Subgroups — C₂×C₁₇×#3209 #16918522

Order 4352.

2134 conjugacy classes of subgroups.

The subgroup lattice has 416 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	C₂²×C₁₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#3209	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₇×#494	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₇×#487	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₇×#462	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₇×#451	C₂	1	4	yes	maximal
8	C₂×C₁₇×#431	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₁₇	C₂²	1	2	yes	—
10	C₂²×Q₁₆×C₁₇	C₂²	1	8	yes	—
11	C₁₇×#533	—	2	4	no	—
12	C₁₇×#533	C₂²	1	8	yes	—
13	C₂×C₁₇×C₄⋊Q₈	—	2	1	no	—
14	C₂×C₁₇×C₄⋊Q₈	—	2	1	no	—
15	C₂×C₁₇×C₄⋊Q₈	—	2	4	no	—
16	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₇×C₄⋊Q₈	C₂²	1	8	yes	—
18	C₂×C₁₇×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₇×C₄⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₇×#125	—	2	1	no	—
22	C₂×C₁₇×C₂²⋊Q₈	—	2	1	no	—
23	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₇	—	2	1	no	—
25	C₂×C₄×Q₈×C₁₇	C₂²	1	2	yes	—
26	C₂×C₁₇×#117	—	2	1	no	—
27	C₂²×C₄⋊C₄×C₁₇	—	2	1	no	—
28	C₂²×C₄⋊C₄×C₁₇	—	2	1	no	—
29	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
30	C₁₇×#494	C₂²	1	16	yes	complemented
31	C₁₇×#487	C₂²	1	16	yes	complemented
32	C₁₇×#462	C₂²	1	32	yes	complemented
33	C₁₇×#451	C₂²	1	32	yes	—
34	C₁₇×#431	C₂²	1	8	yes	—
35	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
36	C₂×C₁₇×#103	C₂²	1	8	yes	—
37	C₂×C₁₇×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₁₇	C₂²	1	2	yes	—
39	C₂²×Q₈×C₁₇	—	2	1	no	—
40	C₂²×Q₈×C₁₇	—	2	4	no	—
41	C₂²×Q₈×C₁₇	—	2	2	no	—
42	C₂²×Q₈×C₁₇	—	4	8	no	—
43	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
44	C₂²×Q₈×C₁₇	C₂³	1	4	yes	—
45	C₂²×Q₈×C₁₇	C₂³	1	8	yes	—
46	C₂³×C₄×C₁₇	—	2	2	no	—
47	C₂³×C₄×C₁₇	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₇	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
50	C₂×Q₁₆×C₁₇	—	4	16	no	—
51	C₂×Q₁₆×C₁₇	C₂³	1	32	yes	—
52	C₂²×C₈×C₁₇	C₂³	1	4	yes	—
53	C₁₇×C₄⋊Q₈	—	2	8	no	—
54	C₁₇×C₄⋊Q₈	—	2	4	no	—
55	C₁₇×C₄⋊Q₈	—	2	8	no	—
56	C₁₇×C₄⋊Q₈	—	2	4	no	—
57	C₁₇×C₄⋊Q₈	—	2	2	no	—
58	C₁₇×C₄⋊Q₈	—	2	2	no	—
59	C₁₇×C₄⋊Q₈	C₂³	1	4	yes	—
60	C₁₇×C₄⋊Q₈	C₂³	1	8	yes	—
61	C₁₇×C₄⋊Q₈	C₂³	1	8	yes	—
62	C₁₇×C₄⋊Q₈	C₂³	1	4	yes	—
63	C₁₇×#125	—	2	8	no	—
64	C₁₇×C₂²⋊Q₈	—	2	8	no	—
65	C₁₇×C₂²⋊Q₈	—	2	4	no	—
66	C₁₇×C₂²⋊Q₈	C₂³	1	8	yes	—
67	C₄×Q₈×C₁₇	—	2	8	no	—
68	C₄×Q₈×C₁₇	—	2	4	no	—
69	C₄×Q₈×C₁₇	C₂³	1	8	yes	—
70	C₁₇×#117	—	2	8	no	—
71	C₂×C₄⋊C₄×C₁₇	—	2	8	no	—
72	C₂×C₄⋊C₄×C₁₇	—	2	8	no	—
73	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
75	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
77	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
82	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
84	C₂×C₄²×C₁₇	—	2	2	no	—
85	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₇	D₄	1	4	yes	—
88	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₁₇	C₂³	1	4	yes	—
91	C₁₇×C₄⋊C₈	C₂³	1	8	yes	—
92	C₁₇×#103	C₂³	1	32	yes	—
93	C₁₇×C₂²⋊C₈	C₂³	1	8	yes	—
94	C₄×C₈×C₁₇	C₂³	1	8	yes	—
95	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
96	C₂×Q₈×C₁₇	—	2	2	no	—
97	C₂×Q₈×C₁₇	—	2	4	no	—
98	C₂×Q₈×C₁₇	—	2	8	no	—
99	C₂×Q₈×C₁₇	—	2	4	no	—
100	C₂×Q₈×C₁₇	—	2	8	no	—
101	C₂×Q₈×C₁₇	—	2	16	no	—
102	C₂×Q₈×C₁₇	—	4	16	no	—
103	C₂×Q₈×C₁₇	—	4	8	no	—
104	C₂×Q₈×C₁₇	—	4	16	no	—
105	C₂×Q₈×C₁₇	—	4	4	no	—
106	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
107	C₂×Q₈×C₁₇	C₂⁴	1	8	yes	—
108	C₂²×C₄×C₁₇	—	2	4	no	—
109	C₂²×C₄×C₁₇	—	2	4	no	—
110	C₂²×C₄×C₁₇	—	2	8	no	—
111	C₂²×C₄×C₁₇	—	2	4	no	—
112	C₂²×C₄×C₁₇	—	2	2	no	—
113	C₂²×C₄×C₁₇	—	2	2	no	—
114	C₂²×C₄×C₁₇	—	4	8	no	—
115	C₂²×C₄×C₁₇	Q₁₆	1	8	yes	complemented
116	C₂²×C₄×C₁₇	C₂×D₄	1	4	yes	—
117	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₇	C₂×D₄	1	4	yes	—
123	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
125	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
126	Q₁₆×C₁₇	—	4	32	no	—
127	C₂×C₈×C₁₇	—	2	8	no	—
128	C₂×C₈×C₁₇	C₂⁴	1	8	yes	—
129	C₄⋊C₄×C₁₇	—	2	8	no	—
130	C₄⋊C₄×C₁₇	—	2	2	no	—
131	C₄⋊C₄×C₁₇	—	2	4	no	—
132	C₄⋊C₄×C₁₇	—	2	8	no	—
133	C₄⋊C₄×C₁₇	—	2	4	no	—
134	C₄⋊C₄×C₁₇	—	2	4	no	—
135	C₄⋊C₄×C₁₇	—	2	8	no	—
136	C₄⋊C₄×C₁₇	—	2	8	no	—
137	C₄⋊C₄×C₁₇	—	2	8	no	—
138	C₄⋊C₄×C₁₇	—	2	8	no	—
139	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
140	C₂²⋊C₄×C₁₇	—	2	8	no	—
141	C₄²×C₁₇	—	2	8	no	—
142	C₄²×C₁₇	C₂×D₄	1	4	yes	—
143	C₄²×C₁₇	C₂×D₄	1	2	yes	—
144	C₄²×C₁₇	C₂×D₄	1	4	yes	—
145	C₄²×C₁₇	C₂×D₄	1	2	yes	—
146	C₄²×C₁₇	C₂⁴	1	2	yes	—
147	C₄²×C₁₇	C₂⁴	1	2	yes	—
148	C₂×#3209	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂³×C₁₇	—	2	2	no	—
150	C₂³×C₁₇	—	2	2	no	—
151	C₂³×C₁₇	C₂×Q₁₆	1	4	yes	—
152	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
153	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
154	Q₈×C₁₇	—	2	8	no	—
155	Q₈×C₁₇	—	2	16	no	—
156	Q₈×C₁₇	—	4	16	no	—
157	Q₈×C₁₇	—	4	4	no	—
158	Q₈×C₁₇	—	4	8	no	—
159	Q₈×C₁₇	—	4	8	no	—
160	C₂×C₄×C₁₇	—	2	2	no	—
161	C₂×C₄×C₁₇	—	2	2	no	—
162	C₂×C₄×C₁₇	—	2	4	no	—
163	C₂×C₄×C₁₇	—	2	8	no	—
164	C₂×C₄×C₁₇	—	2	4	no	—
165	C₂×C₄×C₁₇	—	2	4	no	—
166	C₂×C₄×C₁₇	—	2	4	no	—
167	C₂×C₄×C₁₇	—	2	8	no	—
168	C₂×C₄×C₁₇	—	4	16	no	—
169	C₂×C₄×C₁₇	—	4	8	no	—
170	C₂×C₄×C₁₇	—	4	4	no	—
171	C₂×C₄×C₁₇	—	4	4	no	—
172	C₂×C₄×C₁₇	C₂×Q₁₆	1	4	yes	—
173	C₂×C₄×C₁₇	C₂×Q₁₆	1	4	yes	—
174	C₂×C₄×C₁₇	C₂×Q₁₆	1	16	yes	complemented
175	C₂×C₄×C₁₇	#137	1	4	yes	—
176	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
177	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
178	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
180	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
181	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
182	C₂×C₄×C₁₇	H(5,𝔽₂)	1	4	yes	—
183	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
184	C₈×C₁₇	—	2	8	no	—
185	C₂×#533	C₂×C₁₇	1	1	yes	characteristic
186	C₂²×C₄⋊Q₈	C₂×C₁₇	1	1	yes	characteristic
187	#3209	C₂×C₁₇	1	16	yes	direct product factor
188	C₂×#494	C₂×C₁₇	1	2	yes	complemented
189	C₂×#487	C₂×C₁₇	1	2	yes	complemented
190	C₂×#462	C₂×C₁₇	1	4	yes	complemented
191	C₂×#451	C₂×C₁₇	1	4	yes	—
192	C₂×#431	C₂×C₁₇	1	1	yes	characteristic
193	C₂²×C₁₇	—	2	2	no	—
194	C₂²×C₁₇	—	2	8	no	—
195	C₂²×C₁₇	—	2	2	no	—
196	C₂²×C₁₇	#535	1	2	yes	—
197	C₂²×C₁₇	C₂²×Q₁₆	1	4	yes	—
198	C₂²×C₁₇	C₂²×Q₁₆	1	2	yes	—
199	C₂²×C₁₇	C₂×#137	1	2	yes	—
200	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
201	C₄×C₁₇	—	2	2	no	—
202	C₄×C₁₇	—	2	2	no	—
203	C₄×C₁₇	—	4	8	no	—
204	C₄×C₁₇	—	4	4	no	—
205	C₄×C₁₇	—	4	4	no	—
206	C₄×C₁₇	#535	1	2	yes	—
207	C₄×C₁₇	C₂²×Q₁₆	1	4	yes	—
208	C₄×C₁₇	C₂²×Q₁₆	1	4	yes	—
209	C₄×C₁₇	C₂×#137	1	4	yes	—
210	C₄×C₁₇	C₂×H(5,𝔽₂)	1	2	yes	—
211	C₂³×Q₈	C₂²×C₁₇	1	2	yes	—
212	C₂²×Q₁₆	C₂²×C₁₇	1	8	yes	—
213	#533	—	2	4	no	—
214	#533	C₂²×C₁₇	1	8	yes	—
215	C₂×C₄⋊Q₈	—	2	1	no	—
216	C₂×C₄⋊Q₈	—	2	1	no	—
217	C₂×C₄⋊Q₈	—	2	4	no	—
218	C₂×C₄⋊Q₈	C₂²×C₁₇	1	2	yes	—
219	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
220	C₂×C₄⋊Q₈	C₂²×C₁₇	1	8	yes	—
221	C₂×C₄⋊Q₈	C₂²×C₁₇	1	2	yes	—
222	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
223	C₂×#125	—	2	1	no	—
224	C₂×C₂²⋊Q₈	—	2	1	no	—
225	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	2	yes	—
226	C₂×C₄×Q₈	—	2	1	no	—
227	C₂×C₄×Q₈	C₂²×C₁₇	1	2	yes	—
228	C₂×#117	—	2	1	no	—
229	C₂²×C₄⋊C₄	—	2	1	no	—
230	C₂²×C₄⋊C₄	—	2	1	no	—
231	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic
232	#494	C₂²×C₁₇	1	16	yes	complemented
233	#487	C₂²×C₁₇	1	16	yes	complemented
234	#462	C₂²×C₁₇	1	32	yes	complemented
235	#451	C₂²×C₁₇	1	32	yes	—
236	#431	C₂²×C₁₇	1	8	yes	—
237	C₂×C₄⋊C₈	C₂²×C₁₇	1	2	yes	—
238	C₂×#103	C₂²×C₁₇	1	8	yes	—
239	C₂×C₂²⋊C₈	C₂²×C₁₇	1	2	yes	—
240	C₂×C₄×C₈	C₂²×C₁₇	1	2	yes	—
241	C₂×C₁₇	—	2	4	no	—
242	C₂×C₁₇	#3209	1	4	yes	direct product factor
243	C₂×C₁₇	C₂×#535	1	1	yes	characteristic
244	C₂×C₁₇	C₂³×Q₁₆	1	1	yes	characteristic
245	C₂×C₁₇	C₂²×#137	1	1	yes	characteristic
246	C₂²×Q₈	—	2	1	no	—
247	C₂²×Q₈	—	2	2	no	—
248	C₂²×Q₈	—	2	4	no	—
249	C₂²×Q₈	—	4	8	no	—
250	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
251	C₂²×Q₈	C₂³×C₁₇	1	4	yes	—
252	C₂²×Q₈	C₂³×C₁₇	1	8	yes	—
253	C₂³×C₄	—	2	2	no	—
254	C₂³×C₄	D₄×C₁₇	1	1	yes	characteristic
255	C₂³×C₄	D₄×C₁₇	1	1	yes	characteristic
256	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
257	C₂×Q₁₆	—	4	16	no	—
258	C₂×Q₁₆	C₂³×C₁₇	1	32	yes	—
259	C₂²×C₈	C₂³×C₁₇	1	4	yes	—
260	C₄⋊Q₈	—	2	8	no	—
261	C₄⋊Q₈	—	2	4	no	—
262	C₄⋊Q₈	—	2	8	no	—
263	C₄⋊Q₈	—	2	4	no	—
264	C₄⋊Q₈	—	2	2	no	—
265	C₄⋊Q₈	—	2	2	no	—
266	C₄⋊Q₈	C₂³×C₁₇	1	8	yes	—
267	C₄⋊Q₈	C₂³×C₁₇	1	8	yes	—
268	C₄⋊Q₈	C₂³×C₁₇	1	4	yes	—
269	C₄⋊Q₈	C₂³×C₁₇	1	4	yes	—
270	#125	—	2	8	no	—
271	C₂²⋊Q₈	—	2	8	no	—
272	C₂²⋊Q₈	—	2	4	no	—
273	C₂²⋊Q₈	C₂³×C₁₇	1	8	yes	—
274	C₄×Q₈	—	2	8	no	—
275	C₄×Q₈	—	2	4	no	—
276	C₄×Q₈	C₂³×C₁₇	1	8	yes	—
277	#117	—	2	8	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	8	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	8	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₄²	—	2	2	no	—
292	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
293	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
294	C₂×C₄²	D₄×C₁₇	1	4	yes	—
295	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
296	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
297	C₂×C₄²	C₂³×C₁₇	1	4	yes	—
298	C₄⋊C₈	C₂³×C₁₇	1	8	yes	—
299	#103	C₂³×C₁₇	1	32	yes	—
300	C₂²⋊C₈	C₂³×C₁₇	1	8	yes	—
301	C₄×C₈	C₂³×C₁₇	1	8	yes	—
302	C₁₇	C₂×#3209	1	1	yes	characteristic, direct product factor, Sylow
303	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	—	2	8	no	—
307	C₂×Q₈	—	2	4	no	—
308	C₂×Q₈	—	2	8	no	—
309	C₂×Q₈	—	2	16	no	—
310	C₂×Q₈	—	4	16	no	—
311	C₂×Q₈	—	4	8	no	—
312	C₂×Q₈	—	4	16	no	—
313	C₂×Q₈	—	4	4	no	—
314	C₂×Q₈	C₂⁴×C₁₇	1	8	yes	—
315	C₂×Q₈	C₂⁴×C₁₇	1	4	yes	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	4	8	no	—
323	C₂²×C₄	Q₁₆×C₁₇	1	8	yes	complemented
324	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₁₇	1	4	yes	—
328	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₁₇	1	4	yes	—
331	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
332	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
333	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
334	Q₁₆	—	4	32	no	—
335	C₂×C₈	—	2	8	no	—
336	C₂×C₈	C₂⁴×C₁₇	1	8	yes	—
337	C₄⋊C₄	—	2	8	no	—
338	C₄⋊C₄	—	2	8	no	—
339	C₄⋊C₄	—	2	8	no	—
340	C₄⋊C₄	—	2	8	no	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	2	8	no	—
345	C₄⋊C₄	—	2	8	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
348	C₂²⋊C₄	—	2	8	no	—
349	C₄²	—	2	8	no	—
350	C₄²	C₂×D₄×C₁₇	1	4	yes	—
351	C₄²	C₂×D₄×C₁₇	1	2	yes	—
352	C₄²	C₂×D₄×C₁₇	1	4	yes	—
353	C₄²	C₂×D₄×C₁₇	1	2	yes	—
354	C₄²	C₂⁴×C₁₇	1	2	yes	—
355	C₄²	C₂⁴×C₁₇	1	2	yes	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	C₂×Q₁₆×C₁₇	1	4	yes	—
359	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
360	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
361	Q₈	—	2	8	no	—
362	Q₈	—	2	16	no	—
363	Q₈	—	4	16	no	—
364	Q₈	—	4	8	no	—
365	Q₈	—	4	4	no	—
366	Q₈	—	4	8	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	8	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	4	16	no	—
376	C₂×C₄	—	4	8	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	C₂×Q₁₆×C₁₇	1	4	yes	—
380	C₂×C₄	C₂×Q₁₆×C₁₇	1	4	yes	—
381	C₂×C₄	C₂×Q₁₆×C₁₇	1	16	yes	complemented
382	C₂×C₄	C₁₇×#137	1	4	yes	—
383	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
384	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
385	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
386	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
387	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
388	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
389	C₂×C₄	C₁₇×H(5,𝔽₂)	1	4	yes	—
390	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
391	C₈	—	2	8	no	—
392	C₂²	—	2	8	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	C₁₇×#535	1	2	yes	—
396	C₂²	C₂²×Q₁₆×C₁₇	1	4	yes	—
397	C₂²	C₂²×Q₁₆×C₁₇	1	2	yes	—
398	C₂²	C₂×C₁₇×#137	1	2	yes	—
399	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	4	4	no	—
403	C₄	—	4	8	no	—
404	C₄	—	4	4	no	—
405	C₄	C₁₇×#535	1	2	yes	—
406	C₄	C₂²×Q₁₆×C₁₇	1	4	yes	—
407	C₄	C₂²×Q₁₆×C₁₇	1	4	yes	—
408	C₄	C₂×C₁₇×#137	1	4	yes	—
409	C₄	C₂×C₁₇×H(5,𝔽₂)	1	2	yes	—
410	C₂	—	2	4	no	—
411	C₂	C₁₇×#3209	1	4	yes	direct product factor
412	C₂	C₂×C₁₇×#535	1	1	yes	characteristic
413	C₂	C₂³×Q₁₆×C₁₇	1	1	yes	characteristic
414	C₂	C₂²×C₁₇×#137	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₁₇×#3209	C₂	direct (N × H)
4. C₂×C₁₇×#494	C₂	semidirect
5. C₂×C₁₇×#487	C₂	semidirect
6. C₂×C₁₇×#462	C₂	semidirect
30. C₁₇×#494	C₂²	semidirect
31. C₁₇×#487	C₂²	semidirect
32. C₁₇×#462	C₂²	semidirect
115. C₂²×C₄×C₁₇	Q₁₆	semidirect
148. C₂×#3209	C₁₇	direct (N × H)
174. C₂×C₄×C₁₇	C₂×Q₁₆	semidirect
187. #3209	C₂×C₁₇	direct (N × H)
188. C₂×#494	C₂×C₁₇	semidirect
189. C₂×#487	C₂×C₁₇	semidirect
190. C₂×#462	C₂×C₁₇	semidirect
232. #494	C₂²×C₁₇	semidirect
233. #487	C₂²×C₁₇	semidirect
234. #462	C₂²×C₁₇	semidirect
242. C₂×C₁₇	#3209	direct (N × H)
302. C₁₇	C₂×#3209	direct (N × H)
323. C₂²×C₄	Q₁₆×C₁₇	semidirect
381. C₂×C₄	C₂×Q₁₆×C₁₇	semidirect
411. C₂	C₁₇×#3209	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
C₂²×C₁₇×C₄⋊Q₈	2
C₁₇×#3209	2
C₂×C₁₇×#494	2
C₂×C₁₇×#487	2
C₂×C₁₇×#462	2
C₂×C₁₇×#451	2
C₂×C₁₇×#431	2
C₂×#3209	17

Subgroups — C2×C17×#3209 #16918522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×#3209 #16918522