Subgroups — #17978728

Order 4352.

626 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545169	C₂	1	2	yes	maximal, complemented
2	#14545167	C₂	1	2	yes	maximal, complemented
3	#14545164	C₂	1	2	yes	maximal, complemented
4	#14545162	C₂	1	2	yes	maximal, complemented
5	#14545147	C₂	1	1	yes	maximal, characteristic, complemented
6	#14545144	C₂	1	1	yes	maximal, characteristic, complemented
7	#14545013	C₂	1	1	yes	maximal, characteristic, complemented
8	#14545012	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#11763704	C₂	1	1	yes	maximal, characteristic, complemented
10	#14545009	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₄×D₁₇	C₂	1	1	yes	maximal, characteristic
12	C₂×#10587530	C₂²	1	2	yes	complemented
13	C₂×#10587538	C₂²	1	2	yes	complemented
14	C₂×#10587529	C₂²	1	2	yes	complemented
15	C₂²×#63216	C₂²	1	2	yes	complemented
16	#11763730	C₂²	1	2	yes	complemented
17	C₄⋊#63216	C₂²	1	2	yes	complemented
18	#11763704	C₂²	1	1	yes	characteristic
19	#11763704	C₂²	1	1	yes	characteristic
20	#11763704	C₂²	1	1	yes	characteristic
21	#11763704	C₂²	1	1	yes	characteristic
22	#11763704	C₂²	1	2	yes	complemented
23	#11763704	C₂²	1	2	yes	complemented
24	C₂²⋊#63216	C₂²	1	2	yes	complemented
25	C₂²⋊#63216	C₂²	1	2	yes	complemented
26	#11763697	C₂²	1	2	yes	complemented
27	#11763695	C₂²	1	2	yes	complemented
28	C₂²×C₈×D₁₇	C₂²	1	1	yes	characteristic
29	C₂²×C₈×D₁₇	C₂²	1	1	yes	characteristic
30	C₄×D₄×D₁₇	C₄	1	1	yes	characteristic
31	C₈×D₆₈	C₄	1	1	yes	characteristic
32	D₄×#3622	C₂²	1	1	yes	characteristic
33	#11762874	C₂²	1	1	yes	characteristic
34	C₈×C₂²⋊D₁₇	C₄	1	1	yes	characteristic
35	C₈×C₂²⋊D₁₇	C₄	1	1	yes	characteristic
36	#11762872	C₂²	1	1	yes	characteristic
37	#11762872	C₂²	1	1	yes	characteristic
38	C₄⋊C₈×D₁₇	C₄	1	1	yes	characteristic
39	C₂²⋊C₈×D₁₇	C₄	1	1	yes	characteristic
40	C₂²⋊C₈×D₁₇	C₄	1	1	yes	characteristic
41	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
42	C₈×D₄×C₁₇	C₄	1	1	yes	characteristic
43	C₂×D₄×D₁₇	C₈	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	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
48	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
49	D₄×Dic₁₇	C₈	1	1	yes	characteristic
50	C₄×C₂²⋊D₁₇	C₂×C₄	1	1	yes	characteristic
51	C₄×C₂²⋊D₁₇	C₂×C₄	1	1	yes	characteristic
52	C₂²×#3622	C₂³	1	1	yes	characteristic
53	C₂²×#3622	C₂³	1	1	yes	characteristic
54	C₂×C₈×D₁₇	—	4	2	no	—
55	C₂×C₈×D₁₇	—	4	2	no	—
56	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
63	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
64	#10587579	C₈	1	1	yes	characteristic
65	C₄⋊C₄×D₁₇	C₈	1	1	yes	characteristic
66	#10587567	C₈	1	1	yes	characteristic
67	#10587567	C₈	1	1	yes	characteristic
68	C₂²⋊C₄×D₁₇	C₈	1	1	yes	characteristic
69	C₂²⋊C₄×D₁₇	C₈	1	1	yes	characteristic
70	C₄×D₆₈	C₂×C₄	1	1	yes	characteristic
71	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
72	#10587538	—	4	2	no	—
73	C₂×#63216	—	4	2	no	—
74	C₂×#63216	C₂³	1	2	yes	—
75	C₂×#63216	C₂³	1	2	yes	—
76	C₂×#63216	C₂³	1	2	yes	—
77	C₂×#63216	C₂³	1	2	yes	—
78	#10587530	—	4	2	no	—
79	#10587529	—	4	2	no	—
80	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
81	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
82	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
83	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
84	C₂²⋊#3622	C₂×C₄	1	1	yes	characteristic
85	C₂²⋊#3622	C₂×C₄	1	1	yes	characteristic
86	#10587491	C₂×C₄	1	1	yes	characteristic
87	#10587491	C₂×C₄	1	1	yes	characteristic
88	#10587491	C₂×C₄	1	1	yes	characteristic
89	#10587491	C₂×C₄	1	1	yes	characteristic
90	#10587485	C₂×C₄	1	1	yes	characteristic
91	#10587485	C₂×C₄	1	1	yes	characteristic
92	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
94	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
95	C₄×#3622	C₂³	1	1	yes	characteristic
96	C₂³×D₁₇	C₂×C₈	1	1	yes	characteristic
97	C₂³×D₁₇	C₂×C₈	1	1	yes	characteristic
98	C₂×D₄×C₁₇	C₂×C₈	1	1	yes	characteristic
99	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₂²⋊D₁₇	C₂×C₈	1	1	yes	characteristic
102	C₂×C₂²⋊D₁₇	C₂×C₈	1	1	yes	characteristic
103	C₂²×Dic₁₇	C₂×C₈	1	1	yes	characteristic
104	C₂²×Dic₁₇	C₂×C₈	1	1	yes	characteristic
105	D₄×D₁₇	—	2	4	no	—
106	C₂×D₆₈	C₂×C₈	1	1	yes	characteristic
107	C₂×C₄×D₁₇	—	4	1	no	—
108	C₂×C₄×D₁₇	—	4	1	no	—
109	C₂×C₄×D₁₇	—	4	1	no	—
110	C₂×C₄×D₁₇	—	4	1	no	—
111	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
112	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
113	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
114	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
115	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
116	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
117	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₁₇	—	4	1	no	—
121	C₂×C₈×C₁₇	—	4	1	no	—
122	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
126	C₄⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
127	C₂²⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
128	C₂²⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
129	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
130	C₂²⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
131	C₂²⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
132	#63227	C₂×C₈	1	1	yes	characteristic
133	#63227	C₂×C₈	1	1	yes	characteristic
134	#63227	C₂×C₈	1	1	yes	characteristic
135	#63227	C₂×C₈	1	1	yes	characteristic
136	C₄⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
137	#63225	C₂×C₈	1	1	yes	characteristic
138	#63225	C₂×C₈	1	1	yes	characteristic
139	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
140	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
141	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
142	C₂×#3622	—	2	2	no	—
143	C₂×#3622	—	2	2	no	—
144	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
145	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
146	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
147	C₂×#3622	C₂⁴	1	1	yes	characteristic
148	C₈×D₁₇	—	2	2	no	—
149	C₈×D₁₇	—	2	2	no	—
150	C₈×D₁₇	—	2	2	no	—
151	C₈×D₁₇	—	4	1	no	—
152	C₈×D₁₇	—	4	1	no	—
153	C₈×D₁₇	—	4	1	no	—
154	C₈×D₁₇	—	4	1	no	—
155	C₈×D₁₇	—	4	1	no	—
156	#63216	—	2	2	no	—
157	#63216	—	2	2	no	—
158	#63216	—	2	2	no	—
159	#63216	—	2	2	no	—
160	#33488	—	17	1	no	maximal, Sylow
161	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
162	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
163	C₂²×D₁₇	—	2	2	no	—
164	C₂²×D₁₇	—	2	2	no	—
165	C₂²×D₁₇	—	2	2	no	—
166	C₂²×D₁₇	—	2	2	no	—
167	C₂²×D₁₇	—	4	1	no	—
168	C₂²×D₁₇	—	4	1	no	—
169	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
170	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
171	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
172	D₄×C₁₇	—	2	2	no	—
173	C₂×C₄×C₁₇	—	2	1	no	—
174	C₂×C₄×C₁₇	—	2	1	no	—
175	C₂×C₄×C₁₇	—	2	1	no	—
176	C₂×C₄×C₁₇	—	2	1	no	—
177	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
178	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
179	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
180	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
181	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
182	C₂²⋊D₁₇	—	2	2	no	—
183	C₂²⋊D₁₇	M₃₂	1	4	yes	complemented
184	C₂×Dic₁₇	—	4	1	no	—
185	C₂×Dic₁₇	—	4	1	no	—
186	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
187	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
188	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
189	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
190	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
191	D₆₈	—	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	1	no	—
196	C₄×D₁₇	—	2	1	no	—
197	C₄×D₁₇	—	2	1	no	—
198	C₄×D₁₇	—	2	1	no	—
199	C₄×D₁₇	—	2	2	no	—
200	C₄×D₁₇	—	4	1	no	—
201	C₄×D₁₇	—	4	1	no	—
202	C₄×D₁₇	—	4	1	no	—
203	C₄×D₁₇	—	4	1	no	—
204	C₈×C₁₇	—	2	1	no	—
205	C₈×C₁₇	—	2	1	no	—
206	C₈×C₁₇	—	2	1	no	—
207	C₈×C₁₇	—	2	1	no	—
208	#3622	—	2	1	no	—
209	#3622	—	2	1	no	—
210	#3622	—	2	1	no	—
211	#3622	H(5,𝔽₂)	1	2	yes	—
212	C₂×C₈×D₄	—	17	1	no	—
213	#2169	—	17	2	no	—
214	#2168	—	17	2	no	—
215	#2168	—	17	2	no	—
216	D₄×C₁₆	—	17	2	no	—
217	#2163	—	17	1	no	—
218	#2162	—	17	1	no	—
219	#2112	—	17	1	no	—
220	#2112	—	17	1	no	—
221	C₂×C₂²⋊C₁₆	—	17	1	no	—
222	C₂×C₂²⋊C₁₆	—	17	1	no	—
223	C₂²×C₁₇	—	2	1	no	—
224	C₂²×C₁₇	—	2	1	no	—
225	C₂²×C₁₇	—	2	1	no	—
226	C₂²×C₁₇	—	2	1	no	—
227	C₂²×C₁₇	—	2	1	no	—
228	C₂²×C₁₇	C₂×M₃₂	1	2	yes	—
229	C₂²×C₁₇	C₂³×C₈	1	1	yes	characteristic
230	C₂×D₁₇	—	2	1	no	—
231	C₂×D₁₇	—	2	1	no	—
232	C₂×D₁₇	—	2	1	no	—
233	C₂×D₁₇	—	2	1	no	—
234	C₂×D₁₇	—	2	1	no	—
235	C₂×D₁₇	—	2	1	no	—
236	C₂×D₁₇	—	2	1	no	—
237	C₂×D₁₇	—	4	4	no	—
238	C₂×D₁₇	—	4	4	no	—
239	C₂×D₁₇	C₂×M₃₂	1	2	yes	—
240	C₂×D₁₇	#504	1	2	yes	—
241	C₄×C₁₇	—	2	1	no	—
242	C₄×C₁₇	—	2	1	no	—
243	C₄×C₁₇	—	2	1	no	—
244	C₄×C₁₇	—	2	1	no	—
245	C₄×C₁₇	#518	1	1	yes	characteristic
246	C₄×C₁₇	#568	1	1	yes	characteristic
247	Dic₁₇	—	2	1	no	—
248	Dic₁₇	—	2	1	no	—
249	Dic₁₇	—	2	1	no	—
250	Dic₁₇	—	2	1	no	—
251	Dic₁₇	C₂×M₃₂	1	2	yes	—
252	C₂³×C₈	—	17	1	no	—
253	C₂³×C₈	—	17	1	no	—
254	C₂×C₄×D₄	—	17	1	no	—
255	C₂×M₃₂	—	17	2	no	—
256	C₂×M₃₂	—	17	2	no	—
257	C₂²×C₁₆	—	17	2	no	—
258	C₂²×C₁₆	—	17	2	no	—
259	C₈×D₄	—	17	1	no	—
260	C₈×D₄	—	17	1	no	—
261	C₈×D₄	—	17	1	no	—
262	C₈×D₄	—	17	1	no	—
263	C₈×D₄	—	17	1	no	—
264	C₈×D₄	—	17	1	no	—
265	C₈×D₄	—	17	1	no	—
266	C₈×D₄	#595	1	1	yes	characteristic
267	C₂×C₄⋊C₈	—	17	1	no	—
268	C₂×C₂²⋊C₈	—	17	1	no	—
269	C₂×C₂²⋊C₈	—	17	1	no	—
270	C₂×C₄×C₈	—	17	1	no	—
271	C₄⋊C₁₆	—	17	2	no	—
272	C₄⋊C₁₆	—	17	2	no	—
273	C₂²⋊C₁₆	—	17	1	no	—
274	C₂²⋊C₁₆	—	17	1	no	—
275	C₂²⋊C₁₆	—	17	1	no	—
276	C₂²⋊C₁₆	—	17	2	no	—
277	C₂²⋊C₁₆	—	17	2	no	—
278	C₂²⋊C₁₆	—	17	1	no	—
279	C₂²⋊C₁₆	—	17	2	no	—
280	C₂²⋊C₁₆	—	17	2	no	—
281	#346	—	17	2	no	—
282	C₄×C₁₆	—	17	2	no	—
283	C₂×C₁₇	—	2	2	no	—
284	C₂×C₁₇	—	4	1	no	—
285	C₂×C₁₇	#2972	1	1	yes	characteristic
286	C₂×C₁₇	C₂²×M₃₂	1	1	yes	characteristic
287	C₂×C₁₇	C₂×#504	1	1	yes	characteristic
288	D₁₇	—	2	2	no	—
289	D₁₇	—	2	2	no	—
290	D₁₇	—	4	1	no	—
291	C₂²×D₄	—	17	1	no	—
292	C₂³×C₄	—	17	1	no	—
293	C₂³×C₄	—	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	—	17	1	no	—
303	C₂²×C₈	—	17	1	no	—
304	C₂²×C₈	—	68	2	no	—
305	C₂²×C₈	—	68	2	no	—
306	C₂²×C₈	C₂×#595	1	1	yes	characteristic
307	C₂²×C₈	C₂×#595	1	1	yes	characteristic
308	C₄×D₄	—	17	1	no	—
309	C₄×D₄	—	17	1	no	—
310	C₄×D₄	—	17	1	no	—
311	C₄×D₄	—	17	1	no	—
312	C₄×D₄	—	17	1	no	—
313	C₄×D₄	—	17	1	no	—
314	C₄×D₄	—	17	1	no	—
315	C₄×D₄	C₂×#595	1	1	yes	characteristic
316	C₂×C₄⋊C₄	—	17	1	no	—
317	C₂×C₂²⋊C₄	—	17	1	no	—
318	C₂×C₂²⋊C₄	—	17	1	no	—
319	C₂×C₄²	—	17	1	no	—
320	M₃₂	—	68	2	no	—
321	M₃₂	—	68	2	no	—
322	C₂×C₁₆	—	17	2	no	—
323	C₂×C₁₆	—	17	2	no	—
324	C₂×C₁₆	—	17	2	no	—
325	C₂×C₁₆	—	17	2	no	—
326	C₂×C₁₆	—	68	2	no	—
327	C₂×C₁₆	—	68	2	no	—
328	C₄⋊C₈	—	17	1	no	—
329	C₄⋊C₈	—	17	1	no	—
330	C₄⋊C₈	—	17	1	no	—
331	C₄⋊C₈	C₂×#595	1	1	yes	characteristic
332	C₂²⋊C₈	—	17	1	no	—
333	C₂²⋊C₈	—	17	1	no	—
334	C₂²⋊C₈	—	17	1	no	—
335	C₂²⋊C₈	—	17	1	no	—
336	C₂²⋊C₈	—	17	1	no	—
337	C₂²⋊C₈	—	17	1	no	—
338	C₂²⋊C₈	C₂×#595	1	1	yes	characteristic
339	C₂²⋊C₈	C₂×#595	1	1	yes	characteristic
340	C₄×C₈	—	17	1	no	—
341	C₄×C₈	—	17	1	no	—
342	C₄×C₈	—	17	1	no	—
343	C₄×C₈	C₂×#595	1	1	yes	characteristic
344	C₁₇	#33488	1	1	yes	characteristic, complemented, Sylow
345	C₂⁴	—	17	1	no	—
346	C₂⁴	—	17	1	no	—
347	C₂×D₄	—	17	1	no	—
348	C₂×D₄	—	17	1	no	—
349	C₂×D₄	—	17	1	no	—
350	C₂×D₄	—	34	4	no	—
351	C₂×D₄	#63242	1	1	yes	characteristic
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	—	68	1	no	—
364	C₂²×C₄	—	68	1	no	—
365	C₂²×C₄	—	68	1	no	—
366	C₂²×C₄	—	68	1	no	—
367	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
368	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
369	C₂×C₈	—	4	1	no	—
370	C₂×C₈	—	4	1	no	—
371	C₂×C₈	—	17	1	no	—
372	C₂×C₈	—	17	1	no	—
373	C₂×C₈	—	17	1	no	—
374	C₂×C₈	—	17	1	no	—
375	C₂×C₈	—	34	2	no	—
376	C₂×C₈	—	34	2	no	—
377	C₂×C₈	—	34	2	no	—
378	C₂×C₈	—	34	2	no	—
379	C₂×C₈	—	34	2	no	—
380	C₂×C₈	—	68	1	no	—
381	C₂×C₈	—	68	1	no	—
382	C₂×C₈	—	68	1	no	—
383	C₂×C₈	—	68	1	no	—
384	C₂×C₈	—	68	1	no	—
385	C₂×C₈	C₂²×#595	1	1	yes	characteristic
386	C₂×C₈	C₂²×#595	1	1	yes	characteristic
387	C₂×C₈	C₂²×#595	1	1	yes	characteristic
388	C₂×C₈	C₂²×#595	1	1	yes	characteristic
389	C₄⋊C₄	—	17	1	no	—
390	C₄⋊C₄	—	17	1	no	—
391	C₄⋊C₄	—	17	1	no	—
392	C₄⋊C₄	#63242	1	1	yes	characteristic
393	C₂²⋊C₄	—	17	1	no	—
394	C₂²⋊C₄	—	17	1	no	—
395	C₂²⋊C₄	—	17	1	no	—
396	C₂²⋊C₄	—	17	1	no	—
397	C₂²⋊C₄	—	17	1	no	—
398	C₂²⋊C₄	—	17	1	no	—
399	C₂²⋊C₄	#63242	1	1	yes	characteristic
400	C₂²⋊C₄	#63242	1	1	yes	characteristic
401	C₄²	—	17	1	no	—
402	C₄²	—	17	1	no	—
403	C₄²	—	17	1	no	—
404	C₄²	C₂²×#595	1	1	yes	characteristic
405	C₁₆	—	34	2	no	—
406	C₁₆	—	34	2	no	—
407	C₁₆	—	34	2	no	—
408	C₁₆	—	34	2	no	—
409	C₂³	—	17	1	no	—
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	—	34	2	no	—
416	C₂³	—	68	1	no	—
417	C₂³	—	68	1	no	—
418	C₂³	C₂×#63242	1	1	yes	characteristic
419	C₂³	C₂×#63242	1	1	yes	characteristic
420	D₄	—	2	2	no	—
421	D₄	—	17	4	no	—
422	D₄	—	34	2	no	—
423	D₄	—	34	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	17	1	no	—
429	C₂×C₄	—	17	1	no	—
430	C₂×C₄	—	17	1	no	—
431	C₂×C₄	—	17	1	no	—
432	C₂×C₄	—	17	1	no	—
433	C₂×C₄	—	34	2	no	—
434	C₂×C₄	—	34	2	no	—
435	C₂×C₄	—	34	1	no	—
436	C₂×C₄	—	34	1	no	—
437	C₂×C₄	—	34	1	no	—
438	C₂×C₄	—	34	1	no	—
439	C₂×C₄	—	34	1	no	—
440	C₂×C₄	—	34	1	no	—
441	C₂×C₄	—	68	1	no	—
442	C₂×C₄	—	68	1	no	—
443	C₂×C₄	—	68	1	no	—
444	C₂×C₄	—	68	1	no	—
445	C₂×C₄	—	68	1	no	—
446	C₂×C₄	—	68	1	no	—
447	C₂×C₄	C₂×#63242	1	1	yes	characteristic
448	C₂×C₄	C₂×#63242	1	1	yes	characteristic
449	C₂×C₄	C₂×#63242	1	1	yes	characteristic
450	C₂×C₄	C₂×#63242	1	1	yes	characteristic
451	C₂×C₄	C₂³×#595	1	1	yes	characteristic
452	C₈	—	2	1	no	—
453	C₈	—	2	1	no	—
454	C₈	—	2	1	no	—
455	C₈	—	2	1	no	—
456	C₈	—	17	2	no	—
457	C₈	—	34	1	no	—
458	C₈	—	34	1	no	—
459	C₈	—	34	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	17	2	no	—
466	C₂²	—	17	2	no	—
467	C₂²	—	34	1	no	—
468	C₂²	—	34	1	no	—
469	C₂²	—	34	1	no	—
470	C₂²	—	34	1	no	—
471	C₂²	—	34	1	no	—
472	C₂²	—	34	1	no	—
473	C₂²	—	34	1	no	—
474	C₂²	—	68	4	no	—
475	C₂²	—	68	4	no	—
476	C₂²	#11763865	1	2	yes	—
477	C₂²	C₂²×#63242	1	1	yes	characteristic
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	17	2	no	—
483	C₄	—	34	1	no	—
484	C₄	—	34	1	no	—
485	C₄	—	34	1	no	—
486	C₄	—	34	1	no	—
487	C₄	#11763876	1	1	yes	characteristic
488	C₄	#11763888	1	1	yes	characteristic
489	C₂	—	2	2	no	—
490	C₂	—	4	1	no	—
491	C₂	—	34	2	no	—
492	C₂	—	34	2	no	—
493	C₂	—	68	1	no	—
494	C₂	#14545632	1	1	yes	characteristic
495	C₂	C₂×#11763865	1	1	yes	characteristic
496	C₂	#14545749	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#595
commutator, socle	C₂²×C₁₇	C₂³×C₈
Fitting	C₈×D₄×C₁₇	C₄
prime radical	C₂×D₄×D₁₇	C₈
cosocle	C₂×#3622	C₂⁴
hypercenter	C₈×D₄	#595
hypocenter	C₁₇	#33488
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
1. #14545169	C₂	semidirect
2. #14545167	C₂	semidirect
3. #14545164	C₂	semidirect
4. #14545162	C₂	semidirect
5. #14545147	C₂	semidirect
6. #14545144	C₂	semidirect
7. #14545013	C₂	semidirect
8. #14545012	C₂	semidirect
9. C₂×#11763704	C₂	semidirect
10. #14545009	C₂	semidirect
12. C₂×#10587530	C₂²	semidirect
13. C₂×#10587538	C₂²	semidirect
14. C₂×#10587529	C₂²	semidirect
15. C₂²×#63216	C₂²	semidirect
16. #11763730	C₂²	semidirect
17. C₄⋊#63216	C₂²	semidirect
22. #11763704	C₂²	semidirect
23. #11763704	C₂²	semidirect
24. C₂²⋊#63216	C₂²	semidirect
25. C₂²⋊#63216	C₂²	semidirect
26. #11763697	C₂²	semidirect
27. #11763695	C₂²	semidirect
183. C₂²⋊D₁₇	M₃₂	semidirect
344. C₁₇	#33488	semidirect

Maximal subgroups

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

subgroup	index
#14545169	2
#14545167	2
#14545164	2
#14545162	2
#14545147	2
#14545144	2
#14545013	2
#14545012	2
C₂×#11763704	2
#14545009	2
C₈×D₄×D₁₇	2
#33488	17