Subgroups — #17000043

Order 4352.

814 conjugacy classes of subgroups.

The subgroup lattice has 512 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	C₄×#10587587	C₂	1	1	yes	maximal, characteristic
4	#14527088	C₂	1	1	yes	maximal, characteristic, complemented
5	#14527087	C₂	1	1	yes	maximal, characteristic, complemented
6	#14527080	C₂	1	1	yes	maximal, characteristic, complemented
7	#14527079	C₂	1	1	yes	maximal, characteristic, complemented
8	#14527072	C₂	1	1	yes	maximal, characteristic, complemented
9	#14527070	C₂	1	1	yes	maximal, characteristic, complemented
10	#14527066	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#63223	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈×#63218	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈×#63218	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈²×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×M₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10587587	C₄	1	2	yes	—
17	C₄×#63252	C₂²	1	1	yes	characteristic
18	#11762938	C₄	1	2	yes	—
19	#11762937	C₄	1	2	yes	—
20	#11762885	C₄	1	2	yes	—
21	#11762884	C₄	1	2	yes	—
22	#11762883	C₄	1	2	yes	—
23	#11762882	C₄	1	2	yes	—
24	#11762879	C₄	1	2	yes	—
25	#11762878	C₄	1	2	yes	—
26	#11762862	C₂²	1	1	yes	characteristic
27	#11762860	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	#11762764	C₄	1	2	yes	—
32	#11762763	C₄	1	2	yes	—
33	#11762763	C₄	1	2	yes	—
34	C₄×#63223	C₂²	1	1	yes	characteristic
35	C₄×#63223	C₂²	1	1	yes	characteristic
36	C₄×#63218	C₂²	1	1	yes	characteristic
37	C₄×#63218	C₂²	1	1	yes	characteristic
38	C₄×#63218	C₂²	1	1	yes	characteristic
39	C₄×#63218	C₂²	1	1	yes	characteristic
40	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
41	C₄×C₈×D₁₇	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	C₈×#3622	C₂²	1	1	yes	characteristic
53	C₈×#3622	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	#10587587	—	2	8	no	—
75	C₂×#63218	C₂×C₄	1	2	yes	—
76	C₂×#63218	C₂×C₄	1	2	yes	—
77	C₂×#63218	C₂×C₄	1	2	yes	—
78	C₂×#63218	C₂×C₄	1	2	yes	—
79	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
80	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
81	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
82	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
83	C₄×D₆₈	C₂×C₄	1	1	yes	characteristic
84	C₄×D₆₈	C₂×C₄	1	1	yes	characteristic
85	#10587558	C₂×C₄	1	1	yes	characteristic
86	#10587558	C₂×C₄	1	1	yes	characteristic
87	C₄²×D₁₇	C₂³	1	1	yes	characteristic
88	C₄²×D₁₇	C₂³	1	1	yes	characteristic
89	C₄×Dic₃₄	C₂×C₄	1	1	yes	characteristic
90	C₄×Dic₃₄	C₂×C₄	1	1	yes	characteristic
91	C₁₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
92	C₁₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
93	C₁₇×#97	C₂×C₄	1	2	yes	—
94	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	—
95	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
101	C₂²⋊#3622	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	#10587491	C₂×C₄	1	2	yes	—
106	#10587486	C₂×C₄	1	2	yes	—
107	#10587486	C₂×C₄	1	2	yes	—
108	#10587486	C₂×C₄	1	2	yes	—
109	#10587486	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	C₈×Dic₁₇	C₂×C₄	1	2	yes	—
115	C₈×Dic₁₇	C₂×C₄	1	2	yes	—
116	C₈×Dic₁₇	C₂×C₄	1	2	yes	—
117	C₈×Dic₁₇	C₂×C₄	1	2	yes	—
118	C₄⋊#3622	C₂×C₄	1	2	yes	—
119	#10587474	C₂×C₄	1	2	yes	—
120	#10587474	C₂×C₄	1	2	yes	—
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	C₄×#3622	C₂³	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	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₂²⋊D₁₇	C₄²	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₇	C₄²	1	1	yes	characteristic
132	#63252	—	2	4	no	—
133	C₂×D₆₈	C₄²	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×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
140	C₂×Dic₃₄	C₄²	1	1	yes	characteristic
141	M₁₆×C₁₇	—	2	4	no	—
142	C₂×C₈×C₁₇	—	2	4	no	—
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	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
149	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
150	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
153	C₂²⋊Dic₁₇	C₄²	1	1	yes	characteristic
154	C₂²⋊Dic₁₇	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	#63227	C₄²	1	1	yes	characteristic
159	C₄⋊Dic₁₇	C₄²	1	1	yes	characteristic
160	C₄⋊Dic₁₇	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	#63225	C₄²	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	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
171	#63223	—	2	4	no	—
172	#63223	—	2	4	no	—
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	C₂×#3622	C₂²×C₄	1	2	yes	—
179	#63218	—	2	4	no	—
180	#63218	—	2	4	no	—
181	#63218	—	2	4	no	—
182	#63218	—	2	4	no	—
183	C₈×D₁₇	—	2	4	no	—
184	C₈×D₁₇	—	2	4	no	—
185	C₈×D₁₇	—	2	4	no	—
186	C₈×D₁₇	M₁₆	1	8	yes	complemented
187	#17335	—	17	1	no	maximal, Sylow
188	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
189	C₂²×D₁₇	C₂×C₄²	1	1	yes	characteristic
190	C₂²×D₁₇	C₂×C₄²	1	1	yes	characteristic
191	C₂×C₄×C₁₇	—	2	2	no	—
192	C₂×C₄×C₁₇	—	2	2	no	—
193	C₂×C₄×C₁₇	—	2	2	no	—
194	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
195	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
196	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
197	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
200	C₂²⋊D₁₇	—	2	2	no	—
201	C₂²⋊D₁₇	—	2	2	no	—
202	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
203	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
204	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
205	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
206	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
207	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
208	D₆₈	—	2	2	no	—
209	C₄×D₁₇	—	2	2	no	—
210	C₄×D₁₇	—	2	2	no	—
211	C₄×D₁₇	—	2	2	no	—
212	C₄×D₁₇	—	2	2	no	—
213	C₄×D₁₇	—	2	2	no	—
214	C₄×D₁₇	C₂×M₁₆	1	4	yes	—
215	Dic₃₄	—	2	2	no	—
216	C₈×C₁₇	—	2	2	no	—
217	C₈×C₁₇	—	2	2	no	—
218	C₈×C₁₇	—	2	2	no	—
219	C₈×C₁₇	—	2	2	no	—
220	C₈×C₁₇	C₂×M₁₆	1	4	yes	—
221	C₈×C₁₇	#131	1	4	yes	complemented
222	#3622	—	2	2	no	—
223	#3622	—	2	2	no	—
224	#3622	—	2	2	no	—
225	#3622	—	2	2	no	—
226	#3622	C₂×M₁₆	1	4	yes	—
227	#3622	#131	1	4	yes	complemented
228	#2965	—	17	1	no	—
229	#2965	—	17	1	no	—
230	C₄×#131	—	17	1	no	—
231	#1455	—	17	1	no	—
232	#1455	—	17	1	no	—
233	#1453	—	17	1	no	—
234	#1453	—	17	1	no	—
235	#1451	—	17	1	no	—
236	#1451	—	17	1	no	—
237	#1450	—	17	1	no	—
238	C₈×M₁₆	—	17	1	no	—
239	C₈×M₁₆	—	17	1	no	—
240	C₈×M₁₆	—	17	1	no	—
241	C₈×M₁₆	D₁₇	1	1	yes	characteristic, complemented
242	C₂×C₈²	—	17	1	no	—
243	C₂²×C₁₇	—	2	1	no	—
244	C₂²×C₁₇	—	2	1	no	—
245	C₂²×C₁₇	—	2	1	no	—
246	C₂²×C₁₇	C₂²×C₄²	1	1	yes	characteristic
247	C₂×D₁₇	—	2	1	no	—
248	C₂×D₁₇	—	2	1	no	—
249	C₂×D₁₇	—	2	1	no	—
250	C₂×D₁₇	—	2	1	no	—
251	C₂×D₁₇	—	2	1	no	—
252	C₂×D₁₇	C₄×M₁₆	1	2	yes	—
253	C₄×C₁₇	—	2	1	no	—
254	C₄×C₁₇	—	2	1	no	—
255	C₄×C₁₇	—	2	1	no	—
256	C₄×C₁₇	C₂²×M₁₆	1	2	yes	—
257	C₄×C₁₇	C₂×#131	1	2	yes	—
258	C₄×C₁₇	C₂×#131	1	2	yes	—
259	Dic₁₇	—	2	1	no	—
260	Dic₁₇	—	2	1	no	—
261	Dic₁₇	—	2	1	no	—
262	Dic₁₇	—	2	1	no	—
263	Dic₁₇	—	2	1	no	—
264	Dic₁₇	C₄×M₁₆	1	2	yes	—
265	C₂×#131	—	17	2	no	—
266	C₄×#41	—	17	1	no	—
267	#446	—	17	2	no	—
268	#446	—	17	2	no	—
269	#436	—	17	2	no	—
270	#436	—	17	2	no	—
271	#435	—	17	2	no	—
272	#435	—	17	2	no	—
273	#435	—	17	2	no	—
274	#435	—	17	2	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	#405	—	17	2	no	—
282	#405	—	17	2	no	—
283	#405	—	17	2	no	—
284	C₄×M₁₆	—	17	1	no	—
285	C₄×M₁₆	—	17	1	no	—
286	C₄×M₁₆	—	17	1	no	—
287	C₄×M₁₆	—	17	1	no	—
288	C₄×M₁₆	—	17	1	no	—
289	C₄×M₁₆	—	17	1	no	—
290	C₄×M₁₆	C₂×D₁₇	1	1	yes	characteristic
291	C₂×C₄×C₈	—	17	1	no	—
292	C₂×C₄×C₈	—	17	1	no	—
293	C₂×C₄×C₈	—	17	1	no	—
294	C₂×C₄×C₈	—	17	1	no	—
295	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
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	—	17	1	no	—
302	#322	—	17	1	no	—
303	#322	—	17	1	no	—
304	#322	C₂×D₁₇	1	1	yes	characteristic
305	#322	C₂×D₁₇	1	1	yes	characteristic
306	C₈²	—	17	1	no	—
307	C₈²	—	17	1	no	—
308	C₈²	—	17	1	no	—
309	C₈²	—	17	1	no	—
310	C₈²	C₂×D₁₇	1	1	yes	characteristic
311	C₈²	C₂×D₁₇	1	1	yes	characteristic
312	C₂×C₁₇	—	4	1	no	—
313	C₂×C₁₇	C₂×C₄×M₁₆	1	1	yes	characteristic
314	C₂×C₁₇	C₄×#131	1	1	yes	characteristic
315	C₂×C₁₇	C₄×#131	1	1	yes	characteristic
316	D₁₇	—	2	2	no	—
317	D₁₇	—	4	1	no	—
318	C₂×#41	—	17	1	no	—
319	#131	—	34	8	no	—
320	C₂×M₁₆	—	17	2	no	—
321	C₂×M₁₆	—	17	2	no	—
322	C₂×M₁₆	—	17	2	no	—
323	C₂×M₁₆	—	17	2	no	—
324	C₂×M₁₆	—	17	2	no	—
325	C₂×M₁₆	—	17	2	no	—
326	C₂×M₁₆	C₄×D₁₇	1	2	yes	—
327	C₂²×C₈	—	17	2	no	—
328	C₂²×C₈	—	17	2	no	—
329	C₂²×C₈	—	17	2	no	—
330	C₂²×C₈	—	17	2	no	—
331	C₂²×C₈	C₄×D₁₇	1	2	yes	—
332	C₄×Q₈	—	17	1	no	—
333	C₄×Q₈	—	17	1	no	—
334	C₄×D₄	—	17	1	no	—
335	C₄×D₄	—	17	1	no	—
336	C₄×D₄	—	17	1	no	—
337	C₄×D₄	—	17	1	no	—
338	C₄×D₄	—	17	1	no	—
339	C₄×D₄	—	17	1	no	—
340	#117	—	17	1	no	—
341	#117	—	17	1	no	—
342	#117	—	17	1	no	—
343	C₂×C₄²	—	17	1	no	—
344	C₂×C₄²	—	17	1	no	—
345	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
346	C₄⋊C₈	—	17	2	no	—
347	C₄⋊C₈	—	17	2	no	—
348	C₄⋊C₈	—	17	2	no	—
349	C₄⋊C₈	—	17	2	no	—
350	C₄⋊C₈	—	17	2	no	—
351	C₄⋊C₈	C₄×D₁₇	1	2	yes	—
352	C₂²⋊C₈	—	17	2	no	—
353	C₂²⋊C₈	—	17	2	no	—
354	C₂²⋊C₈	—	17	2	no	—
355	C₂²⋊C₈	—	17	2	no	—
356	C₂²⋊C₈	—	17	2	no	—
357	C₂²⋊C₈	C₄×D₁₇	1	2	yes	—
358	#97	—	17	2	no	—
359	#97	—	17	2	no	—
360	#97	—	17	2	no	—
361	#97	—	17	2	no	—
362	#97	—	17	2	no	—
363	#97	—	17	2	no	—
364	#97	C₄×D₁₇	1	2	yes	—
365	C₄×C₈	—	17	2	no	—
366	C₄×C₈	—	17	2	no	—
367	C₄×C₈	—	17	2	no	—
368	C₄×C₈	—	17	2	no	—
369	C₄×C₈	—	17	1	no	—
370	C₄×C₈	—	17	1	no	—
371	C₄×C₈	—	17	1	no	—
372	C₄×C₈	—	17	1	no	—
373	C₄×C₈	—	17	1	no	—
374	C₄×C₈	—	17	1	no	—
375	C₄×C₈	C₄×D₁₇	1	2	yes	—
376	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
377	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
378	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
379	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
380	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
381	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
382	C₁₇	#17335	1	1	yes	characteristic, complemented, Sylow
383	#41	—	34	4	no	—
384	C₂×Q₈	—	17	1	no	—
385	C₂×D₄	—	17	1	no	—
386	C₂×D₄	—	17	1	no	—
387	C₂×D₄	—	17	1	no	—
388	C₂²×C₄	—	17	1	no	—
389	C₂²×C₄	—	17	1	no	—
390	C₂²×C₄	—	17	1	no	—
391	C₂²×C₄	—	17	1	no	—
392	C₂²×C₄	—	17	1	no	—
393	C₂²×C₄	—	17	1	no	—
394	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
395	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
396	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
397	M₁₆	—	2	4	no	—
398	M₁₆	—	34	4	no	—
399	M₁₆	—	34	4	no	—
400	M₁₆	—	34	4	no	—
401	M₁₆	—	34	4	no	—
402	M₁₆	—	34	4	no	—
403	M₁₆	—	34	4	no	—
404	C₂×C₈	—	2	4	no	—
405	C₂×C₈	—	17	2	no	—
406	C₂×C₈	—	17	2	no	—
407	C₂×C₈	—	17	8	no	—
408	C₂×C₈	—	17	2	no	—
409	C₂×C₈	—	17	2	no	—
410	C₂×C₈	—	17	2	no	—
411	C₂×C₈	—	17	2	no	—
412	C₂×C₈	—	34	4	no	—
413	C₂×C₈	—	34	4	no	—
414	C₂×C₈	—	34	4	no	—
415	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
416	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
417	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
418	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
419	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
420	C₂×C₈	C₂×C₄×D₁₇	1	2	yes	—
421	C₄⋊C₄	—	17	1	no	—
422	C₄⋊C₄	—	17	1	no	—
423	C₄⋊C₄	—	17	1	no	—
424	C₄⋊C₄	—	17	1	no	—
425	C₄⋊C₄	—	17	1	no	—
426	C₄⋊C₄	—	17	1	no	—
427	C₂²⋊C₄	—	17	1	no	—
428	C₂²⋊C₄	—	17	1	no	—
429	C₂²⋊C₄	—	17	1	no	—
430	C₂²⋊C₄	—	17	1	no	—
431	C₂²⋊C₄	—	17	1	no	—
432	C₂²⋊C₄	—	17	1	no	—
433	C₄²	—	17	1	no	—
434	C₄²	—	17	1	no	—
435	C₄²	—	17	1	no	—
436	C₄²	—	17	1	no	—
437	C₄²	—	17	1	no	—
438	C₄²	—	17	1	no	—
439	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
440	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
441	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
442	C₄²	C₂³×D₁₇	1	1	yes	characteristic
443	C₂³	—	17	1	no	—
444	C₂³	—	17	1	no	—
445	C₂³	C₄²×D₁₇	1	1	yes	characteristic
446	Q₈	—	34	2	no	—
447	D₄	—	34	2	no	—
448	D₄	—	34	2	no	—
449	D₄	—	34	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	17	1	no	—
454	C₂×C₄	—	17	4	no	—
455	C₂×C₄	—	17	1	no	—
456	C₂×C₄	—	17	1	no	—
457	C₂×C₄	—	17	1	no	—
458	C₂×C₄	—	17	1	no	—
459	C₂×C₄	—	17	1	no	—
460	C₂×C₄	—	34	2	no	—
461	C₂×C₄	—	34	2	no	—
462	C₂×C₄	—	34	2	no	—
463	C₂×C₄	—	34	2	no	—
464	C₂×C₄	—	34	2	no	—
465	C₂×C₄	C₄²×D₁₇	1	1	yes	characteristic
466	C₂×C₄	C₄²×D₁₇	1	1	yes	characteristic
467	C₂×C₄	C₄²×D₁₇	1	1	yes	characteristic
468	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
469	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
470	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
471	C₈	—	2	2	no	—
472	C₈	—	2	2	no	—
473	C₈	—	2	2	no	—
474	C₈	—	2	2	no	—
475	C₈	—	17	4	no	—
476	C₈	—	17	4	no	—
477	C₈	—	34	2	no	—
478	C₈	—	34	2	no	—
479	C₈	—	34	2	no	—
480	C₈	—	34	2	no	—
481	C₈	#10587587	1	4	yes	complemented
482	C₈	M₁₆×D₁₇	1	4	yes	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	17	2	no	—
487	C₂²	—	34	1	no	—
488	C₂²	—	34	1	no	—
489	C₂²	—	34	1	no	—
490	C₂²	—	34	1	no	—
491	C₂²	—	34	1	no	—
492	C₂²	C₂×C₄²×D₁₇	1	1	yes	characteristic
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	17	2	no	—
497	C₄	—	34	1	no	—
498	C₄	—	34	1	no	—
499	C₄	—	34	1	no	—
500	C₄	—	34	1	no	—
501	C₄	—	34	1	no	—
502	C₄	C₂×M₁₆×D₁₇	1	2	yes	—
503	C₄	#131×D₁₇	1	2	yes	—
504	C₄	C₂×#10587587	1	2	yes	—
505	C₂	—	4	1	no	—
506	C₂	—	34	2	no	—
507	C₂	—	68	1	no	—
508	C₂	C₄×M₁₆×D₁₇	1	1	yes	characteristic
509	C₂	C₄×#10587587	1	1	yes	characteristic
510	C₂	#14537206	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈	C₂²×D₁₇
commutator, socle	C₂²×C₁₇	C₂²×C₄²
Frattini	C₄²	C₂³×D₁₇
Fitting	C₈×M₁₆×C₁₇	C₂
prime radical	C₂×#63252	C₂×C₄
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	C₈×M₁₆	D₁₇
hypocenter	C₁₇	#17335
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄×C₈ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
4. #14527088	C₂	semidirect
5. #14527087	C₂	semidirect
6. #14527080	C₂	semidirect
7. #14527079	C₂	semidirect
8. #14527072	C₂	semidirect
9. #14527070	C₂	semidirect
10. #14527066	C₂	semidirect
11. C₈×#63223	C₂	semidirect
12. C₈×#63218	C₂	semidirect
13. C₈×#63218	C₂	semidirect
14. C₈²×D₁₇	C₂	semidirect
15. C₈×M₁₆×C₁₇	C₂	semidirect
186. C₈×D₁₇	M₁₆	semidirect
221. C₈×C₁₇	#131	semidirect
227. #3622	#131	semidirect
241. C₈×M₁₆	D₁₇	semidirect
382. C₁₇	#17335	semidirect
481. C₈	#10587587	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
C₄×#10587587	2
#14527088	2
#14527087	2
#14527080	2
#14527079	2
#14527072	2
#14527070	2
#14527066	2
C₈×#63223	2
C₈×#63218	2
C₈²×D₁₇	2
C₈×M₁₆×C₁₇	2
#17335	17