Subgroups — #17968698

Order 4352.

990 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₇⋊#432	C₂	1	1	yes	maximal, characteristic
2	#14545231	C₂	1	1	yes	maximal, characteristic
3	#14544578	C₂	1	2	yes	maximal, complemented
4	C₈×C₄⋊#595	C₂	1	2	yes	maximal, complemented
5	#14544520	C₂	1	2	yes	maximal
6	C₈×C₂²⋊#595	C₂	1	2	yes	maximal
7	#14544502	C₂	1	2	yes	maximal, complemented
8	#14544440	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
10	#11763832	C₄	1	2	yes	complemented
11	#11763831	C₄	1	2	yes	complemented
12	#11763830	C₄	1	2	yes	complemented
13	#11763829	C₄	1	2	yes	complemented
14	#11763810	C₂²	1	2	yes	—
15	#11763777	C₂²	1	2	yes	—
16	#11763768	C₂²	1	2	yes	—
17	C₂×#10587532	C₂²	1	4	yes	—
18	C₂×C₈×#595	C₂²	1	4	yes	—
19	#11763754	C₄	1	2	yes	—
20	#11763753	C₄	1	2	yes	—
21	#11763752	C₄	1	2	yes	—
22	#11763751	C₄	1	2	yes	—
23	C₄×C₄⋊#595	C₂²	1	2	yes	—
24	C₄×C₂²⋊#595	C₂²	1	2	yes	—
25	#11763745	C₂²	1	2	yes	—
26	#11763674	C₂²	1	4	yes	—
27	#11763674	C₂²	1	4	yes	—
28	C₂²×C₈×D₁₇	C₂²	1	1	yes	characteristic
29	C₂²×C₈×D₁₇	C₂²	1	1	yes	characteristic
30	C₂×C₄²×D₁₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×#3622	C₄	1	1	yes	characteristic, complemented
32	C₂×C₈×Dic₁₇	C₄	1	1	yes	characteristic, complemented
33	C₂×C₈×Dic₁₇	C₄	1	1	yes	characteristic, complemented
34	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic, complemented
35	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic, complemented
36	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic, complemented
37	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic, complemented
38	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
39	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
40	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
41	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₁₇	C₄	1	1	yes	characteristic, complemented
43	C₂²×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×D₁₇	C₂³	1	1	yes	characteristic
46	C₂×C₂²⋊#595	C₂×C₄	1	4	yes	—
47	C₂×C₄⋊#595	C₂×C₄	1	4	yes	—
48	C₂×C₄×#595	C₂³	1	4	yes	—
49	C₂×#63242	C₂³	1	4	yes	—
50	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
56	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
57	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₁₇	—	2	4	no	—
59	C₂×C₈×D₁₇	—	2	4	no	—
60	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
65	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
66	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
68	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
70	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
71	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
72	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
73	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
74	C₄²×D₁₇	C₂³	1	1	yes	characteristic
75	C₄²×D₁₇	C₂³	1	1	yes	characteristic
76	C₂²⋊#3624	C₂×C₄	1	4	yes	—
77	(C₂×#595)⋊C₄	C₂×C₄	1	4	yes	—
78	(C₂×#595)⋊C₄	C₂×C₄	1	4	yes	—
79	(C₂×#595)⋊C₄	C₂×C₄	1	4	yes	—
80	(C₂×#595)⋊C₄	C₂×C₄	1	4	yes	—
81	#10587544	C₂×C₄	1	4	yes	—
82	#10587543	C₂×C₄	1	4	yes	—
83	#10587542	C₂×C₄	1	4	yes	—
84	#10587542	C₂×C₄	1	4	yes	—
85	C₄⋊#3624	C₂×C₄	1	4	yes	—
86	#10587532	—	2	8	no	—
87	C₈×#595	—	2	8	no	—
88	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
89	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
90	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
92	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
98	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
100	C₄×#3622	C₂×C₄	1	1	yes	characteristic
101	C₄×#3622	C₂×C₄	1	1	yes	characteristic
102	C₄×#3622	C₂×C₄	1	1	yes	characteristic
103	C₄×#3622	C₂×C₄	1	1	yes	characteristic
104	C₂³×D₁₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×#595	C₂²×C₄	1	8	yes	—
106	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
107	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
108	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×Dic₁₇	C₄²	1	1	yes	characteristic
110	C₂²×Dic₁₇	C₄²	1	1	yes	characteristic
111	C₂²×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₄×D₁₇	—	2	4	no	—
113	C₂×C₄×D₁₇	—	2	4	no	—
114	C₂×C₄×D₁₇	—	2	2	no	—
115	C₂×C₄×D₁₇	—	2	2	no	—
116	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
117	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
118	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
119	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
120	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×D₁₇	C₂⁴	1	1	yes	characteristic
128	C₂²⋊#595	—	2	8	no	—
129	C₂×#3624	C₂²×C₄	1	8	yes	—
130	C₄⋊#595	—	2	8	no	—
131	C₄×#595	—	2	4	no	—
132	C₄×#595	—	2	4	no	—
133	#63242	—	2	4	no	—
134	#63242	—	2	4	no	—
135	C₂×C₈×C₁₇	—	2	2	no	—
136	C₂×C₈×C₁₇	—	2	2	no	—
137	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₁₇	C₄²	1	1	yes	characteristic
142	C₄²×C₁₇	C₄²	1	1	yes	characteristic
143	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
144	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
145	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
146	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
147	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
148	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
149	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
150	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
151	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
152	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
153	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
154	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
155	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
156	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
157	C₂×#3622	—	2	2	no	—
158	C₂×#3622	—	2	2	no	—
159	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
160	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
161	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
162	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
163	C₈×D₁₇	—	2	2	no	—
164	C₈×D₁₇	—	2	2	no	—
165	C₈×D₁₇	—	2	2	no	—
166	C₈×D₁₇	—	2	2	no	—
167	C₈×D₁₇	—	2	2	no	—
168	C₈×D₁₇	—	2	2	no	—
169	C₈×D₁₇	#41	1	4	yes	—
170	C₈×D₁₇	#41	1	4	yes	—
171	#20476	—	17	1	no	maximal, Sylow
172	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
173	C₂²×D₁₇	—	2	2	no	—
174	C₂²×D₁₇	—	2	2	no	—
175	C₂²×D₁₇	C₂×C₄²	1	1	yes	characteristic
176	C₂²×D₁₇	#131	1	4	yes	—
177	C₂²×D₁₇	C₂³×C₄	1	1	yes	characteristic
178	C₂×#595	—	2	8	no	—
179	C₂×#595	—	2	8	no	—
180	C₂×#595	—	2	8	no	—
181	C₂×C₄×C₁₇	—	2	2	no	—
182	C₂×C₄×C₁₇	—	2	1	no	—
183	C₂×C₄×C₁₇	—	2	1	no	—
184	C₂×C₄×C₁₇	—	2	2	no	—
185	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
186	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
187	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
188	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
189	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
190	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
191	C₂×Dic₁₇	—	2	2	no	—
192	C₂×Dic₁₇	—	2	2	no	—
193	C₂×Dic₁₇	—	2	2	no	—
194	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
195	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
196	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
197	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
198	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
199	C₂×Dic₁₇	C₂³×C₄	1	1	yes	characteristic
200	C₄×D₁₇	—	2	2	no	—
201	C₄×D₁₇	—	2	2	no	—
202	C₄×D₁₇	—	2	2	no	—
203	C₄×D₁₇	—	2	2	no	—
204	C₄×D₁₇	—	2	2	no	—
205	C₄×D₁₇	—	2	2	no	—
206	C₄×D₁₇	—	2	1	no	—
207	C₄×D₁₇	—	2	1	no	—
208	C₄×D₁₇	—	2	2	no	—
209	C₄×D₁₇	—	2	2	no	—
210	C₄×D₁₇	—	2	2	no	—
211	C₄×D₁₇	#131	1	4	yes	—
212	C₄×D₁₇	C₂×#41	1	2	yes	—
213	C₄×D₁₇	C₂×#41	1	2	yes	—
214	#3624	—	2	8	no	—
215	C₈×C₁₇	—	2	1	no	—
216	C₈×C₁₇	—	2	1	no	—
217	C₈×C₁₇	#117	1	2	yes	—
218	C₈×C₁₇	#117	1	2	yes	—
219	#3622	—	2	1	no	—
220	#3622	—	2	1	no	—
221	#3622	#117	1	2	yes	—
222	#3622	#117	1	2	yes	—
223	C₂×#432	—	17	1	no	—
224	C₂²×C₄×C₈	—	17	1	no	—
225	#2283	—	17	1	no	—
226	#1770	—	17	2	no	—
227	C₈×C₄⋊C₄	—	17	2	no	—
228	#1752	—	17	2	no	—
229	C₈×C₂²⋊C₄	—	17	2	no	—
230	#1746	—	17	2	no	—
231	#1726	—	17	2	no	—
232	C₂²×C₁₇	—	2	1	no	—
233	C₂²×C₁₇	—	2	1	no	—
234	C₂²×C₁₇	#405	1	2	yes	—
235	C₂²×C₁₇	C₂²×C₄²	1	1	yes	characteristic
236	C₂×D₁₇	—	2	1	no	—
237	C₂×D₁₇	—	2	1	no	—
238	C₂×D₁₇	—	2	8	no	—
239	C₂×D₁₇	#405	1	2	yes	—
240	C₂×D₁₇	C₄×#41	1	2	yes	—
241	C₂×D₁₇	C₂×#131	1	2	yes	—
242	C₂×D₁₇	C₂×#131	1	2	yes	—
243	#595	—	4	8	no	—
244	C₄×C₁₇	—	2	1	no	—
245	C₄×C₁₇	—	2	1	no	—
246	C₄×C₁₇	—	2	1	no	—
247	C₄×C₁₇	—	2	1	no	—
248	C₄×C₁₇	#405	1	2	yes	—
249	C₄×C₁₇	C₂×#117	1	1	yes	characteristic
250	C₄×C₁₇	C₂×#117	1	1	yes	characteristic
251	Dic₁₇	—	2	1	no	—
252	Dic₁₇	—	2	1	no	—
253	Dic₁₇	—	2	1	no	—
254	Dic₁₇	—	2	1	no	—
255	Dic₁₇	#405	1	2	yes	—
256	Dic₁₇	C₄×#41	1	2	yes	—
257	C₂³×C₈	—	17	1	no	—
258	C₂³×C₈	—	17	1	no	—
259	C₂²×C₄²	—	17	1	no	—
260	#432	—	17	2	no	—
261	#432	—	17	2	no	—
262	#432	—	17	2	no	—
263	#432	—	17	2	no	—
264	C₂×C₄⋊C₈	—	17	2	no	—
265	C₂×C₂²⋊C₈	—	17	2	no	—
266	C₂×#97	—	17	2	no	—
267	C₂×#97	—	17	4	no	—
268	C₂×C₄×C₈	—	17	1	no	—
269	C₂×C₄×C₈	—	17	1	no	—
270	C₂×C₄×C₈	—	17	1	no	—
271	C₂×C₄×C₈	—	17	1	no	—
272	C₂×C₄×C₈	—	17	1	no	—
273	C₂×C₄×C₈	—	17	1	no	—
274	C₂×C₄×C₈	—	17	1	no	—
275	C₂×C₄×C₈	—	17	1	no	—
276	C₂×C₄×C₈	—	17	1	no	—
277	C₂×C₄×C₈	—	17	1	no	—
278	C₂×C₄×C₈	—	17	1	no	—
279	C₂×C₄×C₈	—	17	4	no	—
280	C₂×C₄×C₈	#595	1	1	yes	characteristic, complemented
281	#383	—	17	2	no	—
282	#382	—	17	2	no	—
283	#381	—	17	2	no	—
284	#380	—	17	2	no	—
285	C₄×C₄⋊C₄	—	17	2	no	—
286	C₄×C₂²⋊C₄	—	17	2	no	—
287	#376	—	17	2	no	—
288	#336	—	17	4	no	—
289	#336	—	17	4	no	—
290	C₂×C₁₇	—	2	2	no	—
291	C₂×C₁₇	C₄×#117	1	1	yes	characteristic
292	C₂×C₁₇	C₂×#405	1	1	yes	characteristic
293	C₂×C₁₇	C₂×#405	1	1	yes	characteristic
294	D₁₇	—	2	2	no	—
295	D₁₇	#2966	1	4	yes	—
296	C₂³×C₄	—	17	1	no	—
297	C₂³×C₄	—	17	1	no	—
298	C₂³×C₄	—	17	1	no	—
299	C₂²×C₈	—	17	1	no	—
300	C₂²×C₈	—	17	1	no	—
301	C₂²×C₈	—	17	4	no	—
302	C₂²×C₈	—	17	1	no	—
303	C₂²×C₈	—	17	1	no	—
304	C₂²×C₈	—	17	1	no	—
305	C₂²×C₈	—	17	1	no	—
306	C₂²×C₈	—	17	1	no	—
307	C₂²×C₈	—	17	1	no	—
308	C₂²×C₈	—	17	1	no	—
309	C₂²×C₈	—	17	1	no	—
310	C₂²×C₈	—	34	4	no	—
311	C₂²×C₈	—	34	4	no	—
312	C₂²×C₈	C₂×#595	1	1	yes	characteristic
313	C₂²×C₈	C₂×#595	1	1	yes	characteristic
314	C₂×C₄⋊C₄	—	17	4	no	—
315	C₂×C₂²⋊C₄	—	17	4	no	—
316	C₂×C₄²	—	17	1	no	—
317	C₂×C₄²	—	17	1	no	—
318	C₂×C₄²	—	17	1	no	—
319	C₂×C₄²	—	17	1	no	—
320	C₂×C₄²	—	17	1	no	—
321	C₂×C₄²	—	17	1	no	—
322	C₂×C₄²	—	17	1	no	—
323	C₂×C₄²	—	17	1	no	—
324	C₂×C₄²	—	17	1	no	—
325	C₂×C₄²	—	17	1	no	—
326	C₂×C₄²	—	17	1	no	—
327	C₂×C₄²	—	17	4	no	—
328	C₂×C₄²	C₂×#595	1	1	yes	characteristic
329	C₄⋊C₈	—	17	4	no	—
330	C₄⋊C₈	—	17	4	no	—
331	C₂²⋊C₈	—	17	4	no	—
332	C₂²⋊C₈	—	17	4	no	—
333	#97	—	17	4	no	—
334	#97	—	17	4	no	—
335	#97	—	34	8	no	—
336	C₄×C₈	—	17	1	no	—
337	C₄×C₈	—	17	1	no	—
338	C₄×C₈	—	17	1	no	—
339	C₄×C₈	—	17	1	no	—
340	C₄×C₈	—	17	1	no	—
341	C₄×C₈	—	17	1	no	—
342	C₄×C₈	—	17	1	no	—
343	C₄×C₈	—	17	1	no	—
344	C₄×C₈	—	17	1	no	—
345	C₄×C₈	—	17	1	no	—
346	C₄×C₈	—	17	1	no	—
347	C₄×C₈	—	17	1	no	—
348	C₄×C₈	—	34	8	no	—
349	C₄×C₈	C₂×#595	1	1	yes	characteristic
350	C₄×C₈	C₂×#595	1	1	yes	characteristic
351	C₄×C₈	C₂×#595	1	1	yes	characteristic
352	C₄×C₈	C₂×#595	1	1	yes	characteristic
353	#95	—	17	4	no	—
354	#95	—	17	4	no	—
355	#95	—	17	4	no	—
356	#95	—	17	4	no	—
357	C₁₇	#20476	1	1	yes	characteristic, complemented, Sylow
358	C₂⁴	—	17	1	no	—
359	C₂²×C₄	—	17	1	no	—
360	C₂²×C₄	—	17	1	no	—
361	C₂²×C₄	—	17	1	no	—
362	C₂²×C₄	—	17	1	no	—
363	C₂²×C₄	—	17	1	no	—
364	C₂²×C₄	—	17	1	no	—
365	C₂²×C₄	—	17	1	no	—
366	C₂²×C₄	—	17	1	no	—
367	C₂²×C₄	—	17	1	no	—
368	C₂²×C₄	—	17	1	no	—
369	C₂²×C₄	—	17	1	no	—
370	C₂²×C₄	—	17	1	no	—
371	C₂²×C₄	—	17	1	no	—
372	C₂²×C₄	—	17	1	no	—
373	C₂²×C₄	—	17	1	no	—
374	C₂²×C₄	—	17	8	no	—
375	C₂²×C₄	—	34	2	no	—
376	C₂²×C₄	—	34	2	no	—
377	C₂²×C₄	—	34	4	no	—
378	C₂²×C₄	—	34	4	no	—
379	C₂²×C₄	C₄×#595	1	1	yes	characteristic
380	C₂²×C₄	C₄×#595	1	1	yes	characteristic
381	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	17	1	no	—
385	C₂×C₈	—	17	1	no	—
386	C₂×C₈	—	17	4	no	—
387	C₂×C₈	—	17	4	no	—
388	C₂×C₈	—	17	8	no	—
389	C₂×C₈	—	17	1	no	—
390	C₂×C₈	—	17	1	no	—
391	C₂×C₈	—	34	2	no	—
392	C₂×C₈	—	34	2	no	—
393	C₂×C₈	—	34	2	no	—
394	C₂×C₈	—	34	2	no	—
395	C₂×C₈	—	34	2	no	—
396	C₂×C₈	—	34	2	no	—
397	C₂×C₈	—	34	4	no	—
398	C₂×C₈	—	34	4	no	—
399	C₂×C₈	—	34	2	no	—
400	C₂×C₈	—	34	2	no	—
401	C₂×C₈	C₂²×#595	1	1	yes	characteristic
402	C₂×C₈	C₂²×#595	1	1	yes	characteristic
403	C₂×C₈	C₂²×#595	1	1	yes	characteristic
404	C₂×C₈	C₂²×#595	1	1	yes	characteristic
405	C₄⋊C₄	—	34	8	no	—
406	C₂²⋊C₄	—	34	8	no	—
407	C₄²	—	17	1	no	—
408	C₄²	—	17	1	no	—
409	C₄²	—	17	1	no	—
410	C₄²	—	17	1	no	—
411	C₄²	—	17	1	no	—
412	C₄²	—	17	1	no	—
413	C₄²	—	17	1	no	—
414	C₄²	—	17	1	no	—
415	C₄²	—	17	1	no	—
416	C₄²	—	17	1	no	—
417	C₄²	—	17	1	no	—
418	C₄²	—	17	1	no	—
419	C₄²	—	34	4	no	—
420	C₄²	—	34	4	no	—
421	C₄²	C₄×#595	1	1	yes	characteristic
422	C₄²	C₄×#595	1	1	yes	characteristic
423	C₄²	C₂²×#595	1	1	yes	characteristic
424	C₄²	C₂²×#595	1	1	yes	characteristic
425	C₂³	—	17	1	no	—
426	C₂³	—	17	4	no	—
427	C₂³	—	17	1	no	—
428	C₂³	—	34	2	no	—
429	C₂³	—	34	2	no	—
430	C₂³	C₂×C₄×#595	1	1	yes	characteristic
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	17	1	no	—
436	C₂×C₄	—	17	1	no	—
437	C₂×C₄	—	17	4	no	—
438	C₂×C₄	—	17	2	no	—
439	C₂×C₄	—	17	2	no	—
440	C₂×C₄	—	17	1	no	—
441	C₂×C₄	—	17	1	no	—
442	C₂×C₄	—	17	1	no	—
443	C₂×C₄	—	17	1	no	—
444	C₂×C₄	—	34	2	no	—
445	C₂×C₄	—	34	2	no	—
446	C₂×C₄	—	34	2	no	—
447	C₂×C₄	—	34	2	no	—
448	C₂×C₄	—	34	2	no	—
449	C₂×C₄	—	34	2	no	—
450	C₂×C₄	—	34	2	no	—
451	C₂×C₄	—	34	2	no	—
452	C₂×C₄	—	34	2	no	—
453	C₂×C₄	—	34	2	no	—
454	C₂×C₄	—	34	2	no	—
455	C₂×C₄	—	34	2	no	—
456	C₂×C₄	—	34	1	no	—
457	C₂×C₄	—	34	1	no	—
458	C₂×C₄	—	34	8	no	—
459	C₂×C₄	—	34	8	no	—
460	C₂×C₄	—	34	8	no	—
461	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
462	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
463	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
464	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
465	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
466	C₂×C₄	C₂³×#595	1	1	yes	characteristic
467	C₈	—	2	1	no	—
468	C₈	—	2	1	no	—
469	C₈	—	17	2	no	—
470	C₈	—	17	2	no	—
471	C₈	—	34	8	no	—
472	C₈	—	34	1	no	—
473	C₈	—	34	1	no	—
474	C₈	#10587677	1	2	yes	—
475	C₈	#10587677	1	2	yes	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	17	2	no	—
479	C₂²	—	17	2	no	—
480	C₂²	—	17	2	no	—
481	C₂²	—	17	2	no	—
482	C₂²	—	34	8	no	—
483	C₂²	—	34	1	no	—
484	C₂²	—	34	1	no	—
485	C₂²	#11763772	1	2	yes	—
486	C₂²	C₂²×C₄×#595	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	17	2	no	—
492	C₄	—	17	2	no	—
493	C₄	—	34	1	no	—
494	C₄	—	34	1	no	—
495	C₄	—	34	1	no	—
496	C₄	—	34	1	no	—
497	C₄	—	68	8	no	—
498	C₄	#11763772	1	2	yes	—
499	C₄	C₂×#10587677	1	1	yes	characteristic
500	C₄	C₂×#10587677	1	1	yes	characteristic
501	C₂	—	2	2	no	—
502	C₂	—	17	4	no	—
503	C₂	—	34	2	no	—
504	C₂	C₄×#10587677	1	1	yes	characteristic
505	C₂	C₂×#11763772	1	1	yes	characteristic
506	C₂	C₂×#11763772	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×#595
commutator, socle	C₂²×C₁₇	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#595
Fitting	C₂×C₄×C₈×C₁₇	C₄
prime radical	C₂³×D₁₇	C₂²×C₄
cosocle	C₂×C₄×D₁₇	C₂⁴
hypercenter	C₂×C₄×C₈	#595
hypocenter	C₁₇	#20476
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #14544578	C₂	semidirect
4. C₈×C₄⋊#595	C₂	semidirect
7. #14544502	C₂	semidirect
8. #14544440	C₂	semidirect
10. #11763832	C₄	semidirect
11. #11763831	C₄	semidirect
12. #11763830	C₄	semidirect
13. #11763829	C₄	semidirect
31. C₂×C₄×#3622	C₄	semidirect
32. C₂×C₈×Dic₁₇	C₄	semidirect
33. C₂×C₈×Dic₁₇	C₄	semidirect
34. C₄×C₈×D₁₇	C₄	semidirect
35. C₄×C₈×D₁₇	C₄	semidirect
36. C₄×C₈×D₁₇	C₄	semidirect
37. C₄×C₈×D₁₇	C₄	semidirect
42. C₂×C₄×C₈×C₁₇	C₄	semidirect
280. C₂×C₄×C₈	#595	semidirect
357. C₁₇	#20476	semidirect

Maximal subgroups

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

subgroup	index
D₁₇⋊#432	2
#14545231	2
#14544578	2
C₈×C₄⋊#595	2
#14544520	2
C₈×C₂²⋊#595	2
#14544502	2
#14544440	2
C₂×C₄×C₈×D₁₇	2
#20476	17