Subgroups — C₁₇×#25408 #16883152

Order 4352.

926 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3153	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₇×#472	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×#471	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#3036	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₇×#463	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#2052	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#2051	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#2019	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#2018	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1967	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1950	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1908	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#1907	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₇×#100	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₇×#137	C₂²	1	1	yes	characteristic
17	C₂×C₁₇×#137	C₂²	1	1	yes	characteristic
18	C₂×C₁₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂×C₁₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
20	C₂×C₁₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
21	C₂×C₁₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
22	C₂²×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
23	C₂²×D₈×C₁₇	C₂²	1	1	yes	characteristic
24	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic
25	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic
26	C₁₇×#532	C₂²	1	1	yes	characteristic
27	C₂×C₁₇×#124	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
29	C₁₇×#497	—	2	1	no	—
30	C₁₇×#496	—	2	1	no	—
31	C₁₇×#495	—	2	1	no	—
32	C₁₇×#495	—	2	1	no	—
33	C₁₇×#472	—	2	4	no	—
34	C₁₇×#471	—	2	4	no	—
35	C₁₇×#463	—	2	1	no	—
36	C₁₇×#463	—	2	1	no	—
37	C₁₇×#463	—	2	1	no	—
38	C₁₇×#463	—	2	1	no	—
39	C₁₇×#463	—	2	1	no	—
40	C₁₇×#463	—	2	1	no	—
41	C₁₇×#461	—	2	1	no	—
42	C₁₇×#459	—	2	1	no	—
43	C₁₇×#436	—	2	1	no	—
44	C₁₇×#435	—	2	1	no	—
45	C₁₇×#435	—	2	1	no	—
46	C₈×D₄×C₁₇	—	2	1	no	—
47	C₂×C₁₇×#108	C₂²	1	1	yes	characteristic
48	C₂×C₁₇×#108	C₂²	1	1	yes	characteristic
49	C₁₇×#423	C₂²	1	1	yes	characteristic
50	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
51	C₁₇×#417	C₂²	1	1	yes	characteristic
52	C₁₇×#417	C₂²	1	1	yes	characteristic
53	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
54	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
55	C₂×C₁₇×#101	C₂²	1	1	yes	characteristic
56	C₂×C₁₇×#101	C₂²	1	1	yes	characteristic
57	C₂×C₁₇×#100	C₂²	1	1	yes	characteristic
58	C₂×C₁₇×#100	C₂²	1	1	yes	characteristic
59	C₂×C₁₇×#100	C₂²	1	1	yes	characteristic
60	C₂×C₁₇×#100	C₂²	1	1	yes	characteristic
61	C₁₇×#408	C₂²	1	1	yes	characteristic
62	C₁₇×#408	C₂²	1	1	yes	characteristic
63	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
64	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
65	C₁₇×#343	C₂²	1	1	yes	characteristic
66	C₁₇×#343	C₂²	1	1	yes	characteristic
67	C₁₇×#341	C₂²	1	1	yes	characteristic
68	C₁₇×#341	C₂²	1	1	yes	characteristic
69	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
70	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₇	—	2	1	no	—
75	C₁₇×#137	—	2	2	no	—
76	C₁₇×#137	—	2	2	no	—
77	C₁₇×#137	—	4	1	no	—
78	C₁₇×#137	—	4	1	no	—
79	C₁₇×AGL(1,ℤ/8)	—	2	2	no	—
80	C₁₇×AGL(1,ℤ/8)	—	2	2	no	—
81	C₁₇×AGL(1,ℤ/8)	—	2	2	no	—
82	C₁₇×AGL(1,ℤ/8)	—	2	2	no	—
83	C₁₇×AGL(1,ℤ/8)	—	4	1	no	—
84	C₁₇×AGL(1,ℤ/8)	—	4	1	no	—
85	C₁₇×AGL(1,ℤ/8)	—	4	1	no	—
86	C₁₇×AGL(1,ℤ/8)	—	4	1	no	—
87	C₂×Q₁₆×C₁₇	—	2	1	no	—
88	C₂×Q₁₆×C₁₇	—	2	1	no	—
89	C₂×SD₁₆×C₁₇	—	2	1	no	—
90	C₂×SD₁₆×C₁₇	—	2	1	no	—
91	C₂×SD₁₆×C₁₇	—	2	1	no	—
92	C₂×SD₁₆×C₁₇	—	2	1	no	—
93	C₂×SD₁₆×C₁₇	—	2	1	no	—
94	C₂×SD₁₆×C₁₇	—	2	1	no	—
95	C₂×SD₁₆×C₁₇	—	2	2	no	—
96	C₂×SD₁₆×C₁₇	—	2	1	no	—
97	C₂×SD₁₆×C₁₇	—	2	1	no	—
98	C₂×SD₁₆×C₁₇	—	4	1	no	—
99	C₂×D₈×C₁₇	—	2	1	no	—
100	C₂×D₈×C₁₇	—	2	1	no	—
101	C₂×D₈×C₁₇	—	2	2	no	—
102	C₂×D₈×C₁₇	—	2	1	no	—
103	C₂×D₈×C₁₇	—	2	1	no	—
104	C₂×D₈×C₁₇	—	2	1	no	—
105	C₂×D₈×C₁₇	—	2	1	no	—
106	C₂×D₈×C₁₇	—	4	1	no	—
107	C₁₇×#131	—	2	2	no	—
108	C₁₇×#131	—	2	2	no	—
109	C₁₇×#131	—	4	1	no	—
110	C₁₇×#131	—	4	1	no	—
111	C₂×M₁₆×C₁₇	—	2	1	no	—
112	C₂×M₁₆×C₁₇	—	2	1	no	—
113	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
114	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
115	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
116	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
117	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₁₇	—	2	1	no	—
120	C₂²×C₈×C₁₇	—	2	1	no	—
121	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
123	C₁₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
124	C₁₇×#127	D₄	1	1	yes	characteristic
125	C₁₇×#124	—	2	1	no	—
126	C₁₇×#124	—	2	1	no	—
127	C₁₇×#124	—	2	1	no	—
128	C₁₇×#124	—	2	1	no	—
129	C₁₇×#124	D₄	1	1	yes	characteristic
130	C₁₇×#124	D₄	1	1	yes	characteristic
131	C₁₇×#121	—	2	1	no	—
132	C₁₇×#121	—	2	1	no	—
133	C₄×D₄×C₁₇	—	2	1	no	—
134	C₄×D₄×C₁₇	—	2	1	no	—
135	C₄×D₄×C₁₇	—	2	1	no	—
136	C₄×D₄×C₁₇	—	2	1	no	—
137	C₄×D₄×C₁₇	—	2	1	no	—
138	C₄×D₄×C₁₇	—	2	1	no	—
139	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
141	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
143	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
144	C₁₇×#108	—	2	2	no	—
145	C₁₇×#108	—	2	2	no	—
146	C₁₇×C₄⋊C₈	—	2	1	no	—
147	C₁₇×C₄⋊C₈	—	2	1	no	—
148	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
149	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
150	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
151	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
152	C₁₇×#103	—	2	1	no	—
153	C₁₇×#103	—	2	1	no	—
154	C₁₇×#103	—	2	1	no	—
155	C₁₇×#103	—	2	1	no	—
156	C₁₇×#102	—	2	1	no	—
157	C₁₇×#102	—	2	1	no	—
158	C₁₇×#102	—	2	1	no	—
159	C₁₇×#102	—	2	1	no	—
160	C₁₇×#101	—	2	2	no	—
161	C₁₇×#101	—	4	1	no	—
162	C₁₇×#100	—	2	2	no	—
163	C₁₇×#100	—	2	2	no	—
164	C₁₇×#100	—	4	1	no	—
165	C₁₇×#100	D₄	1	4	yes	complemented
166	C₁₇×C₂²⋊C₈	—	2	1	no	—
167	C₁₇×C₂²⋊C₈	—	2	1	no	—
168	C₁₇×C₂²⋊C₈	—	2	1	no	—
169	C₁₇×C₂²⋊C₈	—	2	1	no	—
170	C₁₇×#97	—	2	1	no	—
171	C₁₇×#97	—	2	1	no	—
172	C₄×C₈×C₁₇	—	2	1	no	—
173	C₄×C₈×C₁₇	—	2	1	no	—
174	C₂⁴×C₁₇	—	2	1	no	—
175	C₂⁴×C₁₇	—	2	1	no	—
176	#41×C₁₇	—	2	1	no	—
177	#41×C₁₇	—	2	1	no	—
178	#41×C₁₇	—	2	1	no	—
179	#41×C₁₇	—	2	1	no	—
180	#41×C₁₇	—	2	1	no	—
181	#41×C₁₇	—	2	1	no	—
182	#41×C₁₇	—	2	1	no	—
183	#41×C₁₇	—	2	1	no	—
184	C₂×Q₈×C₁₇	—	2	1	no	—
185	C₂×Q₈×C₁₇	—	2	1	no	—
186	C₂×Q₈×C₁₇	—	2	1	no	—
187	C₂×Q₈×C₁₇	—	2	1	no	—
188	C₂×Q₈×C₁₇	—	2	1	no	—
189	C₂×Q₈×C₁₇	—	2	1	no	—
190	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
191	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
192	C₂×D₄×C₁₇	—	2	1	no	—
193	C₂×D₄×C₁₇	—	2	1	no	—
194	C₂×D₄×C₁₇	—	2	1	no	—
195	C₂×D₄×C₁₇	—	2	1	no	—
196	C₂×D₄×C₁₇	—	2	1	no	—
197	C₂×D₄×C₁₇	—	2	1	no	—
198	C₂×D₄×C₁₇	—	2	1	no	—
199	C₂×D₄×C₁₇	—	2	1	no	—
200	C₂×D₄×C₁₇	—	2	1	no	—
201	C₂×D₄×C₁₇	—	2	1	no	—
202	C₂×D₄×C₁₇	—	2	1	no	—
203	C₂×D₄×C₁₇	—	2	1	no	—
204	C₂×D₄×C₁₇	—	2	1	no	—
205	C₂×D₄×C₁₇	—	2	1	no	—
206	C₂×D₄×C₁₇	—	2	1	no	—
207	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
208	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
209	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
210	C₂²×C₄×C₁₇	—	2	1	no	—
211	C₂²×C₄×C₁₇	—	2	1	no	—
212	C₂²×C₄×C₁₇	—	2	1	no	—
213	C₂²×C₄×C₁₇	—	2	1	no	—
214	C₂²×C₄×C₁₇	—	4	1	no	—
215	C₂²×C₄×C₁₇	—	4	1	no	—
216	C₂²×C₄×C₁₇	—	8	2	no	—
217	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
218	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
219	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
220	Q₁₆×C₁₇	—	4	2	no	—
221	Q₁₆×C₁₇	—	4	2	no	—
222	SD₁₆×C₁₇	—	4	2	no	—
223	SD₁₆×C₁₇	—	4	2	no	—
224	SD₁₆×C₁₇	—	4	2	no	—
225	SD₁₆×C₁₇	—	4	2	no	—
226	SD₁₆×C₁₇	—	4	2	no	—
227	SD₁₆×C₁₇	—	4	2	no	—
228	SD₁₆×C₁₇	—	4	2	no	—
229	SD₁₆×C₁₇	—	4	2	no	—
230	D₈×C₁₇	—	4	2	no	—
231	D₈×C₁₇	—	4	2	no	—
232	D₈×C₁₇	—	4	2	no	—
233	D₈×C₁₇	—	4	2	no	—
234	D₈×C₁₇	—	4	2	no	—
235	D₈×C₁₇	—	4	2	no	—
236	M₁₆×C₁₇	—	2	1	no	—
237	M₁₆×C₁₇	—	2	1	no	—
238	M₁₆×C₁₇	—	2	1	no	—
239	M₁₆×C₁₇	—	2	1	no	—
240	M₁₆×C₁₇	—	2	1	no	—
241	M₁₆×C₁₇	—	2	1	no	—
242	M₁₆×C₁₇	—	2	1	no	—
243	M₁₆×C₁₇	—	2	1	no	—
244	M₁₆×C₁₇	—	2	1	no	—
245	M₁₆×C₁₇	—	4	2	no	—
246	M₁₆×C₁₇	—	4	2	no	—
247	M₁₆×C₁₇	C₂×D₄	1	2	yes	—
248	M₁₆×C₁₇	C₂×D₄	1	2	yes	—
249	M₁₆×C₁₇	#41	1	2	yes	—
250	C₂×C₈×C₁₇	—	2	1	no	—
251	C₂×C₈×C₁₇	—	2	1	no	—
252	C₂×C₈×C₁₇	—	2	1	no	—
253	C₂×C₈×C₁₇	—	2	1	no	—
254	C₂×C₈×C₁₇	—	2	1	no	—
255	C₂×C₈×C₁₇	—	2	1	no	—
256	C₂×C₈×C₁₇	—	2	1	no	—
257	C₂×C₈×C₁₇	—	2	1	no	—
258	C₂×C₈×C₁₇	—	2	1	no	—
259	C₂×C₈×C₁₇	—	2	1	no	—
260	C₂×C₈×C₁₇	—	4	2	no	—
261	C₂×C₈×C₁₇	—	4	2	no	—
262	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
263	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
264	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
265	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
266	C₄⋊C₄×C₁₇	—	2	1	no	—
267	C₄⋊C₄×C₁₇	—	2	1	no	—
268	C₄⋊C₄×C₁₇	—	2	1	no	—
269	C₄⋊C₄×C₁₇	—	2	1	no	—
270	C₂²⋊C₄×C₁₇	—	2	1	no	—
271	C₂²⋊C₄×C₁₇	—	2	1	no	—
272	C₂²⋊C₄×C₁₇	—	2	1	no	—
273	C₂²⋊C₄×C₁₇	—	2	1	no	—
274	C₂²⋊C₄×C₁₇	—	4	1	no	—
275	C₂²⋊C₄×C₁₇	—	4	1	no	—
276	C₂²⋊C₄×C₁₇	—	4	1	no	—
277	C₂²⋊C₄×C₁₇	—	4	1	no	—
278	C₂²⋊C₄×C₁₇	—	4	1	no	—
279	C₂²⋊C₄×C₁₇	—	4	1	no	—
280	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
284	#25408	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
285	C₂³×C₁₇	—	2	1	no	—
286	C₂³×C₁₇	—	2	1	no	—
287	C₂³×C₁₇	—	2	2	no	—
288	C₂³×C₁₇	—	4	1	no	—
289	C₂³×C₁₇	—	4	1	no	—
290	C₂³×C₁₇	—	4	1	no	—
291	C₂³×C₁₇	—	4	1	no	—
292	C₂³×C₁₇	—	4	1	no	—
293	C₂³×C₁₇	—	8	1	no	—
294	C₂³×C₁₇	—	8	1	no	—
295	C₂³×C₁₇	—	8	1	no	—
296	C₂³×C₁₇	—	8	1	no	—
297	C₂³×C₁₇	C₂×#41	1	1	yes	characteristic
298	Q₈×C₁₇	—	2	1	no	—
299	Q₈×C₁₇	—	2	1	no	—
300	Q₈×C₁₇	—	2	1	no	—
301	Q₈×C₁₇	—	2	1	no	—
302	Q₈×C₁₇	—	4	1	no	—
303	Q₈×C₁₇	—	4	1	no	—
304	Q₈×C₁₇	—	4	1	no	—
305	Q₈×C₁₇	—	4	1	no	—
306	D₄×C₁₇	—	2	1	no	—
307	D₄×C₁₇	—	2	2	no	—
308	D₄×C₁₇	—	2	2	no	—
309	D₄×C₁₇	—	2	1	no	—
310	D₄×C₁₇	—	2	1	no	—
311	D₄×C₁₇	—	2	1	no	—
312	D₄×C₁₇	—	4	2	no	—
313	D₄×C₁₇	—	4	1	no	—
314	D₄×C₁₇	—	4	1	no	—
315	D₄×C₁₇	—	4	1	no	—
316	D₄×C₁₇	—	4	1	no	—
317	D₄×C₁₇	—	4	1	no	—
318	D₄×C₁₇	—	4	1	no	—
319	D₄×C₁₇	—	4	1	no	—
320	D₄×C₁₇	—	4	1	no	—
321	D₄×C₁₇	—	4	1	no	—
322	D₄×C₁₇	—	4	1	no	—
323	D₄×C₁₇	—	8	1	no	—
324	C₂×C₄×C₁₇	—	2	1	no	—
325	C₂×C₄×C₁₇	—	2	1	no	—
326	C₂×C₄×C₁₇	—	4	1	no	—
327	C₂×C₄×C₁₇	—	4	1	no	—
328	C₂×C₄×C₁₇	—	4	1	no	—
329	C₂×C₄×C₁₇	—	4	1	no	—
330	C₂×C₄×C₁₇	—	4	1	no	—
331	C₂×C₄×C₁₇	—	4	1	no	—
332	C₂×C₄×C₁₇	—	4	1	no	—
333	C₂×C₄×C₁₇	—	4	1	no	—
334	C₂×C₄×C₁₇	—	4	1	no	—
335	C₂×C₄×C₁₇	—	4	1	no	—
336	C₂×C₄×C₁₇	—	8	2	no	—
337	C₂×C₄×C₁₇	—	8	2	no	—
338	C₂×C₄×C₁₇	—	8	1	no	—
339	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
340	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
341	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
342	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
343	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
347	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
348	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
349	C₈×C₁₇	—	2	1	no	—
350	C₈×C₁₇	—	2	1	no	—
351	C₈×C₁₇	—	2	1	no	—
352	C₈×C₁₇	—	2	1	no	—
353	C₈×C₁₇	—	2	2	no	—
354	C₈×C₁₇	—	2	2	no	—
355	C₈×C₁₇	—	2	2	no	—
356	C₈×C₁₇	—	4	1	no	—
357	C₈×C₁₇	—	4	1	no	—
358	C₈×C₁₇	—	4	1	no	—
359	#3153	C₂×C₁₇	1	1	yes	characteristic, complemented
360	C₂×#472	C₂×C₁₇	1	1	yes	characteristic, complemented
361	C₂×#471	C₂×C₁₇	1	1	yes	characteristic, complemented
362	#3036	C₂×C₁₇	1	1	yes	characteristic, complemented
363	C₂×#463	C₂×C₁₇	1	1	yes	characteristic, complemented
364	#2935	C₂×C₁₇	1	1	yes	characteristic, complemented
365	#2052	C₂×C₁₇	1	1	yes	characteristic, complemented
366	#2051	C₂×C₁₇	1	1	yes	characteristic, complemented
367	#2019	C₂×C₁₇	1	1	yes	characteristic, complemented
368	#2018	C₂×C₁₇	1	1	yes	characteristic, complemented
369	#1967	C₂×C₁₇	1	1	yes	characteristic, complemented
370	#1950	C₂×C₁₇	1	1	yes	characteristic, complemented
371	#1908	C₂×C₁₇	1	1	yes	characteristic, complemented
372	#1907	C₂×C₁₇	1	1	yes	characteristic, complemented
373	C₄×#100	C₂×C₁₇	1	1	yes	characteristic, complemented
374	C₂²×C₁₇	—	2	1	no	—
375	C₂²×C₁₇	—	2	1	no	—
376	C₂²×C₁₇	—	4	1	no	—
377	C₂²×C₁₇	—	4	1	no	—
378	C₂²×C₁₇	—	4	2	no	—
379	C₂²×C₁₇	—	4	1	no	—
380	C₂²×C₁₇	—	4	1	no	—
381	C₂²×C₁₇	—	4	1	no	—
382	C₂²×C₁₇	—	4	1	no	—
383	C₂²×C₁₇	—	8	2	no	—
384	C₂²×C₁₇	—	8	2	no	—
385	C₂²×C₁₇	—	8	1	no	—
386	C₂²×C₁₇	—	8	1	no	—
387	C₂²×C₁₇	—	8	1	no	—
388	C₂²×C₁₇	—	8	1	no	—
389	C₂²×C₁₇	—	8	1	no	—
390	C₂²×C₁₇	—	16	1	no	—
391	C₂²×C₁₇	—	16	1	no	—
392	C₂²×C₁₇	C₂×#121	1	1	yes	characteristic
393	C₂²×C₁₇	#532	1	1	yes	characteristic
394	C₂²×C₁₇	#540	1	1	yes	characteristic
395	C₄×C₁₇	—	2	1	no	—
396	C₄×C₁₇	—	2	1	no	—
397	C₄×C₁₇	—	2	1	no	—
398	C₄×C₁₇	—	2	1	no	—
399	C₄×C₁₇	—	4	1	no	—
400	C₄×C₁₇	—	4	1	no	—
401	C₄×C₁₇	—	8	1	no	—
402	C₄×C₁₇	—	8	1	no	—
403	C₄×C₁₇	D₄²	1	1	yes	characteristic
404	C₄×C₁₇	D₄²	1	1	yes	characteristic
405	C₄×C₁₇	#546	1	1	yes	characteristic
406	C₄×C₁₇	#550	1	1	yes	characteristic
407	C₂×#137	C₂²×C₁₇	1	1	yes	characteristic
408	C₂×#137	C₂²×C₁₇	1	1	yes	characteristic
409	C₂×AGL(1,ℤ/8)	C₂²×C₁₇	1	1	yes	characteristic
410	C₂×AGL(1,ℤ/8)	C₂²×C₁₇	1	1	yes	characteristic
411	C₂×AGL(1,ℤ/8)	C₂²×C₁₇	1	1	yes	characteristic
412	C₂×AGL(1,ℤ/8)	C₂²×C₁₇	1	1	yes	characteristic
413	C₂²×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
414	C₂²×D₈	C₂²×C₁₇	1	1	yes	characteristic
415	C₂×#131	C₂²×C₁₇	1	1	yes	characteristic
416	C₂×#131	C₂²×C₁₇	1	1	yes	characteristic
417	#532	C₂²×C₁₇	1	1	yes	characteristic
418	C₂×#124	C₂²×C₁₇	1	1	yes	characteristic
419	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
420	#497	—	2	1	no	—
421	#496	—	2	1	no	—
422	#495	—	2	1	no	—
423	#495	—	2	1	no	—
424	#472	—	2	4	no	—
425	#471	—	2	4	no	—
426	#463	—	2	1	no	—
427	#463	—	2	1	no	—
428	#463	—	2	1	no	—
429	#463	—	2	1	no	—
430	#463	—	2	1	no	—
431	#463	—	2	1	no	—
432	#461	—	2	1	no	—
433	#459	—	2	1	no	—
434	#436	—	2	1	no	—
435	#435	—	2	1	no	—
436	#435	—	2	1	no	—
437	C₈×D₄	—	2	1	no	—
438	C₂×#108	C₂²×C₁₇	1	1	yes	characteristic
439	C₂×#108	C₂²×C₁₇	1	1	yes	characteristic
440	#423	C₂²×C₁₇	1	1	yes	characteristic
441	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
442	#417	C₂²×C₁₇	1	1	yes	characteristic
443	#417	C₂²×C₁₇	1	1	yes	characteristic
444	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
445	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
446	C₂×#101	C₂²×C₁₇	1	1	yes	characteristic
447	C₂×#101	C₂²×C₁₇	1	1	yes	characteristic
448	C₂×#100	C₂²×C₁₇	1	1	yes	characteristic
449	C₂×#100	C₂²×C₁₇	1	1	yes	characteristic
450	C₂×#100	C₂²×C₁₇	1	1	yes	characteristic
451	C₂×#100	C₂²×C₁₇	1	1	yes	characteristic
452	#408	C₂²×C₁₇	1	1	yes	characteristic
453	#408	C₂²×C₁₇	1	1	yes	characteristic
454	C₄×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
455	C₄×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
456	#343	C₂²×C₁₇	1	1	yes	characteristic
457	#343	C₂²×C₁₇	1	1	yes	characteristic
458	#341	C₂²×C₁₇	1	1	yes	characteristic
459	#341	C₂²×C₁₇	1	1	yes	characteristic
460	C₂×C₁₇	—	2	1	no	—
461	C₂×C₁₇	—	2	1	no	—
462	C₂×C₁₇	—	8	1	no	—
463	C₂×C₁₇	—	8	1	no	—
464	C₂×C₁₇	—	8	2	no	—
465	C₂×C₁₇	—	16	1	no	—
466	C₂×C₁₇	#2428	1	1	yes	characteristic
467	C₂×C₁₇	#3067	1	1	yes	characteristic
468	C₂×C₁₇	#3068	1	1	yes	characteristic
469	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
470	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
471	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
472	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
473	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
474	C₂³×C₄	—	2	1	no	—
475	#137	—	2	2	no	—
476	#137	—	2	2	no	—
477	#137	—	4	1	no	—
478	#137	—	4	1	no	—
479	AGL(1,ℤ/8)	—	2	2	no	—
480	AGL(1,ℤ/8)	—	2	2	no	—
481	AGL(1,ℤ/8)	—	2	2	no	—
482	AGL(1,ℤ/8)	—	2	2	no	—
483	AGL(1,ℤ/8)	—	4	1	no	—
484	AGL(1,ℤ/8)	—	4	1	no	—
485	AGL(1,ℤ/8)	—	4	1	no	—
486	AGL(1,ℤ/8)	—	4	1	no	—
487	C₂×Q₁₆	—	2	1	no	—
488	C₂×Q₁₆	—	2	1	no	—
489	C₂×SD₁₆	—	2	1	no	—
490	C₂×SD₁₆	—	2	1	no	—
491	C₂×SD₁₆	—	2	1	no	—
492	C₂×SD₁₆	—	2	1	no	—
493	C₂×SD₁₆	—	2	2	no	—
494	C₂×SD₁₆	—	2	1	no	—
495	C₂×SD₁₆	—	2	1	no	—
496	C₂×SD₁₆	—	2	1	no	—
497	C₂×SD₁₆	—	2	1	no	—
498	C₂×SD₁₆	—	4	1	no	—
499	C₂×D₈	—	2	2	no	—
500	C₂×D₈	—	2	1	no	—
501	C₂×D₈	—	2	1	no	—
502	C₂×D₈	—	2	1	no	—
503	C₂×D₈	—	2	1	no	—
504	C₂×D₈	—	2	1	no	—
505	C₂×D₈	—	2	1	no	—
506	C₂×D₈	—	4	1	no	—
507	#131	—	2	2	no	—
508	#131	—	2	2	no	—
509	#131	—	4	1	no	—
510	#131	—	4	1	no	—
511	C₂×M₁₆	—	2	1	no	—
512	C₂×M₁₆	—	2	1	no	—
513	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
514	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
515	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
516	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
517	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
518	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
519	C₂²×C₈	—	2	1	no	—
520	C₂²×C₈	—	2	1	no	—
521	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
522	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
523	C₄⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
524	#127	D₄×C₁₇	1	1	yes	characteristic
525	#124	—	2	1	no	—
526	#124	—	2	1	no	—
527	#124	—	2	1	no	—
528	#124	—	2	1	no	—
529	#124	D₄×C₁₇	1	1	yes	characteristic
530	#124	D₄×C₁₇	1	1	yes	characteristic
531	#121	—	2	1	no	—
532	#121	—	2	1	no	—
533	C₄×D₄	—	2	1	no	—
534	C₄×D₄	—	2	1	no	—
535	C₄×D₄	—	2	1	no	—
536	C₄×D₄	—	2	1	no	—
537	C₄×D₄	—	2	1	no	—
538	C₄×D₄	—	2	1	no	—
539	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	—	2	1	no	—
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₂²⋊C₄	—	2	1	no	—
543	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
544	#108	—	2	2	no	—
545	#108	—	2	2	no	—
546	C₄⋊C₈	—	2	1	no	—
547	C₄⋊C₈	—	2	1	no	—
548	C₄⋊C₈	D₄×C₁₇	1	1	yes	characteristic
549	C₄⋊C₈	D₄×C₁₇	1	1	yes	characteristic
550	C₄⋊C₈	D₄×C₁₇	1	1	yes	characteristic
551	C₄⋊C₈	D₄×C₁₇	1	1	yes	characteristic
552	#103	—	2	1	no	—
553	#103	—	2	1	no	—
554	#103	—	2	1	no	—
555	#103	—	2	1	no	—
556	#102	—	2	1	no	—
557	#102	—	2	1	no	—
558	#102	—	2	1	no	—
559	#102	—	2	1	no	—
560	#101	—	2	2	no	—
561	#101	—	4	1	no	—
562	#100	—	2	2	no	—
563	#100	—	2	2	no	—
564	#100	—	4	1	no	—
565	#100	D₄×C₁₇	1	4	yes	complemented
566	C₂²⋊C₈	—	2	1	no	—
567	C₂²⋊C₈	—	2	1	no	—
568	C₂²⋊C₈	—	2	1	no	—
569	C₂²⋊C₈	—	2	1	no	—
570	#97	—	2	1	no	—
571	#97	—	2	1	no	—
572	C₄×C₈	—	2	1	no	—
573	C₄×C₈	—	2	1	no	—
574	C₁₇	#25408	1	1	yes	characteristic, direct product factor, Sylow
575	C₂⁴	—	2	1	no	—
576	C₂⁴	—	2	1	no	—
577	#41	—	2	1	no	—
578	#41	—	2	1	no	—
579	#41	—	2	1	no	—
580	#41	—	2	1	no	—
581	#41	—	2	1	no	—
582	#41	—	2	1	no	—
583	#41	—	2	1	no	—
584	#41	—	2	1	no	—
585	C₂×Q₈	—	2	1	no	—
586	C₂×Q₈	—	2	1	no	—
587	C₂×Q₈	—	2	1	no	—
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	—	2	1	no	—
590	C₂×Q₈	—	2	1	no	—
591	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
592	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	1	no	—
596	C₂×D₄	—	2	1	no	—
597	C₂×D₄	—	2	1	no	—
598	C₂×D₄	—	2	1	no	—
599	C₂×D₄	—	2	1	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	2	1	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
609	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
610	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	4	1	no	—
616	C₂²×C₄	—	4	1	no	—
617	C₂²×C₄	—	8	2	no	—
618	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
619	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
621	Q₁₆	—	4	2	no	—
622	Q₁₆	—	4	2	no	—
623	SD₁₆	—	4	2	no	—
624	SD₁₆	—	4	2	no	—
625	SD₁₆	—	4	2	no	—
626	SD₁₆	—	4	2	no	—
627	SD₁₆	—	4	2	no	—
628	SD₁₆	—	4	2	no	—
629	SD₁₆	—	4	2	no	—
630	SD₁₆	—	4	2	no	—
631	D₈	—	4	2	no	—
632	D₈	—	4	2	no	—
633	D₈	—	4	2	no	—
634	D₈	—	4	2	no	—
635	D₈	—	4	2	no	—
636	D₈	—	4	2	no	—
637	M₁₆	—	2	1	no	—
638	M₁₆	—	2	1	no	—
639	M₁₆	—	2	1	no	—
640	M₁₆	—	2	1	no	—
641	M₁₆	—	2	1	no	—
642	M₁₆	—	2	1	no	—
643	M₁₆	—	2	1	no	—
644	M₁₆	—	2	1	no	—
645	M₁₆	—	2	1	no	—
646	M₁₆	—	4	2	no	—
647	M₁₆	—	4	2	no	—
648	M₁₆	C₂×D₄×C₁₇	1	2	yes	—
649	M₁₆	C₂×D₄×C₁₇	1	2	yes	—
650	M₁₆	#41×C₁₇	1	2	yes	—
651	C₂×C₈	—	2	1	no	—
652	C₂×C₈	—	2	1	no	—
653	C₂×C₈	—	2	1	no	—
654	C₂×C₈	—	2	1	no	—
655	C₂×C₈	—	2	1	no	—
656	C₂×C₈	—	2	1	no	—
657	C₂×C₈	—	2	1	no	—
658	C₂×C₈	—	2	1	no	—
659	C₂×C₈	—	2	1	no	—
660	C₂×C₈	—	2	1	no	—
661	C₂×C₈	—	4	2	no	—
662	C₂×C₈	—	4	2	no	—
663	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
664	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
665	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
666	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₂²⋊C₄	—	2	1	no	—
672	C₂²⋊C₄	—	2	1	no	—
673	C₂²⋊C₄	—	2	1	no	—
674	C₂²⋊C₄	—	2	1	no	—
675	C₂²⋊C₄	—	4	1	no	—
676	C₂²⋊C₄	—	4	1	no	—
677	C₂²⋊C₄	—	4	1	no	—
678	C₂²⋊C₄	—	4	1	no	—
679	C₂²⋊C₄	—	4	1	no	—
680	C₂²⋊C₄	—	4	1	no	—
681	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
682	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
683	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
684	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
685	C₂³	—	2	1	no	—
686	C₂³	—	2	1	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	4	1	no	—
689	C₂³	—	4	1	no	—
690	C₂³	—	4	1	no	—
691	C₂³	—	4	1	no	—
692	C₂³	—	4	1	no	—
693	C₂³	—	8	1	no	—
694	C₂³	—	8	1	no	—
695	C₂³	—	8	1	no	—
696	C₂³	—	8	1	no	—
697	C₂³	C₂×#41×C₁₇	1	1	yes	characteristic
698	Q₈	—	2	1	no	—
699	Q₈	—	2	1	no	—
700	Q₈	—	2	1	no	—
701	Q₈	—	2	1	no	—
702	Q₈	—	4	1	no	—
703	Q₈	—	4	1	no	—
704	Q₈	—	4	1	no	—
705	Q₈	—	4	1	no	—
706	D₄	—	2	1	no	—
707	D₄	—	2	2	no	—
708	D₄	—	2	2	no	—
709	D₄	—	2	1	no	—
710	D₄	—	2	1	no	—
711	D₄	—	2	1	no	—
712	D₄	—	4	2	no	—
713	D₄	—	4	1	no	—
714	D₄	—	4	1	no	—
715	D₄	—	4	1	no	—
716	D₄	—	4	1	no	—
717	D₄	—	4	1	no	—
718	D₄	—	4	1	no	—
719	D₄	—	4	1	no	—
720	D₄	—	4	1	no	—
721	D₄	—	4	1	no	—
722	D₄	—	4	1	no	—
723	D₄	—	8	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	8	2	no	—
737	C₂×C₄	—	8	2	no	—
738	C₂×C₄	—	8	1	no	—
739	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
740	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
741	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
742	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
743	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
744	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
745	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
746	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
747	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
748	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
749	C₈	—	2	1	no	—
750	C₈	—	2	1	no	—
751	C₈	—	2	1	no	—
752	C₈	—	2	1	no	—
753	C₈	—	2	2	no	—
754	C₈	—	2	2	no	—
755	C₈	—	2	2	no	—
756	C₈	—	4	1	no	—
757	C₈	—	4	1	no	—
758	C₈	—	4	1	no	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	8	2	no	—
769	C₂²	—	8	2	no	—
770	C₂²	—	8	1	no	—
771	C₂²	—	8	1	no	—
772	C₂²	—	8	1	no	—
773	C₂²	—	8	1	no	—
774	C₂²	—	8	1	no	—
775	C₂²	—	16	1	no	—
776	C₂²	—	16	1	no	—
777	C₂²	C₂×C₁₇×#121	1	1	yes	characteristic
778	C₂²	C₁₇×#532	1	1	yes	characteristic
779	C₂²	C₁₇×#540	1	1	yes	characteristic
780	C₄	—	2	1	no	—
781	C₄	—	2	1	no	—
782	C₄	—	2	1	no	—
783	C₄	—	2	1	no	—
784	C₄	—	4	1	no	—
785	C₄	—	4	1	no	—
786	C₄	—	8	1	no	—
787	C₄	—	8	1	no	—
788	C₄	D₄²×C₁₇	1	1	yes	characteristic
789	C₄	D₄²×C₁₇	1	1	yes	characteristic
790	C₄	C₁₇×#546	1	1	yes	characteristic
791	C₄	C₁₇×#550	1	1	yes	characteristic
792	C₂	—	2	1	no	—
793	C₂	—	2	1	no	—
794	C₂	—	8	1	no	—
795	C₂	—	8	1	no	—
796	C₂	—	8	2	no	—
797	C₂	—	16	1	no	—
798	C₂	C₁₇×#2428	1	1	yes	characteristic
799	C₂	C₁₇×#3067	1	1	yes	characteristic
800	C₂	C₁₇×#3068	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3153	C₂	semidirect
2. C₂×C₁₇×#472	C₂	semidirect
3. C₂×C₁₇×#471	C₂	semidirect
4. C₁₇×#3036	C₂	semidirect
5. C₂×C₁₇×#463	C₂	semidirect
6. C₁₇×#2935	C₂	semidirect
7. C₁₇×#2052	C₂	semidirect
8. C₁₇×#2051	C₂	semidirect
9. C₁₇×#2019	C₂	semidirect
10. C₁₇×#2018	C₂	semidirect
11. C₁₇×#1967	C₂	semidirect
12. C₁₇×#1950	C₂	semidirect
13. C₁₇×#1908	C₂	semidirect
14. C₁₇×#1907	C₂	semidirect
15. C₄×C₁₇×#100	C₂	semidirect
165. C₁₇×#100	D₄	semidirect
284. #25408	C₁₇	direct (N × H)
359. #3153	C₂×C₁₇	semidirect
360. C₂×#472	C₂×C₁₇	semidirect
361. C₂×#471	C₂×C₁₇	semidirect
362. #3036	C₂×C₁₇	semidirect
363. C₂×#463	C₂×C₁₇	semidirect
364. #2935	C₂×C₁₇	semidirect
365. #2052	C₂×C₁₇	semidirect
366. #2051	C₂×C₁₇	semidirect
367. #2019	C₂×C₁₇	semidirect
368. #2018	C₂×C₁₇	semidirect
369. #1967	C₂×C₁₇	semidirect
370. #1950	C₂×C₁₇	semidirect
371. #1908	C₂×C₁₇	semidirect
372. #1907	C₂×C₁₇	semidirect
373. C₄×#100	C₂×C₁₇	semidirect
565. #100	D₄×C₁₇	semidirect
574. C₁₇	#25408	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×#3153	2
C₂×C₁₇×#472	2
C₂×C₁₇×#471	2
C₁₇×#3036	2
C₂×C₁₇×#463	2
C₁₇×#2935	2
C₁₇×#2052	2
C₁₇×#2051	2
C₁₇×#2019	2
C₁₇×#2018	2
C₁₇×#1967	2
C₁₇×#1950	2
C₁₇×#1908	2
C₁₇×#1907	2
C₄×C₁₇×#100	2
#25408	17

Subgroups — C17×#25408 #16883152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#25408 #16883152