Subgroups — #17964161

Order 4352.

798 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545594	C₂	1	1	yes	maximal, characteristic
2	C₄×#10587678	C₂	1	1	yes	maximal, characteristic
3	#14544008	C₂	1	1	yes	maximal, characteristic, complemented
4	#14544007	C₂	1	1	yes	maximal, characteristic, complemented
5	#14544002	C₂	1	1	yes	maximal, characteristic, complemented
6	#14544001	C₂	1	1	yes	maximal, characteristic, complemented
7	#14543999	C₂	1	1	yes	maximal, characteristic, complemented
8	#14543992	C₂	1	1	yes	maximal, characteristic, complemented
9	#14543991	C₂	1	1	yes	maximal, characteristic, complemented
10	#14543986	C₂	1	1	yes	maximal, characteristic, complemented
11	#14543985	C₂	1	1	yes	maximal, characteristic, complemented
12	#14543985	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈×#63247	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#11763651	C₂	1	1	yes	maximal, characteristic, complemented
15	#14537744	C₂	1	1	yes	maximal, characteristic
16	C₂×#10587678	C₄	1	2	yes	—
17	#11763861	C₄	1	2	yes	—
18	#11763842	C₄	1	2	yes	—
19	#11763840	C₄	1	2	yes	—
20	#11763838	C₄	1	2	yes	—
21	#11763827	C₂²	1	1	yes	characteristic
22	#11763826	C₂²	1	1	yes	characteristic
23	#11763825	C₂²	1	1	yes	characteristic
24	#11763774	C₄	1	2	yes	—
25	#11763773	C₄	1	2	yes	—
26	#11763773	C₄	1	2	yes	—
27	C₄×#63243	C₂²	1	1	yes	characteristic
28	C₄×#63243	C₂²	1	1	yes	characteristic
29	C₄×#63247	C₂²	1	1	yes	characteristic
30	C₄×#63247	C₂²	1	1	yes	characteristic
31	C₄×#63247	C₂²	1	1	yes	characteristic
32	C₄×#63242	C₂²	1	1	yes	characteristic
33	C₂×C₄×#3624	C₂²	1	1	yes	characteristic
34	C₂×C₄×#3624	C₂²	1	1	yes	characteristic
35	C₂×C₄×#3624	C₂²	1	1	yes	characteristic
36	#11763651	C₂²	1	1	yes	characteristic
37	#11763651	C₂²	1	1	yes	characteristic
38	#11763651	C₂²	1	1	yes	characteristic
39	#11763651	C₂²	1	1	yes	characteristic
40	#11763651	C₂²	1	1	yes	characteristic
41	#11763651	C₂²	1	1	yes	characteristic
42	#11763651	C₂²	1	1	yes	characteristic
43	#11763651	C₂²	1	1	yes	characteristic
44	#11763651	C₂²	1	1	yes	characteristic
45	#11763651	C₂²	1	1	yes	characteristic
46	#11763650	C₂²	1	1	yes	characteristic
47	#11763650	C₂²	1	1	yes	characteristic
48	C₈×#3624	C₂²	1	1	yes	characteristic
49	C₈×#3624	C₂²	1	1	yes	characteristic
50	C₈×#3624	C₂²	1	1	yes	characteristic
51	C₈×#3624	C₂²	1	1	yes	characteristic
52	C₄×#63254	C₂²	1	1	yes	characteristic
53	#11762938	C₄	1	1	yes	characteristic
54	#11762937	C₄	1	1	yes	characteristic
55	#11762885	C₄	1	1	yes	characteristic
56	#11762884	C₄	1	1	yes	characteristic
57	#11762881	C₄	1	1	yes	characteristic
58	#11762880	C₄	1	1	yes	characteristic
59	#11762877	C₄	1	1	yes	characteristic
60	#11762861	C₂²	1	1	yes	characteristic
61	#11762859	C₂²	1	1	yes	characteristic
62	#11762859	C₂²	1	1	yes	characteristic
63	#11762761	C₂²	1	1	yes	characteristic
64	M₁₆×Dic₁₇	C₂²	1	1	yes	characteristic
65	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
66	C₁₇×#435	C₄	1	1	yes	characteristic
67	C₂×#63254	C₂×C₄	1	1	yes	characteristic
68	C₂×#63247	C₂×C₄	1	2	yes	—
69	C₂×#63247	C₂×C₄	1	2	yes	—
70	C₂×#63247	C₂×C₄	1	2	yes	—
71	C₂²×#3624	C₂×C₄	1	2	yes	—
72	C₂²×#3624	C₂×C₄	1	2	yes	—
73	C₂²×#3624	C₂×C₄	1	2	yes	—
74	#10587678	—	2	8	no	—
75	C₂×#63243	C₂×C₄	1	2	yes	—
76	C₂×#63243	C₂×C₄	1	2	yes	—
77	C₂×#63242	C₂×C₄	1	2	yes	—
78	C₂×M₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
80	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
81	D₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
82	C₄×C₂²⋊D₁₇	C₂×C₄	1	1	yes	characteristic
83	C₄×C₂²⋊D₁₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄×Dic₁₇	C₂³	1	1	yes	characteristic
85	C₂×C₄×Dic₁₇	C₂³	1	1	yes	characteristic
86	C₂×#63223	C₂×C₄	1	1	yes	characteristic
87	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
88	C₂×#63218	C₂×C₄	1	1	yes	characteristic
89	C₂×#63218	C₂×C₄	1	1	yes	characteristic
90	#10587578	C₂×C₄	1	1	yes	characteristic
91	#10587573	C₂×C₄	1	1	yes	characteristic
92	#10587567	C₂×C₄	1	1	yes	characteristic
93	#10587567	C₂×C₄	1	1	yes	characteristic
94	#10587563	C₂×C₄	1	1	yes	characteristic
95	#10587563	C₂×C₄	1	1	yes	characteristic
96	C₄²×D₁₇	C₂³	1	1	yes	characteristic
97	C₄×Dic₃₄	C₂×C₄	1	1	yes	characteristic
98	C₂²⋊#3624	C₂×C₄	1	2	yes	—
99	C₂²⋊#3624	C₂×C₄	1	2	yes	—
100	#10587544	C₂×C₄	1	2	yes	—
101	#10587544	C₂×C₄	1	2	yes	—
102	#10587543	C₂×C₄	1	2	yes	—
103	#10587542	C₂×C₄	1	2	yes	—
104	#10587542	C₂×C₄	1	2	yes	—
105	#10587542	C₂×C₄	1	2	yes	—
106	#10587542	C₂×C₄	1	2	yes	—
107	#10587542	C₂×C₄	1	2	yes	—
108	C₄⋊#3624	C₂×C₄	1	2	yes	—
109	C₄×#3624	C₂×C₄	1	2	yes	—
110	C₄×#3624	C₂×C₄	1	2	yes	—
111	C₄×#3624	C₂×C₄	1	2	yes	—
112	C₄×#3624	C₂×C₄	1	2	yes	—
113	C₄×#3624	C₂³	1	1	yes	characteristic
114	C₄×#3624	C₂³	1	1	yes	characteristic
115	C₄×#3624	C₂³	1	1	yes	characteristic
116	C₄×#3624	C₂³	1	1	yes	characteristic
117	C₄×#3624	C₂³	1	1	yes	characteristic
118	C₄×#3624	C₂³	1	1	yes	characteristic
119	C₄×#3624	C₂³	1	1	yes	characteristic
120	C₄×#3624	C₂³	1	1	yes	characteristic
121	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
122	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
123	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
124	C₁₇×#97	C₂×C₄	1	1	yes	characteristic
125	C₂²⋊#3622	C₂×C₄	1	1	yes	characteristic
126	C₂²⋊#3622	C₂×C₄	1	1	yes	characteristic
127	#10587491	C₂×C₄	1	1	yes	characteristic
128	#10587491	C₂×C₄	1	1	yes	characteristic
129	#10587486	C₂×C₄	1	1	yes	characteristic
130	#10587486	C₂×C₄	1	1	yes	characteristic
131	#10587485	C₂×C₄	1	1	yes	characteristic
132	#10587485	C₂×C₄	1	1	yes	characteristic
133	#10587485	C₂×C₄	1	1	yes	characteristic
134	#10587485	C₂×C₄	1	1	yes	characteristic
135	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
136	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
137	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
138	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
139	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
140	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
141	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
142	#10587474	C₂×C₄	1	1	yes	characteristic
143	C₂×D₄×C₁₇	C₄²	1	1	yes	characteristic
144	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₂²⋊D₁₇	C₄²	1	1	yes	characteristic
147	C₂×C₂²⋊D₁₇	C₄²	1	1	yes	characteristic
148	C₂²×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
150	C₂²×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
151	C₂²×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
152	#63254	—	2	4	no	—
153	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
156	C₂×Dic₃₄	C₄²	1	1	yes	characteristic
157	#63247	—	2	4	no	—
158	#63247	—	2	4	no	—
159	#63247	M₁₆	1	8	yes	complemented
160	C₂×#3624	—	2	4	no	—
161	C₂×#3624	—	2	4	no	—
162	C₂×#3624	—	2	4	no	—
163	C₂×#3624	C₂²×C₄	1	2	yes	—
164	C₂×#3624	C₂²×C₄	1	2	yes	—
165	C₂×#3624	C₂²×C₄	1	2	yes	—
166	C₂×#3624	C₂²×C₄	1	2	yes	—
167	C₂×#3624	C₂²×C₄	1	2	yes	—
168	C₂×#3624	C₂²×C₄	1	2	yes	—
169	C₂×#3624	C₂²×C₄	1	2	yes	—
170	C₂×#3624	C₂²×C₄	1	2	yes	—
171	#63243	—	2	4	no	—
172	#63243	—	2	4	no	—
173	#63242	—	2	4	no	—
174	M₁₆×C₁₇	—	4	1	no	—
175	C₂×C₈×C₁₇	—	4	1	no	—
176	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
180	C₄⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
181	C₂²⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
182	C₂²⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
183	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
184	C₂²⋊Dic₁₇	C₄²	1	1	yes	characteristic
185	C₂²⋊Dic₁₇	C₄²	1	1	yes	characteristic
186	#63227	C₄²	1	1	yes	characteristic
187	#63227	C₄²	1	1	yes	characteristic
188	C₄⋊Dic₁₇	C₄²	1	1	yes	characteristic
189	#63225	C₄²	1	1	yes	characteristic
190	#63225	C₄²	1	1	yes	characteristic
191	#63225	C₄²	1	1	yes	characteristic
192	#63225	C₄²	1	1	yes	characteristic
193	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
194	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
195	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
196	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
197	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
198	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
199	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
200	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
201	C₄×Dic₁₇	C₂⁴	1	1	yes	characteristic
202	#63223	—	4	1	no	—
203	C₂×#3622	—	4	1	no	—
204	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
205	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
206	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
207	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
208	#63218	—	4	1	no	—
209	#63218	—	4	1	no	—
210	#17337	—	17	1	no	maximal, Sylow
211	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
212	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
213	C₂²×D₁₇	C₂×C₄²	1	1	yes	characteristic
214	D₄×C₁₇	—	2	2	no	—
215	C₂×C₄×C₁₇	—	2	1	no	—
216	C₂×C₄×C₁₇	—	2	1	no	—
217	C₂×C₄×C₁₇	—	2	1	no	—
218	C₂×C₄×C₁₇	—	2	1	no	—
219	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
220	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
221	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
222	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
223	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
224	C₂²⋊D₁₇	—	2	2	no	—
225	C₂²⋊D₁₇	—	2	2	no	—
226	C₂×Dic₁₇	—	2	2	no	—
227	C₂×Dic₁₇	—	2	2	no	—
228	C₂×Dic₁₇	—	2	2	no	—
229	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
230	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
231	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
232	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
233	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
234	C₂×Dic₁₇	C₂×M₁₆	1	4	yes	—
235	C₂×Dic₁₇	C₂³×C₄	1	1	yes	characteristic
236	C₂×Dic₁₇	C₂³×C₄	1	1	yes	characteristic
237	C₄×D₁₇	—	2	1	no	—
238	C₄×D₁₇	—	2	1	no	—
239	C₄×D₁₇	—	2	2	no	—
240	C₄×D₁₇	—	2	2	no	—
241	Dic₃₄	—	2	2	no	—
242	#3624	—	2	2	no	—
243	#3624	—	2	2	no	—
244	#3624	—	2	2	no	—
245	#3624	—	2	2	no	—
246	#3624	—	2	2	no	—
247	#3624	C₂×M₁₆	1	4	yes	—
248	#3624	C₂×M₁₆	1	4	yes	—
249	#3624	#131	1	4	yes	complemented
250	C₈×C₁₇	—	2	1	no	—
251	C₈×C₁₇	—	2	1	no	—
252	C₈×C₁₇	—	2	1	no	—
253	C₈×C₁₇	—	2	1	no	—
254	#3622	—	2	1	no	—
255	#3622	—	2	1	no	—
256	#3622	—	2	1	no	—
257	#3622	—	2	1	no	—
258	#2965	—	17	1	no	—
259	#2965	—	17	1	no	—
260	C₄×#131	—	17	1	no	—
261	#1455	—	17	1	no	—
262	#1455	—	17	1	no	—
263	#1453	—	17	1	no	—
264	#1453	—	17	1	no	—
265	#1452	—	17	1	no	—
266	#1451	—	17	1	no	—
267	#1451	—	17	1	no	—
268	C₈×M₁₆	—	17	1	no	—
269	C₈×M₁₆	—	17	1	no	—
270	C₈×M₁₆	—	17	1	no	—
271	C₈×M₁₆	—	17	1	no	—
272	C₂×#322	—	17	1	no	—
273	C₂²×C₁₇	—	2	1	no	—
274	C₂²×C₁₇	—	2	1	no	—
275	C₂²×C₁₇	—	2	1	no	—
276	C₂²×C₁₇	—	2	1	no	—
277	C₂²×C₁₇	—	2	1	no	—
278	C₂²×C₁₇	C₄×M₁₆	1	2	yes	—
279	C₂²×C₁₇	C₂²×C₄²	1	1	yes	characteristic
280	C₂×D₁₇	—	2	1	no	—
281	C₂×D₁₇	—	2	1	no	—
282	C₂×D₁₇	—	2	1	no	—
283	C₄×C₁₇	—	2	1	no	—
284	C₄×C₁₇	—	2	1	no	—
285	C₄×C₁₇	—	2	1	no	—
286	C₄×C₁₇	—	2	1	no	—
287	C₄×C₁₇	#568	1	1	yes	characteristic
288	C₄×C₁₇	#568	1	1	yes	characteristic
289	Dic₁₇	—	2	1	no	—
290	Dic₁₇	—	2	1	no	—
291	Dic₁₇	—	2	1	no	—
292	Dic₁₇	—	2	1	no	—
293	Dic₁₇	C₄×M₁₆	1	2	yes	—
294	Dic₁₇	C₂²×M₁₆	1	2	yes	—
295	Dic₁₇	C₂×#131	1	2	yes	—
296	C₂×#131	—	17	2	no	—
297	C₄×#41	—	17	1	no	—
298	#446	—	17	2	no	—
299	#446	—	17	1	no	—
300	#446	—	17	1	no	—
301	#436	—	17	2	no	—
302	#436	—	17	1	no	—
303	#436	—	17	1	no	—
304	#435	—	17	2	no	—
305	#435	—	17	2	no	—
306	#435	—	17	1	no	—
307	#435	—	17	1	no	—
308	#435	—	17	1	no	—
309	#435	#595	1	1	yes	characteristic
310	#431	—	17	1	no	—
311	#431	—	17	1	no	—
312	#431	—	17	1	no	—
313	#431	—	17	1	no	—
314	#431	—	17	1	no	—
315	#431	—	17	1	no	—
316	#405	—	17	2	no	—
317	#405	—	17	2	no	—
318	#405	—	17	2	no	—
319	C₄×M₁₆	—	17	1	no	—
320	C₄×M₁₆	—	17	1	no	—
321	C₄×M₁₆	—	17	1	no	—
322	C₄×M₁₆	—	17	1	no	—
323	C₄×M₁₆	—	17	1	no	—
324	C₄×M₁₆	—	17	1	no	—
325	C₄×M₁₆	—	17	1	no	—
326	C₂×C₄×C₈	—	17	1	no	—
327	C₂×C₄×C₈	—	17	1	no	—
328	C₂×C₄×C₈	—	17	1	no	—
329	C₂×C₄×C₈	—	17	1	no	—
330	C₂×C₄×C₈	—	17	1	no	—
331	#322	—	17	1	no	—
332	#322	—	17	1	no	—
333	#322	—	17	1	no	—
334	#322	—	17	1	no	—
335	#322	—	17	1	no	—
336	#322	—	17	1	no	—
337	#322	—	17	1	no	—
338	#322	—	17	1	no	—
339	#322	—	17	1	no	—
340	#322	—	17	1	no	—
341	#322	—	17	1	no	—
342	#322	—	17	1	no	—
343	C₈²	—	17	1	no	—
344	C₈²	—	17	1	no	—
345	C₈²	—	17	1	no	—
346	C₈²	—	17	1	no	—
347	C₂×C₁₇	—	2	2	no	—
348	C₂×C₁₇	—	4	1	no	—
349	C₂×C₁₇	C₂×C₄×M₁₆	1	1	yes	characteristic
350	C₂×C₁₇	C₄×#131	1	1	yes	characteristic
351	C₂×C₁₇	#2875	1	1	yes	characteristic
352	D₁₇	—	4	1	no	—
353	C₂×#41	—	17	1	no	—
354	#131	—	34	8	no	—
355	C₂×M₁₆	—	17	2	no	—
356	C₂×M₁₆	—	17	2	no	—
357	C₂×M₁₆	—	17	2	no	—
358	C₂×M₁₆	—	17	2	no	—
359	C₂×M₁₆	—	17	2	no	—
360	C₂×M₁₆	—	17	1	no	—
361	C₂×M₁₆	—	17	1	no	—
362	C₂×M₁₆	—	17	1	no	—
363	C₂×M₁₆	C₂×#595	1	1	yes	characteristic
364	C₂²×C₈	—	17	2	no	—
365	C₂²×C₈	—	17	2	no	—
366	C₂²×C₈	—	17	2	no	—
367	C₂²×C₈	—	17	2	no	—
368	C₂²×C₈	—	17	1	no	—
369	C₂²×C₈	C₂×#595	1	1	yes	characteristic
370	C₄×Q₈	—	17	1	no	—
371	C₄×Q₈	—	17	1	no	—
372	C₄×D₄	—	17	1	no	—
373	C₄×D₄	—	17	1	no	—
374	C₄×D₄	—	17	1	no	—
375	C₄×D₄	—	17	1	no	—
376	C₄×D₄	—	17	1	no	—
377	C₄×D₄	C₂×#595	1	1	yes	characteristic
378	#117	—	17	1	no	—
379	#117	—	17	1	no	—
380	#117	—	17	1	no	—
381	C₂×C₄²	—	17	1	no	—
382	C₂×C₄²	—	17	1	no	—
383	C₂×C₄²	—	17	1	no	—
384	C₄⋊C₈	—	17	2	no	—
385	C₄⋊C₈	—	17	2	no	—
386	C₄⋊C₈	—	17	2	no	—
387	C₄⋊C₈	—	17	1	no	—
388	C₄⋊C₈	—	17	1	no	—
389	C₄⋊C₈	—	17	1	no	—
390	C₄⋊C₈	—	17	1	no	—
391	C₄⋊C₈	—	17	1	no	—
392	C₄⋊C₈	C₂×#595	1	1	yes	characteristic
393	C₂²⋊C₈	—	17	2	no	—
394	C₂²⋊C₈	—	17	2	no	—
395	C₂²⋊C₈	—	17	2	no	—
396	C₂²⋊C₈	—	17	1	no	—
397	C₂²⋊C₈	—	17	1	no	—
398	C₂²⋊C₈	—	17	1	no	—
399	C₂²⋊C₈	—	17	1	no	—
400	C₂²⋊C₈	C₂×#595	1	1	yes	characteristic
401	C₂²⋊C₈	C₂×#595	1	1	yes	characteristic
402	#97	—	17	2	no	—
403	#97	—	17	2	no	—
404	#97	—	17	2	no	—
405	#97	—	17	2	no	—
406	#97	—	17	2	no	—
407	#97	—	17	1	no	—
408	#97	—	17	1	no	—
409	#97	—	17	1	no	—
410	#97	C₂×#595	1	1	yes	characteristic
411	C₄×C₈	—	17	1	no	—
412	C₄×C₈	—	17	1	no	—
413	C₄×C₈	—	17	1	no	—
414	C₄×C₈	—	17	1	no	—
415	C₄×C₈	—	17	1	no	—
416	C₄×C₈	—	17	1	no	—
417	C₄×C₈	—	17	1	no	—
418	C₄×C₈	—	17	1	no	—
419	C₄×C₈	—	17	2	no	—
420	C₄×C₈	—	17	2	no	—
421	C₄×C₈	—	17	2	no	—
422	C₄×C₈	—	17	2	no	—
423	C₄×C₈	—	17	1	no	—
424	C₄×C₈	—	17	1	no	—
425	C₄×C₈	—	17	1	no	—
426	C₄×C₈	—	17	1	no	—
427	C₄×C₈	—	17	1	no	—
428	C₄×C₈	—	17	1	no	—
429	C₁₇	#17337	1	1	yes	characteristic, complemented, Sylow
430	#41	—	34	4	no	—
431	C₂×Q₈	—	17	1	no	—
432	C₂×D₄	—	17	1	no	—
433	C₂×D₄	—	17	1	no	—
434	C₂×D₄	C₄×#595	1	1	yes	characteristic
435	C₂²×C₄	—	17	1	no	—
436	C₂²×C₄	—	17	1	no	—
437	C₂²×C₄	—	17	1	no	—
438	C₂²×C₄	—	17	1	no	—
439	C₂²×C₄	—	17	1	no	—
440	C₂²×C₄	—	17	1	no	—
441	C₂²×C₄	—	17	1	no	—
442	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
443	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
444	M₁₆	—	4	1	no	—
445	M₁₆	—	17	8	no	—
446	M₁₆	—	34	4	no	—
447	M₁₆	—	34	4	no	—
448	M₁₆	—	34	4	no	—
449	M₁₆	—	34	4	no	—
450	M₁₆	—	68	1	no	—
451	M₁₆	—	68	1	no	—
452	M₁₆	—	68	1	no	—
453	C₂×C₈	—	4	1	no	—
454	C₂×C₈	—	17	2	no	—
455	C₂×C₈	—	17	2	no	—
456	C₂×C₈	—	17	2	no	—
457	C₂×C₈	—	17	2	no	—
458	C₂×C₈	—	17	2	no	—
459	C₂×C₈	—	17	2	no	—
460	C₂×C₈	—	17	2	no	—
461	C₂×C₈	—	17	2	no	—
462	C₂×C₈	—	17	1	no	—
463	C₂×C₈	—	17	1	no	—
464	C₂×C₈	—	17	1	no	—
465	C₂×C₈	—	17	1	no	—
466	C₂×C₈	—	34	4	no	—
467	C₂×C₈	—	34	4	no	—
468	C₂×C₈	—	34	4	no	—
469	C₂×C₈	—	34	4	no	—
470	C₂×C₈	—	68	1	no	—
471	C₂×C₈	C₂²×#595	1	1	yes	characteristic
472	C₂×C₈	C₂²×#595	1	1	yes	characteristic
473	C₂×C₈	C₂²×#595	1	1	yes	characteristic
474	C₂×C₈	C₂²×#595	1	1	yes	characteristic
475	C₄⋊C₄	—	17	1	no	—
476	C₄⋊C₄	—	17	1	no	—
477	C₄⋊C₄	—	17	1	no	—
478	C₄⋊C₄	—	17	1	no	—
479	C₄⋊C₄	—	17	1	no	—
480	C₄⋊C₄	C₄×#595	1	1	yes	characteristic
481	C₂²⋊C₄	—	17	1	no	—
482	C₂²⋊C₄	—	17	1	no	—
483	C₂²⋊C₄	—	17	1	no	—
484	C₂²⋊C₄	—	17	1	no	—
485	C₂²⋊C₄	C₄×#595	1	1	yes	characteristic
486	C₂²⋊C₄	C₄×#595	1	1	yes	characteristic
487	C₄²	—	17	1	no	—
488	C₄²	—	17	1	no	—
489	C₄²	—	17	1	no	—
490	C₄²	—	17	1	no	—
491	C₄²	—	17	1	no	—
492	C₄²	—	17	1	no	—
493	C₄²	—	17	1	no	—
494	C₄²	—	17	1	no	—
495	C₄²	—	17	1	no	—
496	C₄²	C₂²×#595	1	1	yes	characteristic
497	C₂³	—	17	1	no	—
498	C₂³	C₂×C₄×#595	1	1	yes	characteristic
499	C₂³	C₂×C₄×#595	1	1	yes	characteristic
500	Q₈	—	34	2	no	—
501	D₄	—	2	2	no	—
502	D₄	—	34	2	no	—
503	D₄	—	34	2	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	17	4	no	—
509	C₂×C₄	—	17	1	no	—
510	C₂×C₄	—	17	1	no	—
511	C₂×C₄	—	17	1	no	—
512	C₂×C₄	—	17	1	no	—
513	C₂×C₄	—	17	1	no	—
514	C₂×C₄	—	17	1	no	—
515	C₂×C₄	—	17	1	no	—
516	C₂×C₄	—	34	2	no	—
517	C₂×C₄	—	34	2	no	—
518	C₂×C₄	—	34	2	no	—
519	C₂×C₄	—	34	2	no	—
520	C₂×C₄	—	34	2	no	—
521	C₂×C₄	—	34	1	no	—
522	C₂×C₄	—	34	1	no	—
523	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
524	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
525	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
526	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
527	C₂×C₄	C₂³×#595	1	1	yes	characteristic
528	C₈	—	2	1	no	—
529	C₈	—	2	1	no	—
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	17	4	no	—
533	C₈	—	17	4	no	—
534	C₈	—	17	4	no	—
535	C₈	—	34	2	no	—
536	C₈	—	34	2	no	—
537	C₈	—	34	2	no	—
538	C₈	—	34	2	no	—
539	C₈	—	34	2	no	—
540	C₈	—	34	1	no	—
541	C₈	—	34	1	no	—
542	C₈	—	34	1	no	—
543	C₈	—	34	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	34	1	no	—
550	C₂²	—	34	1	no	—
551	C₂²	—	34	1	no	—
552	C₂²	M₁₆×#595	1	2	yes	—
553	C₂²	C₂²×C₄×#595	1	1	yes	characteristic
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	17	2	no	—
559	C₄	—	17	2	no	—
560	C₄	—	17	2	no	—
561	C₄	—	34	1	no	—
562	C₄	—	34	1	no	—
563	C₄	—	34	1	no	—
564	C₄	—	34	1	no	—
565	C₄	#11763887	1	1	yes	characteristic
566	C₄	#11763888	1	1	yes	characteristic
567	C₂	—	2	2	no	—
568	C₂	—	4	1	no	—
569	C₂	—	68	1	no	—
570	C₂	C₂×M₁₆×#595	1	1	yes	characteristic
571	C₂	#131×#595	1	1	yes	characteristic
572	C₂	#14545355	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#595
commutator, socle	C₂²×C₁₇	C₂²×C₄²
Fitting	C₁₇×#435	C₄
prime radical	C₂×#63254	C₂×C₄
cosocle	C₄×Dic₁₇	C₂⁴
hypercenter	#435	#595
hypocenter	C₁₇	#17337
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
3. #14544008	C₂	semidirect
4. #14544007	C₂	semidirect
5. #14544002	C₂	semidirect
6. #14544001	C₂	semidirect
7. #14543999	C₂	semidirect
8. #14543992	C₂	semidirect
9. #14543991	C₂	semidirect
10. #14543986	C₂	semidirect
11. #14543985	C₂	semidirect
12. #14543985	C₂	semidirect
13. C₈×#63247	C₂	semidirect
14. C₂×#11763651	C₂	semidirect
159. #63247	M₁₆	semidirect
249. #3624	#131	semidirect
429. C₁₇	#17337	semidirect

Maximal subgroups

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

subgroup	index
#14545594	2
C₄×#10587678	2
#14544008	2
#14544007	2
#14544002	2
#14544001	2
#14543999	2
#14543992	2
#14543991	2
#14543986	2
#14543985	2
C₈×#63247	2
C₂×#11763651	2
#14537744	2
#17337	17