Subgroups — #17000075

Order 4352.

704 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14537748	C₂	1	1	yes	maximal, characteristic
2	#14537746	C₂	1	1	yes	maximal, characteristic
3	#14537426	C₂	1	1	yes	maximal, characteristic
4	#14527087	C₂	1	1	yes	maximal, characteristic, complemented
5	#14527085	C₂	1	1	yes	maximal, characteristic, complemented
6	#14527083	C₂	1	1	yes	maximal, characteristic, complemented
7	#14527082	C₂	1	1	yes	maximal, characteristic, complemented
8	#14527079	C₂	1	1	yes	maximal, characteristic, complemented
9	#14527078	C₂	1	1	yes	maximal, characteristic, complemented
10	#14527075	C₂	1	1	yes	maximal, characteristic, complemented
11	#14527073	C₂	1	1	yes	maximal, characteristic, complemented
12	#14527070	C₂	1	1	yes	maximal, characteristic, complemented
13	#14527066	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#63218	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×M₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#63252	C₂²	1	1	yes	characteristic
17	#11762938	C₄	1	2	yes	—
18	#11762937	C₄	1	2	yes	—
19	#11762885	C₄	1	2	yes	—
20	#11762884	C₄	1	2	yes	—
21	#11762883	C₄	1	2	yes	—
22	#11762882	C₄	1	2	yes	—
23	#11762879	C₄	1	2	yes	—
24	#11762878	C₄	1	2	yes	—
25	#11762868	C₄	1	2	yes	—
26	#11762868	C₄	1	2	yes	—
27	#11762862	C₂²	1	1	yes	characteristic
28	#11762860	C₂²	1	1	yes	characteristic
29	#11762860	C₂²	1	1	yes	characteristic
30	#11762860	C₂²	1	1	yes	characteristic
31	#11762860	C₂²	1	1	yes	characteristic
32	#11762860	C₂²	1	1	yes	characteristic
33	#11762860	C₂²	1	1	yes	characteristic
34	#11762860	C₂²	1	1	yes	characteristic
35	#11762860	C₂²	1	1	yes	characteristic
36	#11762835	C₄	1	2	yes	—
37	#11762775	C₄	1	2	yes	—
38	C₄×#63223	C₂²	1	1	yes	characteristic
39	C₄×#63223	C₂²	1	1	yes	characteristic
40	C₄×#63218	C₂²	1	1	yes	characteristic
41	C₄×#63218	C₂²	1	1	yes	characteristic
42	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
43	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
44	#11762531	C₂²	1	1	yes	characteristic
45	#11762531	C₂²	1	1	yes	characteristic
46	#11762531	C₂²	1	1	yes	characteristic
47	#11762531	C₂²	1	1	yes	characteristic
48	#11762531	C₂²	1	1	yes	characteristic
49	#11762531	C₂²	1	1	yes	characteristic
50	#11762530	C₂²	1	1	yes	characteristic
51	#11762530	C₂²	1	1	yes	characteristic
52	#11762530	C₂²	1	1	yes	characteristic
53	#11762530	C₂²	1	1	yes	characteristic
54	C₈×#3622	C₂²	1	1	yes	characteristic
55	C₈×#3622	C₂²	1	1	yes	characteristic
56	C₁₇×#431	C₂²	1	1	yes	characteristic
57	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
59	C₁₇×#322	C₂²	1	1	yes	characteristic
60	C₁₇×#322	C₂²	1	1	yes	characteristic
61	C₈²×C₁₇	C₂²	1	1	yes	characteristic
62	C₈²×C₁₇	C₂²	1	1	yes	characteristic
63	C₂×#63252	C₂×C₄	1	1	yes	characteristic
64	C₂×M₁₆×C₁₇	C₂×C₄	1	2	yes	—
65	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
67	C₄×C₂²⋊D₁₇	C₂×C₄	1	1	yes	characteristic
68	C₄×C₂²⋊D₁₇	C₂×C₄	1	1	yes	characteristic
69	C₄×C₂²⋊D₁₇	C₂×C₄	1	1	yes	characteristic
70	C₄×C₂²⋊D₁₇	C₂×C₄	1	1	yes	characteristic
71	#10587612	C₂×C₄	1	1	yes	characteristic
72	C₂×#63223	C₂×C₄	1	2	yes	—
73	C₂×#63223	C₂×C₄	1	2	yes	—
74	C₂×#63218	C₂×C₄	1	2	yes	—
75	C₂×#63218	C₂×C₄	1	2	yes	—
76	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
77	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
78	C₄×D₆₈	C₂×C₄	1	1	yes	characteristic
79	C₄×D₆₈	C₂×C₄	1	1	yes	characteristic
80	#10587558	C₂×C₄	1	1	yes	characteristic
81	#10587558	C₂×C₄	1	1	yes	characteristic
82	C₄²×D₁₇	C₂³	1	1	yes	characteristic
83	C₄²×D₁₇	C₂³	1	1	yes	characteristic
84	C₄×Dic₃₄	C₂×C₄	1	1	yes	characteristic
85	C₄×Dic₃₄	C₂×C₄	1	1	yes	characteristic
86	C₁₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
87	C₁₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
88	C₁₇×#97	C₂×C₄	1	2	yes	—
89	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	—
90	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
95	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
96	C₂²⋊#3622	C₂×C₄	1	2	yes	—
97	#10587491	C₂×C₄	1	2	yes	—
98	#10587491	C₂×C₄	1	2	yes	—
99	#10587491	C₂×C₄	1	2	yes	—
100	#10587491	C₂×C₄	1	2	yes	—
101	#10587491	C₂×C₄	1	2	yes	—
102	#10587491	C₂×C₄	1	2	yes	—
103	#10587491	C₂×C₄	1	2	yes	—
104	#10587491	C₂×C₄	1	2	yes	—
105	#10587486	C₂×C₄	1	2	yes	—
106	#10587486	C₂×C₄	1	2	yes	—
107	#10587485	C₂×C₄	1	2	yes	—
108	#10587485	C₂×C₄	1	2	yes	—
109	#10587485	C₂×C₄	1	2	yes	—
110	#10587485	C₂×C₄	1	2	yes	—
111	#10587485	C₂×C₄	1	2	yes	—
112	#10587485	C₂×C₄	1	2	yes	—
113	#10587485	C₂×C₄	1	2	yes	—
114	#10587485	C₂×C₄	1	2	yes	—
115	C₈×Dic₁₇	C₂×C₄	1	2	yes	—
116	C₈×Dic₁₇	C₂×C₄	1	2	yes	—
117	C₄⋊#3622	C₂×C₄	1	2	yes	—
118	#10587474	C₂×C₄	1	2	yes	—
119	#10587474	C₂×C₄	1	2	yes	—
120	C₄×#3622	C₂³	1	1	yes	characteristic
121	C₄×#3622	C₂³	1	1	yes	characteristic
122	C₄×#3622	C₂³	1	1	yes	characteristic
123	C₄×#3622	C₂³	1	1	yes	characteristic
124	C₄×#3622	C₂³	1	1	yes	characteristic
125	C₄×#3622	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₂²⋊D₁₇	C₄²	1	1	yes	characteristic
130	C₂×C₂²⋊D₁₇	C₄²	1	1	yes	characteristic
131	#63252	—	4	2	no	—
132	C₂×D₆₈	C₄²	1	1	yes	characteristic
133	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
139	C₂×Dic₃₄	C₄²	1	1	yes	characteristic
140	M₁₆×C₁₇	—	2	4	no	—
141	C₂×C₈×C₁₇	—	4	2	no	—
142	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
147	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
148	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
150	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
152	C₂²⋊Dic₁₇	C₄²	1	1	yes	characteristic
153	C₂²⋊Dic₁₇	C₄²	1	1	yes	characteristic
154	#63227	C₄²	1	1	yes	characteristic
155	#63227	C₄²	1	1	yes	characteristic
156	#63227	C₄²	1	1	yes	characteristic
157	#63227	C₄²	1	1	yes	characteristic
158	C₄⋊Dic₁₇	C₄²	1	1	yes	characteristic
159	C₄⋊Dic₁₇	C₄²	1	1	yes	characteristic
160	#63225	C₄²	1	1	yes	characteristic
161	#63225	C₄²	1	1	yes	characteristic
162	#63225	C₄²	1	1	yes	characteristic
163	#63225	C₄²	1	1	yes	characteristic
164	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
165	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
166	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
167	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
168	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
169	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
170	#63223	—	4	2	no	—
171	#63223	—	4	2	no	—
172	C₂×#3622	C₂²×C₄	1	2	yes	—
173	C₂×#3622	C₂²×C₄	1	2	yes	—
174	C₂×#3622	C₂²×C₄	1	2	yes	—
175	C₂×#3622	C₂²×C₄	1	2	yes	—
176	C₂×#3622	C₂²×C₄	1	2	yes	—
177	C₂×#3622	C₂²×C₄	1	2	yes	—
178	#63218	—	2	4	no	—
179	#63218	—	4	2	no	—
180	C₈×D₁₇	—	2	4	no	—
181	C₈×D₁₇	—	4	2	no	—
182	#17340	—	17	1	no	maximal, Sylow
183	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
184	C₂²×D₁₇	C₂×C₄²	1	1	yes	characteristic
185	C₂²×D₁₇	C₂×C₄²	1	1	yes	characteristic
186	C₂×C₄×C₁₇	—	2	2	no	—
187	C₂×C₄×C₁₇	—	2	2	no	—
188	C₂×C₄×C₁₇	—	2	2	no	—
189	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
190	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
191	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
192	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
195	C₂²⋊D₁₇	—	4	1	no	—
196	C₂²⋊D₁₇	—	4	1	no	—
197	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
198	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
199	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
200	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
201	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
202	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
203	D₆₈	—	4	1	no	—
204	C₄×D₁₇	—	2	2	no	—
205	C₄×D₁₇	—	2	2	no	—
206	C₄×D₁₇	—	2	2	no	—
207	C₄×D₁₇	—	2	2	no	—
208	C₄×D₁₇	—	2	2	no	—
209	C₄×D₁₇	—	2	2	no	—
210	Dic₃₄	—	4	1	no	—
211	C₈×C₁₇	—	2	2	no	—
212	C₈×C₁₇	—	2	2	no	—
213	C₈×C₁₇	—	2	2	no	—
214	C₈×C₁₇	—	2	2	no	—
215	C₈×C₁₇	—	2	2	no	—
216	C₈×C₁₇	#131	1	4	yes	—
217	#3622	—	2	2	no	—
218	#3622	—	2	2	no	—
219	#3622	—	2	2	no	—
220	#3622	—	2	2	no	—
221	#3622	—	2	2	no	—
222	#3622	—	2	2	no	—
223	#2965	—	17	1	no	—
224	#2965	—	17	1	no	—
225	#2922	—	17	1	no	—
226	#1455	—	17	1	no	—
227	#1454	—	17	1	no	—
228	#1454	—	17	1	no	—
229	#1453	—	17	1	no	—
230	#1453	—	17	1	no	—
231	#1453	—	17	1	no	—
232	#1452	—	17	1	no	—
233	#1451	—	17	1	no	—
234	#1451	—	17	1	no	—
235	#1450	—	17	1	no	—
236	C₈×M₁₆	—	17	1	no	—
237	C₈×M₁₆	D₁₇	1	1	yes	characteristic, complemented
238	C₂²×C₁₇	—	2	1	no	—
239	C₂²×C₁₇	—	2	1	no	—
240	C₂²×C₁₇	—	2	1	no	—
241	C₂²×C₁₇	C₂²×C₄²	1	1	yes	characteristic
242	C₂×D₁₇	—	2	1	no	—
243	C₂×D₁₇	—	2	1	no	—
244	C₂×D₁₇	—	2	1	no	—
245	C₂×D₁₇	—	2	1	no	—
246	C₂×D₁₇	—	2	1	no	—
247	C₂×D₁₇	—	2	1	no	—
248	C₄×C₁₇	—	2	1	no	—
249	C₄×C₁₇	—	2	1	no	—
250	C₄×C₁₇	—	2	1	no	—
251	C₄×C₁₇	C₂×#131	1	2	yes	—
252	C₄×C₁₇	#568	1	2	yes	—
253	C₄×C₁₇	#568	1	2	yes	—
254	Dic₁₇	—	2	1	no	—
255	Dic₁₇	—	2	1	no	—
256	Dic₁₇	—	2	1	no	—
257	Dic₁₇	—	2	1	no	—
258	Dic₁₇	—	2	1	no	—
259	Dic₁₇	—	2	1	no	—
260	C₄×#41	—	17	1	no	—
261	#446	—	17	2	no	—
262	#446	—	17	2	no	—
263	#436	—	17	2	no	—
264	#436	—	17	2	no	—
265	#435	—	17	2	no	—
266	#435	—	17	2	no	—
267	#435	—	17	2	no	—
268	#435	—	17	2	no	—
269	#433	—	17	2	no	—
270	#433	—	17	2	no	—
271	#431	—	17	1	no	—
272	#431	—	17	1	no	—
273	#431	—	17	1	no	—
274	#431	—	17	1	no	—
275	#431	—	17	1	no	—
276	#431	—	17	1	no	—
277	#431	—	17	1	no	—
278	#431	—	17	1	no	—
279	#431	—	17	1	no	—
280	#431	C₂×D₁₇	1	1	yes	characteristic
281	#424	—	17	2	no	—
282	#408	—	17	2	no	—
283	C₄×M₁₆	—	17	1	no	—
284	C₄×M₁₆	—	17	1	no	—
285	C₄×M₁₆	—	17	1	no	—
286	C₄×M₁₆	—	17	1	no	—
287	C₄×M₁₆	C₂×D₁₇	1	1	yes	characteristic
288	C₂×C₄×C₈	—	17	1	no	—
289	C₂×C₄×C₈	—	17	1	no	—
290	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
291	#322	—	17	1	no	—
292	#322	—	17	1	no	—
293	#322	—	17	1	no	—
294	#322	—	17	1	no	—
295	#322	—	17	1	no	—
296	#322	—	17	1	no	—
297	#322	—	17	1	no	—
298	#322	—	17	1	no	—
299	#322	—	17	1	no	—
300	#322	—	17	1	no	—
301	#322	C₂×D₁₇	1	1	yes	characteristic
302	#322	C₂×D₁₇	1	1	yes	characteristic
303	C₈²	—	17	1	no	—
304	C₈²	—	17	1	no	—
305	C₈²	C₂×D₁₇	1	1	yes	characteristic
306	C₈²	C₂×D₁₇	1	1	yes	characteristic
307	C₂×C₁₇	—	4	1	no	—
308	C₂×C₁₇	#2873	1	1	yes	characteristic
309	C₂×C₁₇	C₄×#131	1	1	yes	characteristic
310	C₂×C₁₇	#2875	1	1	yes	characteristic
311	D₁₇	—	4	1	no	—
312	D₁₇	—	4	1	no	—
313	C₂×#41	—	17	1	no	—
314	C₂×M₁₆	—	17	2	no	—
315	C₂×M₁₆	—	17	2	no	—
316	C₂×M₁₆	—	17	2	no	—
317	C₂×M₁₆	—	17	2	no	—
318	C₂×M₁₆	C₄×D₁₇	1	2	yes	—
319	C₂²×C₈	—	17	2	no	—
320	C₂²×C₈	—	17	2	no	—
321	C₂²×C₈	C₄×D₁₇	1	2	yes	—
322	C₄×Q₈	—	17	1	no	—
323	C₄×Q₈	—	17	1	no	—
324	C₄×D₄	—	17	1	no	—
325	C₄×D₄	—	17	1	no	—
326	C₄×D₄	—	17	1	no	—
327	C₄×D₄	—	17	1	no	—
328	C₄×D₄	—	17	1	no	—
329	C₄×D₄	—	17	1	no	—
330	#117	—	17	1	no	—
331	#117	—	17	1	no	—
332	#117	—	17	1	no	—
333	C₂×C₄²	—	17	1	no	—
334	C₂×C₄²	—	17	1	no	—
335	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
336	C₄⋊C₈	—	17	2	no	—
337	C₄⋊C₈	—	17	2	no	—
338	C₄⋊C₈	—	17	2	no	—
339	C₄⋊C₈	—	17	2	no	—
340	C₄⋊C₈	—	17	2	no	—
341	C₄⋊C₈	—	17	2	no	—
342	C₄⋊C₈	—	17	2	no	—
343	C₄⋊C₈	—	17	2	no	—
344	C₄⋊C₈	—	17	2	no	—
345	C₄⋊C₈	C₄×D₁₇	1	2	yes	—
346	C₂²⋊C₈	—	17	2	no	—
347	C₂²⋊C₈	—	17	2	no	—
348	C₂²⋊C₈	—	17	2	no	—
349	C₂²⋊C₈	—	17	2	no	—
350	C₂²⋊C₈	—	17	2	no	—
351	C₂²⋊C₈	—	17	2	no	—
352	C₂²⋊C₈	—	17	2	no	—
353	C₂²⋊C₈	—	17	2	no	—
354	C₂²⋊C₈	—	17	2	no	—
355	C₂²⋊C₈	C₄×D₁₇	1	2	yes	—
356	#97	—	17	2	no	—
357	#97	—	17	2	no	—
358	#97	—	17	2	no	—
359	#97	—	17	2	no	—
360	#97	C₄×D₁₇	1	2	yes	—
361	C₄×C₈	—	17	2	no	—
362	C₄×C₈	—	17	2	no	—
363	C₄×C₈	—	17	1	no	—
364	C₄×C₈	—	17	1	no	—
365	C₄×C₈	—	17	1	no	—
366	C₄×C₈	—	17	1	no	—
367	C₄×C₈	—	17	1	no	—
368	C₄×C₈	—	17	1	no	—
369	C₄×C₈	C₄×D₁₇	1	2	yes	—
370	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
371	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
372	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
373	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
374	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
375	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
376	C₁₇	#17340	1	1	yes	characteristic, complemented, Sylow
377	#41	—	68	2	no	—
378	C₂×Q₈	—	17	1	no	—
379	C₂×D₄	—	17	1	no	—
380	C₂×D₄	—	17	1	no	—
381	C₂×D₄	—	17	1	no	—
382	C₂²×C₄	—	17	1	no	—
383	C₂²×C₄	—	17	1	no	—
384	C₂²×C₄	—	17	1	no	—
385	C₂²×C₄	—	17	1	no	—
386	C₂²×C₄	—	17	1	no	—
387	C₂²×C₄	—	17	1	no	—
388	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
390	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
391	M₁₆	—	2	4	no	—
392	M₁₆	—	34	4	no	—
393	M₁₆	—	68	2	no	—
394	M₁₆	—	68	2	no	—
395	M₁₆	—	68	2	no	—
396	C₂×C₈	—	4	2	no	—
397	C₂×C₈	—	17	2	no	—
398	C₂×C₈	—	17	2	no	—
399	C₂×C₈	—	17	2	no	—
400	C₂×C₈	—	17	2	no	—
401	C₂×C₈	—	17	2	no	—
402	C₂×C₈	—	17	2	no	—
403	C₂×C₈	—	34	4	no	—
404	C₂×C₈	—	68	2	no	—
405	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
406	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
407	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
408	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
409	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
410	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
411	C₄⋊C₄	—	17	1	no	—
412	C₄⋊C₄	—	17	1	no	—
413	C₄⋊C₄	—	17	1	no	—
414	C₄⋊C₄	—	17	1	no	—
415	C₄⋊C₄	—	17	1	no	—
416	C₄⋊C₄	—	17	1	no	—
417	C₂²⋊C₄	—	17	1	no	—
418	C₂²⋊C₄	—	17	1	no	—
419	C₂²⋊C₄	—	17	1	no	—
420	C₂²⋊C₄	—	17	1	no	—
421	C₂²⋊C₄	—	17	1	no	—
422	C₂²⋊C₄	—	17	1	no	—
423	C₄²	—	17	1	no	—
424	C₄²	—	17	1	no	—
425	C₄²	—	17	1	no	—
426	C₄²	—	17	1	no	—
427	C₄²	—	17	1	no	—
428	C₄²	—	17	1	no	—
429	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
430	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
431	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
432	C₄²	C₂³×D₁₇	1	1	yes	characteristic
433	C₂³	—	17	1	no	—
434	C₂³	—	17	1	no	—
435	C₂³	C₄²×D₁₇	1	1	yes	characteristic
436	Q₈	—	68	1	no	—
437	D₄	—	68	1	no	—
438	D₄	—	68	1	no	—
439	D₄	—	68	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	17	1	no	—
444	C₂×C₄	—	17	1	no	—
445	C₂×C₄	—	17	1	no	—
446	C₂×C₄	—	17	1	no	—
447	C₂×C₄	—	17	1	no	—
448	C₂×C₄	—	17	1	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	C₄²×D₁₇	1	1	yes	characteristic
456	C₂×C₄	C₄²×D₁₇	1	1	yes	characteristic
457	C₂×C₄	C₄²×D₁₇	1	1	yes	characteristic
458	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
459	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
460	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	2	2	no	—
463	C₈	—	2	2	no	—
464	C₈	—	2	2	no	—
465	C₈	—	2	2	no	—
466	C₈	—	34	2	no	—
467	C₈	—	34	2	no	—
468	C₈	—	34	2	no	—
469	C₈	—	34	2	no	—
470	C₈	—	34	2	no	—
471	C₈	—	34	2	no	—
472	C₈	#10587587	1	4	yes	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	34	1	no	—
477	C₂²	—	34	1	no	—
478	C₂²	—	34	1	no	—
479	C₂²	—	34	1	no	—
480	C₂²	—	34	1	no	—
481	C₂²	—	34	1	no	—
482	C₂²	C₂×C₄²×D₁₇	1	1	yes	characteristic
483	C₄	—	2	1	no	—
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	34	1	no	—
487	C₄	—	34	1	no	—
488	C₄	—	34	1	no	—
489	C₄	—	34	1	no	—
490	C₄	—	34	1	no	—
491	C₄	—	34	1	no	—
492	C₄	C₂×#10587587	1	2	yes	—
493	C₄	#11763574	1	2	yes	—
494	C₄	#11763575	1	2	yes	—
495	C₂	—	4	1	no	—
496	C₂	—	68	1	no	—
497	C₂	—	68	1	no	—
498	C₂	#14537201	1	1	yes	characteristic
499	C₂	C₄×#10587587	1	1	yes	characteristic
500	C₂	#14537211	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₇
commutator, socle	C₂²×C₁₇	C₂²×C₄²
Fitting	C₈×M₁₆×C₁₇	C₂
prime radical	C₂×#63252	C₂×C₄
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	C₈×M₁₆	D₁₇
hypocenter	C₁₇	#17340
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄² ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
4. #14527087	C₂	semidirect
5. #14527085	C₂	semidirect
6. #14527083	C₂	semidirect
7. #14527082	C₂	semidirect
8. #14527079	C₂	semidirect
9. #14527078	C₂	semidirect
10. #14527075	C₂	semidirect
11. #14527073	C₂	semidirect
12. #14527070	C₂	semidirect
13. #14527066	C₂	semidirect
14. C₈×#63218	C₂	semidirect
15. C₈×M₁₆×C₁₇	C₂	semidirect
237. C₈×M₁₆	D₁₇	semidirect
376. C₁₇	#17340	semidirect

Maximal subgroups

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

subgroup	index
#14537748	2
#14537746	2
#14537426	2
#14527087	2
#14527085	2
#14527083	2
#14527082	2
#14527079	2
#14527078	2
#14527075	2
#14527073	2
#14527070	2
#14527066	2
C₈×#63218	2
C₈×M₁₆×C₁₇	2
#17340	17