Subgroups — #17978539

Order 4352.

710 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11763868	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#10587529	C₂	1	1	yes	maximal, characteristic, complemented
3	#14545167	C₂	1	1	yes	maximal, characteristic, complemented
4	#14545166	C₂	1	1	yes	maximal, characteristic, complemented
5	#14545165	C₂	1	1	yes	maximal, characteristic, complemented
6	#14545164	C₂	1	1	yes	maximal, characteristic, complemented
7	#14545163	C₂	1	1	yes	maximal, characteristic, complemented
8	#14545162	C₂	1	1	yes	maximal, characteristic, complemented
9	#14545162	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×#63216	C₂	1	1	yes	maximal, characteristic, complemented
11	#14545120	C₂	1	1	yes	maximal, characteristic, complemented
12	#14545015	C₂	1	1	yes	maximal, characteristic, complemented
13	#14545012	C₂	1	1	yes	maximal, characteristic, complemented
14	#14544994	C₂	1	1	yes	maximal, characteristic, complemented
15	#14537475	C₂	1	1	yes	maximal, characteristic
16	#11763868	—	2	4	no	—
17	C₂×#10587530	C₂²	1	1	yes	characteristic
18	C₂×#10587530	C₂²	1	1	yes	characteristic
19	C₂×#10587530	C₂²	1	1	yes	characteristic, complemented
20	C₂×#10587538	C₂²	1	1	yes	characteristic, complemented
21	C₂×#10587529	—	2	4	no	—
22	C₂×#10587529	C₂²	1	1	yes	characteristic
23	C₂×#10587529	C₂²	1	1	yes	characteristic
24	C₂×#10587529	C₂²	1	1	yes	characteristic
25	C₂×#10587529	C₂²	1	1	yes	characteristic
26	C₂×#10587529	C₂²	1	1	yes	characteristic, complemented
27	C₂²×#63216	C₂²	1	1	yes	characteristic
28	C₂²×#63216	C₂²	1	1	yes	characteristic
29	C₂²×#63216	C₂²	1	1	yes	characteristic, complemented
30	#11763730	C₂²	1	1	yes	characteristic, complemented
31	#11763730	C₂²	1	1	yes	characteristic, complemented
32	C₄⋊#63216	C₂²	1	1	yes	characteristic, complemented
33	C₄⋊#63216	C₂²	1	1	yes	characteristic, complemented
34	#11763704	C₂²	1	1	yes	characteristic
35	#11763704	C₂²	1	1	yes	characteristic
36	#11763704	C₂²	1	1	yes	characteristic, complemented
37	#11763704	C₂²	1	1	yes	characteristic, complemented
38	C₂²⋊#63216	C₂²	1	1	yes	characteristic
39	C₂²⋊#63216	C₂²	1	1	yes	characteristic
40	C₂²⋊#63216	C₂²	1	1	yes	characteristic, complemented
41	C₂²⋊#63216	C₂²	1	1	yes	characteristic, complemented
42	#11763698	C₂²	1	1	yes	characteristic, complemented
43	#11763697	C₂²	1	1	yes	characteristic, complemented
44	#11763695	C₂²	1	1	yes	characteristic, complemented
45	C₄×#63216	C₂²	1	1	yes	characteristic, complemented
46	C₂×#10587593	C₂²	1	1	yes	characteristic
47	C₂²×C₈×D₁₇	C₂²	1	1	yes	characteristic
48	#11763318	C₄	1	1	yes	characteristic
49	#11762882	C₄	1	1	yes	characteristic
50	#11762880	C₄	1	1	yes	characteristic
51	#11762878	C₄	1	1	yes	characteristic
52	D₄×#3622	C₂²	1	1	yes	characteristic
53	#11762874	C₂²	1	1	yes	characteristic
54	#11762872	C₂²	1	1	yes	characteristic
55	#11762872	C₂²	1	1	yes	characteristic
56	#11762834	C₄	1	1	yes	characteristic
57	#11762774	C₄	1	1	yes	characteristic
58	#11762771	C₄	1	1	yes	characteristic
59	#11762766	C₂²	1	1	yes	characteristic
60	C₁₇×#435	C₄	1	1	yes	characteristic
61	C₂×#63252	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
63	C₂×M₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
65	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
66	#10587625	C₈	1	1	yes	characteristic
67	#10587623	C₈	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	C₂²×#3622	C₂³	1	1	yes	characteristic
71	C₂²×#3622	C₂³	1	1	yes	characteristic
72	#10587593	—	2	2	no	—
73	#10587593	—	2	2	no	—
74	C₂×#63218	C₂×C₄	1	1	yes	characteristic
75	C₂×#63218	C₂×C₄	1	1	yes	characteristic
76	C₂×#63218	C₂×C₄	1	1	yes	characteristic
77	C₂×C₈×D₁₇	—	2	2	no	—
78	C₂×C₈×D₁₇	—	2	2	no	—
79	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
80	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
81	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
82	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
83	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
84	#10587582	C₈	1	1	yes	characteristic
85	#10587580	C₈	1	1	yes	characteristic
86	#10587570	C₈	1	1	yes	characteristic
87	#10587569	C₈	1	1	yes	characteristic
88	#10587568	C₈	1	1	yes	characteristic
89	#10587564	C₈	1	1	yes	characteristic
90	C₄×D₆₈	C₂×C₄	1	1	yes	characteristic
91	#10587558	C₂×C₄	1	1	yes	characteristic
92	#10587538	—	2	2	no	—
93	C₂×#63216	—	2	2	no	—
94	C₂×#63216	—	2	2	no	—
95	C₂×#63216	—	2	2	no	—
96	C₂×#63216	C₂³	1	1	yes	characteristic
97	C₂×#63216	C₂³	1	1	yes	characteristic
98	C₂×#63216	C₂³	1	1	yes	characteristic
99	C₂×#63216	C₂³	1	1	yes	characteristic
100	C₂×#63216	C₂³	1	1	yes	characteristic
101	C₂×#63216	C₂³	1	1	yes	characteristic
102	C₂×#63216	C₂³	1	1	yes	characteristic
103	C₂×#63216	C₂³	1	1	yes	characteristic
104	#10587530	—	2	2	no	—
105	#10587530	—	2	2	no	—
106	#10587530	—	2	2	no	—
107	#10587529	—	2	2	no	—
108	#10587529	—	2	2	no	—
109	#10587529	—	2	2	no	—
110	#10587529	—	2	2	no	—
111	#10587529	D₄	1	4	yes	complemented
112	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
113	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
114	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
115	C₁₇×#97	C₂×C₄	1	1	yes	characteristic
116	C₂²⋊#3622	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊#3622	C₂×C₄	1	1	yes	characteristic
118	#10587491	C₂×C₄	1	1	yes	characteristic
119	#10587491	C₂×C₄	1	1	yes	characteristic
120	#10587491	C₂×C₄	1	1	yes	characteristic
121	#10587491	C₂×C₄	1	1	yes	characteristic
122	#10587486	C₂×C₄	1	1	yes	characteristic
123	#10587485	C₂×C₄	1	1	yes	characteristic
124	#10587485	C₂×C₄	1	1	yes	characteristic
125	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
126	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
127	C₄×#3622	C₂³	1	1	yes	characteristic
128	C₂³×D₁₇	C₂×C₈	1	1	yes	characteristic
129	C₂×D₄×C₁₇	C₂×C₈	1	1	yes	characteristic
130	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₂²⋊D₁₇	C₂×C₈	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₇	C₂×C₈	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₇	C₂×C₈	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₇	C₂×C₈	1	1	yes	characteristic
136	C₂²×Dic₁₇	C₂×C₈	1	1	yes	characteristic
137	#63252	—	2	2	no	—
138	#63252	—	2	2	no	—
139	C₂×D₆₈	C₂×C₈	1	1	yes	characteristic
140	C₂×D₆₈	C₂×C₈	1	1	yes	characteristic
141	C₂×C₄×D₁₇	—	2	2	no	—
142	C₂×C₄×D₁₇	—	2	2	no	—
143	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
144	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
145	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
148	C₂×Dic₃₄	C₂×C₈	1	1	yes	characteristic
149	M₁₆×C₁₇	—	2	2	no	—
150	C₂×C₈×C₁₇	—	2	2	no	—
151	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
155	C₄⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
156	C₂²⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
157	C₂²⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
158	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
159	C₂²⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
160	C₂²⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
161	#63227	C₂×C₈	1	1	yes	characteristic
162	#63227	C₂×C₈	1	1	yes	characteristic
163	#63227	C₂×C₈	1	1	yes	characteristic
164	#63227	C₂×C₈	1	1	yes	characteristic
165	#63227	C₂×C₈	1	1	yes	characteristic
166	#63227	C₂×C₈	1	1	yes	characteristic
167	C₄⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
168	#63225	C₂×C₈	1	1	yes	characteristic
169	#63225	C₂×C₈	1	1	yes	characteristic
170	#63225	C₂×C₈	1	1	yes	characteristic
171	#63225	C₂×C₈	1	1	yes	characteristic
172	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
173	C₂×#3622	—	2	1	no	—
174	C₂×#3622	—	2	1	no	—
175	C₂×#3622	—	2	1	no	—
176	C₂×#3622	—	2	1	no	—
177	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
178	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
179	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
180	C₂×#3622	C₂⁴	1	1	yes	characteristic
181	#63218	—	2	2	no	—
182	#63218	—	2	2	no	—
183	#63218	—	2	2	no	—
184	C₈×D₁₇	—	2	2	no	—
185	C₈×D₁₇	—	2	2	no	—
186	C₈×D₁₇	—	2	1	no	—
187	C₈×D₁₇	—	2	1	no	—
188	C₈×D₁₇	—	2	1	no	—
189	C₈×D₁₇	—	2	1	no	—
190	C₈×D₁₇	C₂×D₄	1	2	yes	—
191	C₈×D₁₇	#41	1	2	yes	—
192	#63216	—	2	1	no	—
193	#63216	—	2	1	no	—
194	#63216	—	2	1	no	—
195	#63216	—	2	1	no	—
196	#63216	—	2	1	no	—
197	#63216	—	2	1	no	—
198	#63216	C₂×D₄	1	2	yes	—
199	#63216	C₂×D₄	1	2	yes	—
200	#33432	—	17	1	no	maximal, Sylow
201	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
202	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
203	C₂²×D₁₇	—	2	2	no	—
204	C₂²×D₁₇	—	2	2	no	—
205	C₂²×D₁₇	—	2	2	no	—
206	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
207	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
208	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
209	D₄×C₁₇	—	2	2	no	—
210	C₂×C₄×C₁₇	—	2	1	no	—
211	C₂×C₄×C₁₇	—	2	1	no	—
212	C₂×C₄×C₁₇	—	2	1	no	—
213	C₂×C₄×C₁₇	—	2	1	no	—
214	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
215	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
216	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
217	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
218	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
219	C₂²⋊D₁₇	—	2	2	no	—
220	C₂²⋊D₁₇	—	2	2	no	—
221	C₂²⋊D₁₇	—	2	2	no	—
222	C₂²⋊D₁₇	—	2	2	no	—
223	C₂×Dic₁₇	—	2	2	no	—
224	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
225	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
226	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
227	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
228	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
229	D₆₈	—	2	2	no	—
230	D₆₈	—	2	2	no	—
231	C₄×D₁₇	—	2	2	no	—
232	C₄×D₁₇	—	2	1	no	—
233	C₄×D₁₇	—	2	1	no	—
234	C₄×D₁₇	—	2	1	no	—
235	C₄×D₁₇	—	2	1	no	—
236	C₄×D₁₇	—	2	2	no	—
237	C₄×D₁₇	C₄×D₄	1	2	yes	—
238	C₄×D₁₇	#131	1	2	yes	—
239	Dic₃₄	—	2	2	no	—
240	C₈×C₁₇	—	2	1	no	—
241	C₈×C₁₇	—	2	1	no	—
242	C₈×C₁₇	—	2	1	no	—
243	C₈×C₁₇	C₄×D₄	1	2	yes	—
244	#3622	—	2	1	no	—
245	#3622	—	2	1	no	—
246	#3622	—	2	1	no	—
247	#3622	C₂²×D₄	1	1	yes	characteristic
248	#3622	C₂×#41	1	1	yes	characteristic
249	C₂×#504	—	17	1	no	—
250	C₂³×C₁₆	—	17	1	no	—
251	#2929	—	17	1	no	—
252	#2168	—	17	1	no	—
253	#2168	—	17	1	no	—
254	#2168	—	17	1	no	—
255	#2168	—	17	1	no	—
256	D₄×C₁₆	—	17	1	no	—
257	D₄×C₁₆	—	17	1	no	—
258	D₄×C₁₆	—	17	1	no	—
259	D₄×C₁₆	—	17	1	no	—
260	#2151	—	17	1	no	—
261	#2113	—	17	1	no	—
262	#2112	—	17	1	no	—
263	#2108	—	17	1	no	—
264	C₂²×C₁₇	—	2	1	no	—
265	C₂²×C₁₇	—	2	1	no	—
266	C₂²×C₁₇	—	2	1	no	—
267	C₂²×C₁₇	—	2	1	no	—
268	C₂²×C₁₇	—	2	1	no	—
269	C₂²×C₁₇	#504	1	2	yes	complemented
270	C₂²×C₁₇	C₂³×C₈	1	1	yes	characteristic
271	C₂×D₁₇	—	2	8	no	—
272	C₂×D₁₇	—	2	1	no	—
273	C₂×D₁₇	—	2	1	no	—
274	C₂×D₁₇	—	2	1	no	—
275	C₂×D₁₇	—	2	1	no	—
276	C₂×D₁₇	—	2	1	no	—
277	C₂×D₁₇	—	2	1	no	—
278	C₂×D₁₇	—	2	1	no	—
279	C₂×D₁₇	C₈×D₄	1	2	yes	—
280	C₂×D₁₇	#504	1	2	yes	complemented
281	C₄×C₁₇	—	2	1	no	—
282	C₄×C₁₇	—	2	1	no	—
283	C₄×C₁₇	—	2	1	no	—
284	C₄×C₁₇	—	2	1	no	—
285	C₄×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
286	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
287	Dic₁₇	—	2	1	no	—
288	Dic₁₇	—	2	1	no	—
289	Dic₁₇	—	2	1	no	—
290	Dic₁₇	—	2	1	no	—
291	Dic₁₇	C₈×D₄	1	2	yes	—
292	C₂×#131	—	17	1	no	—
293	C₂³×C₈	—	17	1	no	—
294	#525	—	17	1	no	—
295	#504	—	34	4	no	—
296	C₂×M₃₂	—	17	1	no	—
297	C₂×M₃₂	—	17	1	no	—
298	C₂×M₃₂	—	17	1	no	—
299	C₂×M₃₂	—	17	1	no	—
300	C₂²×C₁₆	—	17	1	no	—
301	C₂²×C₁₆	—	17	1	no	—
302	C₂²×C₁₆	—	17	1	no	—
303	C₂²×C₁₆	—	17	1	no	—
304	C₂²×C₁₆	—	17	1	no	—
305	C₂²×C₁₆	—	17	1	no	—
306	C₂²×C₁₆	—	17	1	no	—
307	C₂²×C₁₆	—	17	1	no	—
308	C₂²×C₁₆	—	34	4	no	—
309	#435	—	17	1	no	—
310	#435	—	17	1	no	—
311	#435	—	17	1	no	—
312	#435	#595	1	1	yes	characteristic
313	C₈×D₄	—	17	1	no	—
314	C₈×D₄	—	17	1	no	—
315	C₈×D₄	—	17	1	no	—
316	C₈×D₄	—	17	1	no	—
317	#424	—	17	1	no	—
318	#408	—	17	1	no	—
319	#407	—	17	1	no	—
320	#405	—	17	1	no	—
321	C₄⋊C₁₆	—	17	1	no	—
322	C₄⋊C₁₆	—	17	1	no	—
323	C₄⋊C₁₆	—	17	1	no	—
324	C₄⋊C₁₆	—	17	1	no	—
325	C₂²⋊C₁₆	—	17	1	no	—
326	C₂²⋊C₁₆	—	17	1	no	—
327	C₂²⋊C₁₆	—	17	1	no	—
328	C₂²⋊C₁₆	—	17	1	no	—
329	C₂²⋊C₁₆	—	17	1	no	—
330	C₂²⋊C₁₆	—	17	1	no	—
331	C₂²⋊C₁₆	—	17	1	no	—
332	C₂²⋊C₁₆	—	17	1	no	—
333	#346	—	17	1	no	—
334	#346	—	17	1	no	—
335	C₄×C₁₆	—	17	1	no	—
336	C₄×C₁₆	—	17	1	no	—
337	C₂×C₁₇	—	2	2	no	—
338	C₂×C₁₇	—	4	1	no	—
339	C₂×C₁₇	C₂×C₈×D₄	1	1	yes	characteristic
340	C₂×C₁₇	C₂×#504	1	1	yes	characteristic
341	C₂×C₁₇	C₂×#504	1	1	yes	characteristic
342	D₁₇	—	2	2	no	—
343	D₁₇	—	2	2	no	—
344	D₁₇	—	4	1	no	—
345	C₂×#41	—	17	1	no	—
346	C₂³×C₄	—	17	1	no	—
347	#131	—	34	2	no	—
348	#131	—	34	2	no	—
349	C₂×M₁₆	—	17	1	no	—
350	C₂×M₁₆	—	17	1	no	—
351	C₂×M₁₆	—	17	1	no	—
352	C₂×M₁₆	C₂×#595	1	1	yes	characteristic
353	C₂²×C₈	—	17	1	no	—
354	C₂²×C₈	—	17	1	no	—
355	C₂²×C₈	—	17	1	no	—
356	C₂²×C₈	—	17	1	no	—
357	C₂²×C₈	—	17	1	no	—
358	C₂²×C₈	—	17	1	no	—
359	C₂²×C₈	—	17	1	no	—
360	C₂²×C₈	—	34	2	no	—
361	C₂²×C₈	—	34	2	no	—
362	C₂²×C₈	C₂×#595	1	1	yes	characteristic
363	#123	—	17	1	no	—
364	#123	—	17	1	no	—
365	C₂²⋊Q₈	—	17	1	no	—
366	C₂²⋊Q₈	—	17	1	no	—
367	#121	—	17	1	no	—
368	#121	—	17	1	no	—
369	#120	—	17	1	no	—
370	#120	—	17	1	no	—
371	C₄×D₄	—	17	1	no	—
372	C₄×D₄	—	17	1	no	—
373	C₄×D₄	—	17	1	no	—
374	C₄×D₄	C₂×#595	1	1	yes	characteristic
375	#117	—	17	1	no	—
376	M₃₂	—	34	2	no	—
377	M₃₂	—	34	2	no	—
378	M₃₂	—	34	2	no	—
379	M₃₂	—	34	2	no	—
380	C₂×C₁₆	—	17	1	no	—
381	C₂×C₁₆	—	17	1	no	—
382	C₂×C₁₆	—	17	4	no	—
383	C₂×C₁₆	—	17	1	no	—
384	C₂×C₁₆	—	17	1	no	—
385	C₂×C₁₆	—	17	1	no	—
386	C₂×C₁₆	—	17	1	no	—
387	C₂×C₁₆	—	17	1	no	—
388	C₂×C₁₆	—	17	1	no	—
389	C₂×C₁₆	—	34	2	no	—
390	C₂×C₁₆	—	34	2	no	—
391	C₂×C₁₆	—	34	2	no	—
392	C₂×C₁₆	—	34	2	no	—
393	C₂×C₁₆	—	34	2	no	—
394	C₂×C₁₆	—	34	2	no	—
395	C₂×C₁₆	—	34	2	no	—
396	C₄⋊C₈	—	17	1	no	—
397	C₄⋊C₈	—	17	1	no	—
398	C₄⋊C₈	—	17	1	no	—
399	C₄⋊C₈	C₂×#595	1	1	yes	characteristic
400	C₂²⋊C₈	—	17	1	no	—
401	C₂²⋊C₈	—	17	1	no	—
402	C₂²⋊C₈	—	17	1	no	—
403	C₂²⋊C₈	—	17	1	no	—
404	C₂²⋊C₈	—	17	1	no	—
405	C₂²⋊C₈	—	17	1	no	—
406	C₂²⋊C₈	C₂×#595	1	1	yes	characteristic
407	C₂²⋊C₈	C₂×#595	1	1	yes	characteristic
408	#97	—	17	1	no	—
409	#97	C₂×#595	1	1	yes	characteristic
410	C₄×C₈	—	17	1	no	—
411	C₄×C₈	—	17	1	no	—
412	C₁₇	#33432	1	1	yes	characteristic, complemented, Sylow
413	C₂⁴	—	17	1	no	—
414	#41	—	34	2	no	—
415	#41	—	34	2	no	—
416	C₂×Q₈	—	17	1	no	—
417	C₂×D₄	—	17	1	no	—
418	C₂×D₄	—	17	1	no	—
419	C₂×D₄	—	17	1	no	—
420	C₂×D₄	—	17	1	no	—
421	C₂×D₄	—	17	1	no	—
422	C₂×D₄	—	17	1	no	—
423	C₂×D₄	#63242	1	1	yes	characteristic
424	C₂²×C₄	—	17	1	no	—
425	C₂²×C₄	—	17	1	no	—
426	C₂²×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	—	34	2	no	—
431	C₂²×C₄	—	34	2	no	—
432	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
433	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
434	M₁₆	—	2	2	no	—
435	M₁₆	—	34	2	no	—
436	M₁₆	—	34	2	no	—
437	M₁₆	—	34	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	17	1	no	—
440	C₂×C₈	—	17	2	no	—
441	C₂×C₈	—	17	2	no	—
442	C₂×C₈	—	17	1	no	—
443	C₂×C₈	—	17	1	no	—
444	C₂×C₈	—	17	1	no	—
445	C₂×C₈	—	34	1	no	—
446	C₂×C₈	—	34	1	no	—
447	C₂×C₈	—	34	1	no	—
448	C₂×C₈	—	34	1	no	—
449	C₂×C₈	—	34	2	no	—
450	C₂×C₈	—	34	1	no	—
451	C₂×C₈	—	34	1	no	—
452	C₂×C₈	—	34	1	no	—
453	C₂×C₈	—	34	1	no	—
454	C₂×C₈	—	34	2	no	—
455	C₂×C₈	C₂²×#595	1	1	yes	characteristic
456	C₂×C₈	C₂²×#595	1	1	yes	characteristic
457	C₂×C₈	C₂²×#595	1	1	yes	characteristic
458	C₂×C₈	C₂²×#595	1	1	yes	characteristic
459	C₄⋊C₄	—	17	1	no	—
460	C₄⋊C₄	—	17	1	no	—
461	C₄⋊C₄	—	17	1	no	—
462	C₄⋊C₄	—	17	1	no	—
463	C₄⋊C₄	—	17	1	no	—
464	C₄⋊C₄	#63242	1	1	yes	characteristic
465	C₂²⋊C₄	—	17	1	no	—
466	C₂²⋊C₄	—	17	1	no	—
467	C₂²⋊C₄	—	17	1	no	—
468	C₂²⋊C₄	—	17	1	no	—
469	C₂²⋊C₄	—	17	1	no	—
470	C₂²⋊C₄	—	17	1	no	—
471	C₂²⋊C₄	—	17	1	no	—
472	C₂²⋊C₄	—	17	1	no	—
473	C₂²⋊C₄	#63242	1	1	yes	characteristic
474	C₂²⋊C₄	#63242	1	1	yes	characteristic
475	C₄²	—	17	1	no	—
476	C₄²	C₂²×#595	1	1	yes	characteristic
477	C₁₆	—	17	2	no	—
478	C₁₆	—	17	2	no	—
479	C₁₆	—	34	1	no	—
480	C₁₆	—	34	1	no	—
481	C₁₆	—	34	1	no	—
482	C₁₆	—	34	1	no	—
483	C₁₆	—	34	1	no	—
484	C₁₆	—	34	1	no	—
485	C₂³	—	17	1	no	—
486	C₂³	—	17	1	no	—
487	C₂³	—	17	1	no	—
488	C₂³	—	34	2	no	—
489	C₂³	—	34	2	no	—
490	C₂³	—	34	2	no	—
491	C₂³	C₂×#63242	1	1	yes	characteristic
492	C₂³	C₂×#63242	1	1	yes	characteristic
493	Q₈	—	34	2	no	—
494	D₄	—	2	2	no	—
495	D₄	—	34	2	no	—
496	D₄	—	34	2	no	—
497	D₄	—	34	2	no	—
498	D₄	—	34	2	no	—
499	D₄	—	34	2	no	—
500	D₄	—	34	2	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	17	1	no	—
506	C₂×C₄	—	17	2	no	—
507	C₂×C₄	—	17	2	no	—
508	C₂×C₄	—	17	1	no	—
509	C₂×C₄	—	17	1	no	—
510	C₂×C₄	—	17	1	no	—
511	C₂×C₄	—	17	1	no	—
512	C₂×C₄	—	34	2	no	—
513	C₂×C₄	—	34	2	no	—
514	C₂×C₄	—	34	2	no	—
515	C₂×C₄	—	34	1	no	—
516	C₂×C₄	—	34	1	no	—
517	C₂×C₄	—	34	1	no	—
518	C₂×C₄	—	34	1	no	—
519	C₂×C₄	C₂×#63242	1	1	yes	characteristic
520	C₂×C₄	C₂×#63242	1	1	yes	characteristic
521	C₂×C₄	C₂×#63242	1	1	yes	characteristic
522	C₂×C₄	C₂×#63242	1	1	yes	characteristic
523	C₂×C₄	C₂³×#595	1	1	yes	characteristic
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	17	1	no	—
528	C₈	—	17	1	no	—
529	C₈	—	34	1	no	—
530	C₈	—	34	1	no	—
531	C₈	—	34	1	no	—
532	C₈	D₄×#595	1	2	yes	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	17	2	no	—
539	C₂²	—	17	2	no	—
540	C₂²	—	34	8	no	—
541	C₂²	—	34	1	no	—
542	C₂²	—	34	1	no	—
543	C₂²	—	34	1	no	—
544	C₂²	—	34	1	no	—
545	C₂²	—	34	1	no	—
546	C₂²	—	34	1	no	—
547	C₂²	—	34	1	no	—
548	C₂²	#11763868	1	2	yes	complemented
549	C₂²	C₂²×#63242	1	1	yes	characteristic
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	17	2	no	—
555	C₄	—	34	1	no	—
556	C₄	—	34	1	no	—
557	C₄	—	34	1	no	—
558	C₄	—	34	1	no	—
559	C₄	C₂×D₄×#595	1	1	yes	characteristic
560	C₄	D₁₇⋊#131	1	1	yes	characteristic
561	C₂	—	2	2	no	—
562	C₂	—	4	1	no	—
563	C₂	—	34	2	no	—
564	C₂	—	34	2	no	—
565	C₂	—	68	1	no	—
566	C₂	D₄×#63242	1	1	yes	characteristic
567	C₂	#14545749	1	1	yes	characteristic
568	C₂	C₂×#11763868	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#595
commutator, socle	C₂²×C₁₇	C₂³×C₈
Fitting	C₁₇×#435	C₄
prime radical	#11763318	C₄
cosocle	C₂×#3622	C₂⁴
hypercenter	#435	#595
hypocenter	C₁₇	#33432
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
1. C₂×#11763868	C₂	semidirect
2. C₂²×#10587529	C₂	semidirect
3. #14545167	C₂	semidirect
4. #14545166	C₂	semidirect
5. #14545165	C₂	semidirect
6. #14545164	C₂	semidirect
7. #14545163	C₂	semidirect
8. #14545162	C₂	semidirect
9. #14545162	C₂	semidirect
10. D₄×#63216	C₂	semidirect
11. #14545120	C₂	semidirect
12. #14545015	C₂	semidirect
13. #14545012	C₂	semidirect
14. #14544994	C₂	semidirect
19. C₂×#10587530	C₂²	semidirect
20. C₂×#10587538	C₂²	semidirect
26. C₂×#10587529	C₂²	semidirect
29. C₂²×#63216	C₂²	semidirect
30. #11763730	C₂²	semidirect
31. #11763730	C₂²	semidirect
32. C₄⋊#63216	C₂²	semidirect
33. C₄⋊#63216	C₂²	semidirect
36. #11763704	C₂²	semidirect
37. #11763704	C₂²	semidirect
40. C₂²⋊#63216	C₂²	semidirect
41. C₂²⋊#63216	C₂²	semidirect
42. #11763698	C₂²	semidirect
43. #11763697	C₂²	semidirect
44. #11763695	C₂²	semidirect
45. C₄×#63216	C₂²	semidirect
111. #10587529	D₄	semidirect
269. C₂²×C₁₇	#504	semidirect
280. C₂×D₁₇	#504	semidirect
412. C₁₇	#33432	semidirect
548. C₂²	#11763868	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11763868	2
C₂²×#10587529	2
#14545167	2
#14545166	2
#14545165	2
#14545164	2
#14545163	2
#14545162	2
D₄×#63216	2
#14545120	2
#14545015	2
#14545012	2
#14544994	2
#14537475	2
#33432	17