Subgroups — Q₁₆×#41×C₁₇ #16919173

Order 4352.

1826 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#41×C₁₇	C₂	1	2	yes	maximal
2	C₁₇×#3395	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×Q₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#3363	C₂	1	2	yes	maximal, complemented
5	C₁₇×#3338	C₂	1	3	yes	maximal, complemented
6	C₁₇×#3299	C₂	1	6	yes	maximal, complemented
7	D₄×Q₁₆×C₁₇	C₂	1	3	yes	maximal, complemented
8	C₁₇×#3170	C₂	1	3	yes	maximal, complemented
9	C₁₇×#3104	C₂	1	6	yes	maximal, complemented
10	C₈×#41×C₁₇	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄×Q₁₆×C₁₇	C₂	1	3	yes	maximal, complemented
12	C₂²×Q₁₆×C₁₇	C₂²	1	3	yes	—
13	Q₈²×C₁₇	C₂²	1	2	yes	—
14	C₁₇×#557	—	2	2	no	—
15	C₁₇×#557	C₂²	1	2	yes	—
16	C₁₇×#554	—	2	6	no	—
17	C₁₇×#554	C₂²	1	6	yes	—
18	D₄×Q₈×C₁₇	C₂²	1	6	yes	—
19	C₁₇×#533	—	2	6	no	—
20	C₁₇×#533	C₂²	1	6	yes	—
21	C₄×#41×C₁₇	—	2	2	no	—
22	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₇	C₂²	1	6	yes	—
24	C₁₇×#500	C₂²	1	3	yes	—
25	C₁₇×#494	C₂²	1	3	yes	—
26	C₁₇×#487	C₂²	1	6	yes	—
27	C₁₇×#484	C₂²	1	12	yes	—
28	C₁₇×#477	C₂²	1	6	yes	—
29	C₁₇×#477	C₂²	1	6	yes	—
30	C₁₇×#467	C₂²	1	6	yes	—
31	C₁₇×#467	C₂²	1	6	yes	—
32	C₁₇×#462	C₂²	1	6	yes	—
33	C₁₇×#462	C₂²	1	6	yes	—
34	C₁₇×#451	C₂²	1	12	yes	—
35	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
36	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
37	C₄×Q₁₆×C₁₇	C₂²	1	3	yes	—
38	C₄×Q₁₆×C₁₇	C₂²	1	6	yes	—
39	C₄×Q₁₆×C₁₇	C₂²	1	3	yes	—
40	C₄×Q₁₆×C₁₇	C₂²	1	6	yes	—
41	C₄×Q₁₆×C₁₇	C₂²	1	6	yes	—
42	C₄×Q₁₆×C₁₇	C₂²	1	3	yes	—
43	C₄×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic
44	C₈×D₄×C₁₇	C₂²	1	3	yes	—
45	C₈×D₄×C₁₇	C₂²	1	3	yes	—
46	C₁₇×#431	C₂²	1	3	yes	—
47	C₂×C₁₇×#107	C₂²	1	3	yes	—
48	C₂×C₁₇×#103	C₂²	1	6	yes	—
49	C₂×C₄×C₈×C₁₇	C₂²	1	3	yes	—
50	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
51	C₂²×Q₈×C₁₇	C₂³	1	6	yes	—
52	C₂×Q₁₆×C₁₇	—	2	12	no	—
53	C₂×Q₁₆×C₁₇	C₂³	1	3	yes	—
54	C₂×Q₁₆×C₁₇	C₂³	1	6	yes	—
55	C₂×Q₁₆×C₁₇	C₂³	1	6	yes	—
56	C₂×Q₁₆×C₁₇	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₇	C₂³	1	3	yes	—
58	C₂²×C₈×C₁₇	C₂³	1	3	yes	—
59	C₁₇×C₄⋊Q₈	—	2	6	no	—
60	C₁₇×C₄⋊Q₈	—	2	6	no	—
61	C₁₇×C₄⋊Q₈	C₂³	1	6	yes	—
62	C₁₇×C₄⋊Q₈	C₂³	1	6	yes	—
63	C₁₇×#125	—	2	6	no	—
64	C₁₇×#125	—	2	6	no	—
65	C₁₇×#125	—	2	6	no	—
66	C₁₇×C₂²⋊Q₈	—	2	6	no	—
67	C₁₇×C₂²⋊Q₈	—	2	12	no	—
68	C₁₇×C₂²⋊Q₈	—	2	12	no	—
69	C₁₇×C₂²⋊Q₈	C₂³	1	12	yes	—
70	C₄×Q₈×C₁₇	—	2	2	no	—
71	C₄×Q₈×C₁₇	—	2	2	no	—
72	C₄×Q₈×C₁₇	—	2	6	no	—
73	C₄×Q₈×C₁₇	—	2	6	no	—
74	C₄×Q₈×C₁₇	—	2	6	no	—
75	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
76	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
77	C₄×Q₈×C₁₇	C₂³	1	6	yes	—
78	C₄×Q₈×C₁₇	C₂³	1	6	yes	—
79	C₄×Q₈×C₁₇	C₂³	1	6	yes	—
80	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
81	C₄×D₄×C₁₇	—	2	6	no	—
82	C₄×D₄×C₁₇	—	2	6	no	—
83	C₄×D₄×C₁₇	D₄	1	3	yes	—
84	C₄×D₄×C₁₇	C₂³	1	3	yes	—
85	C₁₇×#117	—	2	6	no	—
86	C₁₇×#117	D₄	1	3	yes	—
87	C₂×C₄⋊C₄×C₁₇	—	2	6	no	—
88	C₂×C₄⋊C₄×C₁₇	C₂³	1	6	yes	—
89	C₂×C₄²×C₁₇	—	2	6	no	—
90	C₂×C₄²×C₁₇	C₂³	1	3	yes	—
91	C₁₇×#107	C₂³	1	3	yes	—
92	C₁₇×#107	C₂³	1	6	yes	—
93	C₁₇×#107	C₂³	1	1	yes	characteristic
94	C₁₇×#107	C₂³	1	6	yes	—
95	C₁₇×C₄⋊C₈	C₂³	1	3	yes	—
96	C₁₇×C₄⋊C₈	C₂³	1	3	yes	—
97	C₁₇×#103	C₂³	1	2	yes	—
98	C₁₇×#103	C₂³	1	6	yes	—
99	C₁₇×#103	C₂³	1	6	yes	—
100	C₁₇×#103	C₂³	1	6	yes	—
101	C₁₇×#103	C₂³	1	12	yes	—
102	C₁₇×C₂²⋊C₈	C₂³	1	6	yes	—
103	C₄×C₈×C₁₇	C₂³	1	3	yes	—
104	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
105	C₄×C₈×C₁₇	C₂³	1	3	yes	—
106	C₄×C₈×C₁₇	C₂³	1	3	yes	—
107	#41×C₁₇	Q₁₆	1	8	yes	direct product factor
108	C₂×Q₈×C₁₇	—	2	6	no	—
109	C₂×Q₈×C₁₇	—	2	6	no	—
110	C₂×Q₈×C₁₇	—	2	12	no	—
111	C₂×Q₈×C₁₇	—	4	6	no	—
112	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
113	C₂×Q₈×C₁₇	C₂⁴	1	6	yes	—
114	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
115	C₂×D₄×C₁₇	C₂×D₄	1	3	yes	—
116	C₂²×C₄×C₁₇	—	2	6	no	—
117	C₂²×C₄×C₁₇	—	2	6	no	—
118	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
119	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
120	C₂²×C₄×C₁₇	C₂⁴	1	3	yes	—
121	Q₁₆×C₁₇	—	2	12	no	—
122	Q₁₆×C₁₇	—	2	6	no	—
123	Q₁₆×C₁₇	—	4	6	no	—
124	Q₁₆×C₁₇	#41	1	4	yes	direct product factor
125	C₂×C₈×C₁₇	—	2	6	no	—
126	C₂×C₈×C₁₇	—	4	3	no	—
127	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
128	C₂×C₈×C₁₇	C₂⁴	1	3	yes	—
129	C₂×C₈×C₁₇	C₂⁴	1	3	yes	—
130	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
131	C₄⋊C₄×C₁₇	—	2	6	no	—
132	C₄⋊C₄×C₁₇	—	2	12	no	—
133	C₄⋊C₄×C₁₇	—	2	6	no	—
134	C₄⋊C₄×C₁₇	—	2	6	no	—
135	C₄⋊C₄×C₁₇	—	2	6	no	—
136	C₄⋊C₄×C₁₇	—	2	6	no	—
137	C₄⋊C₄×C₁₇	—	2	6	no	—
138	C₄⋊C₄×C₁₇	—	2	6	no	—
139	C₄⋊C₄×C₁₇	—	2	2	no	—
140	C₄⋊C₄×C₁₇	C₂×D₄	1	3	yes	—
141	C₄⋊C₄×C₁₇	C₂×D₄	1	3	yes	—
142	C₄⋊C₄×C₁₇	C₂⁴	1	6	yes	—
143	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
144	C₂²⋊C₄×C₁₇	—	2	12	no	—
145	C₂²⋊C₄×C₁₇	C₂×D₄	1	6	yes	—
146	C₄²×C₁₇	—	2	6	no	—
147	C₄²×C₁₇	—	2	6	no	—
148	C₄²×C₁₇	—	2	2	no	—
149	C₄²×C₁₇	—	2	6	no	—
150	C₄²×C₁₇	C₂×D₄	1	3	yes	—
151	C₄²×C₁₇	C₂×D₄	1	3	yes	—
152	C₄²×C₁₇	C₂⁴	1	3	yes	—
153	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
154	Q₁₆×#41	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂³×C₁₇	C₂²×D₄	1	3	yes	—
156	Q₈×C₁₇	—	2	2	no	—
157	Q₈×C₁₇	—	2	6	no	—
158	Q₈×C₁₇	—	2	6	no	—
159	Q₈×C₁₇	—	4	12	no	—
160	Q₈×C₁₇	—	8	6	no	—
161	Q₈×C₁₇	C₂×Q₁₆	1	4	yes	complemented
162	Q₈×C₁₇	C₂×#41	1	4	yes	—
163	D₄×C₁₇	C₂×Q₁₆	1	12	yes	complemented
164	C₂×C₄×C₁₇	—	2	2	no	—
165	C₂×C₄×C₁₇	—	2	3	no	—
166	C₂×C₄×C₁₇	—	2	3	no	—
167	C₂×C₄×C₁₇	—	2	2	no	—
168	C₂×C₄×C₁₇	—	2	6	no	—
169	C₂×C₄×C₁₇	—	2	6	no	—
170	C₂×C₄×C₁₇	—	4	3	no	—
171	C₂×C₄×C₁₇	—	4	12	no	—
172	C₂×C₄×C₁₇	—	8	6	no	—
173	C₂×C₄×C₁₇	C₂×Q₁₆	1	12	yes	complemented
174	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
176	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
177	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
178	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
180	C₈×C₁₇	—	2	3	no	—
181	C₈×C₁₇	—	2	1	no	—
182	C₈×C₁₇	—	2	3	no	—
183	C₈×C₁₇	C₂×#41	1	2	yes	—
184	Q₈×#41	C₂×C₁₇	1	2	yes	—
185	#3395	C₂×C₁₇	1	1	yes	characteristic, complemented
186	Q₈×Q₁₆	C₂×C₁₇	1	1	yes	characteristic, complemented
187	#3363	C₂×C₁₇	1	2	yes	complemented
188	#3338	C₂×C₁₇	1	3	yes	complemented
189	#3299	C₂×C₁₇	1	6	yes	complemented
190	D₄×Q₁₆	C₂×C₁₇	1	3	yes	complemented
191	#3170	C₂×C₁₇	1	3	yes	complemented
192	#3104	C₂×C₁₇	1	6	yes	complemented
193	C₈×#41	C₂×C₁₇	1	1	yes	characteristic
194	C₂×C₄×Q₁₆	C₂×C₁₇	1	3	yes	complemented
195	C₂²×C₁₇	—	2	3	no	—
196	C₂²×C₁₇	—	2	3	no	—
197	C₂²×C₁₇	C₂²×Q₁₆	1	6	yes	—
198	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
199	C₄×C₁₇	—	2	1	no	—
200	C₄×C₁₇	—	2	3	no	—
201	C₄×C₁₇	—	2	3	no	—
202	C₄×C₁₇	—	2	4	no	—
203	C₄×C₁₇	—	4	2	no	—
204	C₄×C₁₇	—	4	6	no	—
205	C₄×C₁₇	—	4	6	no	—
206	C₄×C₁₇	C₂²×Q₁₆	1	2	yes	—
207	C₄×C₁₇	C₂²×Q₁₆	1	6	yes	—
208	C₄×C₁₇	C₂²×#41	1	1	yes	characteristic
209	C₄×C₁₇	#585	1	1	yes	characteristic
210	C₂²×Q₁₆	C₂²×C₁₇	1	3	yes	—
211	Q₈²	C₂²×C₁₇	1	2	yes	—
212	#557	—	2	2	no	—
213	#557	C₂²×C₁₇	1	2	yes	—
214	#554	—	2	6	no	—
215	#554	C₂²×C₁₇	1	6	yes	—
216	D₄×Q₈	C₂²×C₁₇	1	6	yes	—
217	#533	—	2	6	no	—
218	#533	C₂²×C₁₇	1	6	yes	—
219	C₄×#41	—	2	2	no	—
220	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
221	C₂×C₄×Q₈	C₂²×C₁₇	1	6	yes	—
222	#500	C₂²×C₁₇	1	3	yes	—
223	#494	C₂²×C₁₇	1	3	yes	—
224	#487	C₂²×C₁₇	1	6	yes	—
225	#484	C₂²×C₁₇	1	12	yes	—
226	#477	C₂²×C₁₇	1	6	yes	—
227	#477	C₂²×C₁₇	1	6	yes	—
228	#467	C₂²×C₁₇	1	6	yes	—
229	#467	C₂²×C₁₇	1	6	yes	—
230	#462	C₂²×C₁₇	1	6	yes	—
231	#462	C₂²×C₁₇	1	6	yes	—
232	#451	C₂²×C₁₇	1	12	yes	—
233	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
234	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
235	C₄×Q₁₆	C₂²×C₁₇	1	3	yes	—
236	C₄×Q₁₆	C₂²×C₁₇	1	6	yes	—
237	C₄×Q₁₆	C₂²×C₁₇	1	6	yes	—
238	C₄×Q₁₆	C₂²×C₁₇	1	6	yes	—
239	C₄×Q₁₆	C₂²×C₁₇	1	3	yes	—
240	C₄×Q₁₆	C₂²×C₁₇	1	3	yes	—
241	C₄×Q₁₆	C₂²×C₁₇	1	1	yes	characteristic
242	C₈×D₄	C₂²×C₁₇	1	3	yes	—
243	C₈×D₄	C₂²×C₁₇	1	3	yes	—
244	#431	C₂²×C₁₇	1	3	yes	—
245	C₂×#107	C₂²×C₁₇	1	3	yes	—
246	C₂×#103	C₂²×C₁₇	1	6	yes	—
247	C₂×C₄×C₈	C₂²×C₁₇	1	3	yes	—
248	C₂×C₁₇	—	2	6	no	—
249	C₂×C₁₇	D₄×#41	1	1	yes	characteristic
250	C₂×C₁₇	C₂³×Q₁₆	1	1	yes	characteristic
251	C₂×C₁₇	#3584	1	1	yes	characteristic
252	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
253	C₂²×Q₈	C₂³×C₁₇	1	6	yes	—
254	C₂×Q₁₆	—	2	12	no	—
255	C₂×Q₁₆	C₂³×C₁₇	1	6	yes	—
256	C₂×Q₁₆	C₂³×C₁₇	1	3	yes	—
257	C₂×Q₁₆	C₂³×C₁₇	1	6	yes	—
258	C₂×Q₁₆	C₂³×C₁₇	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₁₇	1	3	yes	—
260	C₂²×C₈	C₂³×C₁₇	1	3	yes	—
261	C₄⋊Q₈	—	2	6	no	—
262	C₄⋊Q₈	—	2	6	no	—
263	C₄⋊Q₈	C₂³×C₁₇	1	6	yes	—
264	C₄⋊Q₈	C₂³×C₁₇	1	6	yes	—
265	#125	—	2	6	no	—
266	#125	—	2	6	no	—
267	#125	—	2	6	no	—
268	C₂²⋊Q₈	—	2	6	no	—
269	C₂²⋊Q₈	—	2	12	no	—
270	C₂²⋊Q₈	—	2	12	no	—
271	C₂²⋊Q₈	C₂³×C₁₇	1	12	yes	—
272	C₄×Q₈	—	2	2	no	—
273	C₄×Q₈	—	2	2	no	—
274	C₄×Q₈	—	2	6	no	—
275	C₄×Q₈	—	2	6	no	—
276	C₄×Q₈	—	2	6	no	—
277	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
278	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
279	C₄×Q₈	C₂³×C₁₇	1	6	yes	—
280	C₄×Q₈	C₂³×C₁₇	1	6	yes	—
281	C₄×Q₈	C₂³×C₁₇	1	6	yes	—
282	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
283	C₄×D₄	—	2	6	no	—
284	C₄×D₄	—	2	6	no	—
285	C₄×D₄	D₄×C₁₇	1	3	yes	—
286	C₄×D₄	C₂³×C₁₇	1	3	yes	—
287	#117	—	2	6	no	—
288	#117	D₄×C₁₇	1	3	yes	—
289	C₂×C₄⋊C₄	—	2	6	no	—
290	C₂×C₄⋊C₄	C₂³×C₁₇	1	6	yes	—
291	C₂×C₄²	—	2	6	no	—
292	C₂×C₄²	C₂³×C₁₇	1	3	yes	—
293	#107	C₂³×C₁₇	1	1	yes	characteristic
294	#107	C₂³×C₁₇	1	3	yes	—
295	#107	C₂³×C₁₇	1	6	yes	—
296	#107	C₂³×C₁₇	1	6	yes	—
297	C₄⋊C₈	C₂³×C₁₇	1	3	yes	—
298	C₄⋊C₈	C₂³×C₁₇	1	3	yes	—
299	#103	C₂³×C₁₇	1	2	yes	—
300	#103	C₂³×C₁₇	1	6	yes	—
301	#103	C₂³×C₁₇	1	6	yes	—
302	#103	C₂³×C₁₇	1	6	yes	—
303	#103	C₂³×C₁₇	1	12	yes	—
304	C₂²⋊C₈	C₂³×C₁₇	1	6	yes	—
305	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
306	C₄×C₈	C₂³×C₁₇	1	3	yes	—
307	C₄×C₈	C₂³×C₁₇	1	3	yes	—
308	C₄×C₈	C₂³×C₁₇	1	3	yes	—
309	C₁₇	Q₁₆×#41	1	1	yes	characteristic, direct product factor, Sylow
310	#41	Q₁₆×C₁₇	1	8	yes	direct product factor
311	C₂×Q₈	—	2	6	no	—
312	C₂×Q₈	—	2	6	no	—
313	C₂×Q₈	—	2	12	no	—
314	C₂×Q₈	—	4	6	no	—
315	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
316	C₂×Q₈	C₂⁴×C₁₇	1	6	yes	—
317	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
318	C₂×D₄	C₂×D₄×C₁₇	1	3	yes	—
319	C₂²×C₄	—	2	6	no	—
320	C₂²×C₄	—	2	6	no	—
321	C₂²×C₄	C₂×D₄×C₁₇	1	3	yes	—
322	C₂²×C₄	C₂×D₄×C₁₇	1	3	yes	—
323	C₂²×C₄	C₂⁴×C₁₇	1	3	yes	—
324	Q₁₆	—	2	12	no	—
325	Q₁₆	—	2	6	no	—
326	Q₁₆	—	4	6	no	—
327	Q₁₆	#41×C₁₇	1	4	yes	direct product factor
328	C₂×C₈	—	2	6	no	—
329	C₂×C₈	—	4	3	no	—
330	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
331	C₂×C₈	C₂⁴×C₁₇	1	3	yes	—
332	C₂×C₈	C₂⁴×C₁₇	1	3	yes	—
333	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	6	no	—
336	C₄⋊C₄	—	2	6	no	—
337	C₄⋊C₄	—	2	6	no	—
338	C₄⋊C₄	—	2	6	no	—
339	C₄⋊C₄	—	2	6	no	—
340	C₄⋊C₄	—	2	6	no	—
341	C₄⋊C₄	—	2	6	no	—
342	C₄⋊C₄	—	2	12	no	—
343	C₄⋊C₄	C₂×D₄×C₁₇	1	3	yes	—
344	C₄⋊C₄	C₂×D₄×C₁₇	1	3	yes	—
345	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
346	C₄⋊C₄	C₂⁴×C₁₇	1	6	yes	—
347	C₂²⋊C₄	—	2	12	no	—
348	C₂²⋊C₄	C₂×D₄×C₁₇	1	6	yes	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	6	no	—
351	C₄²	—	2	6	no	—
352	C₄²	—	2	6	no	—
353	C₄²	C₂×D₄×C₁₇	1	3	yes	—
354	C₄²	C₂×D₄×C₁₇	1	3	yes	—
355	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
356	C₄²	C₂⁴×C₁₇	1	3	yes	—
357	C₂³	C₂²×D₄×C₁₇	1	3	yes	—
358	Q₈	—	2	2	no	—
359	Q₈	—	2	6	no	—
360	Q₈	—	2	6	no	—
361	Q₈	—	4	12	no	—
362	Q₈	—	8	6	no	—
363	Q₈	C₂×Q₁₆×C₁₇	1	4	yes	complemented
364	Q₈	C₂×#41×C₁₇	1	4	yes	—
365	D₄	C₂×Q₁₆×C₁₇	1	12	yes	complemented
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	3	no	—
368	C₂×C₄	—	2	3	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	6	no	—
371	C₂×C₄	—	2	6	no	—
372	C₂×C₄	—	4	3	no	—
373	C₂×C₄	—	4	12	no	—
374	C₂×C₄	—	8	6	no	—
375	C₂×C₄	C₂×Q₁₆×C₁₇	1	12	yes	complemented
376	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
377	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
378	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
379	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
380	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
381	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
382	C₈	—	2	3	no	—
383	C₈	—	2	1	no	—
384	C₈	—	2	3	no	—
385	C₈	C₂×#41×C₁₇	1	2	yes	—
386	C₂²	—	2	3	no	—
387	C₂²	—	2	3	no	—
388	C₂²	C₂²×Q₁₆×C₁₇	1	6	yes	—
389	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
390	C₄	—	2	3	no	—
391	C₄	—	2	4	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	3	no	—
394	C₄	—	4	6	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	6	no	—
397	C₄	C₂²×Q₁₆×C₁₇	1	2	yes	—
398	C₄	C₂²×Q₁₆×C₁₇	1	6	yes	—
399	C₄	C₂²×#41×C₁₇	1	1	yes	characteristic
400	C₄	C₁₇×#585	1	1	yes	characteristic
401	C₂	—	2	6	no	—
402	C₂	D₄×#41×C₁₇	1	1	yes	characteristic
403	C₂	C₂³×Q₁₆×C₁₇	1	1	yes	characteristic
404	C₂	C₁₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
socle	C₂²×C₁₇	C₂³×D₄
prime radical	C₂×#41×C₁₇	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₄×#41×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₇×#3395	C₂	semidirect
3. Q₈×Q₁₆×C₁₇	C₂	semidirect
4. C₁₇×#3363	C₂	semidirect
5. C₁₇×#3338	C₂	semidirect
6. C₁₇×#3299	C₂	semidirect
7. D₄×Q₁₆×C₁₇	C₂	semidirect
8. C₁₇×#3170	C₂	semidirect
9. C₁₇×#3104	C₂	semidirect
11. C₂×C₄×Q₁₆×C₁₇	C₂	semidirect
107. #41×C₁₇	Q₁₆	direct (N × H)
124. Q₁₆×C₁₇	#41	direct (N × H)
154. Q₁₆×#41	C₁₇	direct (N × H)
161. Q₈×C₁₇	C₂×Q₁₆	semidirect
163. D₄×C₁₇	C₂×Q₁₆	semidirect
173. C₂×C₄×C₁₇	C₂×Q₁₆	semidirect
185. #3395	C₂×C₁₇	semidirect
186. Q₈×Q₁₆	C₂×C₁₇	semidirect
187. #3363	C₂×C₁₇	semidirect
188. #3338	C₂×C₁₇	semidirect
189. #3299	C₂×C₁₇	semidirect
190. D₄×Q₁₆	C₂×C₁₇	semidirect
191. #3170	C₂×C₁₇	semidirect
192. #3104	C₂×C₁₇	semidirect
194. C₂×C₄×Q₁₆	C₂×C₁₇	semidirect
309. C₁₇	Q₁₆×#41	direct (N × H)
310. #41	Q₁₆×C₁₇	direct (N × H)
327. Q₁₆	#41×C₁₇	direct (N × H)
363. Q₈	C₂×Q₁₆×C₁₇	semidirect
365. D₄	C₂×Q₁₆×C₁₇	semidirect
375. C₂×C₄	C₂×Q₁₆×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#41×C₁₇	2
C₁₇×#3395	2
Q₈×Q₁₆×C₁₇	2
C₁₇×#3363	2
C₁₇×#3338	2
C₁₇×#3299	2
D₄×Q₁₆×C₁₇	2
C₁₇×#3170	2
C₁₇×#3104	2
C₈×#41×C₁₇	2
C₂×C₄×Q₁₆×C₁₇	2
Q₁₆×#41	17

Subgroups — Q16×#41×C17 #16919173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₁₆×#41×C₁₇ #16919173