Subgroups — #35375823

Order 21248.

794 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₈×D₈₃	C₂	1	1	yes	maximal, characteristic
2	#24916199	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×#13050573	C₂	1	1	yes	maximal, characteristic, complemented
4	#24906346	C₂	1	1	yes	maximal, characteristic, complemented
5	#24906345	C₂	1	1	yes	maximal, characteristic, complemented
6	#24906294	C₂	1	1	yes	maximal, characteristic, complemented
7	#24906293	C₂	1	1	yes	maximal, characteristic, complemented
8	#24906291	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#13050575	C₂	1	1	yes	maximal, characteristic, complemented
10	#24906255	C₂	1	1	yes	maximal, characteristic, complemented
11	#24906220	C₂	1	1	yes	maximal, characteristic, complemented
12	#24905886	C₂	1	1	yes	maximal, characteristic, complemented
13	#24905886	C₂	1	1	yes	maximal, characteristic, complemented
14	#24905742	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#1581	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₈×D₈₃	C₄	1	1	yes	characteristic
17	C₂²×#13050573	—	2	1	no	—
18	C₂×M₁₆×D₈₃	—	2	1	no	—
19	C₄×D₄×D₈₃	C₂²	1	1	yes	characteristic
20	C₄×D₄×D₈₃	C₂²	1	1	yes	characteristic
21	C₄×D₆₆₄	C₂²	1	1	yes	characteristic
22	D₈×Dic₈₃	C₄	1	1	yes	characteristic
23	#19127783	C₄	1	1	yes	characteristic
24	C₄×#13050575	C₂²	1	1	yes	characteristic
25	C₄×#13050575	C₂²	1	1	yes	characteristic
26	#19127781	C₄	1	1	yes	characteristic
27	#19127781	C₄	1	1	yes	characteristic
28	#19127780	C₂²	1	1	yes	characteristic, complemented
29	#19127779	C₂²	1	1	yes	characteristic, complemented
30	#19127778	C₂²	1	1	yes	characteristic, complemented
31	#19127775	—	2	1	no	—
32	#19127772	—	2	1	no	—
33	#19127770	—	2	1	no	—
34	#19127769	—	2	1	no	—
35	C₈×D₃₃₂	C₂²	1	1	yes	characteristic, complemented
36	D₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
37	#19127766	C₂²	1	1	yes	characteristic, complemented
38	#19127752	C₂²	1	1	yes	characteristic
39	#107×D₈₃	C₄	1	1	yes	characteristic
40	#19127723	C₂²	1	1	yes	characteristic
41	#19127723	C₂²	1	1	yes	characteristic
42	#102×D₈₃	C₄	1	1	yes	characteristic
43	#102×D₈₃	C₄	1	1	yes	characteristic
44	#19127663	—	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, complemented
52	#19127430	C₂²	1	1	yes	characteristic, complemented
53	D₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
54	D₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
55	#19127428	C₂²	1	1	yes	characteristic, complemented
56	#19127428	C₂²	1	1	yes	characteristic, complemented
57	#19127423	C₂²	1	1	yes	characteristic, complemented
58	C₈×C₈₃⋊C₈	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, complemented
62	C₈×D₄×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, complemented
65	D₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
66	#322×C₈₃	C₂²	1	1	yes	characteristic, complemented
67	C₂×D₄×D₈₃	C₂×C₄	1	1	yes	characteristic
68	C₂×D₄×D₈₃	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₄×D₈₃	—	2	1	no	—
70	C₂²×C₄×D₈₃	—	2	1	no	—
71	C₂×D₆₆₄	C₂×C₄	1	1	yes	characteristic
72	C₂×#13050575	C₂×C₄	1	1	yes	characteristic
73	C₂×#13050575	C₂×C₄	1	1	yes	characteristic
74	D₈×D₈₃	—	2	4	no	—
75	C₂×#13050574	—	2	1	no	—
76	C₂×#13050573	—	2	1	no	—
77	C₂×#13050573	—	2	1	no	—
78	C₂×#13050573	—	2	1	no	—
79	C₂×#13050573	—	2	1	no	—
80	C₂×#13050573	—	4	4	no	—
81	C₂×#13050573	D₄	1	1	yes	characteristic
82	C₂×#13050573	D₄	1	1	yes	characteristic
83	M₁₆×D₈₃	—	4	4	no	—
84	C₂²×C₈₃⋊C₈	—	2	1	no	—
85	C₂×C₈×D₈₃	—	2	1	no	—
86	C₂×C₈×D₈₃	—	2	1	no	—
87	C₂×C₈×D₈₃	C₂×C₄	1	1	yes	characteristic
88	C₂×C₈×D₈₃	C₂×C₄	1	1	yes	characteristic
89	C₄×D₃₃₂	C₂³	1	1	yes	characteristic
90	C₄×D₃₃₂	C₂³	1	1	yes	characteristic
91	D₄×Dic₈₃	C₂×C₄	1	1	yes	characteristic
92	D₄×Dic₈₃	C₂×C₄	1	1	yes	characteristic
93	#14581754	C₂×C₄	1	1	yes	characteristic
94	#14581754	C₂×C₄	1	1	yes	characteristic
95	C₄×C₂²⋊D₈₃	—	2	1	no	—
96	C₄×C₂²⋊D₈₃	—	2	1	no	—
97	(C₂²⋊D₈₃)⋊C₄	—	2	1	no	—
98	(C₂²⋊D₈₃)⋊C₄	—	2	1	no	—
99	C₄⋊C₄×D₈₃	C₂×C₄	1	1	yes	characteristic
100	C₄⋊C₄×D₈₃	C₂×C₄	1	1	yes	characteristic
101	C₂²⋊C₄×D₈₃	—	2	1	no	—
102	C₂²⋊C₄×D₈₃	—	2	1	no	—
103	C₄²×D₈₃	C₂³	1	1	yes	characteristic
104	#14581726	C₂×C₄	1	1	yes	characteristic
105	#14581725	C₂×C₄	1	1	yes	characteristic
106	#14581725	C₂×C₄	1	1	yes	characteristic
107	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
108	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
109	Dic₈₃⋊C₈	—	2	1	no	—
110	Dic₈₃⋊C₈	—	2	1	no	—
111	Dic₈₃⋊C₈	—	2	1	no	—
112	#14581714	C₂×C₄	1	1	yes	characteristic
113	#14581714	C₂×C₄	1	1	yes	characteristic
114	#14581713	C₂×C₄	1	1	yes	characteristic
115	#14581713	C₂×C₄	1	1	yes	characteristic
116	#14581712	C₂×C₄	1	1	yes	characteristic
117	#14581712	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
119	C₂²⋊(C₈₃⋊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	—	2	1	no	—
124	(C₂×D₈₃)⋊C₈	—	2	1	no	—
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	C₂×C₄	1	1	yes	characteristic
131	C₈×Dic₈₃	C₂×C₄	1	1	yes	characteristic
132	C₂×D₈×C₈₃	C₂×C₄	1	1	yes	characteristic
133	C₂×M₁₆×C₈₃	—	2	1	no	—
134	C₂²×C₈×C₈₃	—	2	1	no	—
135	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
136	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
137	#107×C₈₃	C₂×C₄	1	1	yes	characteristic
138	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
139	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
140	#102×C₈₃	C₂×C₄	1	1	yes	characteristic
141	#102×C₈₃	C₂×C₄	1	1	yes	characteristic
142	C₂²⋊C₈×C₈₃	—	2	1	no	—
143	C₂²⋊C₈×C₈₃	—	2	1	no	—
144	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
145	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
146	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
147	C₂³×D₈₃	—	2	1	no	—
148	C₂³×D₈₃	—	2	1	no	—
149	C₂×D₃₃₂	C₂²×C₄	1	1	yes	characteristic
150	C₂×D₃₃₂	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₂²⋊D₈₃	—	2	1	no	—
152	C₂×C₂²⋊D₈₃	—	2	1	no	—
153	D₄×D₈₃	—	2	2	no	—
154	D₄×D₈₃	—	2	2	no	—
155	D₄×D₈₃	—	4	1	no	—
156	D₄×D₈₃	—	4	1	no	—
157	C₂²×Dic₈₃	—	2	1	no	—
158	C₂²×Dic₈₃	—	2	1	no	—
159	C₂×C₄×D₈₃	—	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	—	2	1	no	—
165	C₂×C₄×D₈₃	—	4	2	no	—
166	C₂×C₄×D₈₃	—	4	2	no	—
167	C₂×C₄×D₈₃	—	4	2	no	—
168	C₂×C₄×D₈₃	—	4	2	no	—
169	C₂×C₄×D₈₃	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₄×D₈₃	C₂×D₄	1	1	yes	characteristic
171	C₂×C₄×D₈₃	#41	1	1	yes	characteristic
172	D₆₆₄	—	2	2	no	—
173	#13050575	—	2	2	no	—
174	#13050575	M₁₆	1	4	yes	complemented
175	#13050574	—	4	2	no	—
176	#13050573	—	2	2	no	—
177	#13050573	—	4	2	no	—
178	#13050573	—	4	2	no	—
179	#13050573	—	4	2	no	—
180	#13050573	—	4	2	no	—
181	#13050573	D₈	1	4	yes	complemented
182	C₂×C₈₃⋊C₈	—	2	1	no	—
183	C₂×C₈₃⋊C₈	—	2	1	no	—
184	C₂×C₈₃⋊C₈	—	2	1	no	—
185	C₂×C₈₃⋊C₈	—	4	2	no	—
186	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
189	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
190	C₈×D₈₃	—	2	2	no	—
191	C₈×D₈₃	—	4	1	no	—
192	C₈×D₈₃	—	4	2	no	—
193	C₈×D₈₃	—	4	2	no	—
194	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
195	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
196	Dic₈₃⋊C₄	—	2	1	no	—
197	Dic₈₃⋊C₄	—	2	1	no	—
198	C₂²⋊Dic₈₃	—	2	1	no	—
199	C₂²⋊Dic₈₃	—	2	1	no	—
200	(C₂×D₈₃)⋊C₄	—	2	1	no	—
201	(C₂×D₈₃)⋊C₄	—	2	1	no	—
202	(C₂×D₈₃)⋊C₄	—	2	1	no	—
203	(C₂×D₈₃)⋊C₄	—	2	1	no	—
204	C₄×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
205	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
206	C₄×Dic₈₃	#41	1	1	yes	characteristic
207	C₂×D₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
208	C₂×D₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
209	C₂²×C₄×C₈₃	—	2	1	no	—
210	C₂²×C₄×C₈₃	—	2	1	no	—
211	D₈×C₈₃	—	2	2	no	—
212	M₁₆×C₈₃	—	4	2	no	—
213	C₂×C₈×C₈₃	—	2	1	no	—
214	C₂×C₈×C₈₃	—	2	1	no	—
215	C₂×C₈×C₈₃	—	2	1	no	—
216	C₂×C₈×C₈₃	—	4	2	no	—
217	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
219	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
220	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
221	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
222	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
223	C₂²⋊C₄×C₈₃	—	2	1	no	—
224	C₂²⋊C₄×C₈₃	—	2	1	no	—
225	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
226	C₂³×C₈₃	—	2	1	no	—
227	C₂³×C₈₃	—	2	1	no	—
228	C₂²×D₈₃	—	2	1	no	—
229	C₂²×D₈₃	—	2	1	no	—
230	C₂²×D₈₃	—	4	2	no	—
231	C₂²×D₈₃	—	4	2	no	—
232	C₂²×D₈₃	—	4	2	no	—
233	C₂²×D₈₃	—	4	2	no	—
234	C₂²×D₈₃	—	8	1	no	—
235	C₂²×D₈₃	—	8	1	no	—
236	C₂²×D₈₃	C₄×D₄	1	1	yes	characteristic
237	D₄×C₈₃	—	2	1	no	—
238	D₄×C₈₃	—	2	1	no	—
239	D₄×C₈₃	—	2	1	no	—
240	D₄×C₈₃	C₂×M₁₆	1	2	yes	complemented
241	C₂×C₄×C₈₃	—	2	1	no	—
242	C₂×C₄×C₈₃	—	2	1	no	—
243	C₂×C₄×C₈₃	—	4	1	no	—
244	C₂×C₄×C₈₃	—	4	1	no	—
245	C₂×C₄×C₈₃	—	4	1	no	—
246	C₂×C₄×C₈₃	—	4	1	no	—
247	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
248	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
250	C₂²⋊D₈₃	—	4	2	no	—
251	C₂²⋊D₈₃	—	4	2	no	—
252	C₂×Dic₈₃	—	2	1	no	—
253	C₂×Dic₈₃	—	2	1	no	—
254	C₂×Dic₈₃	—	4	2	no	—
255	C₂×Dic₈₃	—	4	2	no	—
256	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
257	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
258	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
259	D₃₃₂	—	2	1	no	—
260	D₃₃₂	—	2	1	no	—
261	D₃₃₂	—	2	1	no	—
262	D₃₃₂	C₂×M₁₆	1	2	yes	complemented
263	C₄×D₈₃	—	2	1	no	—
264	C₄×D₈₃	—	2	1	no	—
265	C₄×D₈₃	—	4	1	no	—
266	C₄×D₈₃	—	4	2	no	—
267	C₄×D₈₃	—	4	2	no	—
268	C₄×D₈₃	—	4	1	no	—
269	C₄×D₈₃	—	4	1	no	—
270	C₄×D₈₃	—	4	1	no	—
271	C₄×D₈₃	—	4	1	no	—
272	C₄×D₈₃	—	4	2	no	—
273	C₄×D₈₃	—	4	2	no	—
274	C₄×D₈₃	C₂×D₈	1	2	yes	—
275	C₄×D₈₃	#135	1	2	yes	—
276	C₈×C₈₃	—	2	1	no	—
277	C₈×C₈₃	—	2	1	no	—
278	C₈×C₈₃	—	2	1	no	—
279	C₈×C₈₃	—	4	1	no	—
280	C₈×C₈₃	—	4	1	no	—
281	C₈×C₈₃	—	4	1	no	—
282	C₈×C₈₃	C₂×D₈	1	2	yes	complemented
283	C₈₃⋊C₈	—	2	1	no	—
284	C₈₃⋊C₈	—	2	1	no	—
285	C₈₃⋊C₈	—	4	1	no	—
286	C₈₃⋊C₈	—	4	1	no	—
287	C₈₃⋊C₈	—	4	1	no	—
288	C₈₃⋊C₈	C₂×M₁₆	1	2	yes	complemented
289	C₈₃⋊C₈	C₂×D₈	1	2	yes	complemented
290	C₂²×C₈₃	—	2	2	no	—
291	C₂²×C₈₃	—	4	1	no	—
292	C₂²×C₈₃	—	4	1	no	—
293	C₂²×C₈₃	—	4	1	no	—
294	C₂²×C₈₃	—	4	1	no	—
295	C₂²×C₈₃	—	4	1	no	—
296	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
297	C₂×D₈₃	—	2	1	no	—
298	C₂×D₈₃	—	2	1	no	—
299	C₂×D₈₃	—	2	2	no	—
300	C₂×D₈₃	—	4	1	no	—
301	C₂×D₈₃	—	4	1	no	—
302	C₂×D₈₃	—	4	1	no	—
303	C₂×D₈₃	—	4	1	no	—
304	C₂×D₈₃	—	4	1	no	—
305	C₂×D₈₃	—	8	4	no	—
306	C₂×D₈₃	—	8	4	no	—
307	C₂×D₈₃	C₄×D₈	1	2	yes	—
308	C₄×C₈₃	—	2	1	no	—
309	C₄×C₈₃	—	4	1	no	—
310	C₄×C₈₃	—	4	1	no	—
311	C₄×C₈₃	C₂²×M₁₆	1	1	yes	characteristic
312	C₄×C₈₃	#568	1	1	yes	characteristic
313	C₄×C₈₃	C₂²×D₈	1	1	yes	characteristic
314	C₄×C₈₃	C₂×#135	1	1	yes	characteristic
315	Dic₈₃	—	2	1	no	—
316	Dic₈₃	—	2	1	no	—
317	Dic₈₃	—	4	1	no	—
318	Dic₈₃	—	4	1	no	—
319	Dic₈₃	C₄×D₈	1	2	yes	—
320	M₁₆×D₈	—	83	1	no	maximal, Sylow
321	C₂×C₈₃	—	4	2	no	—
322	C₂×C₈₃	—	8	1	no	—
323	C₂×C₈₃	D₄×M₁₆	1	1	yes	characteristic
324	C₂×C₈₃	C₂×C₄×D₈	1	1	yes	characteristic
325	C₂×C₈₃	#2957	1	1	yes	characteristic
326	D₈₃	—	2	2	no	—
327	D₈₃	—	4	2	no	—
328	D₈₃	—	8	1	no	—
329	C₂×C₄×D₈	—	83	1	no	—
330	D₄×M₁₆	—	83	1	no	—
331	D₄×M₁₆	—	83	1	no	—
332	#1589	—	83	1	no	—
333	#1589	—	83	1	no	—
334	#1581	—	83	1	no	—
335	#1581	—	83	1	no	—
336	#1581	—	83	1	no	—
337	#1581	D₈₃	1	1	yes	characteristic, complemented
338	C₈×D₈	—	83	1	no	—
339	C₈×D₈	—	83	1	no	—
340	#1567	—	83	1	no	—
341	#1486	—	83	1	no	—
342	#1486	—	83	1	no	—
343	C₈×M₁₆	—	83	1	no	—
344	C₈₃	M₁₆×D₈	1	1	yes	characteristic, complemented, Sylow
345	C₂²×D₈	—	83	1	no	—
346	C₂²×M₁₆	—	166	1	no	—
347	C₂²×M₁₆	—	166	1	no	—
348	C₂×C₄×D₄	—	83	1	no	—
349	C₂×C₄×D₄	—	83	1	no	—
350	C₄×D₈	—	83	1	no	—
351	C₄×D₈	—	83	1	no	—
352	C₄×D₈	—	83	1	no	—
353	C₄×D₈	—	83	1	no	—
354	C₄×D₈	—	83	1	no	—
355	C₄×D₈	—	83	1	no	—
356	C₄×D₈	—	83	1	no	—
357	C₄×D₈	C₂×D₈₃	1	1	yes	characteristic
358	#436	—	83	1	no	—
359	#436	—	83	1	no	—
360	#436	—	83	1	no	—
361	#436	C₂×D₈₃	1	1	yes	characteristic, complemented
362	#435	—	166	1	no	—
363	#435	—	166	1	no	—
364	#435	—	166	1	no	—
365	#435	—	166	1	no	—
366	C₈×D₄	—	83	1	no	—
367	C₈×D₄	—	83	1	no	—
368	C₈×D₄	—	83	1	no	—
369	C₈×D₄	C₂×D₈₃	1	1	yes	characteristic, complemented
370	#431	—	83	1	no	—
371	C₂×#107	—	83	1	no	—
372	#423	—	83	1	no	—
373	#423	—	83	1	no	—
374	C₂×#102	—	83	1	no	—
375	C₂×#102	—	83	1	no	—
376	#407	—	166	1	no	—
377	#407	—	166	1	no	—
378	C₄×M₁₆	—	83	1	no	—
379	C₂×C₄×C₈	—	83	1	no	—
380	#335	—	83	1	no	—
381	#335	—	83	1	no	—
382	#335	—	83	1	no	—
383	#335	C₂×D₈₃	1	1	yes	characteristic, complemented
384	D₄⋊C₈	—	83	1	no	—
385	D₄⋊C₈	—	83	1	no	—
386	D₄⋊C₈	—	83	1	no	—
387	D₄⋊C₈	—	83	1	no	—
388	D₄⋊C₈	—	83	1	no	—
389	D₄⋊C₈	—	83	1	no	—
390	D₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic, complemented
391	D₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic, complemented
392	#322	—	83	1	no	—
393	#322	C₂×D₈₃	1	1	yes	characteristic, complemented
394	C₈²	—	83	1	no	—
395	C₈²	—	83	1	no	—
396	C₂²×D₄	—	83	1	no	—
397	C₂²×D₄	—	83	1	no	—
398	C₂³×C₄	—	166	1	no	—
399	C₂³×C₄	—	166	1	no	—
400	C₂×D₈	—	83	1	no	—
401	C₂×D₈	—	83	1	no	—
402	C₂×D₈	—	83	1	no	—
403	C₂×D₈	—	166	4	no	—
404	C₂×D₈	C₄×D₈₃	1	1	yes	characteristic
405	C₂×M₁₆	—	2	1	no	—
406	C₂×M₁₆	—	332	4	no	—
407	C₂×M₁₆	—	332	4	no	—
408	C₂×M₁₆	—	83	1	no	—
409	C₂×M₁₆	—	83	1	no	—
410	C₂×M₁₆	—	166	1	no	—
411	C₂×M₁₆	—	166	1	no	—
412	C₂×M₁₆	—	166	1	no	—
413	C₂×M₁₆	—	166	1	no	—
414	C₂×M₁₆	—	166	1	no	—
415	C₂²×C₈	—	2	1	no	—
416	C₂²×C₈	—	83	1	no	—
417	C₂²×C₈	—	83	1	no	—
418	C₂²×C₈	—	166	1	no	—
419	C₂²×C₈	—	166	1	no	—
420	C₂²×C₈	—	166	1	no	—
421	C₄×D₄	—	83	1	no	—
422	C₄×D₄	—	83	1	no	—
423	C₄×D₄	—	83	1	no	—
424	C₄×D₄	—	83	1	no	—
425	C₄×D₄	—	83	1	no	—
426	C₄×D₄	—	83	1	no	—
427	C₄×D₄	—	166	1	no	—
428	C₄×D₄	—	166	1	no	—
429	C₄×D₄	—	166	1	no	—
430	C₄×D₄	—	166	1	no	—
431	C₄×D₄	C₂²×D₈₃	1	1	yes	characteristic
432	C₄×D₄	C₂²×D₈₃	1	1	yes	characteristic
433	C₂×C₄⋊C₄	—	83	1	no	—
434	C₂×C₄⋊C₄	—	83	1	no	—
435	C₂×C₂²⋊C₄	—	166	1	no	—
436	C₂×C₂²⋊C₄	—	166	1	no	—
437	C₂×C₄²	—	83	1	no	—
438	#107	—	83	1	no	—
439	#107	—	83	1	no	—
440	#107	—	83	1	no	—
441	#107	C₄×D₈₃	1	1	yes	characteristic
442	C₄⋊C₈	—	83	1	no	—
443	C₄⋊C₈	—	83	1	no	—
444	C₄⋊C₈	—	166	1	no	—
445	C₄⋊C₈	—	166	1	no	—
446	C₄⋊C₈	—	166	1	no	—
447	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
448	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
449	#102	—	83	1	no	—
450	#102	—	83	1	no	—
451	#102	—	83	1	no	—
452	#102	—	83	1	no	—
453	#102	—	83	1	no	—
454	#102	—	83	1	no	—
455	#102	C₄×D₈₃	1	1	yes	characteristic
456	#102	C₄×D₈₃	1	1	yes	characteristic
457	C₂²⋊C₈	—	2	1	no	—
458	C₂²⋊C₈	—	2	1	no	—
459	C₂²⋊C₈	—	166	1	no	—
460	C₂²⋊C₈	—	166	1	no	—
461	C₂²⋊C₈	—	166	1	no	—
462	C₂²⋊C₈	—	166	1	no	—
463	C₂²⋊C₈	—	166	1	no	—
464	C₂²⋊C₈	—	166	1	no	—
465	C₂²⋊C₈	—	166	1	no	—
466	#97	—	83	1	no	—
467	#97	—	83	1	no	—
468	C₄×C₈	—	83	1	no	—
469	C₄×C₈	—	83	1	no	—
470	C₄×C₈	—	83	1	no	—
471	C₄×C₈	—	83	1	no	—
472	C₄×C₈	—	83	1	no	—
473	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
474	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
475	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
476	C₂⁴	—	166	1	no	—
477	C₂⁴	—	166	1	no	—
478	C₂×D₄	—	332	1	no	—
479	C₂×D₄	—	332	1	no	—
480	C₂×D₄	—	83	1	no	—
481	C₂×D₄	—	83	1	no	—
482	C₂×D₄	—	166	1	no	—
483	C₂×D₄	—	166	1	no	—
484	C₂×D₄	—	166	2	no	—
485	C₂×D₄	—	166	2	no	—
486	C₂×D₄	C₂×C₄×D₈₃	1	1	yes	characteristic
487	C₂×D₄	C₂×C₄×D₈₃	1	1	yes	characteristic
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	332	2	no	—
491	C₂²×C₄	—	332	2	no	—
492	C₂²×C₄	—	332	2	no	—
493	C₂²×C₄	—	332	2	no	—
494	C₂²×C₄	—	83	1	no	—
495	C₂²×C₄	—	83	1	no	—
496	C₂²×C₄	—	83	1	no	—
497	C₂²×C₄	—	166	1	no	—
498	C₂²×C₄	—	166	1	no	—
499	C₂²×C₄	—	166	1	no	—
500	C₂²×C₄	—	166	1	no	—
501	C₂²×C₄	—	166	1	no	—
502	C₂²×C₄	—	166	1	no	—
503	C₂²×C₄	—	166	1	no	—
504	C₂²×C₄	—	166	1	no	—
505	D₈	—	2	2	no	—
506	D₈	—	83	4	no	—
507	D₈	—	166	2	no	—
508	D₈	—	166	2	no	—
509	M₁₆	—	4	2	no	—
510	M₁₆	—	332	2	no	—
511	M₁₆	—	332	2	no	—
512	M₁₆	—	332	2	no	—
513	M₁₆	—	332	2	no	—
514	M₁₆	—	332	2	no	—
515	M₁₆	—	83	4	no	—
516	M₁₆	—	166	2	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	4	2	no	—
521	C₂×C₈	—	332	1	no	—
522	C₂×C₈	—	332	2	no	—
523	C₂×C₈	—	332	2	no	—
524	C₂×C₈	—	332	2	no	—
525	C₂×C₈	—	83	1	no	—
526	C₂×C₈	—	83	1	no	—
527	C₂×C₈	—	83	1	no	—
528	C₂×C₈	—	83	1	no	—
529	C₂×C₈	—	166	2	no	—
530	C₂×C₈	—	166	1	no	—
531	C₂×C₈	—	166	1	no	—
532	C₂×C₈	—	166	1	no	—
533	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
534	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
535	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
536	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
537	C₄⋊C₄	—	83	1	no	—
538	C₄⋊C₄	—	83	1	no	—
539	C₄⋊C₄	—	166	1	no	—
540	C₄⋊C₄	—	166	1	no	—
541	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
542	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
543	C₂²⋊C₄	—	2	1	no	—
544	C₂²⋊C₄	—	2	1	no	—
545	C₂²⋊C₄	—	166	1	no	—
546	C₂²⋊C₄	—	166	1	no	—
547	C₂²⋊C₄	—	166	1	no	—
548	C₂²⋊C₄	—	166	1	no	—
549	C₂²⋊C₄	—	166	1	no	—
550	C₂²⋊C₄	—	166	1	no	—
551	C₄²	—	83	1	no	—
552	C₄²	—	83	1	no	—
553	C₄²	—	83	1	no	—
554	C₄²	C₂³×D₈₃	1	1	yes	characteristic
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	332	2	no	—
558	C₂³	—	332	2	no	—
559	C₂³	—	332	2	no	—
560	C₂³	—	332	2	no	—
561	C₂³	—	83	1	no	—
562	C₂³	—	664	1	no	—
563	C₂³	—	664	1	no	—
564	C₂³	—	166	1	no	—
565	C₂³	—	166	1	no	—
566	D₄	—	2	1	no	—
567	D₄	—	2	1	no	—
568	D₄	—	2	1	no	—
569	D₄	—	332	2	no	—
570	D₄	—	332	2	no	—
571	D₄	—	83	2	no	—
572	D₄	—	166	1	no	—
573	D₄	—	166	1	no	—
574	D₄	—	166	1	no	—
575	D₄	M₁₆×D₈₃	1	2	yes	complemented
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	332	1	no	—
583	C₂×C₄	—	332	2	no	—
584	C₂×C₄	—	332	2	no	—
585	C₂×C₄	—	332	2	no	—
586	C₂×C₄	—	332	2	no	—
587	C₂×C₄	—	332	2	no	—
588	C₂×C₄	—	332	2	no	—
589	C₂×C₄	—	332	1	no	—
590	C₂×C₄	—	332	1	no	—
591	C₂×C₄	—	332	1	no	—
592	C₂×C₄	—	332	1	no	—
593	C₂×C₄	—	83	1	no	—
594	C₂×C₄	—	83	2	no	—
595	C₂×C₄	—	83	2	no	—
596	C₂×C₄	—	83	1	no	—
597	C₂×C₄	—	83	1	no	—
598	C₂×C₄	—	166	1	no	—
599	C₂×C₄	—	166	1	no	—
600	C₂×C₄	—	166	1	no	—
601	C₂×C₄	—	166	1	no	—
602	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
603	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
604	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
605	C₈	—	2	1	no	—
606	C₈	—	2	1	no	—
607	C₈	—	2	1	no	—
608	C₈	—	4	1	no	—
609	C₈	—	4	1	no	—
610	C₈	—	4	1	no	—
611	C₈	—	332	1	no	—
612	C₈	—	332	1	no	—
613	C₈	—	332	1	no	—
614	C₈	—	83	2	no	—
615	C₈	—	83	2	no	—
616	C₈	—	166	1	no	—
617	C₈	—	166	1	no	—
618	C₈	D₈×D₈₃	1	2	yes	complemented
619	C₂²	—	2	2	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	1	no	—
625	C₂²	—	332	1	no	—
626	C₂²	—	332	1	no	—
627	C₂²	—	332	1	no	—
628	C₂²	—	332	1	no	—
629	C₂²	—	332	1	no	—
630	C₂²	—	83	2	no	—
631	C₂²	—	664	4	no	—
632	C₂²	—	664	4	no	—
633	C₂²	—	166	2	no	—
634	C₂²	—	166	1	no	—
635	C₂²	—	166	1	no	—
636	C₂²	C₄×D₄×D₈₃	1	1	yes	characteristic
637	C₄	—	2	1	no	—
638	C₄	—	4	1	no	—
639	C₄	—	4	1	no	—
640	C₄	—	332	1	no	—
641	C₄	—	332	1	no	—
642	C₄	—	83	2	no	—
643	C₄	—	166	1	no	—
644	C₄	—	166	1	no	—
645	C₄	C₂×M₁₆×D₈₃	1	1	yes	characteristic
646	C₄	#19128466	1	1	yes	characteristic
647	C₄	C₂×D₈×D₈₃	1	1	yes	characteristic
648	C₄	#135×D₈₃	1	1	yes	characteristic
649	C₂	—	4	2	no	—
650	C₂	—	8	1	no	—
651	C₂	—	332	2	no	—
652	C₂	—	664	1	no	—
653	C₂	—	166	2	no	—
654	C₂	#24916196	1	1	yes	characteristic
655	C₂	C₄×D₈×D₈₃	1	1	yes	characteristic
656	C₂	#24916377	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×#1581	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	C₂×D₈×D₈₃	C₄
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	#1581	D₈₃
hypocenter	C₈₃	M₁₆×D₈
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1581

Complements

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

N	H ≅ G/N	type
2. #24916199	C₂	semidirect
3. D₄×#13050573	C₂	semidirect
4. #24906346	C₂	semidirect
5. #24906345	C₂	semidirect
6. #24906294	C₂	semidirect
7. #24906293	C₂	semidirect
8. #24906291	C₂	semidirect
9. C₈×#13050575	C₂	semidirect
10. #24906255	C₂	semidirect
11. #24906220	C₂	semidirect
12. #24905886	C₂	semidirect
13. #24905886	C₂	semidirect
14. #24905742	C₂	semidirect
15. C₈₃×#1581	C₂	semidirect
28. #19127780	C₂²	semidirect
29. #19127779	C₂²	semidirect
30. #19127778	C₂²	semidirect
35. C₈×D₃₃₂	C₂²	semidirect
36. D₄×C₈₃⋊C₈	C₂²	semidirect
37. #19127766	C₂²	semidirect
48. #19127454	C₂²	semidirect
49. #19127453	C₂²	semidirect
50. #19127453	C₂²	semidirect
51. #19127430	C₂²	semidirect
52. #19127430	C₂²	semidirect
53. D₄⋊(C₈₃⋊C₈)	C₂²	semidirect
54. D₄⋊(C₈₃⋊C₈)	C₂²	semidirect
55. #19127428	C₂²	semidirect
56. #19127428	C₂²	semidirect
57. #19127423	C₂²	semidirect
58. C₈×C₈₃⋊C₈	C₂²	semidirect
59. C₈×C₈₃⋊C₈	C₂²	semidirect
61. #436×C₈₃	C₂²	semidirect
62. C₈×D₄×C₈₃	C₂²	semidirect
63. #335×C₈₃	C₂²	semidirect
64. D₄⋊C₈×C₈₃	C₂²	semidirect
65. D₄⋊C₈×C₈₃	C₂²	semidirect
66. #322×C₈₃	C₂²	semidirect
174. #13050575	M₁₆	semidirect
181. #13050573	D₈	semidirect
240. D₄×C₈₃	C₂×M₁₆	semidirect
262. D₃₃₂	C₂×M₁₆	semidirect
282. C₈×C₈₃	C₂×D₈	semidirect
288. C₈₃⋊C₈	C₂×M₁₆	semidirect
289. C₈₃⋊C₈	C₂×D₈	semidirect
337. #1581	D₈₃	semidirect
344. C₈₃	M₁₆×D₈	semidirect
361. #436	C₂×D₈₃	semidirect
369. C₈×D₄	C₂×D₈₃	semidirect
383. #335	C₂×D₈₃	semidirect
390. D₄⋊C₈	C₂×D₈₃	semidirect
391. D₄⋊C₈	C₂×D₈₃	semidirect
393. #322	C₂×D₈₃	semidirect
575. D₄	M₁₆×D₈₃	semidirect
618. C₈	D₈×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₈×D₈₃	2
#24916199	2
D₄×#13050573	2
#24906346	2
#24906345	2
#24906294	2
#24906293	2
#24906291	2
C₈×#13050575	2
#24906255	2
#24906220	2
#24905886	2
#24905742	2
C₈₃×#1581	2
M₁₆×D₈	83