Subgroups — C₁₇×#17869 #16875613

Order 4352.

748 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#2965	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₁₇×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#1586	C₂	1	2	yes	maximal, complemented
5	C₁₇×#1585	C₂	1	2	yes	maximal, complemented
6	C₁₇×#1582	C₂	1	2	yes	maximal, complemented
7	C₁₇×#1581	C₂	1	2	yes	maximal, complemented
8	C₁₇×#1565	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1477	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₇×AGL(1,ℤ/8)	C₄	1	1	yes	characteristic
13	C₂³×C₈×C₁₇	—	2	1	no	—
14	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
16	C₁₇×#446	C₂²	1	1	yes	characteristic, complemented
17	C₁₇×#446	C₂²	1	1	yes	characteristic, complemented
18	C₁₇×#442	C₄	1	2	yes	—
19	C₁₇×#440	C₄	1	2	yes	—
20	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	—
21	C₄×D₈×C₁₇	C₂²	1	2	yes	—
22	C₁₇×#436	C₂²	1	1	yes	characteristic, complemented
23	C₁₇×#436	C₂²	1	1	yes	characteristic, complemented
24	C₁₇×#435	—	2	1	no	—
25	C₁₇×#435	—	2	1	no	—
26	C₈×D₄×C₁₇	—	2	1	no	—
27	C₈×D₄×C₁₇	—	2	1	no	—
28	C₈×D₄×C₁₇	C₂²	1	2	yes	—
29	C₈×D₄×C₁₇	C₂²	1	2	yes	—
30	C₁₇×#431	—	2	1	no	—
31	C₁₇×#431	C₂²	1	1	yes	characteristic
32	C₁₇×#431	C₂²	1	1	yes	characteristic
33	C₁₇×#428	C₄	1	1	yes	characteristic
34	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₁₇×#418	C₄	1	1	yes	characteristic
36	C₁₇×#417	C₄	1	1	yes	characteristic
37	C₂×C₁₇×C₂²⋊C₈	—	2	1	no	—
38	C₄×M₁₆×C₁₇	—	2	1	no	—
39	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
41	C₁₇×#335	C₂²	1	2	yes	complemented
42	C₁₇×#334	C₂²	1	2	yes	complemented
43	C₁₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
44	C₁₇×D₄⋊C₈	C₂²	1	2	yes	—
45	C₁₇×D₄⋊C₈	C₂²	1	2	yes	—
46	C₁₇×D₄⋊C₈	C₂²	1	2	yes	complemented
47	C₁₇×#322	C₂²	1	2	yes	complemented
48	C₁₇×#322	C₂²	1	2	yes	complemented
49	C₂×#41×C₁₇	C₂×C₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₇	—	2	1	no	—
52	C₁₇×AGL(1,ℤ/8)	—	2	4	no	—
53	C₂×SD₁₆×C₁₇	C₂×C₄	1	2	yes	—
54	C₂×D₈×C₁₇	C₂×C₄	1	2	yes	—
55	C₂×M₁₆×C₁₇	—	2	1	no	—
56	C₂×M₁₆×C₁₇	—	2	1	no	—
57	C₂×M₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
58	C₂×M₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₈×C₁₇	—	2	1	no	—
60	C₂²×C₈×C₁₇	—	2	2	no	—
61	C₂²×C₈×C₁₇	—	2	2	no	—
62	C₂²×C₈×C₁₇	—	4	4	no	—
63	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
64	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
65	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
66	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
67	C₄×D₄×C₁₇	—	2	1	no	—
68	C₄×D₄×C₁₇	—	2	1	no	—
69	C₄×D₄×C₁₇	—	2	1	no	—
70	C₄×D₄×C₁₇	—	2	1	no	—
71	C₄×D₄×C₁₇	C₂×C₄	1	2	yes	—
72	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
73	C₄×D₄×C₁₇	C₂³	1	2	yes	—
74	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
75	C₁₇×#117	—	2	1	no	—
76	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
79	C₂×C₄²×C₁₇	—	2	1	no	—
80	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
81	C₁₇×#107	C₂×C₄	1	2	yes	—
82	C₁₇×#106	C₂×C₄	1	2	yes	—
83	C₁₇×C₄⋊C₈	—	2	1	no	—
84	C₁₇×C₄⋊C₈	—	2	1	no	—
85	C₁₇×C₄⋊C₈	—	2	1	no	—
86	C₁₇×C₄⋊C₈	—	2	1	no	—
87	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
89	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
90	C₁₇×#103	C₂×C₄	1	2	yes	—
91	C₁₇×#102	C₂×C₄	1	2	yes	—
92	C₁₇×#102	C₂×C₄	1	2	yes	—
93	C₁₇×#102	C₂×C₄	1	2	yes	—
94	C₁₇×C₂²⋊C₈	—	2	1	no	—
95	C₁₇×C₂²⋊C₈	—	2	1	no	—
96	C₁₇×C₂²⋊C₈	—	2	2	no	—
97	C₁₇×C₂²⋊C₈	—	2	2	no	—
98	C₁₇×C₂²⋊C₈	—	2	1	no	—
99	C₁₇×C₂²⋊C₈	—	2	1	no	—
100	C₁₇×#97	—	2	1	no	—
101	C₁₇×#97	—	2	1	no	—
102	C₁₇×#97	C₂×C₄	1	2	yes	—
103	C₄×C₈×C₁₇	—	2	1	no	—
104	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
105	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
106	C₄×C₈×C₁₇	C₂³	1	2	yes	—
107	C₄×C₈×C₁₇	C₂³	1	2	yes	—
108	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
110	C₂⁴×C₁₇	—	2	1	no	—
111	#41×C₁₇	—	2	2	no	—
112	#41×C₁₇	—	2	2	no	—
113	C₂×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
114	C₂×D₄×C₁₇	—	2	1	no	—
115	C₂×D₄×C₁₇	—	2	1	no	—
116	C₂×D₄×C₁₇	—	2	2	no	—
117	C₂×D₄×C₁₇	M₁₆	1	4	yes	complemented
118	C₂×D₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
119	C₂×D₄×C₁₇	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₁₇	—	2	1	no	—
121	C₂²×C₄×C₁₇	—	2	2	no	—
122	C₂²×C₄×C₁₇	—	2	1	no	—
123	C₂²×C₄×C₁₇	—	2	1	no	—
124	C₂²×C₄×C₁₇	—	2	2	no	—
125	C₂²×C₄×C₁₇	—	2	1	no	—
126	C₂²×C₄×C₁₇	—	4	2	no	—
127	C₂²×C₄×C₁₇	—	4	2	no	—
128	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
131	SD₁₆×C₁₇	—	2	4	no	—
132	D₈×C₁₇	—	2	4	no	—
133	M₁₆×C₁₇	—	2	2	no	—
134	M₁₆×C₁₇	—	2	2	no	—
135	M₁₆×C₁₇	—	4	2	no	—
136	M₁₆×C₁₇	—	4	2	no	—
137	C₂×C₈×C₁₇	—	2	2	no	—
138	C₂×C₈×C₁₇	—	2	2	no	—
139	C₂×C₈×C₁₇	—	2	1	no	—
140	C₂×C₈×C₁₇	—	2	1	no	—
141	C₂×C₈×C₁₇	—	2	2	no	—
142	C₂×C₈×C₁₇	—	4	1	no	—
143	C₂×C₈×C₁₇	—	4	4	no	—
144	C₂×C₈×C₁₇	—	4	2	no	—
145	C₂×C₈×C₁₇	—	4	4	no	—
146	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
147	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
148	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
152	C₄⋊C₄×C₁₇	—	2	1	no	—
153	C₄⋊C₄×C₁₇	—	2	1	no	—
154	C₄⋊C₄×C₁₇	—	2	1	no	—
155	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
156	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
157	C₄⋊C₄×C₁₇	C₂²×C₄	1	2	yes	—
158	C₂²⋊C₄×C₁₇	—	2	1	no	—
159	C₂²⋊C₄×C₁₇	—	2	2	no	—
160	C₂²⋊C₄×C₁₇	—	2	1	no	—
161	C₂²⋊C₄×C₁₇	—	2	2	no	—
162	C₂²⋊C₄×C₁₇	—	2	1	no	—
163	C₄²×C₁₇	—	2	1	no	—
164	C₄²×C₁₇	—	2	1	no	—
165	C₄²×C₁₇	—	2	1	no	—
166	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₁₇	#41	1	1	yes	characteristic
169	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
170	#17869	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂³×C₁₇	—	2	2	no	—
172	C₂³×C₁₇	—	2	4	no	—
173	C₂³×C₁₇	—	2	1	no	—
174	C₂³×C₁₇	—	4	2	no	—
175	C₂³×C₁₇	—	4	2	no	—
176	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
177	Q₈×C₁₇	—	2	1	no	—
178	Q₈×C₁₇	—	2	1	no	—
179	D₄×C₁₇	—	2	1	no	—
180	D₄×C₁₇	—	2	2	no	—
181	D₄×C₁₇	—	2	1	no	—
182	D₄×C₁₇	—	2	4	no	—
183	D₄×C₁₇	—	4	2	no	—
184	D₄×C₁₇	C₂×M₁₆	1	4	yes	—
185	C₂×C₄×C₁₇	—	2	1	no	—
186	C₂×C₄×C₁₇	—	2	1	no	—
187	C₂×C₄×C₁₇	—	2	1	no	—
188	C₂×C₄×C₁₇	—	2	1	no	—
189	C₂×C₄×C₁₇	—	2	1	no	—
190	C₂×C₄×C₁₇	—	2	2	no	—
191	C₂×C₄×C₁₇	—	4	1	no	—
192	C₂×C₄×C₁₇	—	4	2	no	—
193	C₂×C₄×C₁₇	—	4	4	no	—
194	C₂×C₄×C₁₇	—	4	2	no	—
195	C₂×C₄×C₁₇	—	4	2	no	—
196	C₂×C₄×C₁₇	—	4	1	no	—
197	C₂×C₄×C₁₇	—	4	1	no	—
198	C₂×C₄×C₁₇	—	4	2	no	—
199	C₂×C₄×C₁₇	—	4	2	no	—
200	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
204	C₂×C₄×C₁₇	#131	1	2	yes	—
205	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
208	C₈×C₁₇	—	2	2	no	—
209	C₈×C₁₇	—	2	2	no	—
210	C₈×C₁₇	—	2	1	no	—
211	C₈×C₁₇	—	2	1	no	—
212	C₈×C₁₇	—	2	1	no	—
213	C₈×C₁₇	—	4	2	no	—
214	C₈×C₁₇	—	4	2	no	—
215	C₈×C₁₇	—	4	1	no	—
216	C₈×C₁₇	—	4	1	no	—
217	C₈×C₁₇	AGL(1,ℤ/8)	1	2	yes	complemented
218	#2965	C₂×C₁₇	1	1	yes	characteristic, complemented
219	C₄×AGL(1,ℤ/8)	C₂×C₁₇	1	1	yes	characteristic
220	C₂×C₈×D₄	C₂×C₁₇	1	1	yes	characteristic, complemented
221	#1586	C₂×C₁₇	1	2	yes	complemented
222	#1585	C₂×C₁₇	1	2	yes	complemented
223	#1582	C₂×C₁₇	1	2	yes	complemented
224	#1581	C₂×C₁₇	1	2	yes	complemented
225	#1565	C₂×C₁₇	1	1	yes	characteristic, complemented
226	#1478	C₂×C₁₇	1	1	yes	characteristic, complemented
227	#1477	C₂×C₁₇	1	1	yes	characteristic, complemented
228	#1451	C₂×C₁₇	1	1	yes	characteristic, complemented
229	C₂²×C₁₇	—	2	1	no	—
230	C₂²×C₁₇	—	2	1	no	—
231	C₂²×C₁₇	—	2	4	no	—
232	C₂²×C₁₇	—	4	8	no	—
233	C₂²×C₁₇	—	4	2	no	—
234	C₂²×C₁₇	—	4	2	no	—
235	C₂²×C₁₇	—	4	1	no	—
236	C₂²×C₁₇	—	4	1	no	—
237	C₂²×C₁₇	—	4	1	no	—
238	C₂²×C₁₇	#435	1	2	yes	—
239	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
240	C₄×C₁₇	—	2	1	no	—
241	C₄×C₁₇	—	2	1	no	—
242	C₄×C₁₇	—	2	1	no	—
243	C₄×C₁₇	—	4	1	no	—
244	C₄×C₁₇	—	4	1	no	—
245	C₄×C₁₇	—	4	2	no	—
246	C₄×C₁₇	—	4	1	no	—
247	C₄×C₁₇	#435	1	2	yes	—
248	C₄×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
249	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
250	C₄×C₁₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
251	C₄×C₁₇	#575	1	1	yes	characteristic
252	C₂×AGL(1,ℤ/8)	C₄×C₁₇	1	1	yes	characteristic
253	C₂³×C₈	—	2	1	no	—
254	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
255	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
256	#446	C₂²×C₁₇	1	1	yes	characteristic, complemented
257	#446	C₂²×C₁₇	1	1	yes	characteristic, complemented
258	#442	C₄×C₁₇	1	2	yes	—
259	#440	C₄×C₁₇	1	2	yes	—
260	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	—
261	C₄×D₈	C₂²×C₁₇	1	2	yes	—
262	#436	C₂²×C₁₇	1	1	yes	characteristic, complemented
263	#436	C₂²×C₁₇	1	1	yes	characteristic, complemented
264	#435	—	2	1	no	—
265	#435	—	2	1	no	—
266	C₈×D₄	—	2	1	no	—
267	C₈×D₄	—	2	1	no	—
268	C₈×D₄	C₂²×C₁₇	1	2	yes	—
269	C₈×D₄	C₂²×C₁₇	1	2	yes	—
270	#431	—	2	1	no	—
271	#431	C₂²×C₁₇	1	1	yes	characteristic
272	#431	C₂²×C₁₇	1	1	yes	characteristic
273	#428	C₄×C₁₇	1	1	yes	characteristic
274	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
275	#418	C₄×C₁₇	1	1	yes	characteristic
276	#417	C₄×C₁₇	1	1	yes	characteristic
277	C₂×C₂²⋊C₈	—	2	1	no	—
278	C₄×M₁₆	—	2	1	no	—
279	C₄×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
280	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
281	#335	C₂²×C₁₇	1	2	yes	complemented
282	#334	C₂²×C₁₇	1	2	yes	complemented
283	Q₈⋊C₈	C₂²×C₁₇	1	2	yes	complemented
284	D₄⋊C₈	C₂²×C₁₇	1	2	yes	—
285	D₄⋊C₈	C₂²×C₁₇	1	2	yes	—
286	D₄⋊C₈	C₂²×C₁₇	1	2	yes	complemented
287	#322	C₂²×C₁₇	1	2	yes	complemented
288	#322	C₂²×C₁₇	1	2	yes	complemented
289	C₂×C₁₇	—	2	2	no	—
290	C₂×C₁₇	—	4	4	no	—
291	C₂×C₁₇	—	8	1	no	—
292	C₂×C₁₇	C₂×#435	1	1	yes	characteristic
293	C₂×C₁₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
294	C₂×C₁₇	#2955	1	1	yes	characteristic
295	C₂×#41	C₂×C₄×C₁₇	1	1	yes	characteristic
296	C₂²×D₄	C₂×C₄×C₁₇	1	1	yes	characteristic
297	C₂³×C₄	—	2	1	no	—
298	AGL(1,ℤ/8)	—	2	4	no	—
299	C₂×SD₁₆	C₂×C₄×C₁₇	1	2	yes	—
300	C₂×D₈	C₂×C₄×C₁₇	1	2	yes	—
301	C₂×M₁₆	—	2	1	no	—
302	C₂×M₁₆	—	2	1	no	—
303	C₂×M₁₆	C₂×C₄×C₁₇	1	1	yes	characteristic
304	C₂×M₁₆	C₂×C₄×C₁₇	1	1	yes	characteristic
305	C₂²×C₈	—	2	1	no	—
306	C₂²×C₈	—	2	2	no	—
307	C₂²×C₈	—	2	2	no	—
308	C₂²×C₈	—	4	4	no	—
309	C₂²×C₈	D₄×C₁₇	1	1	yes	characteristic
310	C₂²×C₈	D₄×C₁₇	1	1	yes	characteristic
311	C₄×Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
312	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
313	C₄×D₄	—	2	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	C₂×C₄×C₁₇	1	2	yes	—
318	C₄×D₄	C₂×C₄×C₁₇	1	1	yes	characteristic
319	C₄×D₄	C₂³×C₁₇	1	2	yes	—
320	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
321	#117	—	2	1	no	—
322	#117	C₂×C₄×C₁₇	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
327	#107	C₂×C₄×C₁₇	1	2	yes	—
328	#106	C₂×C₄×C₁₇	1	2	yes	—
329	C₄⋊C₈	—	2	1	no	—
330	C₄⋊C₈	—	2	1	no	—
331	C₄⋊C₈	—	2	1	no	—
332	C₄⋊C₈	—	2	1	no	—
333	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
334	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
335	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
336	#103	C₂×C₄×C₁₇	1	2	yes	—
337	#102	C₂×C₄×C₁₇	1	2	yes	—
338	#102	C₂×C₄×C₁₇	1	2	yes	—
339	#102	C₂×C₄×C₁₇	1	2	yes	—
340	C₂²⋊C₈	—	2	1	no	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₂²⋊C₈	—	2	2	no	—
343	C₂²⋊C₈	—	2	2	no	—
344	C₂²⋊C₈	—	2	1	no	—
345	C₂²⋊C₈	—	2	1	no	—
346	#97	—	2	1	no	—
347	#97	—	2	1	no	—
348	#97	C₂×C₄×C₁₇	1	2	yes	—
349	C₄×C₈	—	2	1	no	—
350	C₄×C₈	D₄×C₁₇	1	1	yes	characteristic
351	C₄×C₈	D₄×C₁₇	1	1	yes	characteristic
352	C₄×C₈	C₂³×C₁₇	1	2	yes	—
353	C₄×C₈	C₂³×C₁₇	1	2	yes	—
354	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
355	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
356	C₁₇	#17869	1	1	yes	characteristic, direct product factor, Sylow
357	C₂⁴	—	2	1	no	—
358	#41	—	2	2	no	—
359	#41	—	2	2	no	—
360	C₂×Q₈	C₂²×C₄×C₁₇	1	1	yes	characteristic
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	M₁₆×C₁₇	1	4	yes	complemented
365	C₂×D₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
366	C₂×D₄	C₂²×C₄×C₁₇	1	2	yes	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
377	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
378	SD₁₆	—	2	4	no	—
379	D₈	—	2	4	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	—	2	2	no	—
382	M₁₆	—	4	2	no	—
383	M₁₆	—	4	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	4	1	no	—
390	C₂×C₈	—	4	4	no	—
391	C₂×C₈	—	4	2	no	—
392	C₂×C₈	—	4	4	no	—
393	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
394	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
395	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
396	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
397	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
398	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
403	C₄⋊C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
404	C₄⋊C₄	C₂²×C₄×C₁₇	1	2	yes	—
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	1	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	2	1	no	—
413	C₄²	C₂²×C₄×C₁₇	1	1	yes	characteristic
414	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
415	C₄²	#41×C₁₇	1	1	yes	characteristic
416	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
417	C₂³	—	2	2	no	—
418	C₂³	—	2	4	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	C₄×D₄×C₁₇	1	1	yes	characteristic
423	Q₈	—	2	1	no	—
424	Q₈	—	2	1	no	—
425	D₄	—	2	1	no	—
426	D₄	—	2	2	no	—
427	D₄	—	2	1	no	—
428	D₄	—	2	4	no	—
429	D₄	—	4	2	no	—
430	D₄	C₂×M₁₆×C₁₇	1	4	yes	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
447	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
448	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
449	C₂×C₄	C₂×M₁₆×C₁₇	1	2	yes	—
450	C₂×C₄	C₁₇×#131	1	2	yes	—
451	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
452	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
453	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
454	C₈	—	2	2	no	—
455	C₈	—	2	2	no	—
456	C₈	—	2	1	no	—
457	C₈	—	2	1	no	—
458	C₈	—	2	1	no	—
459	C₈	—	4	2	no	—
460	C₈	—	4	2	no	—
461	C₈	—	4	1	no	—
462	C₈	—	4	1	no	—
463	C₈	C₁₇×AGL(1,ℤ/8)	1	2	yes	complemented
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	4	no	—
467	C₂²	—	4	8	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	C₁₇×#435	1	2	yes	—
474	C₂²	C₂×C₄×D₄×C₁₇	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	4	1	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	1	no	—
482	C₄	C₁₇×#435	1	2	yes	—
483	C₄	C₂²×M₁₆×C₁₇	1	1	yes	characteristic
484	C₄	C₂×C₁₇×#131	1	1	yes	characteristic
485	C₄	C₂×C₁₇×AGL(1,ℤ/8)	1	1	yes	characteristic
486	C₄	C₁₇×#575	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	4	4	no	—
489	C₂	—	8	1	no	—
490	C₂	C₂×C₁₇×#435	1	1	yes	characteristic
491	C₂	C₄×C₁₇×AGL(1,ℤ/8)	1	1	yes	characteristic
492	C₂	C₁₇×#2955	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	C₂×C₄×D₄
prime radical	C₂×C₁₇×AGL(1,ℤ/8)	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#2965	C₂	semidirect
3. C₂×C₈×D₄×C₁₇	C₂	semidirect
4. C₁₇×#1586	C₂	semidirect
5. C₁₇×#1585	C₂	semidirect
6. C₁₇×#1582	C₂	semidirect
7. C₁₇×#1581	C₂	semidirect
8. C₁₇×#1565	C₂	semidirect
9. C₁₇×#1478	C₂	semidirect
10. C₁₇×#1477	C₂	semidirect
11. C₁₇×#1451	C₂	semidirect
16. C₁₇×#446	C₂²	semidirect
17. C₁₇×#446	C₂²	semidirect
22. C₁₇×#436	C₂²	semidirect
23. C₁₇×#436	C₂²	semidirect
41. C₁₇×#335	C₂²	semidirect
42. C₁₇×#334	C₂²	semidirect
43. C₁₇×Q₈⋊C₈	C₂²	semidirect
46. C₁₇×D₄⋊C₈	C₂²	semidirect
47. C₁₇×#322	C₂²	semidirect
48. C₁₇×#322	C₂²	semidirect
117. C₂×D₄×C₁₇	M₁₆	semidirect
170. #17869	C₁₇	direct (N × H)
217. C₈×C₁₇	AGL(1,ℤ/8)	semidirect
218. #2965	C₂×C₁₇	semidirect
220. C₂×C₈×D₄	C₂×C₁₇	semidirect
221. #1586	C₂×C₁₇	semidirect
222. #1585	C₂×C₁₇	semidirect
223. #1582	C₂×C₁₇	semidirect
224. #1581	C₂×C₁₇	semidirect
225. #1565	C₂×C₁₇	semidirect
226. #1478	C₂×C₁₇	semidirect
227. #1477	C₂×C₁₇	semidirect
228. #1451	C₂×C₁₇	semidirect
256. #446	C₂²×C₁₇	semidirect
257. #446	C₂²×C₁₇	semidirect
262. #436	C₂²×C₁₇	semidirect
263. #436	C₂²×C₁₇	semidirect
281. #335	C₂²×C₁₇	semidirect
282. #334	C₂²×C₁₇	semidirect
283. Q₈⋊C₈	C₂²×C₁₇	semidirect
286. D₄⋊C₈	C₂²×C₁₇	semidirect
287. #322	C₂²×C₁₇	semidirect
288. #322	C₂²×C₁₇	semidirect
356. C₁₇	#17869	direct (N × H)
364. C₂×D₄	M₁₆×C₁₇	semidirect
463. C₈	C₁₇×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#2965	2
C₄×C₁₇×AGL(1,ℤ/8)	2
C₂×C₈×D₄×C₁₇	2
C₁₇×#1586	2
C₁₇×#1585	2
C₁₇×#1582	2
C₁₇×#1581	2
C₁₇×#1565	2
C₁₇×#1478	2
C₁₇×#1477	2
C₁₇×#1451	2
#17869	17

Subgroups — C17×#17869 #16875613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#17869 #16875613