Subgroups — C₁₇×#17810 #16875554

Order 4352.

648 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#2920	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₇×#432	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₇×#431	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#1573	C₂	1	4	yes	maximal, complemented
5	C₁₇×#1572	C₂	1	4	yes	maximal, complemented
6	C₁₇×#1565	C₂	1	4	yes	maximal, complemented
7	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
8	C₁₇×#432	—	2	1	no	—
9	C₁₇×#432	—	2	1	no	—
10	C₁₇×#432	C₄	1	2	yes	—
11	C₁₇×#432	C₄	1	2	yes	—
12	C₁₇×#432	C₂²	1	2	yes	—
13	C₁₇×#432	C₂²	1	2	yes	—
14	C₁₇×#431	—	2	1	no	—
15	C₁₇×#431	—	2	1	no	—
16	C₁₇×#431	C₂²	1	2	yes	—
17	C₁₇×#431	C₂²	1	2	yes	—
18	C₁₇×#431	C₂²	1	2	yes	—
19	C₁₇×#431	C₂²	1	2	yes	—
20	C₁₇×#423	C₄	1	2	yes	—
21	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
23	C₁₇×#407	C₄	1	2	yes	—
24	C₂×C₁₇×C₂²⋊C₈	—	2	1	no	—
25	C₂×C₁₇×C₂²⋊C₈	—	2	1	no	—
26	C₄×M₁₆×C₁₇	C₂²	1	2	yes	—
27	C₂×C₁₇×#97	—	2	1	no	—
28	C₂×C₄×C₈×C₁₇	—	2	1	no	—
29	C₁₇×#335	C₂²	1	8	yes	complemented
30	C₁₇×#334	C₂²	1	8	yes	complemented
31	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₇	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₇	Q₈	1	1	yes	characteristic
34	C₂×M₁₆×C₁₇	C₂×C₄	1	4	yes	—
35	C₂²×C₈×C₁₇	—	2	2	no	—
36	C₂²×C₈×C₁₇	—	2	2	no	—
37	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₇	Q₈	1	1	yes	characteristic
44	C₂×C₄²×C₁₇	Q₈	1	1	yes	characteristic
45	C₂×C₄²×C₁₇	Q₈	1	1	yes	characteristic
46	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
47	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
48	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
49	C₁₇×C₄⋊C₈	—	2	2	no	—
50	C₁₇×C₄⋊C₈	—	2	2	no	—
51	C₁₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
52	C₁₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
53	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
54	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
55	C₁₇×C₂²⋊C₈	—	2	2	no	—
56	C₁₇×C₂²⋊C₈	—	2	2	no	—
57	C₁₇×C₂²⋊C₈	—	2	2	no	—
58	C₁₇×C₂²⋊C₈	—	2	2	no	—
59	C₁₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
60	C₁₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
61	C₁₇×#97	—	2	2	no	—
62	C₁₇×#97	—	2	2	no	—
63	C₁₇×#97	C₂×C₄	1	4	yes	—
64	C₄×C₈×C₁₇	—	2	2	no	—
65	C₄×C₈×C₁₇	—	2	2	no	—
66	C₄×C₈×C₁₇	C₂³	1	4	yes	—
67	C₂⁴×C₁₇	C₄⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₇	—	2	4	no	—
69	C₂²×C₄×C₁₇	—	4	2	no	—
70	C₂²×C₄×C₁₇	—	4	2	no	—
71	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
89	M₁₆×C₁₇	—	2	8	no	—
90	C₂×C₈×C₁₇	—	2	4	no	—
91	C₂×C₈×C₁₇	—	2	4	no	—
92	C₂×C₈×C₁₇	—	4	4	no	—
93	C₂×C₈×C₁₇	—	4	4	no	—
94	C₂×C₈×C₁₇	C₂²×C₄	1	8	yes	—
95	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
96	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
97	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
102	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₁₇	C₂×Q₈	1	1	yes	characteristic
108	C₄²×C₁₇	C₂×Q₈	1	1	yes	characteristic
109	C₄²×C₁₇	C₂×Q₈	1	1	yes	characteristic
110	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
111	#17810	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂³×C₁₇	—	2	2	no	—
113	C₂³×C₁₇	—	2	2	no	—
114	C₂³×C₁₇	—	4	1	no	—
115	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
116	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
117	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₄×C₁₇	—	2	2	no	—
119	C₂×C₄×C₁₇	—	2	2	no	—
120	C₂×C₄×C₁₇	—	2	2	no	—
121	C₂×C₄×C₁₇	—	2	2	no	—
122	C₂×C₄×C₁₇	—	2	2	no	—
123	C₂×C₄×C₁₇	—	2	2	no	—
124	C₂×C₄×C₁₇	—	2	2	no	—
125	C₂×C₄×C₁₇	—	2	2	no	—
126	C₂×C₄×C₁₇	—	2	2	no	—
127	C₂×C₄×C₁₇	—	2	2	no	—
128	C₂×C₄×C₁₇	—	4	1	no	—
129	C₂×C₄×C₁₇	—	4	1	no	—
130	C₂×C₄×C₁₇	—	4	1	no	—
131	C₂×C₄×C₁₇	—	4	1	no	—
132	C₂×C₄×C₁₇	—	4	1	no	—
133	C₂×C₄×C₁₇	—	4	1	no	—
134	C₂×C₄×C₁₇	—	4	1	no	—
135	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₇	#131	1	4	yes	—
145	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₇	C₂²×Q₈	1	1	yes	characteristic
148	C₈×C₁₇	—	2	8	no	—
149	C₈×C₁₇	—	4	4	no	—
150	C₈×C₁₇	—	4	4	no	—
151	#2920	C₂×C₁₇	1	1	yes	characteristic
152	C₂×#432	C₂×C₁₇	1	1	yes	characteristic
153	C₂×#431	C₂×C₁₇	1	1	yes	characteristic
154	#1573	C₂×C₁₇	1	4	yes	complemented
155	#1572	C₂×C₁₇	1	4	yes	complemented
156	#1565	C₂×C₁₇	1	4	yes	complemented
157	C₂²×C₁₇	—	2	1	no	—
158	C₂²×C₁₇	—	2	1	no	—
159	C₂²×C₁₇	—	2	1	no	—
160	C₂²×C₁₇	—	2	1	no	—
161	C₂²×C₁₇	—	2	1	no	—
162	C₂²×C₁₇	—	2	1	no	—
163	C₂²×C₁₇	—	2	1	no	—
164	C₂²×C₁₇	—	4	4	no	—
165	C₂²×C₁₇	#424	1	2	yes	—
166	C₂²×C₁₇	#430	1	2	yes	—
167	C₂²×C₁₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
168	C₄×C₁₇	—	2	1	no	—
169	C₄×C₁₇	—	2	1	no	—
170	C₄×C₁₇	—	2	1	no	—
171	C₄×C₁₇	—	2	1	no	—
172	C₄×C₁₇	—	2	1	no	—
173	C₄×C₁₇	—	2	1	no	—
174	C₄×C₁₇	—	2	1	no	—
175	C₄×C₁₇	—	2	1	no	—
176	C₄×C₁₇	—	2	1	no	—
177	C₄×C₁₇	#424	1	2	yes	—
178	C₄×C₁₇	C₂×#131	1	2	yes	—
179	C₄×C₁₇	#575	1	2	yes	—
180	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic
181	#432	—	2	1	no	—
182	#432	—	2	1	no	—
183	#432	C₄×C₁₇	1	2	yes	—
184	#432	C₄×C₁₇	1	2	yes	—
185	#432	C₂²×C₁₇	1	2	yes	—
186	#432	C₂²×C₁₇	1	2	yes	—
187	#431	—	2	1	no	—
188	#431	—	2	1	no	—
189	#431	C₂²×C₁₇	1	2	yes	—
190	#431	C₂²×C₁₇	1	2	yes	—
191	#431	C₂²×C₁₇	1	2	yes	—
192	#431	C₂²×C₁₇	1	2	yes	—
193	#423	C₄×C₁₇	1	2	yes	—
194	C₂×C₄⋊C₈	C₂²×C₁₇	1	2	yes	—
195	C₂×C₄⋊C₈	C₂²×C₁₇	1	2	yes	—
196	#407	C₄×C₁₇	1	2	yes	—
197	C₂×C₂²⋊C₈	—	2	1	no	—
198	C₂×C₂²⋊C₈	—	2	1	no	—
199	C₄×M₁₆	C₂²×C₁₇	1	2	yes	—
200	C₂×#97	—	2	1	no	—
201	C₂×C₄×C₈	—	2	1	no	—
202	#335	C₂²×C₁₇	1	8	yes	complemented
203	#334	C₂²×C₁₇	1	8	yes	complemented
204	C₂×C₁₇	—	2	2	no	—
205	C₂×C₁₇	—	2	2	no	—
206	C₂×C₁₇	—	4	1	no	—
207	C₂×C₁₇	C₂×#424	1	1	yes	characteristic
208	C₂×C₁₇	#2911	1	1	yes	characteristic
209	C₂×C₁₇	C₂×#430	1	1	yes	characteristic
210	C₂³×C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
211	C₂³×C₄	D₄×C₁₇	1	1	yes	characteristic
212	C₂³×C₄	Q₈×C₁₇	1	1	yes	characteristic
213	C₂×M₁₆	C₂×C₄×C₁₇	1	4	yes	—
214	C₂²×C₈	—	2	2	no	—
215	C₂²×C₈	—	2	2	no	—
216	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
217	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
218	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
219	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
220	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
221	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
222	C₂×C₄²	Q₈×C₁₇	1	1	yes	characteristic
223	C₂×C₄²	Q₈×C₁₇	1	1	yes	characteristic
224	C₂×C₄²	Q₈×C₁₇	1	1	yes	characteristic
225	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
226	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
227	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
228	C₄⋊C₈	—	2	2	no	—
229	C₄⋊C₈	—	2	2	no	—
230	C₄⋊C₈	C₂×C₄×C₁₇	1	4	yes	—
231	C₄⋊C₈	C₂×C₄×C₁₇	1	4	yes	—
232	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
233	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
234	C₂²⋊C₈	—	2	2	no	—
235	C₂²⋊C₈	—	2	2	no	—
236	C₂²⋊C₈	—	2	2	no	—
237	C₂²⋊C₈	—	2	2	no	—
238	C₂²⋊C₈	C₂×C₄×C₁₇	1	4	yes	—
239	C₂²⋊C₈	C₂×C₄×C₁₇	1	4	yes	—
240	#97	—	2	2	no	—
241	#97	—	2	2	no	—
242	#97	C₂×C₄×C₁₇	1	4	yes	—
243	C₄×C₈	—	2	2	no	—
244	C₄×C₈	—	2	2	no	—
245	C₄×C₈	C₂³×C₁₇	1	4	yes	—
246	C₁₇	#17810	1	1	yes	characteristic, direct product factor, Sylow
247	C₂⁴	C₄⋊C₄×C₁₇	1	1	yes	characteristic
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	4	2	no	—
250	C₂²×C₄	—	4	2	no	—
251	C₂²×C₄	C₄⋊C₄×C₁₇	1	1	yes	characteristic
252	C₂²×C₄	C₄⋊C₄×C₁₇	1	1	yes	characteristic
253	C₂²×C₄	C₄⋊C₄×C₁₇	1	1	yes	characteristic
254	C₂²×C₄	C₄⋊C₄×C₁₇	1	1	yes	characteristic
255	C₂²×C₄	C₄⋊C₄×C₁₇	1	1	yes	characteristic
256	C₂²×C₄	C₄⋊C₄×C₁₇	1	1	yes	characteristic
257	C₂²×C₄	C₄⋊C₄×C₁₇	1	1	yes	characteristic
258	C₂²×C₄	C₄⋊C₄×C₁₇	1	1	yes	characteristic
259	C₂²×C₄	C₄⋊C₄×C₁₇	1	1	yes	characteristic
260	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
261	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
262	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
264	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
266	C₂²×C₄	C₂×Q₈×C₁₇	1	1	yes	characteristic
267	C₂²×C₄	C₂×Q₈×C₁₇	1	1	yes	characteristic
268	C₂²×C₄	C₂×Q₈×C₁₇	1	1	yes	characteristic
269	M₁₆	—	2	8	no	—
270	C₂×C₈	—	2	4	no	—
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	—	4	4	no	—
273	C₂×C₈	—	4	4	no	—
274	C₂×C₈	C₂²×C₄×C₁₇	1	8	yes	—
275	C₄²	C₄⋊C₄×C₁₇	1	1	yes	characteristic
276	C₄²	C₄⋊C₄×C₁₇	1	1	yes	characteristic
277	C₄²	C₄⋊C₄×C₁₇	1	1	yes	characteristic
278	C₄²	C₄⋊C₄×C₁₇	1	1	yes	characteristic
279	C₄²	C₄⋊C₄×C₁₇	1	1	yes	characteristic
280	C₄²	C₄⋊C₄×C₁₇	1	1	yes	characteristic
281	C₄²	C₂²×C₄×C₁₇	1	1	yes	characteristic
282	C₄²	C₂²×C₄×C₁₇	1	1	yes	characteristic
283	C₄²	C₂²×C₄×C₁₇	1	1	yes	characteristic
284	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
285	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
286	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
287	C₄²	C₂×Q₈×C₁₇	1	1	yes	characteristic
288	C₄²	C₂×Q₈×C₁₇	1	1	yes	characteristic
289	C₄²	C₂×Q₈×C₁₇	1	1	yes	characteristic
290	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
291	C₂³	—	2	2	no	—
292	C₂³	—	2	2	no	—
293	C₂³	—	4	1	no	—
294	C₂³	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
295	C₂³	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
296	C₂³	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	4	1	no	—
308	C₂×C₄	—	4	1	no	—
309	C₂×C₄	—	4	1	no	—
310	C₂×C₄	—	4	1	no	—
311	C₂×C₄	—	4	1	no	—
312	C₂×C₄	—	4	1	no	—
313	C₂×C₄	—	4	1	no	—
314	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
315	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
316	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
317	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
318	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
319	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
320	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
321	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
322	C₂×C₄	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
323	C₂×C₄	C₁₇×#131	1	4	yes	—
324	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
325	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
326	C₂×C₄	C₂²×Q₈×C₁₇	1	1	yes	characteristic
327	C₈	—	2	8	no	—
328	C₈	—	4	4	no	—
329	C₈	—	4	4	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	1	no	—
332	C₂²	—	2	1	no	—
333	C₂²	—	2	1	no	—
334	C₂²	—	2	1	no	—
335	C₂²	—	2	1	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	4	4	no	—
338	C₂²	C₁₇×#424	1	2	yes	—
339	C₂²	C₁₇×#430	1	2	yes	—
340	C₂²	C₂²×C₄⋊C₄×C₁₇	1	1	yes	characteristic
341	C₄	—	2	1	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	1	no	—
344	C₄	—	2	1	no	—
345	C₄	—	2	1	no	—
346	C₄	—	2	1	no	—
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	C₁₇×#424	1	2	yes	—
351	C₄	C₂×C₁₇×#131	1	2	yes	—
352	C₄	C₁₇×#575	1	2	yes	—
353	C₂	—	2	2	no	—
354	C₂	—	2	2	no	—
355	C₂	—	4	1	no	—
356	C₂	C₂×C₁₇×#424	1	1	yes	characteristic
357	C₂	C₁₇×#2911	1	1	yes	characteristic
358	C₂	C₂×C₁₇×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₇
Frattini, cosocle	C₄²	C₂⁴×C₁₇
socle	C₂²×C₁₇	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₇	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ 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
4. C₁₇×#1573	C₂	semidirect
5. C₁₇×#1572	C₂	semidirect
6. C₁₇×#1565	C₂	semidirect
29. C₁₇×#335	C₂²	semidirect
30. C₁₇×#334	C₂²	semidirect
111. #17810	C₁₇	direct (N × H)
154. #1573	C₂×C₁₇	semidirect
155. #1572	C₂×C₁₇	semidirect
156. #1565	C₂×C₁₇	semidirect
202. #335	C₂²×C₁₇	semidirect
203. #334	C₂²×C₁₇	semidirect
246. C₁₇	#17810	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₇×#2920	2
C₂×C₁₇×#432	2
C₂×C₁₇×#431	2
C₁₇×#1573	2
C₁₇×#1572	2
C₁₇×#1565	2
#17810	17

Subgroups — C17×#17810 #16875554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#17810 #16875554