Subgroups — C₁₇×#22587 #16880331

Order 4352.

906 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#2924	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₇×#416	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#2880	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#1937	C₂	1	2	yes	maximal, complemented
5	C₁₇×#1929	C₂	1	2	yes	maximal, complemented
6	C₁₇×#1866	C₂	1	2	yes	maximal, complemented
7	C₁₇×#1826	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1810	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1789	C₂	1	1	yes	maximal, characteristic
10	C₁₇×#1764	C₂	1	2	yes	maximal, complemented
11	C₈×C₂²⋊C₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₇	C₂²	1	1	yes	characteristic
13	C₂×C₁₇×#131	C₂²	1	2	yes	—
14	C₂³×C₈×C₁₇	C₂²	1	1	yes	characteristic
15	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
16	C₁₇×#433	—	2	2	no	—
17	C₁₇×#432	—	2	1	no	—
18	C₁₇×#431	—	2	1	no	—
19	C₂×C₁₇×#108	C₂²	1	2	yes	complemented
20	C₁₇×#424	C₂²	1	2	yes	complemented
21	C₂×C₁₇×#104	C₂²	1	2	yes	—
22	C₂×C₁₇×#104	C₂²	1	2	yes	—
23	C₁₇×#416	C₄	1	1	yes	characteristic, complemented
24	C₁₇×#416	C₄	1	1	yes	characteristic, complemented
25	C₁₇×#416	C₄	1	1	yes	characteristic, complemented
26	C₁₇×#416	C₄	1	1	yes	characteristic, complemented
27	C₁₇×#416	C₂²	1	1	yes	characteristic
28	C₁₇×#416	C₂²	1	1	yes	characteristic
29	C₁₇×#416	C₂²	1	1	yes	characteristic
30	C₁₇×#416	C₂²	1	1	yes	characteristic
31	C₂×C₁₇×#103	C₄	1	1	yes	characteristic, complemented
32	C₂×C₁₇×#103	C₄	1	1	yes	characteristic, complemented
33	C₂×C₁₇×#102	C₄	1	1	yes	characteristic, complemented
34	C₂×C₁₇×#102	C₄	1	1	yes	characteristic, complemented
35	C₁₇×#408	—	2	2	no	—
36	C₁₇×#408	C₂²	1	2	yes	—
37	C₁₇×#407	—	2	1	no	—
38	C₁₇×#407	C₂²	1	1	yes	characteristic
39	C₁₇×#407	C₂²	1	1	yes	characteristic
40	C₂×C₁₇×C₂²⋊C₈	—	2	1	no	—
41	C₂×C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
42	C₁₇×#405	C₂²	1	2	yes	complemented
43	C₂×C₄×C₈×C₁₇	C₂²	1	2	yes	complemented
44	C₄×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
45	C₁₇×#341	C₂²	1	2	yes	complemented
46	C₁₇×#339	C₂²	1	2	yes	complemented
47	C₁₇×#339	C₂²	1	2	yes	complemented
48	C₁₇×#336	C₂²	1	2	yes	complemented
49	C₂×#41×C₁₇	—	2	1	no	—
50	C₂×#41×C₁₇	—	2	1	no	—
51	C₂×#41×C₁₇	—	2	4	no	—
52	C₂×#41×C₁₇	—	4	2	no	—
53	C₂×#41×C₁₇	C₂×C₄	1	1	yes	characteristic
54	C₂×#41×C₁₇	C₂×C₄	1	1	yes	characteristic
55	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
56	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
58	C₂²×D₄×C₁₇	—	2	1	no	—
59	C₂²×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₇	—	2	1	no	—
61	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
62	C₁₇×#131	—	2	4	no	—
63	C₁₇×#131	—	4	2	no	—
64	C₂×M₁₆×C₁₇	—	2	2	no	—
65	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
66	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
67	C₂²×C₈×C₁₇	—	2	2	no	—
68	C₂²×C₈×C₁₇	—	4	2	no	—
69	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
72	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
76	C₁₇×#117	—	2	1	no	—
77	C₁₇×#117	—	2	1	no	—
78	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
79	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
80	C₁₇×#117	C₂³	1	1	yes	characteristic
81	C₁₇×#117	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
86	C₂×C₄²×C₁₇	—	2	1	no	—
87	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
88	C₁₇×#108	—	4	2	no	—
89	C₁₇×C₄⋊C₈	—	2	2	no	—
90	C₁₇×C₄⋊C₈	—	2	2	no	—
91	C₁₇×#104	—	2	4	no	—
92	C₁₇×#104	—	4	2	no	—
93	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
94	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
95	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
96	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
97	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
98	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
99	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
100	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
101	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
102	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
103	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
104	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
105	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
106	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
107	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
108	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
109	C₁₇×C₂²⋊C₈	—	2	1	no	—
110	C₁₇×C₂²⋊C₈	—	2	1	no	—
111	C₁₇×C₂²⋊C₈	—	2	1	no	—
112	C₁₇×C₂²⋊C₈	—	2	1	no	—
113	C₁₇×C₂²⋊C₈	—	2	2	no	—
114	C₁₇×C₂²⋊C₈	—	2	2	no	—
115	C₁₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
116	C₁₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
117	C₁₇×C₂²⋊C₈	D₄	1	2	yes	—
118	C₁₇×#97	—	2	2	no	—
119	C₄×C₈×C₁₇	—	2	2	no	—
120	C₄×C₈×C₁₇	—	4	2	no	—
121	C₁₇×#95	—	2	1	no	—
122	C₂⁴×C₁₇	—	2	1	no	—
123	C₂⁴×C₁₇	#41	1	1	yes	characteristic
124	#41×C₁₇	—	2	2	no	—
125	#41×C₁₇	—	2	2	no	—
126	#41×C₁₇	—	2	2	no	—
127	#41×C₁₇	—	2	2	no	—
128	#41×C₁₇	—	2	2	no	—
129	#41×C₁₇	—	4	4	no	—
130	#41×C₁₇	—	4	1	no	—
131	#41×C₁₇	—	4	1	no	—
132	#41×C₁₇	—	4	4	no	—
133	#41×C₁₇	#41	1	4	yes	—
134	C₂×Q₈×C₁₇	—	2	1	no	—
135	C₂×Q₈×C₁₇	—	2	2	no	—
136	C₂×Q₈×C₁₇	—	4	1	no	—
137	C₂×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
138	C₂×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
139	C₂×D₄×C₁₇	—	2	1	no	—
140	C₂×D₄×C₁₇	—	2	2	no	—
141	C₂×D₄×C₁₇	—	2	1	no	—
142	C₂×D₄×C₁₇	—	2	1	no	—
143	C₂×D₄×C₁₇	—	2	1	no	—
144	C₂×D₄×C₁₇	—	2	1	no	—
145	C₂×D₄×C₁₇	—	4	1	no	—
146	C₂×D₄×C₁₇	—	4	4	no	—
147	C₂×D₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₇	—	2	1	no	—
150	C₂²×C₄×C₁₇	—	2	2	no	—
151	C₂²×C₄×C₁₇	—	2	2	no	—
152	C₂²×C₄×C₁₇	—	2	1	no	—
153	C₂²×C₄×C₁₇	—	2	1	no	—
154	C₂²×C₄×C₁₇	—	2	2	no	—
155	C₂²×C₄×C₁₇	—	2	1	no	—
156	C₂²×C₄×C₁₇	—	2	1	no	—
157	C₂²×C₄×C₁₇	—	2	1	no	—
158	C₂²×C₄×C₁₇	—	2	1	no	—
159	C₂²×C₄×C₁₇	—	4	4	no	—
160	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
165	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
166	M₁₆×C₁₇	—	2	2	no	—
167	M₁₆×C₁₇	—	2	2	no	—
168	M₁₆×C₁₇	—	2	2	no	—
169	M₁₆×C₁₇	—	2	2	no	—
170	M₁₆×C₁₇	—	4	4	no	—
171	C₂×C₈×C₁₇	—	2	2	no	—
172	C₂×C₈×C₁₇	—	2	2	no	—
173	C₂×C₈×C₁₇	—	2	2	no	—
174	C₂×C₈×C₁₇	—	2	2	no	—
175	C₂×C₈×C₁₇	—	2	2	no	—
176	C₂×C₈×C₁₇	—	2	2	no	—
177	C₂×C₈×C₁₇	—	4	1	no	—
178	C₂×C₈×C₁₇	—	4	1	no	—
179	C₂×C₈×C₁₇	—	4	1	no	—
180	C₂×C₈×C₁₇	—	4	1	no	—
181	C₂×C₈×C₁₇	—	4	4	no	—
182	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
187	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
188	C₄⋊C₄×C₁₇	—	2	1	no	—
189	C₄⋊C₄×C₁₇	—	2	1	no	—
190	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
191	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
192	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
193	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
194	C₂²⋊C₄×C₁₇	—	2	4	no	—
195	C₂²⋊C₄×C₁₇	—	2	1	no	—
196	C₂²⋊C₄×C₁₇	—	2	1	no	—
197	C₂²⋊C₄×C₁₇	—	2	1	no	—
198	C₂²⋊C₄×C₁₇	—	2	1	no	—
199	C₄²×C₁₇	—	2	1	no	—
200	C₄²×C₁₇	—	2	1	no	—
201	C₄²×C₁₇	—	2	1	no	—
202	C₄²×C₁₇	—	2	1	no	—
203	C₄²×C₁₇	—	2	2	no	—
204	C₄²×C₁₇	—	2	2	no	—
205	#22587	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂³×C₁₇	—	2	1	no	—
207	C₂³×C₁₇	—	2	2	no	—
208	C₂³×C₁₇	—	2	2	no	—
209	C₂³×C₁₇	—	2	1	no	—
210	C₂³×C₁₇	—	4	1	no	—
211	C₂³×C₁₇	—	4	2	no	—
212	C₂³×C₁₇	—	4	2	no	—
213	C₂³×C₁₇	—	8	1	no	—
214	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
215	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
216	C₂³×C₁₇	C₂×#41	1	1	yes	characteristic
217	Q₈×C₁₇	—	2	1	no	—
218	Q₈×C₁₇	—	2	1	no	—
219	Q₈×C₁₇	—	2	1	no	—
220	Q₈×C₁₇	—	4	2	no	—
221	Q₈×C₁₇	#117	1	2	yes	—
222	D₄×C₁₇	—	2	4	no	—
223	D₄×C₁₇	—	2	1	no	—
224	D₄×C₁₇	—	2	1	no	—
225	D₄×C₁₇	—	2	1	no	—
226	D₄×C₁₇	—	4	2	no	—
227	D₄×C₁₇	—	4	2	no	—
228	D₄×C₁₇	—	4	2	no	—
229	D₄×C₁₇	—	4	2	no	—
230	D₄×C₁₇	#117	1	2	yes	—
231	C₂×C₄×C₁₇	—	2	1	no	—
232	C₂×C₄×C₁₇	—	2	2	no	—
233	C₂×C₄×C₁₇	—	2	1	no	—
234	C₂×C₄×C₁₇	—	2	1	no	—
235	C₂×C₄×C₁₇	—	2	1	no	—
236	C₂×C₄×C₁₇	—	2	1	no	—
237	C₂×C₄×C₁₇	—	2	4	no	—
238	C₂×C₄×C₁₇	—	2	2	no	—
239	C₂×C₄×C₁₇	—	2	2	no	—
240	C₂×C₄×C₁₇	—	2	4	no	—
241	C₂×C₄×C₁₇	—	2	1	no	—
242	C₂×C₄×C₁₇	—	2	1	no	—
243	C₂×C₄×C₁₇	—	2	1	no	—
244	C₂×C₄×C₁₇	—	2	1	no	—
245	C₂×C₄×C₁₇	—	2	1	no	—
246	C₂×C₄×C₁₇	—	4	2	no	—
247	C₂×C₄×C₁₇	—	4	2	no	—
248	C₂×C₄×C₁₇	—	4	2	no	—
249	C₂×C₄×C₁₇	—	4	2	no	—
250	C₂×C₄×C₁₇	—	4	2	no	—
251	C₂×C₄×C₁₇	—	4	2	no	—
252	C₂×C₄×C₁₇	—	4	2	no	—
253	C₂×C₄×C₁₇	—	8	1	no	—
254	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
257	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
259	C₂×C₄×C₁₇	H(5,𝔽₂)	1	2	yes	—
260	C₈×C₁₇	—	2	1	no	—
261	C₈×C₁₇	—	2	1	no	—
262	C₈×C₁₇	—	2	1	no	—
263	C₈×C₁₇	—	2	1	no	—
264	C₈×C₁₇	—	2	2	no	—
265	C₈×C₁₇	—	2	2	no	—
266	C₈×C₁₇	—	4	2	no	—
267	C₈×C₁₇	—	4	2	no	—
268	#2924	C₂×C₁₇	1	1	yes	characteristic, complemented
269	C₂×#416	C₂×C₁₇	1	1	yes	characteristic
270	#2880	C₂×C₁₇	1	1	yes	characteristic
271	#1937	C₂×C₁₇	1	2	yes	complemented
272	#1929	C₂×C₁₇	1	2	yes	complemented
273	#1866	C₂×C₁₇	1	2	yes	complemented
274	#1826	C₂×C₁₇	1	1	yes	characteristic, complemented
275	#1810	C₂×C₁₇	1	1	yes	characteristic, complemented
276	#1789	C₂×C₁₇	1	1	yes	characteristic
277	#1764	C₂×C₁₇	1	2	yes	complemented
278	C₈×C₂²⋊C₄	C₂×C₁₇	1	1	yes	characteristic, complemented
279	C₂²×C₁₇	—	2	1	no	—
280	C₂²×C₁₇	—	2	1	no	—
281	C₂²×C₁₇	—	2	1	no	—
282	C₂²×C₁₇	—	2	1	no	—
283	C₂²×C₁₇	—	2	1	no	—
284	C₂²×C₁₇	—	2	2	no	—
285	C₂²×C₁₇	—	2	1	no	—
286	C₂²×C₁₇	—	2	1	no	—
287	C₂²×C₁₇	—	4	4	no	—
288	C₂²×C₁₇	—	4	1	no	—
289	C₂²×C₁₇	—	4	1	no	—
290	C₂²×C₁₇	—	4	1	no	—
291	C₂²×C₁₇	—	4	1	no	—
292	C₂²×C₁₇	—	4	1	no	—
293	C₂²×C₁₇	—	8	4	no	—
294	C₂²×C₁₇	#443	1	2	yes	—
295	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
296	C₂²×C₁₇	#551	1	2	yes	—
297	C₄×C₁₇	—	2	1	no	—
298	C₄×C₁₇	—	2	1	no	—
299	C₄×C₁₇	—	2	2	no	—
300	C₄×C₁₇	—	4	4	no	—
301	C₄×C₁₇	—	4	1	no	—
302	C₄×C₁₇	—	4	1	no	—
303	C₄×C₁₇	—	4	1	no	—
304	C₄×C₁₇	—	4	1	no	—
305	C₄×C₁₇	—	4	1	no	—
306	C₄×C₁₇	C₂×#117	1	1	yes	characteristic
307	C₄×C₁₇	#518	1	1	yes	characteristic
308	C₄×C₁₇	#546	1	2	yes	—
309	C₂²×#41	C₂²×C₁₇	1	1	yes	characteristic
310	C₂×#131	C₂²×C₁₇	1	2	yes	—
311	C₂³×C₈	C₂²×C₁₇	1	1	yes	characteristic
312	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
313	#433	—	2	2	no	—
314	#432	—	2	1	no	—
315	#431	—	2	1	no	—
316	C₂×#108	C₂²×C₁₇	1	2	yes	complemented
317	#424	C₂²×C₁₇	1	2	yes	complemented
318	C₂×#104	C₂²×C₁₇	1	2	yes	—
319	C₂×#104	C₂²×C₁₇	1	2	yes	—
320	#416	C₄×C₁₇	1	1	yes	characteristic, complemented
321	#416	C₄×C₁₇	1	1	yes	characteristic, complemented
322	#416	C₄×C₁₇	1	1	yes	characteristic, complemented
323	#416	C₄×C₁₇	1	1	yes	characteristic, complemented
324	#416	C₂²×C₁₇	1	1	yes	characteristic
325	#416	C₂²×C₁₇	1	1	yes	characteristic
326	#416	C₂²×C₁₇	1	1	yes	characteristic
327	#416	C₂²×C₁₇	1	1	yes	characteristic
328	C₂×#103	C₄×C₁₇	1	1	yes	characteristic, complemented
329	C₂×#103	C₄×C₁₇	1	1	yes	characteristic, complemented
330	C₂×#102	C₄×C₁₇	1	1	yes	characteristic, complemented
331	C₂×#102	C₄×C₁₇	1	1	yes	characteristic, complemented
332	#408	—	2	2	no	—
333	#408	C₂²×C₁₇	1	2	yes	—
334	#407	—	2	1	no	—
335	#407	C₂²×C₁₇	1	1	yes	characteristic
336	#407	C₂²×C₁₇	1	1	yes	characteristic
337	C₂×C₂²⋊C₈	—	2	1	no	—
338	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
339	#405	C₂²×C₁₇	1	2	yes	complemented
340	C₂×C₄×C₈	C₂²×C₁₇	1	2	yes	complemented
341	C₄×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
342	#341	C₂²×C₁₇	1	2	yes	complemented
343	#339	C₂²×C₁₇	1	2	yes	complemented
344	#339	C₂²×C₁₇	1	2	yes	complemented
345	#336	C₂²×C₁₇	1	2	yes	complemented
346	C₂×C₁₇	—	2	2	no	—
347	C₂×C₁₇	—	2	2	no	—
348	C₂×C₁₇	—	4	1	no	—
349	C₂×C₁₇	—	4	2	no	—
350	C₂×C₁₇	—	8	1	no	—
351	C₂×C₁₇	#2342	1	1	yes	characteristic
352	C₂×C₁₇	C₂×#443	1	1	yes	characteristic
353	C₂×C₁₇	#2957	1	1	yes	characteristic
354	C₂×#41	—	2	1	no	—
355	C₂×#41	—	2	1	no	—
356	C₂×#41	—	2	4	no	—
357	C₂×#41	—	4	2	no	—
358	C₂×#41	C₂×C₄×C₁₇	1	1	yes	characteristic
359	C₂×#41	C₂×C₄×C₁₇	1	1	yes	characteristic
360	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
361	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
362	C₂²×Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
363	C₂²×D₄	—	2	1	no	—
364	C₂²×D₄	C₂×C₄×C₁₇	1	1	yes	characteristic
365	C₂³×C₄	—	2	1	no	—
366	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
367	#131	—	2	4	no	—
368	#131	—	4	2	no	—
369	C₂×M₁₆	—	2	2	no	—
370	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
371	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
372	C₂²×C₈	—	2	2	no	—
373	C₂²×C₈	—	4	2	no	—
374	C₂²×C₈	C₂×C₄×C₁₇	1	1	yes	characteristic
375	C₂²×C₈	C₂×C₄×C₁₇	1	1	yes	characteristic
376	C₂²×C₈	C₂×C₄×C₁₇	1	1	yes	characteristic
377	C₂²×C₈	C₂×C₄×C₁₇	1	1	yes	characteristic
378	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
379	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
380	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
381	#117	—	2	1	no	—
382	#117	—	2	1	no	—
383	#117	C₂×C₄×C₁₇	1	1	yes	characteristic
384	#117	C₂×C₄×C₁₇	1	1	yes	characteristic
385	#117	C₂³×C₁₇	1	1	yes	characteristic
386	#117	C₂³×C₁₇	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₄²	—	2	1	no	—
392	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
393	#108	—	4	2	no	—
394	C₄⋊C₈	—	2	2	no	—
395	C₄⋊C₈	—	2	2	no	—
396	#104	—	2	4	no	—
397	#104	—	4	2	no	—
398	#103	C₂×C₄×C₁₇	1	1	yes	characteristic
399	#103	C₂×C₄×C₁₇	1	1	yes	characteristic
400	#103	C₂×C₄×C₁₇	1	1	yes	characteristic
401	#103	C₂×C₄×C₁₇	1	1	yes	characteristic
402	#103	C₂×C₄×C₁₇	1	1	yes	characteristic
403	#103	C₂×C₄×C₁₇	1	1	yes	characteristic
404	#103	C₂×C₄×C₁₇	1	1	yes	characteristic
405	#103	C₂×C₄×C₁₇	1	1	yes	characteristic
406	#102	C₂×C₄×C₁₇	1	1	yes	characteristic
407	#102	C₂×C₄×C₁₇	1	1	yes	characteristic
408	#102	C₂×C₄×C₁₇	1	1	yes	characteristic
409	#102	C₂×C₄×C₁₇	1	1	yes	characteristic
410	#102	C₂×C₄×C₁₇	1	1	yes	characteristic
411	#102	C₂×C₄×C₁₇	1	1	yes	characteristic
412	#102	C₂×C₄×C₁₇	1	1	yes	characteristic
413	#102	C₂×C₄×C₁₇	1	1	yes	characteristic
414	C₂²⋊C₈	—	2	1	no	—
415	C₂²⋊C₈	—	2	1	no	—
416	C₂²⋊C₈	—	2	1	no	—
417	C₂²⋊C₈	—	2	1	no	—
418	C₂²⋊C₈	—	2	2	no	—
419	C₂²⋊C₈	—	2	2	no	—
420	C₂²⋊C₈	D₄×C₁₇	1	1	yes	characteristic
421	C₂²⋊C₈	D₄×C₁₇	1	1	yes	characteristic
422	C₂²⋊C₈	D₄×C₁₇	1	2	yes	—
423	#97	—	2	2	no	—
424	C₄×C₈	—	2	2	no	—
425	C₄×C₈	—	4	2	no	—
426	#95	—	2	1	no	—
427	C₁₇	#22587	1	1	yes	characteristic, direct product factor, Sylow
428	C₂⁴	—	2	1	no	—
429	C₂⁴	#41×C₁₇	1	1	yes	characteristic
430	#41	—	2	2	no	—
431	#41	—	2	2	no	—
432	#41	—	2	2	no	—
433	#41	—	2	2	no	—
434	#41	—	2	2	no	—
435	#41	—	4	4	no	—
436	#41	—	4	1	no	—
437	#41	—	4	1	no	—
438	#41	—	4	4	no	—
439	#41	#41×C₁₇	1	4	yes	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	2	no	—
442	C₂×Q₈	—	4	1	no	—
443	C₂×Q₈	C₂²×C₄×C₁₇	1	1	yes	characteristic
444	C₂×Q₈	C₂²×C₄×C₁₇	1	1	yes	characteristic
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	4	1	no	—
452	C₂×D₄	—	4	4	no	—
453	C₂×D₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
454	C₂×D₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	4	4	no	—
466	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
467	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
470	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
471	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
472	M₁₆	—	2	2	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	—	2	2	no	—
475	M₁₆	—	2	2	no	—
476	M₁₆	—	4	4	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	2	2	no	—
483	C₂×C₈	—	4	1	no	—
484	C₂×C₈	—	4	1	no	—
485	C₂×C₈	—	4	1	no	—
486	C₂×C₈	—	4	1	no	—
487	C₂×C₈	—	4	4	no	—
488	C₂×C₈	C₂²×C₄×C₁₇	1	1	yes	characteristic
489	C₂×C₈	C₂²×C₄×C₁₇	1	1	yes	characteristic
490	C₂×C₈	C₂²×C₄×C₁₇	1	1	yes	characteristic
491	C₂×C₈	C₂²×C₄×C₁₇	1	1	yes	characteristic
492	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
493	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	2	no	—
510	C₄²	—	2	2	no	—
511	C₂³	—	2	1	no	—
512	C₂³	—	2	2	no	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	2	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	8	1	no	—
519	C₂³	C₄×D₄×C₁₇	1	1	yes	characteristic
520	C₂³	C₄×D₄×C₁₇	1	1	yes	characteristic
521	C₂³	C₂×#41×C₁₇	1	1	yes	characteristic
522	Q₈	—	2	1	no	—
523	Q₈	—	2	1	no	—
524	Q₈	—	2	1	no	—
525	Q₈	—	4	2	no	—
526	Q₈	C₁₇×#117	1	2	yes	—
527	D₄	—	2	4	no	—
528	D₄	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	2	1	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	2	no	—
535	D₄	C₁₇×#117	1	2	yes	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	8	1	no	—
559	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
560	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
561	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
562	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
563	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
564	C₂×C₄	C₁₇×H(5,𝔽₂)	1	2	yes	—
565	C₈	—	2	1	no	—
566	C₈	—	2	1	no	—
567	C₈	—	2	1	no	—
568	C₈	—	2	1	no	—
569	C₈	—	2	2	no	—
570	C₈	—	2	2	no	—
571	C₈	—	4	2	no	—
572	C₈	—	4	2	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	8	4	no	—
588	C₂²	C₁₇×#443	1	2	yes	—
589	C₂²	C₂×C₄×D₄×C₁₇	1	1	yes	characteristic
590	C₂²	C₁₇×#551	1	2	yes	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	2	no	—
594	C₄	—	4	4	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	1	no	—
600	C₄	C₂×C₁₇×#117	1	1	yes	characteristic
601	C₄	C₁₇×#518	1	1	yes	characteristic
602	C₄	C₁₇×#546	1	2	yes	—
603	C₂	—	2	2	no	—
604	C₂	—	2	2	no	—
605	C₂	—	4	1	no	—
606	C₂	—	4	2	no	—
607	C₂	—	8	1	no	—
608	C₂	C₁₇×#2342	1	1	yes	characteristic
609	C₂	C₂×C₁₇×#443	1	1	yes	characteristic
610	C₂	C₁₇×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	C₂²×#41×C₁₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₁₇×C₂²⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#2924	C₂	semidirect
4. C₁₇×#1937	C₂	semidirect
5. C₁₇×#1929	C₂	semidirect
6. C₁₇×#1866	C₂	semidirect
7. C₁₇×#1826	C₂	semidirect
8. C₁₇×#1810	C₂	semidirect
10. C₁₇×#1764	C₂	semidirect
11. C₈×C₂²⋊C₄×C₁₇	C₂	semidirect
19. C₂×C₁₇×#108	C₂²	semidirect
20. C₁₇×#424	C₂²	semidirect
23. C₁₇×#416	C₄	semidirect
24. C₁₇×#416	C₄	semidirect
25. C₁₇×#416	C₄	semidirect
26. C₁₇×#416	C₄	semidirect
31. C₂×C₁₇×#103	C₄	semidirect
32. C₂×C₁₇×#103	C₄	semidirect
33. C₂×C₁₇×#102	C₄	semidirect
34. C₂×C₁₇×#102	C₄	semidirect
42. C₁₇×#405	C₂²	semidirect
43. C₂×C₄×C₈×C₁₇	C₂²	semidirect
45. C₁₇×#341	C₂²	semidirect
46. C₁₇×#339	C₂²	semidirect
47. C₁₇×#339	C₂²	semidirect
48. C₁₇×#336	C₂²	semidirect
205. #22587	C₁₇	direct (N × H)
268. #2924	C₂×C₁₇	semidirect
271. #1937	C₂×C₁₇	semidirect
272. #1929	C₂×C₁₇	semidirect
273. #1866	C₂×C₁₇	semidirect
274. #1826	C₂×C₁₇	semidirect
275. #1810	C₂×C₁₇	semidirect
277. #1764	C₂×C₁₇	semidirect
278. C₈×C₂²⋊C₄	C₂×C₁₇	semidirect
316. C₂×#108	C₂²×C₁₇	semidirect
317. #424	C₂²×C₁₇	semidirect
320. #416	C₄×C₁₇	semidirect
321. #416	C₄×C₁₇	semidirect
322. #416	C₄×C₁₇	semidirect
323. #416	C₄×C₁₇	semidirect
328. C₂×#103	C₄×C₁₇	semidirect
329. C₂×#103	C₄×C₁₇	semidirect
330. C₂×#102	C₄×C₁₇	semidirect
331. C₂×#102	C₄×C₁₇	semidirect
339. #405	C₂²×C₁₇	semidirect
340. C₂×C₄×C₈	C₂²×C₁₇	semidirect
342. #341	C₂²×C₁₇	semidirect
343. #339	C₂²×C₁₇	semidirect
344. #339	C₂²×C₁₇	semidirect
345. #336	C₂²×C₁₇	semidirect
427. C₁₇	#22587	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×#2924	2
C₂×C₁₇×#416	2
C₁₇×#2880	2
C₁₇×#1937	2
C₁₇×#1929	2
C₁₇×#1866	2
C₁₇×#1826	2
C₁₇×#1810	2
C₁₇×#1789	2
C₁₇×#1764	2
C₈×C₂²⋊C₄×C₁₇	2
#22587	17

Subgroups — C17×#22587 #16880331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#22587 #16880331