Subgroups — #35375294

Order 21248.

748 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24917461	C₂	1	1	yes	maximal, characteristic
2	#24916208	C₂	1	1	yes	maximal, characteristic, complemented
3	#24916199	C₂	1	1	yes	maximal, characteristic, complemented
4	#24906345	C₂	1	1	yes	maximal, characteristic, complemented
5	#24906293	C₂	1	1	yes	maximal, characteristic, complemented
6	#24906291	C₂	1	1	yes	maximal, characteristic, complemented
7	#24906290	C₂	1	1	yes	maximal, characteristic, complemented
8	#24906290	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×D₆₆₄	C₂	1	1	yes	maximal, characteristic, complemented
10	#24906255	C₂	1	1	yes	maximal, characteristic, complemented
11	#24906236	C₂	1	1	yes	maximal, characteristic, complemented
12	#24905912	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄⋊C₈×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#13050573	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#1589	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14581800	—	2	1	no	—
17	C₂×M₁₆×D₈₃	—	2	1	no	—
18	#19128248	C₂²	1	1	yes	characteristic
19	C₄×D₄×D₈₃	C₂²	1	1	yes	characteristic
20	#19128016	C₄	1	1	yes	characteristic
21	#19128013	C₄	1	1	yes	characteristic
22	#19127980	C₄	1	1	yes	characteristic
23	#19127979	C₄	1	1	yes	characteristic
24	#19127895	C₄	1	1	yes	characteristic
25	#19127894	C₄	1	1	yes	characteristic
26	#19127836	C₄	1	1	yes	characteristic
27	#19127833	C₄	1	1	yes	characteristic
28	C₄×D₆₆₄	C₂²	1	1	yes	characteristic
29	C₄×#13050575	C₂²	1	1	yes	characteristic
30	C₄×#13050575	C₂²	1	1	yes	characteristic
31	#19127779	C₂²	1	1	yes	characteristic
32	#19127778	C₂²	1	1	yes	characteristic, complemented
33	#19127775	—	2	1	no	—
34	#19127770	—	2	1	no	—
35	#19127770	—	2	1	no	—
36	#19127769	—	2	1	no	—
37	C₈×D₃₃₂	C₂²	1	1	yes	characteristic
38	C₈×D₃₃₂	C₂²	1	1	yes	characteristic, complemented
39	D₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	#19127766	C₂²	1	1	yes	characteristic
41	#19127752	C₂²	1	1	yes	characteristic
42	#19127723	C₂²	1	1	yes	characteristic
43	C₄⋊C₈×D₈₃	C₂²	1	1	yes	characteristic
44	#19127666	—	2	1	no	—
45	#19127663	—	2	1	no	—
46	C₄×#13050573	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₈₃	C₂²	1	1	yes	characteristic
48	#19127454	C₂²	1	1	yes	characteristic, complemented
49	#19127453	C₂²	1	1	yes	characteristic, complemented
50	#19127453	C₂²	1	1	yes	characteristic, complemented
51	#19127430	C₂²	1	1	yes	characteristic
52	#19127430	C₂²	1	1	yes	characteristic, complemented
53	D₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
54	D₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
55	#19127428	C₂²	1	1	yes	characteristic
56	#19127428	C₂²	1	1	yes	characteristic, complemented
57	#19127423	C₂²	1	1	yes	characteristic, complemented
58	#19127422	C₂²	1	1	yes	characteristic, complemented
59	C₈×C₈₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic
61	#436×C₈₃	C₂²	1	1	yes	characteristic
62	#436×C₈₃	C₂²	1	1	yes	characteristic, complemented
63	#335×C₈₃	C₂²	1	1	yes	characteristic, complemented
64	D₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
65	D₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
66	C₈²×C₈₃	C₂²	1	1	yes	characteristic, complemented
67	C₂×#13050590	—	2	1	no	—
68	C₂×D₄×D₈₃	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₄×D₈₃	—	2	1	no	—
70	C₂×D₆₆₄	C₂×C₄	1	1	yes	characteristic
71	C₂×#13050575	C₂×C₄	1	1	yes	characteristic
72	C₂×#13050575	C₂×C₄	1	1	yes	characteristic
73	#14581800	—	4	4	no	—
74	C₂×#13050574	—	2	1	no	—
75	C₂×#13050573	—	2	1	no	—
76	C₂×#13050573	—	2	1	no	—
77	C₂×#13050573	D₄	1	1	yes	characteristic
78	C₂×#13050573	D₄	1	1	yes	characteristic
79	M₁₆×D₈₃	—	4	4	no	—
80	C₂²×C₈₃⋊C₈	—	2	1	no	—
81	C₂×C₈×D₈₃	—	2	1	no	—
82	C₂×C₈×D₈₃	—	2	1	no	—
83	C₂×C₈×D₈₃	—	2	1	no	—
84	C₂×C₈×D₈₃	—	2	1	no	—
85	C₂×C₈×D₈₃	—	2	1	no	—
86	#14581791	C₂×C₄	1	1	yes	characteristic
87	#14581788	C₂×C₄	1	1	yes	characteristic
88	#14581778	—	2	1	no	—
89	#14581767	C₂×C₄	1	1	yes	characteristic
90	#14581765	—	2	1	no	—
91	#14581763	C₂×C₄	1	1	yes	characteristic
92	C₄×D₃₃₂	C₂³	1	1	yes	characteristic
93	C₄×D₃₃₂	C₂³	1	1	yes	characteristic
94	D₄×Dic₈₃	C₂×C₄	1	1	yes	characteristic
95	#14581754	C₂×C₄	1	1	yes	characteristic
96	C₄×C₂²⋊D₈₃	—	2	1	no	—
97	C₄×C₂²⋊D₈₃	—	2	1	no	—
98	(C₂²⋊D₈₃)⋊C₄	—	2	1	no	—
99	C₄⋊C₄×D₈₃	C₂×C₄	1	1	yes	characteristic
100	C₂²⋊C₄×D₈₃	—	2	1	no	—
101	C₄²×D₈₃	C₂³	1	1	yes	characteristic
102	#14581726	C₂×C₄	1	1	yes	characteristic
103	#14581725	C₂×C₄	1	1	yes	characteristic
104	#14581725	C₂×C₄	1	1	yes	characteristic
105	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
106	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
107	Dic₈₃⋊C₈	—	2	1	no	—
108	Dic₈₃⋊C₈	—	2	1	no	—
109	Dic₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
110	Dic₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
111	#14581714	C₂×C₄	1	1	yes	characteristic
112	#14581714	C₂×C₄	1	1	yes	characteristic
113	#14581713	C₂×C₄	1	1	yes	characteristic
114	#14581713	C₂×C₄	1	1	yes	characteristic
115	#14581712	C₂×C₄	1	1	yes	characteristic
116	#14581712	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
118	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
119	(C₂×D₈₃)⋊C₈	—	2	1	no	—
120	(C₂×D₈₃)⋊C₈	—	2	1	no	—
121	(C₂×D₈₃)⋊C₈	—	2	1	no	—
122	(C₂×D₈₃)⋊C₈	—	2	1	no	—
123	(C₂×D₈₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
124	(C₂×D₈₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
125	#14581702	D₄	1	1	yes	characteristic
126	#14581702	D₄	1	1	yes	characteristic
127	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
128	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
129	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
130	C₈×Dic₈₃	—	2	1	no	—
131	C₂×D₈×C₈₃	C₂×C₄	1	1	yes	characteristic
132	C₂×M₁₆×C₈₃	—	2	1	no	—
133	C₂×M₁₆×C₈₃	—	2	1	no	—
134	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
135	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
136	#107×C₈₃	C₂×C₄	1	1	yes	characteristic
137	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
138	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
139	#102×C₈₃	C₂×C₄	1	1	yes	characteristic
140	#102×C₈₃	C₂×C₄	1	1	yes	characteristic
141	C₂²⋊C₈×C₈₃	—	2	1	no	—
142	C₂²⋊C₈×C₈₃	—	2	1	no	—
143	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
145	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
146	C₂³×D₈₃	—	2	1	no	—
147	#13050590	—	4	2	no	—
148	#13050590	—	4	2	no	—
149	C₂×Dic₁₆₆	—	2	1	no	—
150	C₂×D₃₃₂	—	2	1	no	—
151	C₂×D₃₃₂	C₂²×C₄	1	1	yes	characteristic
152	C₂×D₃₃₂	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₂²⋊D₈₃	—	2	1	no	—
154	C₂×C₂²⋊D₈₃	—	2	1	no	—
155	C₂×C₂²⋊D₈₃	—	2	1	no	—
156	C₂×C₂²⋊D₈₃	—	2	1	no	—
157	D₄×D₈₃	—	2	2	no	—
158	D₄×D₈₃	—	4	1	no	—
159	C₂²×Dic₈₃	—	2	1	no	—
160	C₂×C₄×D₈₃	—	2	1	no	—
161	C₂×C₄×D₈₃	—	2	1	no	—
162	C₂×C₄×D₈₃	—	2	1	no	—
163	C₂×C₄×D₈₃	—	2	1	no	—
164	C₂×C₄×D₈₃	—	4	2	no	—
165	C₂×C₄×D₈₃	—	4	2	no	—
166	C₂×C₄×D₈₃	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₄×D₈₃	C₂×D₄	1	1	yes	characteristic
168	C₂×C₄×D₈₃	#41	1	1	yes	characteristic
169	D₆₆₄	—	2	2	no	—
170	#13050575	—	2	2	no	—
171	#13050575	—	4	1	no	—
172	#13050574	—	4	2	no	—
173	#13050573	—	2	2	no	—
174	#13050573	—	4	2	no	—
175	#13050573	—	4	2	no	—
176	#13050573	D₈	1	4	yes	complemented
177	C₂×C₈₃⋊C₈	—	2	1	no	—
178	C₂×C₈₃⋊C₈	—	2	1	no	—
179	C₂×C₈₃⋊C₈	—	2	1	no	—
180	C₂×C₈₃⋊C₈	—	4	2	no	—
181	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
185	C₈×D₈₃	—	4	2	no	—
186	C₈×D₈₃	—	4	2	no	—
187	C₈×D₈₃	—	4	2	no	—
188	C₈×D₈₃	—	4	2	no	—
189	C₈×D₈₃	—	4	2	no	—
190	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
191	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
192	Dic₈₃⋊C₄	—	2	1	no	—
193	Dic₈₃⋊C₄	—	2	1	no	—
194	C₂²⋊Dic₈₃	—	2	1	no	—
195	C₂²⋊Dic₈₃	—	2	1	no	—
196	(C₂×D₈₃)⋊C₄	—	2	1	no	—
197	(C₂×D₈₃)⋊C₄	—	2	1	no	—
198	(C₂×D₈₃)⋊C₄	—	2	1	no	—
199	(C₂×D₈₃)⋊C₄	—	2	1	no	—
200	C₄×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
201	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
202	C₄×Dic₈₃	#41	1	1	yes	characteristic
203	C₂×D₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
204	C₂×D₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₄×C₈₃	—	2	1	no	—
206	C₂²×C₄×C₈₃	—	2	1	no	—
207	D₈×C₈₃	—	4	1	no	—
208	M₁₆×C₈₃	—	4	2	no	—
209	M₁₆×C₈₃	—	4	2	no	—
210	C₂×C₈×C₈₃	—	2	1	no	—
211	C₂×C₈×C₈₃	—	2	1	no	—
212	C₂×C₈×C₈₃	—	2	1	no	—
213	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
214	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
215	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
216	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
217	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
218	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
219	C₂²⋊C₄×C₈₃	—	2	1	no	—
220	C₂²⋊C₄×C₈₃	—	2	1	no	—
221	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
222	C₂³×C₈₃	—	2	1	no	—
223	C₂³×C₈₃	—	2	1	no	—
224	C₂²×D₈₃	—	2	1	no	—
225	C₂²×D₈₃	—	2	1	no	—
226	C₂²×D₈₃	—	4	2	no	—
227	C₂²×D₈₃	—	4	2	no	—
228	C₂²×D₈₃	—	8	1	no	—
229	C₂²×D₈₃	C₄×D₄	1	1	yes	characteristic
230	D₄×C₈₃	—	2	1	no	—
231	D₄×C₈₃	—	2	1	no	—
232	D₄×C₈₃	—	2	1	no	—
233	D₄×C₈₃	—	2	1	no	—
234	C₂×C₄×C₈₃	—	2	1	no	—
235	C₂×C₄×C₈₃	—	2	1	no	—
236	C₂×C₄×C₈₃	—	4	1	no	—
237	C₂×C₄×C₈₃	—	4	1	no	—
238	C₂×C₄×C₈₃	—	4	1	no	—
239	C₂×C₄×C₈₃	—	4	1	no	—
240	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
241	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
243	C₂²⋊D₈₃	—	4	2	no	—
244	C₂²⋊D₈₃	—	4	2	no	—
245	C₂²⋊D₈₃	—	4	2	no	—
246	C₂²⋊D₈₃	—	8	1	no	—
247	C₂×Dic₈₃	—	2	1	no	—
248	C₂×Dic₈₃	—	2	1	no	—
249	C₂×Dic₈₃	—	4	2	no	—
250	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
251	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
252	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
253	D₃₃₂	—	2	1	no	—
254	D₃₃₂	—	2	1	no	—
255	D₃₃₂	—	2	1	no	—
256	D₃₃₂	—	4	2	no	—
257	D₃₃₂	#131	1	2	yes	complemented
258	C₄×D₈₃	—	2	1	no	—
259	C₄×D₈₃	—	2	1	no	—
260	C₄×D₈₃	—	4	1	no	—
261	C₄×D₈₃	—	4	2	no	—
262	C₄×D₈₃	—	4	1	no	—
263	C₄×D₈₃	—	4	1	no	—
264	C₄×D₈₃	—	4	1	no	—
265	C₄×D₈₃	—	4	1	no	—
266	C₄×D₈₃	—	4	2	no	—
267	C₄×D₈₃	C₂×D₈	1	2	yes	—
268	C₄×D₈₃	#135	1	2	yes	—
269	Dic₁₆₆	—	4	2	no	—
270	C₈×C₈₃	—	2	2	no	—
271	C₈×C₈₃	—	2	1	no	—
272	C₈×C₈₃	—	2	1	no	—
273	C₈×C₈₃	—	2	1	no	—
274	C₈×C₈₃	—	4	1	no	—
275	C₈×C₈₃	—	4	1	no	—
276	C₈×C₈₃	C₂×D₈	1	2	yes	—
277	C₈₃⋊C₈	—	2	1	no	—
278	C₈₃⋊C₈	—	2	1	no	—
279	C₈₃⋊C₈	—	2	1	no	—
280	C₈₃⋊C₈	—	4	1	no	—
281	C₈₃⋊C₈	—	4	1	no	—
282	C₈₃⋊C₈	—	4	1	no	—
283	C₈₃⋊C₈	C₂×D₈	1	2	yes	—
284	C₂²×C₈₃	—	4	1	no	—
285	C₂²×C₈₃	—	4	1	no	—
286	C₂²×C₈₃	—	4	1	no	—
287	C₂²×C₈₃	—	4	1	no	—
288	C₂²×C₈₃	—	4	1	no	—
289	C₂²×C₈₃	—	4	1	no	—
290	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
291	C₂×D₈₃	—	2	1	no	—
292	C₂×D₈₃	—	2	1	no	—
293	C₂×D₈₃	—	2	2	no	—
294	C₂×D₈₃	—	4	1	no	—
295	C₂×D₈₃	—	4	1	no	—
296	C₂×D₈₃	—	4	1	no	—
297	C₂×D₈₃	—	4	1	no	—
298	C₂×D₈₃	—	4	1	no	—
299	C₂×D₈₃	—	8	4	no	—
300	C₂×D₈₃	C₄×D₈	1	2	yes	—
301	C₄×C₈₃	—	2	1	no	—
302	C₄×C₈₃	—	4	1	no	—
303	C₄×C₈₃	—	4	1	no	—
304	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
305	C₄×C₈₃	#568	1	1	yes	characteristic
306	C₄×C₈₃	C₂²×D₈	1	1	yes	characteristic
307	C₄×C₈₃	C₂×#135	1	1	yes	characteristic
308	Dic₈₃	—	2	1	no	—
309	Dic₈₃	—	2	1	no	—
310	Dic₈₃	—	4	1	no	—
311	Dic₈₃	—	4	1	no	—
312	Dic₈₃	C₄×D₈	1	2	yes	—
313	#17994	—	83	1	no	maximal, Sylow
314	C₂×C₈₃	—	8	1	no	—
315	C₂×C₈₃	—	8	1	no	—
316	C₂×C₈₃	#2933	1	1	yes	characteristic
317	C₂×C₈₃	C₂×C₄×D₈	1	1	yes	characteristic
318	C₂×C₈₃	#2956	1	1	yes	characteristic
319	D₈₃	—	2	2	no	—
320	D₈₃	—	4	2	no	—
321	D₈₃	—	8	1	no	—
322	#3100	—	83	1	no	—
323	#2935	—	83	1	no	—
324	D₄×M₁₆	—	83	1	no	—
325	#1589	—	83	1	no	—
326	#1589	D₈₃	1	1	yes	characteristic, complemented
327	#1581	—	83	1	no	—
328	#1581	—	83	1	no	—
329	#1581	—	83	1	no	—
330	#1581	—	83	1	no	—
331	C₈×D₈	—	83	1	no	—
332	C₈×D₈	—	83	1	no	—
333	#1571	—	83	1	no	—
334	#1492	—	83	1	no	—
335	C₂×D₄⋊C₈	—	83	1	no	—
336	C₈×M₁₆	—	83	1	no	—
337	C₈₃	#17994	1	1	yes	characteristic, complemented, Sylow
338	C₂×#131	—	166	1	no	—
339	C₂²×M₁₆	—	166	1	no	—
340	#532	—	83	1	no	—
341	C₂×C₄×D₄	—	83	1	no	—
342	#480	—	83	1	no	—
343	#480	—	83	1	no	—
344	#474	—	83	1	no	—
345	#474	—	83	1	no	—
346	#459	—	83	1	no	—
347	#459	—	83	1	no	—
348	#447	—	83	1	no	—
349	#447	—	83	1	no	—
350	C₄×D₈	—	83	1	no	—
351	C₄×D₈	—	83	1	no	—
352	C₄×D₈	—	83	1	no	—
353	C₄×D₈	C₂×D₈₃	1	1	yes	characteristic
354	#436	—	83	1	no	—
355	#436	—	83	1	no	—
356	#436	C₂×D₈₃	1	1	yes	characteristic
357	#436	C₂×D₈₃	1	1	yes	characteristic, complemented
358	#435	—	166	1	no	—
359	#435	—	166	1	no	—
360	#435	—	166	1	no	—
361	#435	—	166	1	no	—
362	C₈×D₄	—	83	1	no	—
363	C₈×D₄	—	83	1	no	—
364	C₈×D₄	—	83	1	no	—
365	C₈×D₄	—	83	1	no	—
366	#431	—	83	1	no	—
367	#423	—	83	1	no	—
368	C₂×C₄⋊C₈	—	83	1	no	—
369	#408	—	166	1	no	—
370	#407	—	166	1	no	—
371	C₄×M₁₆	—	83	1	no	—
372	C₂×C₄×C₈	—	83	1	no	—
373	#335	—	83	1	no	—
374	#335	—	83	1	no	—
375	#335	—	83	1	no	—
376	#335	C₂×D₈₃	1	1	yes	characteristic, complemented
377	D₄⋊C₈	—	83	1	no	—
378	D₄⋊C₈	—	83	1	no	—
379	D₄⋊C₈	—	83	1	no	—
380	D₄⋊C₈	—	83	1	no	—
381	D₄⋊C₈	—	83	1	no	—
382	D₄⋊C₈	—	83	1	no	—
383	D₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic
384	D₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic, complemented
385	#322	—	83	1	no	—
386	#322	—	83	1	no	—
387	C₈²	—	83	1	no	—
388	C₈²	C₂×D₈₃	1	1	yes	characteristic, complemented
389	C₂×#41	—	166	1	no	—
390	C₂²×D₄	—	83	1	no	—
391	C₂³×C₄	—	166	1	no	—
392	C₂×D₈	—	83	1	no	—
393	C₂×D₈	—	83	1	no	—
394	C₂×D₈	—	83	1	no	—
395	C₂×D₈	C₄×D₈₃	1	1	yes	characteristic
396	#131	—	332	4	no	—
397	C₂×M₁₆	—	2	1	no	—
398	C₂×M₁₆	—	2	1	no	—
399	C₂×M₁₆	—	332	4	no	—
400	C₂×M₁₆	—	83	1	no	—
401	C₂×M₁₆	—	83	1	no	—
402	C₂×M₁₆	—	166	1	no	—
403	C₂×M₁₆	—	166	1	no	—
404	C₂×M₁₆	—	166	1	no	—
405	C₂²×C₈	—	166	1	no	—
406	C₂²×C₈	—	166	1	no	—
407	C₂²×C₈	—	166	1	no	—
408	C₂²×C₈	—	166	1	no	—
409	C₂²×C₈	—	166	1	no	—
410	C₂²×C₈	—	166	1	no	—
411	C₄⋊Q₈	—	83	1	no	—
412	#127	—	83	1	no	—
413	#124	—	166	1	no	—
414	#121	—	83	1	no	—
415	#121	—	83	1	no	—
416	#121	—	166	1	no	—
417	C₄×D₄	—	83	1	no	—
418	C₄×D₄	—	83	1	no	—
419	C₄×D₄	—	83	1	no	—
420	C₄×D₄	—	83	1	no	—
421	C₄×D₄	—	166	1	no	—
422	C₄×D₄	—	166	1	no	—
423	C₄×D₄	—	166	1	no	—
424	C₄×D₄	C₂²×D₈₃	1	1	yes	characteristic
425	C₄×D₄	C₂²×D₈₃	1	1	yes	characteristic
426	C₂×C₄⋊C₄	—	83	1	no	—
427	C₂×C₂²⋊C₄	—	166	1	no	—
428	C₂×C₄²	—	83	1	no	—
429	#107	—	83	1	no	—
430	#107	—	83	1	no	—
431	#107	—	83	1	no	—
432	#107	C₄×D₈₃	1	1	yes	characteristic
433	C₄⋊C₈	—	83	1	no	—
434	C₄⋊C₈	—	83	1	no	—
435	C₄⋊C₈	—	83	1	no	—
436	C₄⋊C₈	—	83	1	no	—
437	C₄⋊C₈	—	166	1	no	—
438	C₄⋊C₈	—	166	1	no	—
439	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
440	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
441	#102	—	83	1	no	—
442	#102	—	83	1	no	—
443	#102	—	83	1	no	—
444	#102	—	83	1	no	—
445	#102	—	83	1	no	—
446	#102	—	83	1	no	—
447	#102	C₄×D₈₃	1	1	yes	characteristic
448	#102	C₄×D₈₃	1	1	yes	characteristic
449	C₂²⋊C₈	—	2	1	no	—
450	C₂²⋊C₈	—	2	1	no	—
451	C₂²⋊C₈	—	83	1	no	—
452	C₂²⋊C₈	—	83	1	no	—
453	C₂²⋊C₈	—	166	1	no	—
454	C₂²⋊C₈	—	166	1	no	—
455	C₂²⋊C₈	—	166	1	no	—
456	C₂²⋊C₈	—	166	1	no	—
457	C₂²⋊C₈	—	166	1	no	—
458	C₂²⋊C₈	—	166	1	no	—
459	#97	—	83	1	no	—
460	#97	—	83	1	no	—
461	C₄×C₈	—	83	1	no	—
462	C₄×C₈	—	83	1	no	—
463	C₄×C₈	—	83	1	no	—
464	C₄×C₈	—	166	1	no	—
465	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
466	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
467	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
468	C₂⁴	—	166	1	no	—
469	#41	—	332	2	no	—
470	#41	—	332	2	no	—
471	C₂×Q₈	—	166	1	no	—
472	C₂×D₄	—	332	1	no	—
473	C₂×D₄	—	83	1	no	—
474	C₂×D₄	—	83	1	no	—
475	C₂×D₄	—	166	1	no	—
476	C₂×D₄	—	166	1	no	—
477	C₂×D₄	—	166	1	no	—
478	C₂×D₄	—	166	1	no	—
479	C₂×D₄	—	166	2	no	—
480	C₂×D₄	—	166	1	no	—
481	C₂×D₄	C₂×C₄×D₈₃	1	1	yes	characteristic
482	C₂×D₄	C₂×C₄×D₈₃	1	1	yes	characteristic
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	332	2	no	—
486	C₂²×C₄	—	332	2	no	—
487	C₂²×C₄	—	83	1	no	—
488	C₂²×C₄	—	83	1	no	—
489	C₂²×C₄	—	83	1	no	—
490	C₂²×C₄	—	166	1	no	—
491	C₂²×C₄	—	166	1	no	—
492	C₂²×C₄	—	166	1	no	—
493	C₂²×C₄	—	166	1	no	—
494	C₂²×C₄	—	166	1	no	—
495	D₈	—	4	1	no	—
496	D₈	—	332	1	no	—
497	D₈	—	166	2	no	—
498	D₈	—	166	2	no	—
499	M₁₆	—	4	2	no	—
500	M₁₆	—	4	2	no	—
501	M₁₆	—	332	2	no	—
502	M₁₆	—	332	2	no	—
503	M₁₆	—	332	2	no	—
504	M₁₆	—	83	4	no	—
505	M₁₆	—	166	2	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	332	2	no	—
510	C₂×C₈	—	332	2	no	—
511	C₂×C₈	—	332	2	no	—
512	C₂×C₈	—	332	2	no	—
513	C₂×C₈	—	332	2	no	—
514	C₂×C₈	—	332	2	no	—
515	C₂×C₈	—	83	1	no	—
516	C₂×C₈	—	83	1	no	—
517	C₂×C₈	—	83	1	no	—
518	C₂×C₈	—	83	1	no	—
519	C₂×C₈	—	166	1	no	—
520	C₂×C₈	—	166	1	no	—
521	C₂×C₈	—	166	1	no	—
522	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
523	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
524	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
525	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
526	C₄⋊C₄	—	83	1	no	—
527	C₄⋊C₄	—	83	1	no	—
528	C₄⋊C₄	—	166	1	no	—
529	C₄⋊C₄	—	166	1	no	—
530	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
531	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
532	C₂²⋊C₄	—	2	1	no	—
533	C₂²⋊C₄	—	2	1	no	—
534	C₂²⋊C₄	—	166	1	no	—
535	C₂²⋊C₄	—	166	1	no	—
536	C₂²⋊C₄	—	166	1	no	—
537	C₂²⋊C₄	—	166	1	no	—
538	C₂²⋊C₄	—	166	1	no	—
539	C₂²⋊C₄	—	166	1	no	—
540	C₄²	—	83	1	no	—
541	C₄²	—	83	1	no	—
542	C₄²	—	83	1	no	—
543	C₄²	C₂³×D₈₃	1	1	yes	characteristic
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	332	2	no	—
547	C₂³	—	332	2	no	—
548	C₂³	—	83	1	no	—
549	C₂³	—	664	1	no	—
550	C₂³	—	166	1	no	—
551	C₂³	—	166	1	no	—
552	Q₈	—	332	2	no	—
553	D₄	—	2	1	no	—
554	D₄	—	2	1	no	—
555	D₄	—	2	1	no	—
556	D₄	—	2	1	no	—
557	D₄	—	332	2	no	—
558	D₄	—	332	2	no	—
559	D₄	—	332	2	no	—
560	D₄	—	332	2	no	—
561	D₄	—	83	2	no	—
562	D₄	—	664	1	no	—
563	D₄	—	166	1	no	—
564	D₄	—	166	1	no	—
565	D₄	—	166	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	332	1	no	—
573	C₂×C₄	—	332	2	no	—
574	C₂×C₄	—	332	2	no	—
575	C₂×C₄	—	332	2	no	—
576	C₂×C₄	—	332	1	no	—
577	C₂×C₄	—	332	1	no	—
578	C₂×C₄	—	332	1	no	—
579	C₂×C₄	—	332	1	no	—
580	C₂×C₄	—	83	1	no	—
581	C₂×C₄	—	83	2	no	—
582	C₂×C₄	—	83	2	no	—
583	C₂×C₄	—	83	1	no	—
584	C₂×C₄	—	83	1	no	—
585	C₂×C₄	—	166	1	no	—
586	C₂×C₄	—	166	1	no	—
587	C₂×C₄	—	166	1	no	—
588	C₂×C₄	—	166	1	no	—
589	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
590	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
591	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
592	C₈	—	2	2	no	—
593	C₈	—	2	1	no	—
594	C₈	—	2	1	no	—
595	C₈	—	2	1	no	—
596	C₈	—	4	1	no	—
597	C₈	—	4	1	no	—
598	C₈	—	332	1	no	—
599	C₈	—	332	1	no	—
600	C₈	—	332	1	no	—
601	C₈	—	83	2	no	—
602	C₈	—	166	1	no	—
603	C₈	—	166	1	no	—
604	C₈	—	166	1	no	—
605	C₈	D₈×D₈₃	1	2	yes	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	1	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	332	1	no	—
613	C₂²	—	332	1	no	—
614	C₂²	—	332	1	no	—
615	C₂²	—	332	1	no	—
616	C₂²	—	332	1	no	—
617	C₂²	—	83	2	no	—
618	C₂²	—	664	4	no	—
619	C₂²	—	166	2	no	—
620	C₂²	—	166	1	no	—
621	C₂²	—	166	1	no	—
622	C₂²	C₄×D₄×D₈₃	1	1	yes	characteristic
623	C₄	—	2	1	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	1	no	—
626	C₄	—	332	1	no	—
627	C₄	—	332	1	no	—
628	C₄	—	83	2	no	—
629	C₄	—	166	1	no	—
630	C₄	—	166	1	no	—
631	C₄	#131×D₈₃	1	1	yes	characteristic
632	C₄	#19128467	1	1	yes	characteristic
633	C₄	C₂×D₈×D₈₃	1	1	yes	characteristic
634	C₄	#135×D₈₃	1	1	yes	characteristic
635	C₂	—	8	1	no	—
636	C₂	—	8	1	no	—
637	C₂	—	332	2	no	—
638	C₂	—	664	1	no	—
639	C₂	—	166	2	no	—
640	C₂	#24916192	1	1	yes	characteristic
641	C₂	C₄×D₈×D₈₃	1	1	yes	characteristic
642	C₂	#24916368	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₃
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₄²	C₂³×D₈₃
Fitting	C₈₃×#1589	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	#24917461	C₂
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	#1589	D₈₃
hypocenter	C₈₃	#17994
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1589

Complements

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

N	H ≅ G/N	type
2. #24916208	C₂	semidirect
3. #24916199	C₂	semidirect
4. #24906345	C₂	semidirect
5. #24906293	C₂	semidirect
6. #24906291	C₂	semidirect
7. #24906290	C₂	semidirect
8. #24906290	C₂	semidirect
9. C₈×D₆₆₄	C₂	semidirect
10. #24906255	C₂	semidirect
11. #24906236	C₂	semidirect
12. #24905912	C₂	semidirect
13. D₄⋊C₈×D₈₃	C₂	semidirect
14. C₈×#13050573	C₂	semidirect
15. C₈₃×#1589	C₂	semidirect
32. #19127778	C₂²	semidirect
38. C₈×D₃₃₂	C₂²	semidirect
39. D₄×C₈₃⋊C₈	C₂²	semidirect
48. #19127454	C₂²	semidirect
49. #19127453	C₂²	semidirect
50. #19127453	C₂²	semidirect
52. #19127430	C₂²	semidirect
54. D₄⋊(C₈₃⋊C₈)	C₂²	semidirect
56. #19127428	C₂²	semidirect
57. #19127423	C₂²	semidirect
58. #19127422	C₂²	semidirect
59. C₈×C₈₃⋊C₈	C₂²	semidirect
62. #436×C₈₃	C₂²	semidirect
63. #335×C₈₃	C₂²	semidirect
65. D₄⋊C₈×C₈₃	C₂²	semidirect
66. C₈²×C₈₃	C₂²	semidirect
176. #13050573	D₈	semidirect
257. D₃₃₂	#131	semidirect
326. #1589	D₈₃	semidirect
337. C₈₃	#17994	semidirect
357. #436	C₂×D₈₃	semidirect
376. #335	C₂×D₈₃	semidirect
384. D₄⋊C₈	C₂×D₈₃	semidirect
388. C₈²	C₂×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
#24917461	2
#24916208	2
#24916199	2
#24906345	2
#24906293	2
#24906291	2
#24906290	2
C₈×D₆₆₄	2
#24906255	2
#24906236	2
#24905912	2
D₄⋊C₈×D₈₃	2
C₈×#13050573	2
C₈₃×#1589	2
#17994	83