	4	no	—
438	#41	—	2	4	no	—
439	#41	—	2	4	no	—
440	#41	—	2	4	no	—
441	#41	—	2	4	no	—
442	#41	—	2	4	no	—
443	#41	—	2	8	no	—
444	#41	—	2	8	no	—
445	#41	—	2	8	no	—
446	#41	—	2	8	no	—
447	C₂×Q₈	—	2	4	no	—
448	C₂×Q₈	—	2	4	no	—
449	C₂×Q₈	C₂²×C₄×C₁₇	1	2	yes	—
450	C₂×Q₈	C₂²×C₄×C₁₇	1	2	yes	—
451	C₂×Q₈	C₂²×C₄×C₁₇	1	2	yes	—
452	C₂×Q₈	C₂²×C₄×C₁₇	1	2	yes	—
453	C₂×D₄	—	2	8	no	—
454	C₂×D₄	—	2	8	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	C₂²×C₄×C₁₇	1	4	yes	—
458	C₂×D₄	C₂²×C₄×C₁₇	1	4	yes	—
459	C₂×D₄	C₂²×C₄×C₁₇	1	4	yes	—
460	C₂×D₄	C₂²×C₄×C₁₇	1	4	yes	—
461	C₂×D₄	C₂²×C₄×C₁₇	1	2	yes	—
462	C₂×D₄	C₂²×C₄×C₁₇	1	2	yes	—
463	C₂×D₄	C₂²×C₄×C₁₇	1	2	yes	—
464	C₂×D₄	C₂²×C₄×C₁₇	1	2	yes	—
465	C₂×D₄	C₂²×C₄×C₁₇	1	16	yes	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	C₂²×C₄×C₁₇	1	4	yes	—
471	C₂²×C₄	C₂²×C₄×C₁₇	1	4	yes	—
472	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
473	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
474	C₂²×C₄	C₂²×C₄×C₁₇	1	4	yes	—
475	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
476	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
477	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₁₇	1	4	yes	—
479	C₂²×C₄	#41×C₁₇	1	4	yes	—
480	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
481	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
482	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
483	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
484	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
485	M₁₆	—	2	4	no	—
486	M₁₆	—	2	4	no	—
487	M₁₆	—	2	4	no	—
488	M₁₆	—	2	4	no	—
489	M₁₆	—	2	16	no	—
490	M₁₆	—	2	16	no	—
491	M₁₆	C₂×D₄×C₁₇	1	8	yes	—
492	M₁₆	C₂×D₄×C₁₇	1	8	yes	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	2	4	no	—
496	C₂×C₈	—	2	4	no	—
497	C₂×C₈	—	2	4	no	—
498	C₂×C₈	—	2	4	no	—
499	C₂×C₈	—	2	16	no	—
500	C₂×C₈	—	2	16	no	—
501	C₂×C₈	C₂×D₄×C₁₇	1	8	yes	—
502	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
503	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
504	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
505	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
506	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
507	C₄⋊C₄	C₂²×C₄×C₁₇	1	4	yes	—
508	C₄⋊C₄	C₂²×C₄×C₁₇	1	4	yes	—
509	C₄⋊C₄	C₂²×C₄×C₁₇	1	16	yes	—
510	C₂²⋊C₄	C₂²×C₄×C₁₇	1	4	yes	—
511	C₂²⋊C₄	C₂²×C₄×C₁₇	1	4	yes	—
512	C₂²⋊C₄	C₂²×C₄×C₁₇	1	16	yes	—
513	C₂²⋊C₄	C₂²×C₄×C₁₇	1	16	yes	—
514	C₄²	C₂²×C₄×C₁₇	1	4	yes	—
515	C₄²	C₂⁴×C₁₇	1	4	yes	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	4	2	no	—
519	C₂³	—	4	4	no	—
520	C₂³	—	4	4	no	—
521	C₂³	C₄×D₄×C₁₇	1	4	yes	—
522	C₂³	C₂³×C₄×C₁₇	1	4	yes	—
523	C₂³	C₂³×C₄×C₁₇	1	4	yes	—
524	C₂³	C₂³×C₄×C₁₇	1	1	yes	characteristic
525	C₂³	C₂³×C₄×C₁₇	1	1	yes	characteristic
526	C₂³	C₂³×C₄×C₁₇	1	1	yes	characteristic
527	Q₈	—	2	4	no	—
528	Q₈	—	2	4	no	—
529	Q₈	—	2	4	no	—
530	Q₈	—	2	4	no	—
531	D₄	—	2	8	no	—
532	D₄	—	2	8	no	—
533	D₄	—	2	8	no	—
534	D₄	—	2	8	no	—
535	D₄	—	2	4	no	—
536	D₄	—	2	4	no	—
537	D₄	—	2	4	no	—
538	D₄	—	2	4	no	—
539	D₄	—	4	16	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	8	no	—
543	C₂×C₄	—	2	8	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	4	4	no	—
549	C₂×C₄	C₄×D₄×C₁₇	1	4	yes	—
550	C₂×C₄	C₄×D₄×C₁₇	1	4	yes	—
551	C₂×C₄	C₄×D₄×C₁₇	1	4	yes	—
552	C₂×C₄	C₂³×C₄×C₁₇	1	8	yes	—
553	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
554	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
555	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
556	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
557	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
558	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
559	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
560	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
561	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
562	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
563	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
564	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
565	C₈	—	2	2	no	—
566	C₈	—	2	2	no	—
567	C₈	—	2	4	no	—
568	C₈	—	2	4	no	—
569	C₈	C₂²×D₄×C₁₇	1	8	yes	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	8	no	—
574	C₂²	—	2	8	no	—
575	C₂²	—	2	4	no	—
576	C₂²	—	2	4	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	4	8	no	—
579	C₂²	—	8	4	no	—
580	C₂²	C₂×C₄×D₄×C₁₇	1	2	yes	—
581	C₂²	C₂×C₄×D₄×C₁₇	1	2	yes	—
582	C₂²	C₂×C₄×D₄×C₁₇	1	2	yes	—
583	C₂²	C₂⁴×C₄×C₁₇	1	1	yes	characteristic
584	C₄	—	2	8	no	—
585	C₄	—	2	4	no	—
586	C₄	—	2	4	no	—
587	C₄	C₂×C₄×D₄×C₁₇	1	2	yes	—
588	C₄	C₂×C₄×D₄×C₁₇	1	2	yes	—
589	C₄	C₂×C₄×D₄×C₁₇	1	2	yes	—
590	C₄	C₂³×D₄×C₁₇	1	1	yes	characteristic
591	C₄	C₂²×#41×C₁₇	1	1	yes	characteristic
592	C₂	—	2	2	no	—
593	C₂	—	2	2	no	—
594	C₂	—	2	2	no	—
595	C₂	—	4	4	no	—
596	C₂	—	4	4	no	—
597	C₂	C₂²×C₄×D₄×C₁₇	1	1	yes	characteristic
598	C₂	C₁₇×#3573	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
socle	C₂²×C₁₇	C₂⁴×C₄
prime radical	C₁₇×#3449	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×#568	C₂	semidirect
2. C₂²×C₁₇×#131	C₂	semidirect
4. C₁₇×#2935	C₂	semidirect
5. C₁₇×#2933	C₂	semidirect
6. C₁₇×#2930	C₂	semidirect
7. C₁₇×#2929	C₂	semidirect
8. C₂×C₁₇×#424	C₂	semidirect
9. C₁₇×#2879	C₂	semidirect
10. C₂×C₁₇×#408	C₂	semidirect
11. C₁₇×#2873	C₂	semidirect
18. C₂×C₁₇×#131	C₂²	semidirect
19. C₂×C₁₇×#131	C₂²	semidirect
23. C₂²×M₁₆×C₁₇	C₂²	semidirect
24. C₂²×M₁₆×C₁₇	C₂²	semidirect
26. C₂³×C₈×C₁₇	C₂²	semidirect
37. C₁₇×#436	C₂²	semidirect
38. C₁₇×#435	C₂²	semidirect
39. C₁₇×#435	C₂²	semidirect
40. C₈×D₄×C₁₇	C₂²	semidirect
41. C₁₇×#424	C₂²	semidirect
42. C₁₇×#424	C₂²	semidirect
43. C₁₇×#424	C₂²	semidirect
44. C₂×C₁₇×C₄⋊C₈	C₂²	semidirect
48. C₁₇×#408	C₂²	semidirect
49. C₁₇×#408	C₂²	semidirect
50. C₁₇×#407	C₂²	semidirect
51. C₂×C₁₇×C₂²⋊C₈	C₂²	semidirect
52. C₁₇×#405	C₂²	semidirect
53. C₁₇×#405	C₂²	semidirect
54. C₄×M₁₆×C₁₇	C₂²	semidirect
84. C₂×M₁₆×C₁₇	D₄	semidirect
216. #60142	C₁₇	direct (N × H)
271. C₂×#568	C₂×C₁₇	semidirect
272. C₂²×#131	C₂×C₁₇	semidirect
274. #2935	C₂×C₁₇	semidirect
275. #2933	C₂×C₁₇	semidirect
276. #2930	C₂×C₁₇	semidirect
277. #2929	C₂×C₁₇	semidirect
278. C₂×#424	C₂×C₁₇	semidirect
279. #2879	C₂×C₁₇	semidirect
280. C₂×#408	C₂×C₁₇	semidirect
281. #2873	C₂×C₁₇	semidirect
310. C₂×#131	C₂²×C₁₇	semidirect
311. C₂×#131	C₂²×C₁₇	semidirect
315. C₂²×M₁₆	C₂²×C₁₇	semidirect
316. C₂²×M₁₆	C₂²×C₁₇	semidirect
318. C₂³×C₈	C₂²×C₁₇	semidirect
329. #436	C₂²×C₁₇	semidirect
330. #435	C₂²×C₁₇	semidirect
331. #435	C₂²×C₁₇	semidirect
332. C₈×D₄	C₂²×C₁₇	semidirect
333. #424	C₂²×C₁₇	semidirect
334. #424	C₂²×C₁₇	semidirect
335. #424	C₂²×C₁₇	semidirect
336. C₂×C₄⋊C₈	C₂²×C₁₇	semidirect
340. #408	C₂²×C₁₇	semidirect
341. #408	C₂²×C₁₇	semidirect
342. #407	C₂²×C₁₇	semidirect
343. C₂×C₂²⋊C₈	C₂²×C₁₇	semidirect
344. #405	C₂²×C₁₇	semidirect
345. #405	C₂²×C₁₇	semidirect
346. C₄×M₁₆	C₂²×C₁₇	semidirect
383. C₂×M₁₆	D₄×C₁₇	semidirect
431. C₁₇	#60142	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×#568	2
C₂²×C₁₇×#131	2
C₁₇×#3449	2
C₁₇×#2935	2
C₁₇×#2933	2
C₁₇×#2930	2
C₁₇×#2929	2
C₂×C₁₇×#424	2
C₁₇×#2879	2
C₂×C₁₇×#408	2
C₁₇×#2873	2
#60142	17

Subgroups — C17×#60142 #16917886

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#60142 #16917886