Subgroups — C₁₇×#17863 #16875607

Order 4352.

688 conjugacy classes of subgroups.

The subgroup lattice has 500 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	C₈×#41×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₇×#135	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#1584	C₂	1	2	yes	maximal, complemented
5	C₁₇×#1583	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×#1564	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1476	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₇×#322	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₇×#135	C₄	1	1	yes	characteristic
13	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
14	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
15	C₁₇×#446	C₂²	1	2	yes	—
16	C₈×Q₈×C₁₇	C₂²	1	2	yes	—
17	C₄×Q₁₆×C₁₇	C₄	1	1	yes	characteristic
18	C₄×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic
19	C₄×SD₁₆×C₁₇	C₄	1	1	yes	characteristic
20	C₄×SD₁₆×C₁₇	C₄	1	1	yes	characteristic
21	C₄×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
22	C₄×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
23	C₄×D₈×C₁₇	C₄	1	1	yes	characteristic
24	C₄×D₈×C₁₇	C₂²	1	1	yes	characteristic
25	C₁₇×#436	C₂²	1	2	yes	—
26	C₁₇×#435	—	2	2	no	—
27	C₈×D₄×C₁₇	—	2	2	no	—
28	C₈×D₄×C₁₇	C₂²	1	2	yes	—
29	C₁₇×#431	—	2	1	no	—
30	C₁₇×#431	—	2	1	no	—
31	C₁₇×#431	C₂²	1	1	yes	characteristic
32	C₁₇×#431	C₂²	1	1	yes	characteristic
33	C₁₇×#427	C₄	1	1	yes	characteristic
34	C₁₇×#416	C₄	1	1	yes	characteristic
35	C₁₇×#416	C₄	1	1	yes	characteristic
36	C₄×M₁₆×C₁₇	—	2	1	no	—
37	C₂×C₄×C₈×C₁₇	—	2	1	no	—
38	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
41	C₁₇×#335	C₂²	1	2	yes	—
42	C₁₇×#334	C₂²	1	2	yes	—
43	C₁₇×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₁₇×Q₈⋊C₈	C₂²	1	2	yes	—
45	C₁₇×D₄⋊C₈	C₂²	1	2	yes	—
46	C₁₇×D₄⋊C₈	C₂²	1	2	yes	—
47	C₁₇×#322	C₂²	1	2	yes	—
48	C₁₇×#322	C₂²	1	2	yes	—
49	C₂×#41×C₁₇	C₂×C₄	1	1	yes	characteristic
50	C₂×#41×C₁₇	C₂×C₄	1	1	yes	characteristic
51	C₁₇×#135	—	2	4	no	—
52	C₂×Q₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
53	C₂×SD₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
54	C₂×SD₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
55	C₂×D₈×C₁₇	C₂×C₄	1	1	yes	characteristic
56	C₂×M₁₆×C₁₇	—	2	2	no	—
57	C₂²×C₈×C₁₇	—	2	1	no	—
58	C₂²×C₈×C₁₇	—	2	2	no	—
59	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₈×C₁₇	D₄	1	2	yes	—
62	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
63	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
64	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
65	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
66	C₄×D₄×C₁₇	—	2	1	no	—
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	C₂×C₄	1	1	yes	characteristic
71	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
72	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
73	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
74	C₁₇×#117	—	2	1	no	—
75	C₁₇×#117	—	2	1	no	—
76	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
77	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×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	1	yes	characteristic
82	C₁₇×#107	C₂×C₄	1	1	yes	characteristic
83	C₁₇×#106	C₂×C₄	1	1	yes	characteristic
84	C₁₇×#106	C₂×C₄	1	1	yes	characteristic
85	C₁₇×C₄⋊C₈	—	2	2	no	—
86	C₁₇×C₄⋊C₈	—	2	2	no	—
87	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
88	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
89	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
90	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
91	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
92	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
93	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
94	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
95	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
96	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
97	C₁₇×C₂²⋊C₈	—	2	1	no	—
98	C₁₇×C₂²⋊C₈	—	2	1	no	—
99	C₁₇×C₂²⋊C₈	—	2	2	no	—
100	C₁₇×C₂²⋊C₈	—	2	2	no	—
101	C₁₇×#97	—	2	2	no	—
102	C₄×C₈×C₁₇	—	2	2	no	—
103	C₄×C₈×C₁₇	—	2	1	no	—
104	C₄×C₈×C₁₇	—	2	1	no	—
105	C₄×C₈×C₁₇	—	2	1	no	—
106	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
107	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
108	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
109	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
110	C₄×C₈×C₁₇	C₂³	1	2	yes	—
111	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
112	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
113	C₄×C₈×C₁₇	C₂³	1	2	yes	—
114	#41×C₁₇	—	2	2	no	—
115	#41×C₁₇	—	2	2	no	—
116	#41×C₁₇	—	2	2	no	—
117	#41×C₁₇	M₁₆	1	4	yes	complemented
118	C₂×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
119	C₂×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
120	C₂×D₄×C₁₇	—	2	1	no	—
121	C₂×D₄×C₁₇	—	2	1	no	—
122	C₂×D₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
123	C₂×D₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₇	—	2	1	no	—
125	C₂²×C₄×C₁₇	—	2	1	no	—
126	C₂²×C₄×C₁₇	—	2	1	no	—
127	C₂²×C₄×C₁₇	—	2	1	no	—
128	C₂²×C₄×C₁₇	—	2	1	no	—
129	C₂²×C₄×C₁₇	—	2	1	no	—
130	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
133	Q₁₆×C₁₇	—	2	2	no	—
134	SD₁₆×C₁₇	—	2	2	no	—
135	SD₁₆×C₁₇	—	2	2	no	—
136	D₈×C₁₇	—	2	2	no	—
137	M₁₆×C₁₇	—	4	4	no	—
138	C₂×C₈×C₁₇	—	2	2	no	—
139	C₂×C₈×C₁₇	—	2	2	no	—
140	C₂×C₈×C₁₇	—	2	4	no	—
141	C₂×C₈×C₁₇	—	2	2	no	—
142	C₂×C₈×C₁₇	—	2	2	no	—
143	C₂×C₈×C₁₇	—	2	2	no	—
144	C₂×C₈×C₁₇	—	4	2	no	—
145	C₂×C₈×C₁₇	—	4	4	no	—
146	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
156	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
157	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
158	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
159	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
160	C₂²⋊C₄×C₁₇	—	2	1	no	—
161	C₂²⋊C₄×C₁₇	—	2	1	no	—
162	C₂²⋊C₄×C₁₇	—	2	1	no	—
163	C₂²⋊C₄×C₁₇	—	2	1	no	—
164	C₂²⋊C₄×C₁₇	—	2	1	no	—
165	C₂²⋊C₄×C₁₇	—	2	1	no	—
166	C₄²×C₁₇	—	2	1	no	—
167	C₄²×C₁₇	—	2	1	no	—
168	C₄²×C₁₇	—	2	1	no	—
169	C₄²×C₁₇	—	2	1	no	—
170	C₄²×C₁₇	—	2	1	no	—
171	C₄²×C₁₇	—	2	1	no	—
172	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₁₇	#41	1	1	yes	characteristic
175	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
176	#17863	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂³×C₁₇	—	2	1	no	—
178	C₂³×C₁₇	—	2	1	no	—
179	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
180	Q₈×C₁₇	—	2	1	no	—
181	Q₈×C₁₇	—	2	1	no	—
182	Q₈×C₁₇	—	2	1	no	—
183	Q₈×C₁₇	C₂×M₁₆	1	2	yes	—
184	D₄×C₁₇	—	2	4	no	—
185	D₄×C₁₇	—	2	1	no	—
186	D₄×C₁₇	—	2	1	no	—
187	D₄×C₁₇	—	2	1	no	—
188	D₄×C₁₇	—	4	2	no	—
189	D₄×C₁₇	C₂×M₁₆	1	2	yes	—
190	C₂×C₄×C₁₇	—	2	1	no	—
191	C₂×C₄×C₁₇	—	2	2	no	—
192	C₂×C₄×C₁₇	—	2	4	no	—
193	C₂×C₄×C₁₇	—	2	2	no	—
194	C₂×C₄×C₁₇	—	2	1	no	—
195	C₂×C₄×C₁₇	—	2	1	no	—
196	C₂×C₄×C₁₇	—	2	1	no	—
197	C₂×C₄×C₁₇	—	2	1	no	—
198	C₂×C₄×C₁₇	—	2	1	no	—
199	C₂×C₄×C₁₇	—	4	2	no	—
200	C₂×C₄×C₁₇	—	4	2	no	—
201	C₂×C₄×C₁₇	—	4	2	no	—
202	C₂×C₄×C₁₇	—	4	2	no	—
203	C₂×C₄×C₁₇	—	4	2	no	—
204	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
208	C₂×C₄×C₁₇	#131	1	2	yes	—
209	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
212	C₈×C₁₇	—	2	1	no	—
213	C₈×C₁₇	—	2	1	no	—
214	C₈×C₁₇	—	2	1	no	—
215	C₈×C₁₇	—	2	1	no	—
216	C₈×C₁₇	—	2	2	no	—
217	C₈×C₁₇	—	4	2	no	—
218	C₈×C₁₇	—	4	2	no	—
219	C₈×C₁₇	—	4	2	no	—
220	C₈×C₁₇	#135	1	4	yes	complemented
221	#2965	C₂×C₁₇	1	1	yes	characteristic, complemented
222	C₈×#41	C₂×C₁₇	1	1	yes	characteristic, complemented
223	C₄×#135	C₂×C₁₇	1	1	yes	characteristic
224	#1584	C₂×C₁₇	1	2	yes	complemented
225	#1583	C₂×C₁₇	1	2	yes	complemented
226	#1582	C₂×C₁₇	1	2	yes	complemented
227	#1581	C₂×C₁₇	1	2	yes	complemented
228	#1564	C₂×C₁₇	1	1	yes	characteristic, complemented
229	#1476	C₂×C₁₇	1	1	yes	characteristic, complemented
230	#1476	C₂×C₁₇	1	1	yes	characteristic, complemented
231	C₂×#322	C₂×C₁₇	1	1	yes	characteristic, complemented
232	C₂²×C₁₇	—	2	1	no	—
233	C₂²×C₁₇	—	2	1	no	—
234	C₂²×C₁₇	—	2	2	no	—
235	C₂²×C₁₇	—	4	1	no	—
236	C₂²×C₁₇	—	4	1	no	—
237	C₂²×C₁₇	—	4	1	no	—
238	C₂²×C₁₇	—	4	1	no	—
239	C₂²×C₁₇	—	4	1	no	—
240	C₂²×C₁₇	#435	1	2	yes	—
241	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
242	C₄×C₁₇	—	2	2	no	—
243	C₄×C₁₇	—	2	1	no	—
244	C₄×C₁₇	—	2	1	no	—
245	C₄×C₁₇	—	4	1	no	—
246	C₄×C₁₇	—	4	1	no	—
247	C₄×C₁₇	—	4	1	no	—
248	C₄×C₁₇	—	4	1	no	—
249	C₄×C₁₇	—	4	1	no	—
250	C₄×C₁₇	#435	1	2	yes	—
251	C₄×C₁₇	#444	1	2	yes	—
252	C₄×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
253	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
254	C₄×C₁₇	C₂×#135	1	2	yes	—
255	C₂×#135	C₄×C₁₇	1	1	yes	characteristic
256	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
257	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
258	#446	C₂²×C₁₇	1	2	yes	—
259	C₈×Q₈	C₂²×C₁₇	1	2	yes	—
260	C₄×Q₁₆	C₄×C₁₇	1	1	yes	characteristic
261	C₄×Q₁₆	C₂²×C₁₇	1	1	yes	characteristic
262	C₄×SD₁₆	C₄×C₁₇	1	1	yes	characteristic
263	C₄×SD₁₆	C₄×C₁₇	1	1	yes	characteristic
264	C₄×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
265	C₄×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
266	C₄×D₈	C₄×C₁₇	1	1	yes	characteristic
267	C₄×D₈	C₂²×C₁₇	1	1	yes	characteristic
268	#436	C₂²×C₁₇	1	2	yes	—
269	#435	—	2	2	no	—
270	C₈×D₄	—	2	2	no	—
271	C₈×D₄	C₂²×C₁₇	1	2	yes	—
272	#431	—	2	1	no	—
273	#431	—	2	1	no	—
274	#431	C₂²×C₁₇	1	1	yes	characteristic
275	#431	C₂²×C₁₇	1	1	yes	characteristic
276	#427	C₄×C₁₇	1	1	yes	characteristic
277	#416	C₄×C₁₇	1	1	yes	characteristic
278	#416	C₄×C₁₇	1	1	yes	characteristic
279	C₄×M₁₆	—	2	1	no	—
280	C₂×C₄×C₈	—	2	1	no	—
281	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
282	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
283	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
284	#335	C₂²×C₁₇	1	2	yes	—
285	#334	C₂²×C₁₇	1	2	yes	—
286	Q₈⋊C₈	C₂²×C₁₇	1	2	yes	—
287	Q₈⋊C₈	C₂²×C₁₇	1	2	yes	—
288	D₄⋊C₈	C₂²×C₁₇	1	2	yes	—
289	D₄⋊C₈	C₂²×C₁₇	1	2	yes	—
290	#322	C₂²×C₁₇	1	2	yes	—
291	#322	C₂²×C₁₇	1	2	yes	—
292	C₂×C₁₇	—	2	2	no	—
293	C₂×C₁₇	—	4	2	no	—
294	C₂×C₁₇	—	8	1	no	—
295	C₂×C₁₇	C₂×#435	1	1	yes	characteristic
296	C₂×C₁₇	C₄×#135	1	1	yes	characteristic
297	C₂×C₁₇	C₂×#444	1	1	yes	characteristic
298	C₂×#41	C₂×C₄×C₁₇	1	1	yes	characteristic
299	C₂×#41	C₂×C₄×C₁₇	1	1	yes	characteristic
300	#135	—	2	4	no	—
301	C₂×Q₁₆	C₂×C₄×C₁₇	1	1	yes	characteristic
302	C₂×SD₁₆	C₂×C₄×C₁₇	1	1	yes	characteristic
303	C₂×SD₁₆	C₂×C₄×C₁₇	1	1	yes	characteristic
304	C₂×D₈	C₂×C₄×C₁₇	1	1	yes	characteristic
305	C₂×M₁₆	—	2	2	no	—
306	C₂²×C₈	—	2	1	no	—
307	C₂²×C₈	—	2	2	no	—
308	C₂²×C₈	C₂×C₄×C₁₇	1	1	yes	characteristic
309	C₂²×C₈	C₂×C₄×C₁₇	1	1	yes	characteristic
310	C₂²×C₈	D₄×C₁₇	1	2	yes	—
311	C₄×Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
312	C₄×Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
313	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
314	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	—	2	1	no	—
319	C₄×D₄	C₂×C₄×C₁₇	1	1	yes	characteristic
320	C₄×D₄	C₂×C₄×C₁₇	1	1	yes	characteristic
321	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
322	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
323	#117	—	2	1	no	—
324	#117	—	2	1	no	—
325	#117	C₂×C₄×C₁₇	1	1	yes	characteristic
326	#117	C₂×C₄×C₁₇	1	1	yes	characteristic
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
330	#107	C₂×C₄×C₁₇	1	1	yes	characteristic
331	#107	C₂×C₄×C₁₇	1	1	yes	characteristic
332	#106	C₂×C₄×C₁₇	1	1	yes	characteristic
333	#106	C₂×C₄×C₁₇	1	1	yes	characteristic
334	C₄⋊C₈	—	2	2	no	—
335	C₄⋊C₈	—	2	2	no	—
336	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
337	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
338	#103	C₂×C₄×C₁₇	1	1	yes	characteristic
339	#103	C₂×C₄×C₁₇	1	1	yes	characteristic
340	#103	C₂×C₄×C₁₇	1	1	yes	characteristic
341	#103	C₂×C₄×C₁₇	1	1	yes	characteristic
342	#102	C₂×C₄×C₁₇	1	1	yes	characteristic
343	#102	C₂×C₄×C₁₇	1	1	yes	characteristic
344	#102	C₂×C₄×C₁₇	1	1	yes	characteristic
345	#102	C₂×C₄×C₁₇	1	1	yes	characteristic
346	C₂²⋊C₈	—	2	1	no	—
347	C₂²⋊C₈	—	2	1	no	—
348	C₂²⋊C₈	—	2	2	no	—
349	C₂²⋊C₈	—	2	2	no	—
350	#97	—	2	2	no	—
351	C₄×C₈	—	2	2	no	—
352	C₄×C₈	—	2	1	no	—
353	C₄×C₈	—	2	1	no	—
354	C₄×C₈	—	2	1	no	—
355	C₄×C₈	C₂×C₄×C₁₇	1	1	yes	characteristic
356	C₄×C₈	C₂×C₄×C₁₇	1	1	yes	characteristic
357	C₄×C₈	D₄×C₁₇	1	1	yes	characteristic
358	C₄×C₈	D₄×C₁₇	1	1	yes	characteristic
359	C₄×C₈	C₂³×C₁₇	1	2	yes	—
360	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
361	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
362	C₄×C₈	C₂³×C₁₇	1	2	yes	—
363	C₁₇	#17863	1	1	yes	characteristic, direct product factor, Sylow
364	#41	—	2	2	no	—
365	#41	—	2	2	no	—
366	#41	—	2	2	no	—
367	#41	M₁₆×C₁₇	1	4	yes	complemented
368	C₂×Q₈	C₂²×C₄×C₁₇	1	1	yes	characteristic
369	C₂×Q₈	C₂²×C₄×C₁₇	1	1	yes	characteristic
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
373	C₂×D₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
382	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
383	Q₁₆	—	2	2	no	—
384	SD₁₆	—	2	2	no	—
385	SD₁₆	—	2	2	no	—
386	D₈	—	2	2	no	—
387	M₁₆	—	4	4	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	4	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	4	2	no	—
395	C₂×C₈	—	4	4	no	—
396	C₂×C₈	C₂²×C₄×C₁₇	1	1	yes	characteristic
397	C₂×C₈	C₂²×C₄×C₁₇	1	1	yes	characteristic
398	C₂×C₈	C₂²×C₄×C₁₇	1	1	yes	characteristic
399	C₂×C₈	C₂²×C₄×C₁₇	1	1	yes	characteristic
400	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
401	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
407	C₄⋊C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
408	C₄⋊C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
409	C₄⋊C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	2	1	no	—
420	C₄²	—	2	1	no	—
421	C₄²	—	2	1	no	—
422	C₄²	C₂²×C₄×C₁₇	1	1	yes	characteristic
423	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
424	C₄²	#41×C₁₇	1	1	yes	characteristic
425	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
426	C₂³	—	2	1	no	—
427	C₂³	—	2	1	no	—
428	C₂³	C₄×D₄×C₁₇	1	1	yes	characteristic
429	Q₈	—	2	1	no	—
430	Q₈	—	2	1	no	—
431	Q₈	—	2	1	no	—
432	Q₈	C₂×M₁₆×C₁₇	1	2	yes	—
433	D₄	—	2	4	no	—
434	D₄	—	2	1	no	—
435	D₄	—	2	1	no	—
436	D₄	—	2	1	no	—
437	D₄	—	4	2	no	—
438	D₄	C₂×M₁₆×C₁₇	1	2	yes	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
454	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
455	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
456	C₂×C₄	C₂×M₁₆×C₁₇	1	2	yes	—
457	C₂×C₄	C₁₇×#131	1	2	yes	—
458	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
459	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
460	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
461	C₈	—	2	1	no	—
462	C₈	—	2	1	no	—
463	C₈	—	2	1	no	—
464	C₈	—	2	1	no	—
465	C₈	—	2	2	no	—
466	C₈	—	4	2	no	—
467	C₈	—	4	2	no	—
468	C₈	—	4	2	no	—
469	C₈	C₁₇×#135	1	4	yes	complemented
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	1	no	—
477	C₂²	—	4	1	no	—
478	C₂²	C₁₇×#435	1	2	yes	—
479	C₂²	C₂×C₄×D₄×C₁₇	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	2	2	no	—
482	C₄	—	2	1	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	1	no	—
487	C₄	—	4	1	no	—
488	C₄	C₁₇×#435	1	2	yes	—
489	C₄	C₁₇×#444	1	2	yes	—
490	C₄	C₂²×M₁₆×C₁₇	1	1	yes	characteristic
491	C₄	C₂×C₁₇×#131	1	1	yes	characteristic
492	C₄	C₂×C₁₇×#135	1	2	yes	—
493	C₂	—	2	2	no	—
494	C₂	—	4	2	no	—
495	C₂	—	8	1	no	—
496	C₂	C₂×C₁₇×#435	1	1	yes	characteristic
497	C₂	C₄×C₁₇×#135	1	1	yes	characteristic
498	C₂	C₂×C₁₇×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₁₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₇
Frattini, cosocle	C₄²	C₂⁴×C₁₇
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	C₂×C₁₇×#135	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×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
2. C₈×#41×C₁₇	C₂	semidirect
4. C₁₇×#1584	C₂	semidirect
5. C₁₇×#1583	C₂	semidirect
6. C₁₇×#1582	C₂	semidirect
7. C₁₇×#1581	C₂	semidirect
8. C₁₇×#1564	C₂	semidirect
9. C₁₇×#1476	C₂	semidirect
10. C₁₇×#1476	C₂	semidirect
11. C₂×C₁₇×#322	C₂	semidirect
117. #41×C₁₇	M₁₆	semidirect
176. #17863	C₁₇	direct (N × H)
220. C₈×C₁₇	#135	semidirect
221. #2965	C₂×C₁₇	semidirect
222. C₈×#41	C₂×C₁₇	semidirect
224. #1584	C₂×C₁₇	semidirect
225. #1583	C₂×C₁₇	semidirect
226. #1582	C₂×C₁₇	semidirect
227. #1581	C₂×C₁₇	semidirect
228. #1564	C₂×C₁₇	semidirect
229. #1476	C₂×C₁₇	semidirect
230. #1476	C₂×C₁₇	semidirect
231. C₂×#322	C₂×C₁₇	semidirect
363. C₁₇	#17863	direct (N × H)
367. #41	M₁₆×C₁₇	semidirect
469. C₈	C₁₇×#135	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
C₈×#41×C₁₇	2
C₄×C₁₇×#135	2
C₁₇×#1584	2
C₁₇×#1583	2
C₁₇×#1582	2
C₁₇×#1581	2
C₁₇×#1564	2
C₁₇×#1476	2
C₂×C₁₇×#322	2
#17863	17

Subgroups — C17×#17863 #16875607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#17863 #16875607