Subgroups — #17968864

Order 4352.

838 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₇⋊#446	C₂	1	1	yes	maximal, characteristic
2	#14545243	C₂	1	1	yes	maximal, characteristic
3	#14544585	C₂	1	1	yes	maximal, characteristic
4	#14544585	C₂	1	1	yes	maximal, characteristic
5	#14544582	C₂	1	1	yes	maximal, characteristic
6	#14544582	C₂	1	1	yes	maximal, characteristic
7	#14544581	C₂	1	1	yes	maximal, characteristic
8	#14544578	C₂	1	1	yes	maximal, characteristic
9	#14544573	C₂	1	1	yes	maximal, characteristic
10	#14544573	C₂	1	1	yes	maximal, characteristic
11	#14544571	C₂	1	1	yes	maximal, characteristic
12	#14544442	C₂	1	1	yes	maximal, characteristic
13	#14544440	C₂	1	1	yes	maximal, characteristic
14	#97×#595	C₂	1	1	yes	maximal, characteristic
15	D₁₇×#446	C₂	1	1	yes	maximal, characteristic
16	#11763861	C₄	1	2	yes	complemented
17	#11763861	C₄	1	2	yes	complemented
18	#11763860	C₄	1	2	yes	complemented
19	#11763859	C₄	1	2	yes	complemented
20	#11763810	C₂²	1	1	yes	characteristic
21	#11763810	C₂²	1	1	yes	characteristic
22	#11763810	C₂²	1	1	yes	characteristic
23	#11763768	C₂²	1	1	yes	characteristic
24	#11763768	C₂²	1	1	yes	characteristic
25	C₂×#10587532	C₂²	1	1	yes	characteristic
26	C₂×#10587532	C₂²	1	1	yes	characteristic
27	C₂×#10587532	C₂²	1	1	yes	characteristic
28	C₂×#10587532	C₂²	1	1	yes	characteristic
29	C₂×#10587532	C₂²	1	1	yes	characteristic
30	C₂×#10587532	C₂²	1	1	yes	characteristic
31	C₄×#63242	C₂²	1	1	yes	characteristic
32	C₂×C₈×#595	C₂²	1	1	yes	characteristic
33	C₂×C₈×#595	C₂²	1	1	yes	characteristic
34	C₂×C₈×#595	C₂²	1	1	yes	characteristic
35	C₂×C₈×#595	C₂²	1	1	yes	characteristic
36	(C₂×#595)⋊Q₈	C₄	1	2	yes	—
37	#11763760	C₄	1	2	yes	—
38	#11763758	C₄	1	2	yes	—
39	#11763758	C₄	1	2	yes	—
40	C₄×C₄⋊#595	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊#595	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊#595	C₂²	1	1	yes	characteristic
43	#11763745	C₂²	1	1	yes	characteristic
44	#11763745	C₂²	1	1	yes	characteristic
45	C₄²×#595	C₂²	1	1	yes	characteristic
46	#11763674	C₂²	1	1	yes	characteristic
47	#11763674	C₂²	1	1	yes	characteristic
48	#11763674	C₂²	1	1	yes	characteristic
49	#11763674	C₂²	1	1	yes	characteristic
50	#11763674	C₂²	1	1	yes	characteristic
51	#11763674	C₂²	1	1	yes	characteristic
52	C₄×Q₈×D₁₇	C₂²	1	1	yes	characteristic
53	#11762940	C₄	1	1	yes	characteristic, complemented
54	#11762939	C₄	1	1	yes	characteristic, complemented
55	#11762938	C₄	1	1	yes	characteristic, complemented
56	#11762938	C₄	1	1	yes	characteristic, complemented
57	#11762937	C₄	1	1	yes	characteristic, complemented
58	#11762937	C₄	1	1	yes	characteristic, complemented
59	#11762936	C₄	1	1	yes	characteristic, complemented
60	C₄⋊C₈×D₁₇	C₂²	1	1	yes	characteristic
61	C₄⋊C₈×D₁₇	C₂²	1	1	yes	characteristic
62	C₄⋊C₈×D₁₇	C₂²	1	1	yes	characteristic
63	#97×D₁₇	C₂²	1	1	yes	characteristic
64	#97×D₁₇	C₂²	1	1	yes	characteristic
65	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
66	C₁₇×#446	C₄	1	1	yes	characteristic, complemented
67	C₂×Q₈×D₁₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄⋊#595	C₂×C₄	1	2	yes	—
69	C₂×C₄⋊#595	C₂×C₄	1	2	yes	—
70	C₂×C₄⋊#595	C₂×C₄	1	2	yes	—
71	C₂×C₄×#595	C₂×C₄	1	2	yes	—
72	C₂×C₄×#595	C₂×C₄	1	2	yes	—
73	C₂×C₄×#595	C₂³	1	1	yes	characteristic
74	C₂×C₄×#595	C₂³	1	1	yes	characteristic
75	C₂×C₄×#595	C₂³	1	1	yes	characteristic
76	C₂×C₄×#595	C₂³	1	1	yes	characteristic
77	C₂×#63242	C₂³	1	1	yes	characteristic
78	C₂×#63242	C₂³	1	1	yes	characteristic
79	C₂×#63242	C₂³	1	1	yes	characteristic
80	C₂×#63242	C₂³	1	1	yes	characteristic
81	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
82	Q₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
83	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
84	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
85	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
86	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
87	C₄⋊C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
89	C₄⋊C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
90	#10587573	C₂×C₄	1	1	yes	characteristic
91	#10587573	C₂×C₄	1	1	yes	characteristic
92	#10587573	C₂×C₄	1	1	yes	characteristic
93	C₄²×D₁₇	C₂³	1	1	yes	characteristic
94	C₄²×D₁₇	C₂³	1	1	yes	characteristic
95	C₄²×D₁₇	C₂³	1	1	yes	characteristic
96	C₄×Dic₃₄	C₂×C₄	1	1	yes	characteristic
97	C₄×Dic₃₄	C₂×C₄	1	1	yes	characteristic
98	C₄×Dic₃₄	C₂×C₄	1	1	yes	characteristic
99	(C₂×#595)⋊C₄	C₂×C₄	1	2	yes	—
100	(C₂×#595)⋊C₄	C₂×C₄	1	2	yes	—
101	(C₂×#595)⋊C₄	C₂×C₄	1	2	yes	—
102	(C₂×#595)⋊C₄	C₂×C₄	1	2	yes	—
103	(C₂×#595)⋊C₄	C₂×C₄	1	2	yes	—
104	(C₂×#595)⋊C₄	C₂×C₄	1	2	yes	—
105	(C₂×#595)⋊C₄	C₂×C₄	1	2	yes	—
106	#10587544	C₂×C₄	1	2	yes	—
107	#10587544	C₂×C₄	1	2	yes	—
108	#10587544	C₂×C₄	1	2	yes	—
109	#10587542	C₂×C₄	1	2	yes	—
110	#10587542	C₂×C₄	1	2	yes	—
111	#10587542	C₂×C₄	1	2	yes	—
112	#10587542	C₂×C₄	1	2	yes	—
113	C₄⋊#3624	C₂×C₄	1	2	yes	—
114	C₄⋊#3624	C₂×C₄	1	2	yes	—
115	C₄⋊#3624	C₂×C₄	1	2	yes	—
116	C₄×#3624	C₂×C₄	1	2	yes	—
117	C₄×#3624	C₂×C₄	1	2	yes	—
118	#10587532	—	2	2	no	—
119	#10587532	—	2	2	no	—
120	#10587532	—	2	2	no	—
121	#10587532	—	2	2	no	—
122	#10587532	—	2	2	no	—
123	#10587532	—	2	2	no	—
124	C₈×#595	—	2	2	no	—
125	C₈×#595	—	2	2	no	—
126	C₈×#595	—	2	2	no	—
127	C₈×#595	Q₈	1	4	yes	complemented
128	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
129	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
130	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
131	C₁₇×#97	C₂×C₄	1	1	yes	characteristic
132	C₁₇×#97	C₂×C₄	1	1	yes	characteristic
133	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
134	#10587486	C₂×C₄	1	1	yes	characteristic
135	#10587486	C₂×C₄	1	1	yes	characteristic
136	#10587486	C₂×C₄	1	1	yes	characteristic
137	#10587486	C₂×C₄	1	1	yes	characteristic
138	#10587485	C₂×C₄	1	1	yes	characteristic
139	#10587485	C₂×C₄	1	1	yes	characteristic
140	#10587485	C₂×C₄	1	1	yes	characteristic
141	#10587485	C₂×C₄	1	1	yes	characteristic
142	#10587485	C₂×C₄	1	1	yes	characteristic
143	#10587485	C₂×C₄	1	1	yes	characteristic
144	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
145	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
146	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
147	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
148	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
149	#10587474	C₂×C₄	1	1	yes	characteristic
150	#10587474	C₂×C₄	1	1	yes	characteristic
151	C₄×#3622	C₂×C₄	1	1	yes	characteristic
152	C₂²×#595	C₂²×C₄	1	2	yes	—
153	C₂²×#595	C₂²×C₄	1	2	yes	—
154	C₂²×#595	C₂²×C₄	1	2	yes	—
155	C₂²×#595	C₂²×C₄	1	2	yes	—
156	C₂×Q₈×C₁₇	C₄²	1	1	yes	characteristic
157	Q₈×D₁₇	—	4	2	no	—
158	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₄×D₁₇	C₂⁴	1	1	yes	characteristic
165	C₂×Dic₃₄	C₄²	1	1	yes	characteristic
166	C₂×Dic₃₄	C₄²	1	1	yes	characteristic
167	C₂×Dic₃₄	C₄²	1	1	yes	characteristic
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	C₂×#3624	C₂²×C₄	1	2	yes	—
172	C₄⋊#595	—	4	2	no	—
173	C₄⋊#595	—	4	2	no	—
174	C₄⋊#595	—	4	2	no	—
175	C₄×#595	—	2	1	no	—
176	C₄×#595	—	2	1	no	—
177	C₄×#595	—	2	1	no	—
178	C₄×#595	—	2	1	no	—
179	C₄×#595	—	2	1	no	—
180	C₄×#595	—	2	1	no	—
181	C₄×#595	—	4	2	no	—
182	C₄×#595	—	4	2	no	—
183	C₄×#595	C₂×Q₈	1	2	yes	—
184	C₄×#595	#41	1	2	yes	—
185	#63242	—	2	1	no	—
186	#63242	—	2	1	no	—
187	#63242	—	2	1	no	—
188	#63242	—	2	1	no	—
189	#63242	—	2	1	no	—
190	#63242	—	2	1	no	—
191	#63242	C₂×Q₈	1	2	yes	—
192	#63242	#41	1	2	yes	—
193	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
197	C₄⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
198	C₄⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
199	C₄⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
200	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
201	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
202	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
203	C₄⋊Dic₁₇	C₄²	1	1	yes	characteristic
204	C₄⋊Dic₁₇	C₄²	1	1	yes	characteristic
205	C₄⋊Dic₁₇	C₄²	1	1	yes	characteristic
206	#63225	C₄²	1	1	yes	characteristic
207	#63225	C₄²	1	1	yes	characteristic
208	#63225	C₄²	1	1	yes	characteristic
209	#63225	C₄²	1	1	yes	characteristic
210	#63225	C₄²	1	1	yes	characteristic
211	#63225	C₄²	1	1	yes	characteristic
212	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
213	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
214	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
215	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
216	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
217	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
218	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
219	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
220	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
221	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
222	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
223	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
224	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
225	C₈×D₁₇	—	2	1	no	—
226	C₈×D₁₇	—	2	1	no	—
227	C₈×D₁₇	—	2	1	no	—
228	C₈×D₁₇	—	2	1	no	—
229	C₈×D₁₇	—	2	1	no	—
230	C₈×D₁₇	—	2	1	no	—
231	C₈×D₁₇	C₂×Q₈	1	2	yes	—
232	C₈×D₁₇	#41	1	2	yes	—
233	#20518	—	17	1	no	maximal, Sylow
234	C₂²×D₁₇	C₂³×C₄	1	1	yes	characteristic
235	C₂×#595	—	2	2	no	—
236	C₂×#595	—	2	2	no	—
237	C₂×#595	—	2	2	no	—
238	C₂×#595	—	2	2	no	—
239	C₂×#595	—	2	2	no	—
240	C₂×#595	—	2	2	no	—
241	C₂×#595	—	2	2	no	—
242	C₂×#595	—	2	2	no	—
243	C₂×#595	—	2	2	no	—
244	C₂×#595	—	2	2	no	—
245	C₂×#595	—	2	2	no	—
246	C₂×#595	C₄×Q₈	1	4	yes	—
247	Q₈×C₁₇	—	4	1	no	—
248	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
249	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
250	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
251	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
252	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
253	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
254	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
255	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
256	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
257	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
258	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
259	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
260	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
261	C₂×Dic₁₇	C₂³×C₄	1	1	yes	characteristic
262	C₄×D₁₇	—	2	2	no	—
263	C₄×D₁₇	—	2	2	no	—
264	C₄×D₁₇	—	2	2	no	—
265	C₄×D₁₇	—	2	2	no	—
266	C₄×D₁₇	—	2	2	no	—
267	C₄×D₁₇	—	2	2	no	—
268	C₄×D₁₇	C₂²×Q₈	1	1	yes	characteristic
269	C₄×D₁₇	C₂×#41	1	1	yes	characteristic
270	C₄×D₁₇	C₂×#41	1	1	yes	characteristic
271	C₄×D₁₇	C₂×#41	1	1	yes	characteristic
272	Dic₃₄	—	4	1	no	—
273	Dic₃₄	—	4	1	no	—
274	Dic₃₄	—	4	1	no	—
275	#3624	—	2	2	no	—
276	#3624	—	2	2	no	—
277	#3624	—	2	2	no	—
278	#3624	C₄×Q₈	1	4	yes	—
279	C₈×C₁₇	—	2	1	no	—
280	C₈×C₁₇	—	2	1	no	—
281	C₈×C₁₇	—	2	1	no	—
282	C₈×C₁₇	C₄×Q₈	1	2	yes	—
283	#3622	—	2	1	no	—
284	#3622	—	2	1	no	—
285	#3622	—	2	1	no	—
286	#3622	C₄×Q₈	1	2	yes	—
287	C₂×#446	—	17	1	no	—
288	C₂×#446	—	17	1	no	—
289	#2295	—	17	1	no	—
290	#1771	—	17	1	no	—
291	#1771	—	17	1	no	—
292	#1771	—	17	1	no	—
293	#1771	—	17	1	no	—
294	#1770	—	17	1	no	—
295	#1770	—	17	1	no	—
296	#1768	—	17	1	no	—
297	#1768	—	17	1	no	—
298	#1767	—	17	1	no	—
299	#1726	—	17	1	no	—
300	#1726	—	17	1	no	—
301	C₄×#97	—	17	1	no	—
302	C₂²×C₁₇	C₂²×C₄²	1	1	yes	characteristic
303	C₂×D₁₇	C₂×C₄×Q₈	1	1	yes	characteristic
304	C₂×D₁₇	C₄×#41	1	1	yes	characteristic
305	C₂×D₁₇	#568	1	2	yes	—
306	C₂×D₁₇	#568	1	2	yes	—
307	#595	—	2	4	no	—
308	#595	—	4	2	no	—
309	#595	—	4	2	no	—
310	#595	—	4	2	no	—
311	C₄×C₁₇	—	2	1	no	—
312	C₄×C₁₇	—	2	1	no	—
313	C₄×C₁₇	—	2	1	no	—
314	C₄×C₁₇	—	2	1	no	—
315	C₄×C₁₇	—	2	1	no	—
316	C₄×C₁₇	—	2	1	no	—
317	C₄×C₁₇	C₂×C₄×Q₈	1	1	yes	characteristic
318	C₄×C₁₇	C₄×#41	1	1	yes	characteristic
319	Dic₁₇	—	2	1	no	—
320	Dic₁₇	—	2	1	no	—
321	Dic₁₇	—	2	1	no	—
322	Dic₁₇	—	2	1	no	—
323	Dic₁₇	—	2	1	no	—
324	Dic₁₇	—	2	1	no	—
325	Dic₁₇	C₂×C₄×Q₈	1	1	yes	characteristic
326	Dic₁₇	C₄×#41	1	1	yes	characteristic
327	C₂×C₄×Q₈	—	17	1	no	—
328	#446	—	17	2	no	—
329	#446	—	17	2	no	—
330	#446	—	17	2	no	—
331	#446	—	17	2	no	—
332	#446	—	17	1	no	—
333	#446	—	17	1	no	—
334	#446	—	17	1	no	—
335	#446	—	17	1	no	—
336	#446	—	17	1	no	—
337	#446	—	17	1	no	—
338	#446	—	17	1	no	—
339	#446	#595	1	1	yes	characteristic, complemented
340	C₂×C₄⋊C₈	—	17	1	no	—
341	C₂×C₄⋊C₈	—	17	1	no	—
342	C₂×C₄⋊C₈	—	17	1	no	—
343	C₂×C₄⋊C₈	—	17	1	no	—
344	C₂×C₄⋊C₈	—	17	1	no	—
345	C₂×C₄⋊C₈	—	17	1	no	—
346	C₂×#97	—	17	1	no	—
347	C₂×#97	—	17	1	no	—
348	C₂×#97	—	17	1	no	—
349	C₂×#97	—	17	1	no	—
350	C₂×#97	—	17	1	no	—
351	C₂×#97	—	17	1	no	—
352	C₂×#97	—	17	1	no	—
353	C₂×#97	—	17	1	no	—
354	C₂×#97	—	17	1	no	—
355	C₂×#97	—	17	1	no	—
356	C₂×C₄×C₈	—	17	1	no	—
357	C₂×C₄×C₈	—	17	1	no	—
358	C₂×C₄×C₈	—	17	1	no	—
359	C₂×C₄×C₈	—	17	1	no	—
360	C₂×C₄×C₈	—	17	1	no	—
361	C₂×C₄×C₈	—	17	1	no	—
362	#391	—	17	2	no	—
363	#389	—	17	2	no	—
364	#387	—	17	2	no	—
365	#387	—	17	2	no	—
366	C₄×C₄⋊C₄	—	17	1	no	—
367	C₄×C₄⋊C₄	—	17	1	no	—
368	C₄×C₄⋊C₄	—	17	1	no	—
369	#376	—	17	1	no	—
370	#376	—	17	1	no	—
371	C₄³	—	17	1	no	—
372	#336	—	17	1	no	—
373	#336	—	17	1	no	—
374	#336	—	17	1	no	—
375	#336	—	17	1	no	—
376	#336	—	17	1	no	—
377	#336	—	17	1	no	—
378	C₂×C₁₇	C₄²×Q₈	1	1	yes	characteristic
379	C₂×C₁₇	#2873	1	1	yes	characteristic
380	C₂×C₁₇	#2875	1	1	yes	characteristic
381	D₁₇	#2961	1	2	yes	—
382	D₁₇	#2967	1	2	yes	—
383	C₂²×Q₈	—	17	1	no	—
384	C₂²×C₈	—	17	1	no	—
385	C₂²×C₈	—	17	1	no	—
386	C₂²×C₈	—	17	1	no	—
387	C₂²×C₈	—	17	1	no	—
388	C₂²×C₈	—	17	1	no	—
389	C₂²×C₈	—	17	1	no	—
390	C₂²×C₈	—	17	1	no	—
391	C₂²×C₈	—	17	1	no	—
392	C₄×Q₈	—	17	1	no	—
393	C₄×Q₈	—	17	1	no	—
394	C₄×Q₈	—	17	1	no	—
395	C₄×Q₈	—	17	1	no	—
396	C₄×Q₈	—	17	1	no	—
397	C₄×Q₈	—	17	1	no	—
398	C₄×Q₈	—	17	1	no	—
399	C₄×Q₈	C₂×#595	1	1	yes	characteristic
400	C₂×C₄⋊C₄	—	17	1	no	—
401	C₂×C₄⋊C₄	—	17	1	no	—
402	C₂×C₄⋊C₄	—	17	1	no	—
403	C₂×C₄⋊C₄	—	17	2	no	—
404	C₂×C₄⋊C₄	—	17	2	no	—
405	C₂×C₄⋊C₄	—	17	2	no	—
406	C₂×C₄²	—	17	1	no	—
407	C₂×C₄²	—	17	1	no	—
408	C₂×C₄²	—	17	1	no	—
409	C₂×C₄²	—	17	1	no	—
410	C₂×C₄²	—	17	1	no	—
411	C₂×C₄²	—	17	1	no	—
412	C₂×C₄²	—	17	1	no	—
413	C₂×C₄²	—	17	2	no	—
414	C₂×C₄²	—	17	2	no	—
415	C₄⋊C₈	—	17	2	no	—
416	C₄⋊C₈	—	17	2	no	—
417	C₄⋊C₈	—	17	2	no	—
418	C₄⋊C₈	—	17	2	no	—
419	C₄⋊C₈	—	17	2	no	—
420	C₄⋊C₈	—	17	2	no	—
421	C₄⋊C₈	—	17	1	no	—
422	C₄⋊C₈	—	17	1	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	C₄⋊C₈	—	17	1	no	—
430	C₄⋊C₈	C₂×#595	1	1	yes	characteristic
431	C₄⋊C₈	C₂×#595	1	1	yes	characteristic
432	C₄⋊C₈	C₂×#595	1	1	yes	characteristic
433	#97	—	17	2	no	—
434	#97	—	17	2	no	—
435	#97	—	17	2	no	—
436	#97	—	17	2	no	—
437	#97	—	17	1	no	—
438	#97	—	17	1	no	—
439	#97	—	17	1	no	—
440	#97	—	17	1	no	—
441	#97	—	17	1	no	—
442	#97	—	17	1	no	—
443	#97	—	34	2	no	—
444	#97	—	34	2	no	—
445	#97	—	34	2	no	—
446	#97	—	34	2	no	—
447	#97	—	34	2	no	—
448	#97	—	34	2	no	—
449	#97	C₂×#595	1	1	yes	characteristic
450	#97	C₂×#595	1	1	yes	characteristic
451	C₄×C₈	—	17	4	no	—
452	C₄×C₈	—	17	2	no	—
453	C₄×C₈	—	17	2	no	—
454	C₄×C₈	—	17	1	no	—
455	C₄×C₈	—	17	1	no	—
456	C₄×C₈	—	17	1	no	—
457	C₄×C₈	—	34	2	no	—
458	C₄×C₈	—	34	2	no	—
459	C₄×C₈	—	34	2	no	—
460	C₄×C₈	C₂×#595	1	1	yes	characteristic
461	#95	—	17	2	no	—
462	#95	—	17	2	no	—
463	#95	—	17	2	no	—
464	#95	—	17	2	no	—
465	#95	—	17	2	no	—
466	#95	—	17	2	no	—
467	#95	—	17	2	no	—
468	C₁₇	#20518	1	1	yes	characteristic, complemented, Sylow
469	C₂×Q₈	—	17	1	no	—
470	C₂×Q₈	—	17	1	no	—
471	C₂×Q₈	—	17	1	no	—
472	C₂×Q₈	—	68	2	no	—
473	C₂×Q₈	C₄×#595	1	1	yes	characteristic
474	C₂²×C₄	—	17	1	no	—
475	C₂²×C₄	—	17	2	no	—
476	C₂²×C₄	—	17	1	no	—
477	C₂²×C₄	—	17	1	no	—
478	C₂²×C₄	—	17	1	no	—
479	C₂²×C₄	—	17	1	no	—
480	C₂²×C₄	—	17	1	no	—
481	C₂²×C₄	—	17	1	no	—
482	C₂²×C₄	—	17	2	no	—
483	C₂²×C₄	—	17	2	no	—
484	C₂²×C₄	—	17	2	no	—
485	C₂×C₈	—	17	2	no	—
486	C₂×C₈	—	17	2	no	—
487	C₂×C₈	—	17	2	no	—
488	C₂×C₈	—	17	1	no	—
489	C₂×C₈	—	17	2	no	—
490	C₂×C₈	—	17	2	no	—
491	C₂×C₈	—	17	2	no	—
492	C₂×C₈	—	17	2	no	—
493	C₂×C₈	—	17	2	no	—
494	C₂×C₈	—	17	1	no	—
495	C₂×C₈	—	17	1	no	—
496	C₂×C₈	—	17	1	no	—
497	C₂×C₈	—	34	1	no	—
498	C₂×C₈	—	34	1	no	—
499	C₂×C₈	—	34	1	no	—
500	C₂×C₈	—	34	1	no	—
501	C₂×C₈	—	34	1	no	—
502	C₂×C₈	—	34	1	no	—
503	C₂×C₈	—	34	1	no	—
504	C₂×C₈	—	34	1	no	—
505	C₂×C₈	—	34	1	no	—
506	C₂×C₈	—	34	1	no	—
507	C₂×C₈	—	34	1	no	—
508	C₂×C₈	—	34	1	no	—
509	C₂×C₈	C₂²×#595	1	1	yes	characteristic
510	C₂×C₈	C₂²×#595	1	1	yes	characteristic
511	C₂×C₈	C₂²×#595	1	1	yes	characteristic
512	C₂×C₈	C₂²×#595	1	1	yes	characteristic
513	C₄⋊C₄	—	17	1	no	—
514	C₄⋊C₄	—	17	1	no	—
515	C₄⋊C₄	—	17	1	no	—
516	C₄⋊C₄	—	17	1	no	—
517	C₄⋊C₄	—	17	1	no	—
518	C₄⋊C₄	—	17	1	no	—
519	C₄⋊C₄	—	17	1	no	—
520	C₄⋊C₄	—	17	1	no	—
521	C₄⋊C₄	—	17	1	no	—
522	C₄⋊C₄	—	68	2	no	—
523	C₄⋊C₄	—	68	2	no	—
524	C₄⋊C₄	—	68	2	no	—
525	C₄⋊C₄	C₄×#595	1	1	yes	characteristic
526	C₄⋊C₄	C₄×#595	1	1	yes	characteristic
527	C₄⋊C₄	C₄×#595	1	1	yes	characteristic
528	C₄²	—	17	2	no	—
529	C₄²	—	17	2	no	—
530	C₄²	—	17	1	no	—
531	C₄²	—	17	1	no	—
532	C₄²	—	17	1	no	—
533	C₄²	—	17	1	no	—
534	C₄²	—	17	1	no	—
535	C₄²	—	17	1	no	—
536	C₄²	—	17	1	no	—
537	C₄²	—	17	1	no	—
538	C₄²	—	17	1	no	—
539	C₄²	—	34	1	no	—
540	C₄²	—	34	1	no	—
541	C₄²	—	34	1	no	—
542	C₄²	—	34	1	no	—
543	C₄²	—	34	1	no	—
544	C₄²	—	34	1	no	—
545	C₄²	—	68	2	no	—
546	C₄²	—	68	2	no	—
547	C₄²	C₂²×#595	1	1	yes	characteristic
548	C₄²	C₂²×#595	1	1	yes	characteristic
549	C₄²	C₂²×#595	1	1	yes	characteristic
550	C₂³	—	17	1	no	—
551	Q₈	—	4	1	no	—
552	Q₈	—	68	1	no	—
553	Q₈	—	68	1	no	—
554	Q₈	—	68	1	no	—
555	C₂×C₄	—	17	1	no	—
556	C₂×C₄	—	17	1	no	—
557	C₂×C₄	—	17	1	no	—
558	C₂×C₄	—	17	1	no	—
559	C₂×C₄	—	17	1	no	—
560	C₂×C₄	—	17	4	no	—
561	C₂×C₄	—	17	1	no	—
562	C₂×C₄	—	17	1	no	—
563	C₂×C₄	—	17	1	no	—
564	C₂×C₄	—	17	1	no	—
565	C₂×C₄	—	17	1	no	—
566	C₂×C₄	—	17	1	no	—
567	C₂×C₄	—	34	2	no	—
568	C₂×C₄	—	34	2	no	—
569	C₂×C₄	—	34	2	no	—
570	C₂×C₄	—	34	2	no	—
571	C₂×C₄	—	34	2	no	—
572	C₂×C₄	—	34	2	no	—
573	C₂×C₄	—	34	2	no	—
574	C₂×C₄	—	34	2	no	—
575	C₂×C₄	—	34	2	no	—
576	C₂×C₄	—	34	2	no	—
577	C₂×C₄	—	34	2	no	—
578	C₂×C₄	—	34	2	no	—
579	C₂×C₄	—	34	2	no	—
580	C₂×C₄	—	34	2	no	—
581	C₂×C₄	—	34	2	no	—
582	C₂×C₄	—	34	2	no	—
583	C₂×C₄	—	34	2	no	—
584	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
585	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
586	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
587	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
588	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
589	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
590	C₂×C₄	C₂³×#595	1	1	yes	characteristic
591	C₈	—	2	1	no	—
592	C₈	—	2	1	no	—
593	C₈	—	2	1	no	—
594	C₈	—	17	4	no	—
595	C₈	—	17	2	no	—
596	C₈	—	34	2	no	—
597	C₈	—	34	2	no	—
598	C₈	—	34	2	no	—
599	C₈	—	34	1	no	—
600	C₈	—	34	1	no	—
601	C₈	—	34	1	no	—
602	C₈	Q₈×#595	1	2	yes	—
603	C₂²	—	17	1	no	—
604	C₂²	—	17	1	no	—
605	C₂²	—	17	2	no	—
606	C₂²	—	17	2	no	—
607	C₂²	C₂²×C₄×#595	1	1	yes	characteristic
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	2	1	no	—
613	C₄	—	2	1	no	—
614	C₄	—	17	1	no	—
615	C₄	—	17	1	no	—
616	C₄	—	34	4	no	—
617	C₄	—	34	1	no	—
618	C₄	—	34	1	no	—
619	C₄	—	34	1	no	—
620	C₄	—	34	1	no	—
621	C₄	—	34	1	no	—
622	C₄	—	34	1	no	—
623	C₄	—	68	2	no	—
624	C₄	—	68	2	no	—
625	C₄	—	68	2	no	—
626	C₄	C₂×Q₈×#595	1	1	yes	characteristic
627	C₄	#41×#595	1	1	yes	characteristic
628	C₂	—	17	2	no	—
629	C₂	—	17	2	no	—
630	C₂	C₄×Q₈×#595	1	1	yes	characteristic
631	C₂	#14545347	1	1	yes	characteristic
632	C₂	#14545354	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#595
commutator, socle	C₂²×C₁₇	C₂²×C₄²
Fitting	C₁₇×#446	C₄
prime radical	C₂²×D₁₇	C₂³×C₄
cosocle	C₂×C₄×D₁₇	C₂⁴
hypercenter	#446	#595
hypocenter	C₁₇	#20518
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #446

Complements

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

N	H ≅ G/N	type
16. #11763861	C₄	semidirect
17. #11763861	C₄	semidirect
18. #11763860	C₄	semidirect
19. #11763859	C₄	semidirect
53. #11762940	C₄	semidirect
54. #11762939	C₄	semidirect
55. #11762938	C₄	semidirect
56. #11762938	C₄	semidirect
57. #11762937	C₄	semidirect
58. #11762937	C₄	semidirect
59. #11762936	C₄	semidirect
66. C₁₇×#446	C₄	semidirect
127. C₈×#595	Q₈	semidirect
339. #446	#595	semidirect
468. C₁₇	#20518	semidirect

Maximal subgroups

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

subgroup	index
D₁₇⋊#446	2
#14545243	2
#14544585	2
#14544582	2
#14544581	2
#14544578	2
#14544573	2
#14544571	2
#14544442	2
#14544440	2
#97×#595	2
D₁₇×#446	2
#20518	17