Subgroups — #17964045

Order 4352.

874 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545463	C₂	1	1	yes	maximal, characteristic
2	#14545462	C₂	1	1	yes	maximal, characteristic
3	#14543998	C₂	1	2	yes	maximal, complemented
4	#14543994	C₂	1	2	yes	maximal, complemented
5	#14543993	C₂	1	2	yes	maximal, complemented
6	#14543988	C₂	1	2	yes	maximal, complemented
7	C₈×#63243	C₂	1	2	yes	maximal, complemented
8	C₈×#63247	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
10	#11763832	C₄	1	2	yes	—
11	#11763832	C₄	1	2	yes	—
12	#11763831	C₄	1	2	yes	—
13	#11763829	C₄	1	2	yes	—
14	#11763828	C₂²	1	2	yes	—
15	#11763827	C₂²	1	2	yes	—
16	#11763827	C₂²	1	2	yes	—
17	#11763826	C₂²	1	2	yes	—
18	#11763814	C₄	1	2	yes	—
19	#11763812	C₄	1	2	yes	—
20	#11763781	C₄	1	2	yes	—
21	#11763780	C₄	1	2	yes	—
22	C₄×#63243	C₂²	1	2	yes	—
23	C₄×#63247	C₂²	1	2	yes	—
24	#11763651	C₂²	1	4	yes	complemented
25	#11763651	C₂²	1	4	yes	complemented
26	#11763650	C₂²	1	4	yes	complemented
27	C₈×#3624	C₂²	1	4	yes	complemented
28	C₂²×C₈×D₁₇	C₄	1	1	yes	characteristic
29	C₂²×C₈×D₁₇	C₄	1	1	yes	characteristic
30	C₂×C₄²×D₁₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×#3622	C₄	1	1	yes	characteristic
32	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic
35	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic
36	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic
37	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic
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
43	C₂²×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
46	C₂×#63247	C₂×C₄	1	4	yes	—
47	C₂×#63243	C₂×C₄	1	4	yes	—
48	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₁₇	C₂³	1	1	yes	characteristic
54	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
55	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₁₇	—	2	4	no	—
57	C₂×C₈×D₁₇	—	2	4	no	—
58	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
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	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
66	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
67	C₄²×D₁₇	C₂×C₄	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	C₂³	1	1	yes	characteristic
73	C₄²×D₁₇	C₂³	1	1	yes	characteristic
74	C₂²⋊#3624	C₂×C₄	1	4	yes	—
75	#10587544	C₂×C₄	1	4	yes	—
76	#10587544	C₂×C₄	1	4	yes	—
77	#10587544	C₂×C₄	1	4	yes	—
78	#10587543	C₂×C₄	1	4	yes	—
79	#10587543	C₂×C₄	1	4	yes	—
80	#10587543	C₂×C₄	1	4	yes	—
81	#10587542	C₂×C₄	1	4	yes	—
82	#10587542	C₂×C₄	1	4	yes	—
83	C₄⋊#3624	C₂×C₄	1	4	yes	—
84	C₄×#3624	C₂³	1	4	yes	—
85	C₄×#3624	C₂³	1	4	yes	—
86	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
87	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
88	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
89	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
90	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
91	C₈×Dic₁₇	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	C₂³	1	1	yes	characteristic
95	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
96	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
97	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
98	C₄×#3622	C₂×C₄	1	1	yes	characteristic
99	C₄×#3622	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	C₂³×D₁₇	C₄²	1	1	yes	characteristic
103	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
104	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
105	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×Dic₁₇	C₄²	1	1	yes	characteristic
107	C₂²×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₄×D₁₇	—	2	4	no	—
110	C₂×C₄×D₁₇	—	2	2	no	—
111	C₂×C₄×D₁₇	—	2	2	no	—
112	C₂×C₄×D₁₇	—	2	4	no	—
113	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
114	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
115	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
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	C₂²×C₄	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	#63247	—	2	8	no	—
126	C₂×#3624	C₂²×C₄	1	8	yes	—
127	C₂×#3624	C₂²×C₄	1	8	yes	—
128	#63243	—	2	8	no	—
129	C₂×C₈×C₁₇	—	2	2	no	—
130	C₂×C₈×C₁₇	—	2	2	no	—
131	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₁₇	C₄²	1	1	yes	characteristic
136	C₄²×C₁₇	C₄²	1	1	yes	characteristic
137	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
139	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
140	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
141	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
142	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
143	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
144	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
145	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
146	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
147	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
148	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
149	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
150	C₄×Dic₁₇	C₂⁴	1	1	yes	characteristic
151	C₂×#3622	—	2	2	no	—
152	C₂×#3622	—	2	2	no	—
153	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
154	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
155	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
156	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
157	C₈×D₁₇	—	2	2	no	—
158	C₈×D₁₇	—	2	2	no	—
159	C₈×D₁₇	—	2	2	no	—
160	C₈×D₁₇	—	2	2	no	—
161	C₈×D₁₇	—	2	2	no	—
162	C₈×D₁₇	—	2	2	no	—
163	C₈×D₁₇	M₁₆	1	4	yes	complemented
164	C₈×D₁₇	M₁₆	1	4	yes	complemented
165	#17323	—	17	1	no	maximal, Sylow
166	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
167	C₂²×D₁₇	—	2	2	no	—
168	C₂²×D₁₇	—	2	2	no	—
169	C₂²×D₁₇	—	2	2	no	—
170	C₂²×D₁₇	C₂×C₄²	1	1	yes	characteristic
171	C₂²×D₁₇	C₂×C₄²	1	1	yes	characteristic
172	C₂×C₄×C₁₇	—	2	2	no	—
173	C₂×C₄×C₁₇	—	2	1	no	—
174	C₂×C₄×C₁₇	—	2	1	no	—
175	C₂×C₄×C₁₇	—	2	2	no	—
176	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
177	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
178	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
179	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
180	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
181	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
182	C₂×Dic₁₇	—	2	2	no	—
183	C₂×Dic₁₇	—	2	2	no	—
184	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
185	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
186	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
187	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
188	C₂×Dic₁₇	#131	1	4	yes	—
189	C₂×Dic₁₇	C₂³×C₄	1	1	yes	characteristic
190	C₂×Dic₁₇	C₂³×C₄	1	1	yes	characteristic
191	C₄×D₁₇	—	2	2	no	—
192	C₄×D₁₇	—	2	2	no	—
193	C₄×D₁₇	—	2	1	no	—
194	C₄×D₁₇	—	2	1	no	—
195	C₄×D₁₇	—	2	2	no	—
196	C₄×D₁₇	—	2	2	no	—
197	C₄×D₁₇	—	2	2	no	—
198	C₄×D₁₇	—	2	2	no	—
199	C₄×D₁₇	—	2	2	no	—
200	C₄×D₁₇	—	2	2	no	—
201	C₄×D₁₇	—	2	2	no	—
202	C₄×D₁₇	C₂×M₁₆	1	2	yes	—
203	C₄×D₁₇	C₂×M₁₆	1	2	yes	—
204	C₄×D₁₇	#131	1	4	yes	—
205	#3624	—	2	8	no	—
206	#3624	—	2	8	no	—
207	C₈×C₁₇	—	2	1	no	—
208	C₈×C₁₇	—	2	1	no	—
209	C₈×C₁₇	C₂×M₁₆	1	2	yes	—
210	C₈×C₁₇	C₂×M₁₆	1	2	yes	—
211	#3622	—	2	1	no	—
212	#3622	—	2	1	no	—
213	#3622	C₂×M₁₆	1	2	yes	—
214	#3622	C₂×M₁₆	1	2	yes	—
215	#2920	—	17	1	no	—
216	#2920	—	17	1	no	—
217	C₂²×C₄×C₈	—	17	1	no	—
218	#1452	—	17	2	no	—
219	#1451	—	17	2	no	—
220	#1451	—	17	2	no	—
221	#1450	—	17	2	no	—
222	C₈×M₁₆	—	17	2	no	—
223	C₈×M₁₆	—	17	2	no	—
224	C₂²×C₁₇	—	2	1	no	—
225	C₂²×C₁₇	—	2	1	no	—
226	C₂²×C₁₇	#405	1	2	yes	—
227	C₂²×C₁₇	C₂²×C₄²	1	1	yes	characteristic
228	C₂×D₁₇	—	2	8	no	—
229	C₂×D₁₇	—	2	1	no	—
230	C₂×D₁₇	—	2	1	no	—
231	C₂×D₁₇	—	2	1	no	—
232	C₂×D₁₇	—	2	1	no	—
233	C₂×D₁₇	C₄×M₁₆	1	2	yes	—
234	C₂×D₁₇	#405	1	2	yes	—
235	C₄×C₁₇	—	2	1	no	—
236	C₄×C₁₇	—	2	1	no	—
237	C₄×C₁₇	—	2	1	no	—
238	C₄×C₁₇	—	2	1	no	—
239	C₄×C₁₇	#405	1	2	yes	—
240	C₄×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
241	C₄×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
242	Dic₁₇	—	2	1	no	—
243	Dic₁₇	—	2	1	no	—
244	Dic₁₇	C₄×M₁₆	1	2	yes	—
245	Dic₁₇	#405	1	2	yes	—
246	Dic₁₇	C₂×#131	1	2	yes	—
247	Dic₁₇	C₂×#131	1	2	yes	—
248	C₂³×C₈	—	17	1	no	—
249	C₂³×C₈	—	17	1	no	—
250	C₂²×C₄²	—	17	1	no	—
251	#432	—	17	2	no	—
252	#432	—	17	2	no	—
253	#432	—	17	2	no	—
254	#432	—	17	2	no	—
255	#431	—	17	2	no	—
256	#431	—	17	2	no	—
257	#431	—	17	2	no	—
258	#431	—	17	2	no	—
259	#423	—	17	2	no	—
260	#423	—	17	2	no	—
261	#407	—	17	2	no	—
262	#407	—	17	2	no	—
263	C₄×M₁₆	—	17	2	no	—
264	C₄×M₁₆	—	17	2	no	—
265	C₂×C₄×C₈	—	17	1	no	—
266	C₂×C₄×C₈	—	17	1	no	—
267	C₂×C₄×C₈	—	17	1	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	#595	1	1	yes	characteristic
277	#322	—	17	4	no	—
278	#322	—	17	4	no	—
279	#322	—	17	4	no	—
280	C₈²	—	17	4	no	—
281	C₂×C₁₇	—	2	2	no	—
282	C₂×C₁₇	C₂×C₄×M₁₆	1	1	yes	characteristic
283	C₂×C₁₇	C₂×#405	1	1	yes	characteristic
284	C₂×C₁₇	C₂×#405	1	1	yes	characteristic
285	D₁₇	—	2	2	no	—
286	D₁₇	—	2	2	no	—
287	C₂³×C₄	—	17	1	no	—
288	C₂³×C₄	—	17	1	no	—
289	C₂³×C₄	—	17	1	no	—
290	C₂×M₁₆	—	17	4	no	—
291	C₂×M₁₆	—	17	4	no	—
292	C₂²×C₈	—	17	1	no	—
293	C₂²×C₈	—	17	1	no	—
294	C₂²×C₈	—	17	1	no	—
295	C₂²×C₈	—	17	1	no	—
296	C₂²×C₈	—	17	1	no	—
297	C₂²×C₈	—	17	1	no	—
298	C₂²×C₈	—	17	1	no	—
299	C₂²×C₈	—	17	1	no	—
300	C₂²×C₈	—	17	1	no	—
301	C₂²×C₈	—	17	1	no	—
302	C₂²×C₈	—	34	4	no	—
303	C₂²×C₈	—	34	4	no	—
304	C₂²×C₈	C₂×#595	1	1	yes	characteristic
305	C₂²×C₈	C₂×#595	1	1	yes	characteristic
306	C₂×C₄²	—	17	1	no	—
307	C₂×C₄²	—	17	1	no	—
308	C₂×C₄²	—	17	1	no	—
309	C₂×C₄²	—	17	1	no	—
310	C₂×C₄²	—	17	1	no	—
311	C₂×C₄²	—	17	1	no	—
312	C₂×C₄²	—	17	1	no	—
313	C₂×C₄²	—	17	1	no	—
314	C₂×C₄²	—	17	1	no	—
315	C₂×C₄²	—	17	1	no	—
316	C₂×C₄²	—	17	1	no	—
317	C₂×C₄²	C₂×#595	1	1	yes	characteristic
318	C₄⋊C₈	—	17	4	no	—
319	C₄⋊C₈	—	17	4	no	—
320	C₄⋊C₈	—	17	4	no	—
321	C₄⋊C₈	—	17	4	no	—
322	C₂²⋊C₈	—	17	4	no	—
323	C₂²⋊C₈	—	17	4	no	—
324	C₂²⋊C₈	—	17	4	no	—
325	C₂²⋊C₈	—	17	4	no	—
326	#97	—	17	4	no	—
327	#97	—	17	4	no	—
328	C₄×C₈	—	17	4	no	—
329	C₄×C₈	—	17	4	no	—
330	C₄×C₈	—	17	1	no	—
331	C₄×C₈	—	17	1	no	—
332	C₄×C₈	—	17	1	no	—
333	C₄×C₈	—	17	1	no	—
334	C₄×C₈	—	17	1	no	—
335	C₄×C₈	—	17	1	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	C₂×#595	1	1	yes	characteristic
343	C₄×C₈	C₂×#595	1	1	yes	characteristic
344	C₄×C₈	C₂×#595	1	1	yes	characteristic
345	C₄×C₈	C₂×#595	1	1	yes	characteristic
346	C₁₇	#17323	1	1	yes	characteristic, complemented, Sylow
347	C₂⁴	—	17	1	no	—
348	C₂²×C₄	—	17	1	no	—
349	C₂²×C₄	—	17	1	no	—
350	C₂²×C₄	—	17	1	no	—
351	C₂²×C₄	—	17	1	no	—
352	C₂²×C₄	—	17	1	no	—
353	C₂²×C₄	—	17	1	no	—
354	C₂²×C₄	—	17	1	no	—
355	C₂²×C₄	—	17	1	no	—
356	C₂²×C₄	—	17	1	no	—
357	C₂²×C₄	—	17	1	no	—
358	C₂²×C₄	—	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	—	34	2	no	—
364	C₂²×C₄	—	34	2	no	—
365	C₂²×C₄	—	34	4	no	—
366	C₂²×C₄	—	34	4	no	—
367	C₂²×C₄	C₄×#595	1	1	yes	characteristic
368	C₂²×C₄	C₄×#595	1	1	yes	characteristic
369	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
370	M₁₆	—	34	8	no	—
371	M₁₆	—	34	8	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	17	1	no	—
375	C₂×C₈	—	17	1	no	—
376	C₂×C₈	—	17	4	no	—
377	C₂×C₈	—	17	4	no	—
378	C₂×C₈	—	17	8	no	—
379	C₂×C₈	—	17	8	no	—
380	C₂×C₈	—	17	1	no	—
381	C₂×C₈	—	17	1	no	—
382	C₂×C₈	—	34	2	no	—
383	C₂×C₈	—	34	2	no	—
384	C₂×C₈	—	34	2	no	—
385	C₂×C₈	—	34	2	no	—
386	C₂×C₈	—	34	2	no	—
387	C₂×C₈	—	34	2	no	—
388	C₂×C₈	—	34	2	no	—
389	C₂×C₈	—	34	2	no	—
390	C₂×C₈	C₂²×#595	1	1	yes	characteristic
391	C₂×C₈	C₂²×#595	1	1	yes	characteristic
392	C₂×C₈	C₂²×#595	1	1	yes	characteristic
393	C₂×C₈	C₂²×#595	1	1	yes	characteristic
394	C₄²	—	17	1	no	—
395	C₄²	—	17	1	no	—
396	C₄²	—	17	1	no	—
397	C₄²	—	17	1	no	—
398	C₄²	—	17	1	no	—
399	C₄²	—	17	1	no	—
400	C₄²	—	17	1	no	—
401	C₄²	—	17	1	no	—
402	C₄²	—	17	1	no	—
403	C₄²	—	17	1	no	—
404	C₄²	—	17	1	no	—
405	C₄²	—	17	1	no	—
406	C₄²	C₄×#595	1	1	yes	characteristic
407	C₄²	C₄×#595	1	1	yes	characteristic
408	C₄²	C₂²×#595	1	1	yes	characteristic
409	C₄²	C₂²×#595	1	1	yes	characteristic
410	C₂³	—	17	1	no	—
411	C₂³	—	17	1	no	—
412	C₂³	—	34	2	no	—
413	C₂³	—	34	2	no	—
414	C₂³	—	34	2	no	—
415	C₂³	C₂×C₄×#595	1	1	yes	characteristic
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	17	4	no	—
421	C₂×C₄	—	17	1	no	—
422	C₂×C₄	—	17	1	no	—
423	C₂×C₄	—	17	1	no	—
424	C₂×C₄	—	17	1	no	—
425	C₂×C₄	—	17	4	no	—
426	C₂×C₄	—	17	2	no	—
427	C₂×C₄	—	17	2	no	—
428	C₂×C₄	—	17	1	no	—
429	C₂×C₄	—	17	1	no	—
430	C₂×C₄	—	34	2	no	—
431	C₂×C₄	—	34	2	no	—
432	C₂×C₄	—	34	2	no	—
433	C₂×C₄	—	34	2	no	—
434	C₂×C₄	—	34	2	no	—
435	C₂×C₄	—	34	2	no	—
436	C₂×C₄	—	34	2	no	—
437	C₂×C₄	—	34	2	no	—
438	C₂×C₄	—	34	2	no	—
439	C₂×C₄	—	34	2	no	—
440	C₂×C₄	—	34	2	no	—
441	C₂×C₄	—	34	1	no	—
442	C₂×C₄	—	34	1	no	—
443	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
444	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
445	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
446	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
447	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
448	C₂×C₄	C₂³×#595	1	1	yes	characteristic
449	C₈	—	2	1	no	—
450	C₈	—	2	1	no	—
451	C₈	—	17	2	no	—
452	C₈	—	17	2	no	—
453	C₈	—	34	8	no	—
454	C₈	—	34	8	no	—
455	C₈	—	34	1	no	—
456	C₈	—	34	1	no	—
457	C₈	D₁₇⋊M₁₆	1	2	yes	—
458	C₈	D₁₇⋊M₁₆	1	2	yes	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	17	2	no	—
462	C₂²	—	17	2	no	—
463	C₂²	—	34	8	no	—
464	C₂²	—	34	1	no	—
465	C₂²	—	34	1	no	—
466	C₂²	—	34	1	no	—
467	C₂²	—	34	1	no	—
468	C₂²	#11763772	1	2	yes	—
469	C₂²	C₂²×C₄×#595	1	1	yes	characteristic
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	17	2	no	—
475	C₄	—	17	2	no	—
476	C₄	—	17	2	no	—
477	C₄	—	17	2	no	—
478	C₄	—	34	1	no	—
479	C₄	—	34	1	no	—
480	C₄	#11763772	1	2	yes	—
481	C₄	C₂×D₁₇⋊M₁₆	1	1	yes	characteristic
482	C₄	C₂×D₁₇⋊M₁₆	1	1	yes	characteristic
483	C₂	—	2	2	no	—
484	C₂	—	34	2	no	—
485	C₂	—	34	2	no	—
486	C₂	C₄×D₁₇⋊M₁₆	1	1	yes	characteristic
487	C₂	C₂×#11763772	1	1	yes	characteristic
488	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	C₄²
cosocle	C₄×Dic₁₇	C₂⁴
hypercenter	C₂×C₄×C₈	#595
hypocenter	C₁₇	#17323
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. #14543998	C₂	semidirect
4. #14543994	C₂	semidirect
5. #14543993	C₂	semidirect
6. #14543988	C₂	semidirect
7. C₈×#63243	C₂	semidirect
8. C₈×#63247	C₂	semidirect
24. #11763651	C₂²	semidirect
25. #11763651	C₂²	semidirect
26. #11763650	C₂²	semidirect
27. C₈×#3624	C₂²	semidirect
163. C₈×D₁₇	M₁₆	semidirect
164. C₈×D₁₇	M₁₆	semidirect
346. C₁₇	#17323	semidirect

Maximal subgroups

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

subgroup	index
#14545463	2
#14545462	2
#14543998	2
#14543994	2
#14543993	2
#14543988	2
C₈×#63243	2
C₈×#63247	2
C₂×C₄×C₈×D₁₇	2
#17323	17