Subgroups — C₈₃×#21466 #35249290

Order 21248.

1354 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#131×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₃×#3002	C₂	1	1	yes	maximal, characteristic
3	C₂×#443×C₈₃	C₂	1	2	yes	maximal, complemented
4	C₈₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₃×#1876	C₂	1	2	yes	maximal, complemented
6	C₈₃×#1871	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₃×#1866	C₂	1	2	yes	maximal, complemented
8	C₈₃×#1855	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₃×#1789	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₃×#1764	C₂	1	2	yes	maximal, complemented
11	C₈×C₂²⋊C₄×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₈₃	C₂²	1	1	yes	characteristic
13	C₂×#135×C₈₃	C₂²	1	2	yes	—
14	C₂×#131×C₈₃	—	2	8	no	—
15	C₂×#131×C₈₃	—	2	1	no	—
16	C₂×#131×C₈₃	—	2	1	no	—
17	C₂×#131×C₈₃	C₂²	1	2	yes	—
18	C₂×#131×C₈₃	C₂²	1	2	yes	—
19	C₂×#131×C₈₃	C₂²	1	1	yes	characteristic, complemented
20	C₂²×M₁₆×C₈₃	—	2	1	no	—
21	C₂²×M₁₆×C₈₃	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₈₃	—	2	1	no	—
23	C₂³×C₈×C₈₃	C₂²	1	1	yes	characteristic
24	#525×C₈₃	C₂²	1	1	yes	characteristic
25	#452×C₈₃	C₄	1	2	yes	complemented
26	#451×C₈₃	C₄	1	1	yes	characteristic, complemented
27	#450×C₈₃	C₄	1	1	yes	characteristic, complemented
28	#449×C₈₃	C₄	1	2	yes	complemented
29	#448×C₈₃	C₄	1	1	yes	characteristic, complemented
30	#447×C₈₃	C₄	1	1	yes	characteristic, complemented
31	#443×C₈₃	—	2	8	no	—
32	#435×C₈₃	—	2	1	no	—
33	#435×C₈₃	—	2	1	no	—
34	C₈×D₄×C₈₃	—	2	1	no	—
35	C₈×D₄×C₈₃	—	2	1	no	—
36	C₂×#108×C₈₃	C₂²	1	2	yes	complemented
37	#424×C₈₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×#104×C₈₃	C₂²	1	2	yes	—
39	C₂×#104×C₈₃	C₂²	1	2	yes	—
40	C₂×#104×C₈₃	C₂²	1	2	yes	complemented
41	#416×C₈₃	C₂²	1	2	yes	—
42	#408×C₈₃	C₂²	1	1	yes	characteristic, complemented
43	#407×C₈₃	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
45	#405×C₈₃	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×C₈×C₈₃	C₂²	1	2	yes	complemented
47	C₄×C₂²⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
48	#341×C₈₃	C₂²	1	2	yes	complemented
49	#339×C₈₃	C₂²	1	2	yes	complemented
50	#336×C₈₃	C₂²	1	2	yes	complemented
51	C₂×#41×C₈₃	—	2	4	no	—
52	C₂×#41×C₈₃	—	2	4	no	—
53	C₂×#41×C₈₃	—	2	1	no	—
54	C₂×#41×C₈₃	—	2	1	no	—
55	C₂×#41×C₈₃	C₂×C₄	1	2	yes	—
56	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
57	C₂×#41×C₈₃	C₂³	1	2	yes	—
58	C₂²×Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
59	C₂²×D₄×C₈₃	—	2	1	no	—
60	C₂²×D₄×C₈₃	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₈₃	—	2	1	no	—
62	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
63	#135×C₈₃	—	2	4	no	—
64	#135×C₈₃	—	2	4	no	—
65	C₂×Q₁₆×C₈₃	C₂×C₄	1	2	yes	—
66	C₂×SD₁₆×C₈₃	C₂×C₄	1	2	yes	—
67	C₂×SD₁₆×C₈₃	C₂×C₄	1	2	yes	—
68	C₂×D₈×C₈₃	C₂×C₄	1	2	yes	—
69	#131×C₈₃	—	2	8	no	—
70	#131×C₈₃	—	2	8	no	—
71	#131×C₈₃	—	2	4	no	—
72	#131×C₈₃	—	2	4	no	—
73	#131×C₈₃	—	2	4	no	—
74	#131×C₈₃	—	2	4	no	—
75	#131×C₈₃	D₄	1	8	yes	complemented
76	C₂×M₁₆×C₈₃	—	2	8	no	—
77	C₂×M₁₆×C₈₃	—	2	1	no	—
78	C₂×M₁₆×C₈₃	—	2	4	no	—
79	C₂×M₁₆×C₈₃	—	2	2	no	—
80	C₂×M₁₆×C₈₃	—	2	2	no	—
81	C₂×M₁₆×C₈₃	—	2	1	no	—
82	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
83	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
85	C₂²×C₈×C₈₃	—	2	8	no	—
86	C₂²×C₈×C₈₃	—	2	1	no	—
87	C₂²×C₈×C₈₃	—	2	2	no	—
88	C₂²×C₈×C₈₃	—	2	4	no	—
89	C₂²×C₈×C₈₃	—	2	2	no	—
90	C₂²×C₈×C₈₃	—	2	1	no	—
91	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
92	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
93	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
94	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
95	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
96	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
98	#123×C₈₃	—	2	1	no	—
99	C₂²⋊Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
100	C₂²⋊Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
101	#121×C₈₃	C₂×C₄	1	1	yes	characteristic
102	#121×C₈₃	C₂×C₄	1	1	yes	characteristic
103	#120×C₈₃	—	2	1	no	—
104	C₄×D₄×C₈₃	—	2	1	no	—
105	C₄×D₄×C₈₃	—	2	1	no	—
106	#117×C₈₃	C₂³	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
108	C₂×C₄²×C₈₃	C₂³	1	2	yes	—
109	#108×C₈₃	—	2	4	no	—
110	C₄⋊C₈×C₈₃	—	2	1	no	—
111	C₄⋊C₈×C₈₃	—	2	1	no	—
112	#104×C₈₃	—	2	4	no	—
113	#104×C₈₃	—	2	4	no	—
114	#104×C₈₃	—	2	4	no	—
115	#103×C₈₃	C₂×C₄	1	2	yes	—
116	#103×C₈₃	C₂×C₄	1	2	yes	—
117	#102×C₈₃	C₂×C₄	1	2	yes	—
118	#102×C₈₃	C₂×C₄	1	2	yes	—
119	C₂²⋊C₈×C₈₃	—	2	1	no	—
120	C₂²⋊C₈×C₈₃	—	2	1	no	—
121	C₂²⋊C₈×C₈₃	—	2	1	no	—
122	C₂²⋊C₈×C₈₃	—	2	1	no	—
123	C₂²⋊C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
124	C₂²⋊C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
125	C₂²⋊C₈×C₈₃	C₂×C₄	1	2	yes	—
126	#97×C₈₃	—	2	1	no	—
127	C₄×C₈×C₈₃	—	2	4	no	—
128	C₄×C₈×C₈₃	—	2	1	no	—
129	#95×C₈₃	—	2	1	no	—
130	C₂⁴×C₈₃	—	2	1	no	—
131	C₂⁴×C₈₃	#41	1	1	yes	characteristic
132	#41×C₈₃	—	2	4	no	—
133	#41×C₈₃	—	2	8	no	—
134	#41×C₈₃	—	2	4	no	—
135	#41×C₈₃	—	2	4	no	—
136	#41×C₈₃	—	2	4	no	—
137	#41×C₈₃	—	2	2	no	—
138	#41×C₈₃	—	2	2	no	—
139	#41×C₈₃	—	2	2	no	—
140	#41×C₈₃	—	2	2	no	—
141	#41×C₈₃	C₂×D₄	1	4	yes	—
142	#41×C₈₃	#41	1	4	yes	—
143	C₂×Q₈×C₈₃	—	2	4	no	—
144	C₂×Q₈×C₈₃	—	2	1	no	—
145	C₂×Q₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
146	C₂×Q₈×C₈₃	C₂²×C₄	1	2	yes	—
147	C₂×D₄×C₈₃	—	2	8	no	—
148	C₂×D₄×C₈₃	—	2	2	no	—
149	C₂×D₄×C₈₃	—	2	2	no	—
150	C₂×D₄×C₈₃	—	2	4	no	—
151	C₂×D₄×C₈₃	—	2	1	no	—
152	C₂×D₄×C₈₃	—	2	1	no	—
153	C₂×D₄×C₈₃	—	2	1	no	—
154	C₂×D₄×C₈₃	—	2	1	no	—
155	C₂×D₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
156	C₂×D₄×C₈₃	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₈₃	—	2	4	no	—
158	C₂²×C₄×C₈₃	—	2	4	no	—
159	C₂²×C₄×C₈₃	—	2	1	no	—
160	C₂²×C₄×C₈₃	—	2	2	no	—
161	C₂²×C₄×C₈₃	—	2	2	no	—
162	C₂²×C₄×C₈₃	—	2	2	no	—
163	C₂²×C₄×C₈₃	—	2	2	no	—
164	C₂²×C₄×C₈₃	—	2	2	no	—
165	C₂²×C₄×C₈₃	—	2	1	no	—
166	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
171	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
172	Q₁₆×C₈₃	—	2	4	no	—
173	SD₁₆×C₈₃	—	2	4	no	—
174	SD₁₆×C₈₃	—	2	4	no	—
175	D₈×C₈₃	—	2	4	no	—
176	M₁₆×C₈₃	—	2	4	no	—
177	M₁₆×C₈₃	—	2	8	no	—
178	M₁₆×C₈₃	—	2	2	no	—
179	M₁₆×C₈₃	—	2	8	no	—
180	M₁₆×C₈₃	—	2	2	no	—
181	M₁₆×C₈₃	—	2	2	no	—
182	M₁₆×C₈₃	—	4	2	no	—
183	M₁₆×C₈₃	C₂×D₄	1	4	yes	—
184	C₂×C₈×C₈₃	—	2	4	no	—
185	C₂×C₈×C₈₃	—	2	8	no	—
186	C₂×C₈×C₈₃	—	2	2	no	—
187	C₂×C₈×C₈₃	—	2	2	no	—
188	C₂×C₈×C₈₃	—	2	2	no	—
189	C₂×C₈×C₈₃	—	2	2	no	—
190	C₂×C₈×C₈₃	—	2	2	no	—
191	C₂×C₈×C₈₃	—	2	8	no	—
192	C₂×C₈×C₈₃	—	2	2	no	—
193	C₂×C₈×C₈₃	—	2	2	no	—
194	C₂×C₈×C₈₃	—	2	2	no	—
195	C₂×C₈×C₈₃	—	2	1	no	—
196	C₂×C₈×C₈₃	—	2	1	no	—
197	C₂×C₈×C₈₃	—	4	2	no	—
198	C₂×C₈×C₈₃	C₂²×C₄	1	2	yes	—
199	C₂×C₈×C₈₃	C₂²×C₄	1	2	yes	—
200	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
201	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
202	C₂×C₈×C₈₃	C₂×D₄	1	4	yes	—
203	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
204	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
205	C₄⋊C₄×C₈₃	—	2	1	no	—
206	C₄⋊C₄×C₈₃	—	2	1	no	—
207	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
208	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
209	C₂²⋊C₄×C₈₃	—	2	4	no	—
210	C₂²⋊C₄×C₈₃	—	2	1	no	—
211	C₂²⋊C₄×C₈₃	—	2	1	no	—
212	C₂²⋊C₄×C₈₃	—	2	1	no	—
213	C₂²⋊C₄×C₈₃	—	2	1	no	—
214	C₂²⋊C₄×C₈₃	—	2	1	no	—
215	C₄²×C₈₃	—	2	1	no	—
216	C₄²×C₈₃	—	2	2	no	—
217	C₄²×C₈₃	—	2	2	no	—
218	C₂³×C₈₃	—	2	4	no	—
219	C₂³×C₈₃	—	2	2	no	—
220	C₂³×C₈₃	—	2	2	no	—
221	C₂³×C₈₃	—	2	2	no	—
222	C₂³×C₈₃	—	2	1	no	—
223	C₂³×C₈₃	—	4	1	no	—
224	C₂³×C₈₃	—	4	2	no	—
225	C₂³×C₈₃	—	4	2	no	—
226	C₂³×C₈₃	C₄×D₄	1	1	yes	characteristic
227	C₂³×C₈₃	C₄×D₄	1	1	yes	characteristic
228	C₂³×C₈₃	C₂×#41	1	1	yes	characteristic
229	Q₈×C₈₃	—	2	4	no	—
230	Q₈×C₈₃	—	2	2	no	—
231	Q₈×C₈₃	—	2	2	no	—
232	Q₈×C₈₃	C₄×D₄	1	4	yes	—
233	D₄×C₈₃	—	2	8	no	—
234	D₄×C₈₃	—	2	4	no	—
235	D₄×C₈₃	—	2	4	no	—
236	D₄×C₈₃	—	2	4	no	—
237	D₄×C₈₃	—	2	2	no	—
238	D₄×C₈₃	—	2	2	no	—
239	D₄×C₈₃	—	4	2	no	—
240	D₄×C₈₃	—	4	2	no	—
241	D₄×C₈₃	—	4	2	no	—
242	D₄×C₈₃	C₄×D₄	1	4	yes	—
243	C₂×C₄×C₈₃	—	2	4	no	—
244	C₂×C₄×C₈₃	—	2	8	no	—
245	C₂×C₄×C₈₃	—	2	2	no	—
246	C₂×C₄×C₈₃	—	2	2	no	—
247	C₂×C₄×C₈₃	—	2	2	no	—
248	C₂×C₄×C₈₃	—	2	2	no	—
249	C₂×C₄×C₈₃	—	2	1	no	—
250	C₂×C₄×C₈₃	—	2	4	no	—
251	C₂×C₄×C₈₃	—	2	1	no	—
252	C₂×C₄×C₈₃	—	2	1	no	—
253	C₂×C₄×C₈₃	—	2	4	no	—
254	C₂×C₄×C₈₃	—	2	1	no	—
255	C₂×C₄×C₈₃	—	2	4	no	—
256	C₂×C₄×C₈₃	—	2	1	no	—
257	C₂×C₄×C₈₃	—	2	1	no	—
258	C₂×C₄×C₈₃	—	2	1	no	—
259	C₂×C₄×C₈₃	—	4	2	no	—
260	C₂×C₄×C₈₃	—	4	2	no	—
261	C₂×C₄×C₈₃	—	4	1	no	—
262	C₂×C₄×C₈₃	—	4	1	no	—
263	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
264	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
265	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
266	C₂×C₄×C₈₃	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₈₃	C₂×#41	1	2	yes	—
269	C₈×C₈₃	—	2	2	no	—
270	C₈×C₈₃	—	2	2	no	—
271	C₈×C₈₃	—	2	1	no	—
272	C₈×C₈₃	—	2	4	no	—
273	C₈×C₈₃	—	2	1	no	—
274	C₈×C₈₃	—	4	1	no	—
275	C₈×C₈₃	—	4	1	no	—
276	C₈×C₈₃	#120	1	2	yes	—
277	C₈×C₈₃	#120	1	2	yes	—
278	C₂²×C₈₃	—	2	1	no	—
279	C₂²×C₈₃	—	2	1	no	—
280	C₂²×C₈₃	—	2	1	no	—
281	C₂²×C₈₃	—	2	1	no	—
282	C₂²×C₈₃	—	2	1	no	—
283	C₂²×C₈₃	—	2	1	no	—
284	C₂²×C₈₃	—	2	1	no	—
285	C₂²×C₈₃	—	2	4	no	—
286	C₂²×C₈₃	—	4	4	no	—
287	C₂²×C₈₃	—	4	8	no	—
288	C₂²×C₈₃	—	4	2	no	—
289	C₂²×C₈₃	—	4	2	no	—
290	C₂²×C₈₃	—	4	1	no	—
291	C₂²×C₈₃	—	4	1	no	—
292	C₂²×C₈₃	—	4	1	no	—
293	C₂²×C₈₃	#443	1	2	yes	complemented
294	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
295	C₂²×C₈₃	#525	1	2	yes	—
296	C₄×C₈₃	—	2	1	no	—
297	C₄×C₈₃	—	2	4	no	—
298	C₄×C₈₃	—	2	1	no	—
299	C₄×C₈₃	—	4	4	no	—
300	C₄×C₈₃	—	4	1	no	—
301	C₄×C₈₃	—	4	1	no	—
302	C₄×C₈₃	—	4	1	no	—
303	C₄×C₈₃	C₂×C₄×D₄	1	2	yes	—
304	C₄×C₈₃	C₂×#120	1	1	yes	characteristic
305	C₄×C₈₃	#525	1	1	yes	characteristic
306	#21466	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
307	C₂×C₈₃	—	2	2	no	—
308	C₂×C₈₃	—	2	2	no	—
309	C₂×C₈₃	—	4	1	no	—
310	C₂×C₈₃	—	4	4	no	—
311	C₂×C₈₃	—	8	1	no	—
312	C₂×C₈₃	C₄×#120	1	1	yes	characteristic
313	C₂×C₈₃	C₂×#443	1	1	yes	characteristic
314	C₂×C₈₃	#2955	1	1	yes	characteristic
315	C₂²×#131	C₂×C₈₃	1	1	yes	characteristic, complemented
316	#3002	C₂×C₈₃	1	1	yes	characteristic
317	C₂×#443	C₂×C₈₃	1	2	yes	complemented
318	#2929	C₂×C₈₃	1	1	yes	characteristic, complemented
319	#1876	C₂×C₈₃	1	2	yes	complemented
320	#1871	C₂×C₈₃	1	1	yes	characteristic, complemented
321	#1866	C₂×C₈₃	1	2	yes	complemented
322	#1855	C₂×C₈₃	1	1	yes	characteristic, complemented
323	#1789	C₂×C₈₃	1	1	yes	characteristic, complemented
324	#1764	C₂×C₈₃	1	2	yes	complemented
325	C₈×C₂²⋊C₄	C₂×C₈₃	1	1	yes	characteristic, complemented
326	C₈₃	#21466	1	1	yes	characteristic, direct product factor, Sylow
327	C₂²×#41	C₂²×C₈₃	1	1	yes	characteristic
328	C₂×#135	C₂²×C₈₃	1	2	yes	—
329	C₂×#131	—	2	8	no	—
330	C₂×#131	—	2	1	no	—
331	C₂×#131	—	2	1	no	—
332	C₂×#131	C₂²×C₈₃	1	2	yes	—
333	C₂×#131	C₂²×C₈₃	1	2	yes	—
334	C₂×#131	C₂²×C₈₃	1	1	yes	characteristic, complemented
335	C₂²×M₁₆	—	2	1	no	—
336	C₂²×M₁₆	C₂²×C₈₃	1	1	yes	characteristic
337	C₂³×C₈	—	2	1	no	—
338	C₂³×C₈	C₂²×C₈₃	1	1	yes	characteristic
339	#525	C₂²×C₈₃	1	1	yes	characteristic
340	#452	C₄×C₈₃	1	2	yes	complemented
341	#451	C₄×C₈₃	1	1	yes	characteristic, complemented
342	#450	C₄×C₈₃	1	1	yes	characteristic, complemented
343	#449	C₄×C₈₃	1	2	yes	complemented
344	#448	C₄×C₈₃	1	1	yes	characteristic, complemented
345	#447	C₄×C₈₃	1	1	yes	characteristic, complemented
346	#443	—	2	8	no	—
347	#435	—	2	1	no	—
348	#435	—	2	1	no	—
349	C₈×D₄	—	2	1	no	—
350	C₈×D₄	—	2	1	no	—
351	C₂×#108	C₂²×C₈₃	1	2	yes	complemented
352	#424	C₂²×C₈₃	1	1	yes	characteristic, complemented
353	C₂×#104	C₂²×C₈₃	1	2	yes	—
354	C₂×#104	C₂²×C₈₃	1	2	yes	—
355	C₂×#104	C₂²×C₈₃	1	2	yes	complemented
356	#416	C₂²×C₈₃	1	2	yes	—
357	#408	C₂²×C₈₃	1	1	yes	characteristic, complemented
358	#407	C₂²×C₈₃	1	1	yes	characteristic
359	C₂×C₂²⋊C₈	C₂²×C₈₃	1	1	yes	characteristic
360	#405	C₂²×C₈₃	1	1	yes	characteristic, complemented
361	C₂×C₄×C₈	C₂²×C₈₃	1	2	yes	complemented
362	C₄×C₂²⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
363	#341	C₂²×C₈₃	1	2	yes	complemented
364	#339	C₂²×C₈₃	1	2	yes	complemented
365	#336	C₂²×C₈₃	1	2	yes	complemented
366	C₂×#41	—	2	4	no	—
367	C₂×#41	—	2	4	no	—
368	C₂×#41	—	2	1	no	—
369	C₂×#41	—	2	1	no	—
370	C₂×#41	C₂×C₄×C₈₃	1	2	yes	—
371	C₂×#41	C₂³×C₈₃	1	1	yes	characteristic
372	C₂×#41	C₂³×C₈₃	1	2	yes	—
373	C₂²×Q₈	C₂×C₄×C₈₃	1	1	yes	characteristic
374	C₂²×D₄	—	2	1	no	—
375	C₂²×D₄	C₂×C₄×C₈₃	1	1	yes	characteristic
376	C₂³×C₄	—	2	1	no	—
377	C₂³×C₄	C₂³×C₈₃	1	1	yes	characteristic
378	#135	—	2	4	no	—
379	#135	—	2	4	no	—
380	C₂×Q₁₆	C₂×C₄×C₈₃	1	2	yes	—
381	C₂×SD₁₆	C₂×C₄×C₈₃	1	2	yes	—
382	C₂×SD₁₆	C₂×C₄×C₈₃	1	2	yes	—
383	C₂×D₈	C₂×C₄×C₈₃	1	2	yes	—
384	#131	—	2	8	no	—
385	#131	—	2	8	no	—
386	#131	—	2	4	no	—
387	#131	—	2	4	no	—
388	#131	—	2	4	no	—
389	#131	—	2	4	no	—
390	#131	D₄×C₈₃	1	8	yes	complemented
391	C₂×M₁₆	—	2	8	no	—
392	C₂×M₁₆	—	2	1	no	—
393	C₂×M₁₆	—	2	4	no	—
394	C₂×M₁₆	—	2	2	no	—
395	C₂×M₁₆	—	2	2	no	—
396	C₂×M₁₆	—	2	1	no	—
397	C₂×M₁₆	C₂³×C₈₃	1	1	yes	characteristic
398	C₂×M₁₆	C₂³×C₈₃	1	1	yes	characteristic
399	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
400	C₂²×C₈	—	2	8	no	—
401	C₂²×C₈	—	2	1	no	—
402	C₂²×C₈	—	2	2	no	—
403	C₂²×C₈	—	2	2	no	—
404	C₂²×C₈	—	2	4	no	—
405	C₂²×C₈	—	2	1	no	—
406	C₂²×C₈	D₄×C₈₃	1	1	yes	characteristic
407	C₂²×C₈	D₄×C₈₃	1	1	yes	characteristic
408	C₂²×C₈	D₄×C₈₃	1	1	yes	characteristic
409	C₂²×C₈	D₄×C₈₃	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
411	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
412	C₂²×C₈	C₂³×C₈₃	1	1	yes	characteristic
413	#123	—	2	1	no	—
414	C₂²⋊Q₈	C₂×C₄×C₈₃	1	1	yes	characteristic
415	C₂²⋊Q₈	C₂×C₄×C₈₃	1	1	yes	characteristic
416	#121	C₂×C₄×C₈₃	1	1	yes	characteristic
417	#121	C₂×C₄×C₈₃	1	1	yes	characteristic
418	#120	—	2	1	no	—
419	C₄×D₄	—	2	1	no	—
420	C₄×D₄	—	2	1	no	—
421	#117	C₂³×C₈₃	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₄²	C₂³×C₈₃	1	2	yes	—
424	#108	—	2	4	no	—
425	C₄⋊C₈	—	2	1	no	—
426	C₄⋊C₈	—	2	1	no	—
427	#104	—	2	4	no	—
428	#104	—	2	4	no	—
429	#104	—	2	4	no	—
430	#103	C₂×C₄×C₈₃	1	2	yes	—
431	#103	C₂×C₄×C₈₃	1	2	yes	—
432	#102	C₂×C₄×C₈₃	1	2	yes	—
433	#102	C₂×C₄×C₈₃	1	2	yes	—
434	C₂²⋊C₈	—	2	1	no	—
435	C₂²⋊C₈	—	2	1	no	—
436	C₂²⋊C₈	—	2	1	no	—
437	C₂²⋊C₈	—	2	1	no	—
438	C₂²⋊C₈	C₂×C₄×C₈₃	1	1	yes	characteristic
439	C₂²⋊C₈	C₂×C₄×C₈₃	1	1	yes	characteristic
440	C₂²⋊C₈	C₂×C₄×C₈₃	1	2	yes	—
441	#97	—	2	1	no	—
442	C₄×C₈	—	2	4	no	—
443	C₄×C₈	—	2	1	no	—
444	#95	—	2	1	no	—
445	C₂⁴	—	2	1	no	—
446	C₂⁴	#41×C₈₃	1	1	yes	characteristic
447	#41	—	2	4	no	—
448	#41	—	2	8	no	—
449	#41	—	2	4	no	—
450	#41	—	2	4	no	—
451	#41	—	2	4	no	—
452	#41	—	2	2	no	—
453	#41	—	2	2	no	—
454	#41	—	2	2	no	—
455	#41	—	2	2	no	—
456	#41	C₂×D₄×C₈₃	1	4	yes	—
457	#41	#41×C₈₃	1	4	yes	—
458	C₂×Q₈	—	2	4	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	C₂²×C₄×C₈₃	1	1	yes	characteristic
461	C₂×Q₈	C₂²×C₄×C₈₃	1	2	yes	—
462	C₂×D₄	—	2	8	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	4	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	C₂²×C₄×C₈₃	1	1	yes	characteristic
471	C₂×D₄	C₂²×C₄×C₈₃	1	2	yes	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	C₂²×C₄×C₈₃	1	1	yes	characteristic
482	C₂²×C₄	C₂²×C₄×C₈₃	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
485	C₂²×C₄	#41×C₈₃	1	1	yes	characteristic
486	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
487	Q₁₆	—	2	4	no	—
488	SD₁₆	—	2	4	no	—
489	SD₁₆	—	2	4	no	—
490	D₈	—	2	4	no	—
491	M₁₆	—	2	4	no	—
492	M₁₆	—	2	8	no	—
493	M₁₆	—	2	2	no	—
494	M₁₆	—	2	8	no	—
495	M₁₆	—	2	2	no	—
496	M₁₆	—	2	2	no	—
497	M₁₆	—	4	2	no	—
498	M₁₆	C₂×D₄×C₈₃	1	4	yes	—
499	C₂×C₈	—	2	4	no	—
500	C₂×C₈	—	2	8	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	2	2	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	2	2	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	2	8	no	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	—	2	2	no	—
509	C₂×C₈	—	2	2	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	4	2	no	—
513	C₂×C₈	C₂²×C₄×C₈₃	1	2	yes	—
514	C₂×C₈	C₂²×C₄×C₈₃	1	2	yes	—
515	C₂×C₈	C₂×D₄×C₈₃	1	1	yes	characteristic
516	C₂×C₈	C₂×D₄×C₈₃	1	1	yes	characteristic
517	C₂×C₈	C₂×D₄×C₈₃	1	1	yes	characteristic
518	C₂×C₈	C₂×D₄×C₈₃	1	4	yes	—
519	C₂×C₈	C₂×D₄×C₈₃	1	1	yes	characteristic
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	C₂²×C₄×C₈₃	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×C₄×C₈₃	1	1	yes	characteristic
524	C₂²⋊C₄	—	2	4	no	—
525	C₂²⋊C₄	—	2	1	no	—
526	C₂²⋊C₄	—	2	1	no	—
527	C₂²⋊C₄	—	2	1	no	—
528	C₂²⋊C₄	—	2	1	no	—
529	C₂²⋊C₄	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	2	2	no	—
532	C₄²	—	2	2	no	—
533	C₂³	—	2	4	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	4	1	no	—
539	C₂³	—	4	2	no	—
540	C₂³	—	4	2	no	—
541	C₂³	C₄×D₄×C₈₃	1	1	yes	characteristic
542	C₂³	C₄×D₄×C₈₃	1	1	yes	characteristic
543	C₂³	C₂×#41×C₈₃	1	1	yes	characteristic
544	Q₈	—	2	4	no	—
545	Q₈	—	2	2	no	—
546	Q₈	—	2	2	no	—
547	Q₈	C₄×D₄×C₈₃	1	4	yes	—
548	D₄	—	2	8	no	—
549	D₄	—	2	4	no	—
550	D₄	—	2	4	no	—
551	D₄	—	2	4	no	—
552	D₄	—	2	2	no	—
553	D₄	—	2	2	no	—
554	D₄	—	4	2	no	—
555	D₄	—	4	2	no	—
556	D₄	—	4	2	no	—
557	D₄	C₄×D₄×C₈₃	1	4	yes	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	8	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	C₄×D₄×C₈₃	1	1	yes	characteristic
579	C₂×C₄	C₄×D₄×C₈₃	1	1	yes	characteristic
580	C₂×C₄	C₂³×C₄×C₈₃	1	1	yes	characteristic
581	C₂×C₄	C₂²×D₄×C₈₃	1	2	yes	—
582	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
583	C₂×C₄	C₂×#41×C₈₃	1	2	yes	—
584	C₈	—	2	2	no	—
585	C₈	—	2	2	no	—
586	C₈	—	2	1	no	—
587	C₈	—	2	4	no	—
588	C₈	—	2	1	no	—
589	C₈	—	4	1	no	—
590	C₈	—	4	1	no	—
591	C₈	#120×C₈₃	1	2	yes	—
592	C₈	#120×C₈₃	1	2	yes	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	2	1	no	—
598	C₂²	—	2	4	no	—
599	C₂²	—	2	1	no	—
600	C₂²	—	2	1	no	—
601	C₂²	—	4	4	no	—
602	C₂²	—	4	8	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	#443×C₈₃	1	2	yes	complemented
609	C₂²	C₂×C₄×D₄×C₈₃	1	1	yes	characteristic
610	C₂²	#525×C₈₃	1	2	yes	—
611	C₄	—	2	1	no	—
612	C₄	—	2	4	no	—
613	C₄	—	2	1	no	—
614	C₄	—	4	4	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	1	no	—
617	C₄	—	4	1	no	—
618	C₄	C₂×C₄×D₄×C₈₃	1	2	yes	—
619	C₄	C₂×#120×C₈₃	1	1	yes	characteristic
620	C₄	#525×C₈₃	1	1	yes	characteristic
621	C₂	—	2	2	no	—
622	C₂	—	2	2	no	—
623	C₂	—	4	1	no	—
624	C₂	—	4	4	no	—
625	C₂	—	8	1	no	—
626	C₂	C₄×#120×C₈₃	1	1	yes	characteristic
627	C₂	C₂×#443×C₈₃	1	1	yes	characteristic
628	C₂	C₈₃×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₈₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₈₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₃
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	C₈₃×#3002	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₈₃ ◁ C₂³×C₈×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#131×C₈₃	C₂	semidirect
3. C₂×#443×C₈₃	C₂	semidirect
4. C₈₃×#2929	C₂	semidirect
5. C₈₃×#1876	C₂	semidirect
6. C₈₃×#1871	C₂	semidirect
7. C₈₃×#1866	C₂	semidirect
8. C₈₃×#1855	C₂	semidirect
9. C₈₃×#1789	C₂	semidirect
10. C₈₃×#1764	C₂	semidirect
11. C₈×C₂²⋊C₄×C₈₃	C₂	semidirect
19. C₂×#131×C₈₃	C₂²	semidirect
25. #452×C₈₃	C₄	semidirect
26. #451×C₈₃	C₄	semidirect
27. #450×C₈₃	C₄	semidirect
28. #449×C₈₃	C₄	semidirect
29. #448×C₈₃	C₄	semidirect
30. #447×C₈₃	C₄	semidirect
36. C₂×#108×C₈₃	C₂²	semidirect
37. #424×C₈₃	C₂²	semidirect
40. C₂×#104×C₈₃	C₂²	semidirect
42. #408×C₈₃	C₂²	semidirect
45. #405×C₈₃	C₂²	semidirect
46. C₂×C₄×C₈×C₈₃	C₂²	semidirect
48. #341×C₈₃	C₂²	semidirect
49. #339×C₈₃	C₂²	semidirect
50. #336×C₈₃	C₂²	semidirect
75. #131×C₈₃	D₄	semidirect
293. C₂²×C₈₃	#443	semidirect
306. #21466	C₈₃	direct (N × H)
315. C₂²×#131	C₂×C₈₃	semidirect
317. C₂×#443	C₂×C₈₃	semidirect
318. #2929	C₂×C₈₃	semidirect
319. #1876	C₂×C₈₃	semidirect
320. #1871	C₂×C₈₃	semidirect
321. #1866	C₂×C₈₃	semidirect
322. #1855	C₂×C₈₃	semidirect
323. #1789	C₂×C₈₃	semidirect
324. #1764	C₂×C₈₃	semidirect
325. C₈×C₂²⋊C₄	C₂×C₈₃	semidirect
326. C₈₃	#21466	direct (N × H)
334. C₂×#131	C₂²×C₈₃	semidirect
340. #452	C₄×C₈₃	semidirect
341. #451	C₄×C₈₃	semidirect
342. #450	C₄×C₈₃	semidirect
343. #449	C₄×C₈₃	semidirect
344. #448	C₄×C₈₃	semidirect
345. #447	C₄×C₈₃	semidirect
351. C₂×#108	C₂²×C₈₃	semidirect
352. #424	C₂²×C₈₃	semidirect
355. C₂×#104	C₂²×C₈₃	semidirect
357. #408	C₂²×C₈₃	semidirect
360. #405	C₂²×C₈₃	semidirect
361. C₂×C₄×C₈	C₂²×C₈₃	semidirect
363. #341	C₂²×C₈₃	semidirect
364. #339	C₂²×C₈₃	semidirect
365. #336	C₂²×C₈₃	semidirect
390. #131	D₄×C₈₃	semidirect
608. C₂²	#443×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#131×C₈₃	2
C₈₃×#3002	2
C₂×#443×C₈₃	2
C₈₃×#2929	2
C₈₃×#1876	2
C₈₃×#1871	2
C₈₃×#1866	2
C₈₃×#1855	2
C₈₃×#1789	2
C₈₃×#1764	2
C₈×C₂²⋊C₄×C₈₃	2
#21466	83

Subgroups — C83×#21466 #35249290

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#21466 #35249290