Subgroups — C₈₃×#21655 #35249479

Order 21248.

886 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#489×C₈₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊Q₈×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#124×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₈₃×#1993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₃×#1959	C₂	1	1	yes	maximal, characteristic
6	C₈₃×#1934	C₂	1	2	yes	maximal
7	C₈₃×#1933	C₂	1	2	yes	maximal, complemented
8	C₈₃×#1836	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₃×#1763	C₂	1	2	yes	maximal, complemented
10	C₈₃×#1762	C₂	1	2	yes	maximal
11	C₄×#97×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
13	C₂×#124×C₈₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₈₃	—	2	1	no	—
15	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
17	#489×C₈₃	C₄	1	8	yes	complemented
18	C₂×#103×C₈₃	C₂²	1	2	yes	—
19	C₂×#103×C₈₃	C₂²	1	2	yes	—
20	C₂×#102×C₈₃	C₂²	1	2	yes	—
21	C₂×#102×C₈₃	C₂²	1	2	yes	—
22	C₂×#97×C₈₃	C₂²	1	2	yes	—
23	C₂×#97×C₈₃	C₂²	1	1	yes	characteristic
24	C₂×#97×C₈₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₈₃	C₂²	1	2	yes	—
26	#391×C₈₃	—	2	1	no	—
27	#391×C₈₃	C₂²	1	1	yes	characteristic
28	#390×C₈₃	C₂²	1	1	yes	characteristic
29	#389×C₈₃	—	2	1	no	—
30	#389×C₈₃	C₂²	1	2	yes	—
31	#388×C₈₃	—	2	1	no	—
32	#388×C₈₃	—	2	1	no	—
33	#384×C₈₃	C₂²	1	1	yes	characteristic
34	#382×C₈₃	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₈₃	—	2	1	no	—
36	C₄×C₄⋊C₄×C₈₃	C₂²	1	2	yes	—
37	C₄×C₂²⋊C₄×C₈₃	—	2	1	no	—
38	C₄×C₂²⋊C₄×C₈₃	—	2	1	no	—
39	C₄³×C₈₃	C₂²	1	1	yes	characteristic
40	#340×C₈₃	C₂²	1	2	yes	—
41	#340×C₈₃	C₂²	1	2	yes	—
42	#340×C₈₃	C₂²	1	2	yes	—
43	#340×C₈₃	C₂²	1	2	yes	—
44	C₂²×Q₈×C₈₃	—	2	1	no	—
45	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₈₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₈₃	—	2	1	no	—
48	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
49	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
50	C₄⋊Q₈×C₈₃	—	2	2	no	—
51	C₄⋊Q₈×C₈₃	C₂×C₄	1	4	yes	complemented
52	#124×C₈₃	—	2	2	no	—
53	#124×C₈₃	C₂×C₄	1	4	yes	—
54	C₄×Q₈×C₈₃	—	2	4	no	—
55	C₄×Q₈×C₈₃	—	4	4	no	—
56	C₄×D₄×C₈₃	—	2	4	no	—
57	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
60	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
71	C₂×C₄²×C₈₃	—	2	2	no	—
72	C₂×C₄²×C₈₃	—	2	1	no	—
73	C₂×C₄²×C₈₃	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₈₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₈₃	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₈₃	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
80	#103×C₈₃	—	2	4	no	—
81	#103×C₈₃	C₂×C₄	1	8	yes	complemented
82	#102×C₈₃	—	2	4	no	—
83	#102×C₈₃	C₂×C₄	1	8	yes	—
84	#97×C₈₃	—	2	2	no	—
85	#97×C₈₃	—	2	4	no	—
86	#97×C₈₃	C₂×C₄	1	4	yes	complemented
87	C₄×C₈×C₈₃	—	2	4	no	—
88	#95×C₈₃	—	2	1	no	—
89	#95×C₈₃	—	2	1	no	—
90	#95×C₈₃	—	2	1	no	—
91	#95×C₈₃	—	2	1	no	—
92	#95×C₈₃	—	2	2	no	—
93	#95×C₈₃	—	2	2	no	—
94	C₂⁴×C₈₃	—	2	1	no	—
95	C₂×Q₈×C₈₃	—	2	4	no	—
96	C₂×Q₈×C₈₃	—	2	1	no	—
97	C₂×Q₈×C₈₃	—	2	2	no	—
98	C₂×Q₈×C₈₃	—	2	2	no	—
99	C₂×Q₈×C₈₃	—	4	2	no	—
100	C₂×Q₈×C₈₃	—	4	2	no	—
101	C₂×Q₈×C₈₃	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₈₃	—	2	2	no	—
103	C₂×D₄×C₈₃	—	2	2	no	—
104	C₂×D₄×C₈₃	—	2	1	no	—
105	C₂×D₄×C₈₃	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₈₃	—	2	1	no	—
107	C₂²×C₄×C₈₃	—	2	2	no	—
108	C₂²×C₄×C₈₃	—	2	1	no	—
109	C₂²×C₄×C₈₃	—	2	1	no	—
110	C₂²×C₄×C₈₃	—	2	2	no	—
111	C₂²×C₄×C₈₃	—	4	2	no	—
112	C₂²×C₄×C₈₃	—	4	2	no	—
113	C₂²×C₄×C₈₃	—	4	2	no	—
114	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
121	C₂×C₈×C₈₃	—	2	2	no	—
122	C₂×C₈×C₈₃	—	2	2	no	—
123	C₂×C₈×C₈₃	—	2	2	no	—
124	C₂×C₈×C₈₃	—	2	2	no	—
125	C₂×C₈×C₈₃	C₂²×C₄	1	4	yes	—
126	C₂×C₈×C₈₃	#41	1	4	yes	—
127	C₄⋊C₄×C₈₃	—	2	4	no	—
128	C₄⋊C₄×C₈₃	—	2	2	no	—
129	C₄⋊C₄×C₈₃	—	2	2	no	—
130	C₄⋊C₄×C₈₃	—	2	2	no	—
131	C₄⋊C₄×C₈₃	—	2	2	no	—
132	C₄⋊C₄×C₈₃	—	2	2	no	—
133	C₄⋊C₄×C₈₃	—	4	2	no	—
134	C₄⋊C₄×C₈₃	—	4	2	no	—
135	C₄⋊C₄×C₈₃	—	4	2	no	—
136	C₄⋊C₄×C₈₃	—	4	4	no	—
137	C₄⋊C₄×C₈₃	C₂²×C₄	1	4	yes	—
138	C₂²⋊C₄×C₈₃	—	2	4	no	—
139	C₂²⋊C₄×C₈₃	—	2	4	no	—
140	C₂²⋊C₄×C₈₃	—	4	2	no	—
141	C₂²⋊C₄×C₈₃	—	4	2	no	—
142	C₂²⋊C₄×C₈₃	—	4	2	no	—
143	C₄²×C₈₃	—	2	2	no	—
144	C₄²×C₈₃	—	2	2	no	—
145	C₄²×C₈₃	—	2	2	no	—
146	C₄²×C₈₃	—	4	1	no	—
147	C₄²×C₈₃	—	4	1	no	—
148	C₄²×C₈₃	—	4	4	no	—
149	C₄²×C₈₃	—	4	2	no	—
150	C₄²×C₈₃	C₂²×C₄	1	2	yes	—
151	C₄²×C₈₃	#41	1	2	yes	—
152	C₄²×C₈₃	#41	1	4	yes	—
153	C₂³×C₈₃	—	2	2	no	—
154	C₂³×C₈₃	—	4	1	no	—
155	C₂³×C₈₃	—	4	1	no	—
156	C₂³×C₈₃	—	4	1	no	—
157	C₂³×C₈₃	—	4	1	no	—
158	C₂³×C₈₃	—	4	1	no	—
159	C₂³×C₈₃	—	4	1	no	—
160	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
161	Q₈×C₈₃	—	2	4	no	—
162	Q₈×C₈₃	—	4	8	no	—
163	Q₈×C₈₃	—	4	2	no	—
164	D₄×C₈₃	—	2	4	no	—
165	D₄×C₈₃	—	4	2	no	—
166	C₂×C₄×C₈₃	—	2	1	no	—
167	C₂×C₄×C₈₃	—	2	1	no	—
168	C₂×C₄×C₈₃	—	2	1	no	—
169	C₂×C₄×C₈₃	—	2	1	no	—
170	C₂×C₄×C₈₃	—	2	1	no	—
171	C₂×C₄×C₈₃	—	2	1	no	—
172	C₂×C₄×C₈₃	—	2	1	no	—
173	C₂×C₄×C₈₃	—	2	1	no	—
174	C₂×C₄×C₈₃	—	2	1	no	—
175	C₂×C₄×C₈₃	—	2	1	no	—
176	C₂×C₄×C₈₃	—	2	1	no	—
177	C₂×C₄×C₈₃	—	2	1	no	—
178	C₂×C₄×C₈₃	—	2	2	no	—
179	C₂×C₄×C₈₃	—	2	4	no	—
180	C₂×C₄×C₈₃	—	4	1	no	—
181	C₂×C₄×C₈₃	—	4	1	no	—
182	C₂×C₄×C₈₃	—	4	2	no	—
183	C₂×C₄×C₈₃	—	4	2	no	—
184	C₂×C₄×C₈₃	—	4	1	no	—
185	C₂×C₄×C₈₃	—	4	1	no	—
186	C₂×C₄×C₈₃	—	4	2	no	—
187	C₂×C₄×C₈₃	—	4	2	no	—
188	C₂×C₄×C₈₃	—	4	1	no	—
189	C₂×C₄×C₈₃	—	4	1	no	—
190	C₂×C₄×C₈₃	—	4	2	no	—
191	C₂×C₄×C₈₃	—	4	1	no	—
192	C₂×C₄×C₈₃	—	4	1	no	—
193	C₂×C₄×C₈₃	—	8	4	no	—
194	C₂×C₄×C₈₃	C₄×D₄	1	2	yes	—
195	C₂×C₄×C₈₃	C₄×D₄	1	2	yes	—
196	C₂×C₄×C₈₃	#124	1	2	yes	—
197	C₂×C₄×C₈₃	#124	1	2	yes	—
198	C₂×C₄×C₈₃	AGL(1,ℤ/8)	1	2	yes	—
199	C₂×C₄×C₈₃	#137	1	2	yes	—
200	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₈₃	C₂×#41	1	2	yes	—
202	C₂×C₄×C₈₃	C₂×#41	1	2	yes	—
203	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
204	C₈×C₈₃	—	2	4	no	—
205	C₈×C₈₃	—	2	4	no	—
206	C₂²×C₈₃	—	4	2	no	—
207	C₂²×C₈₃	—	4	2	no	—
208	C₂²×C₈₃	—	4	2	no	—
209	C₂²×C₈₃	—	8	1	no	—
210	C₂²×C₈₃	—	8	1	no	—
211	C₂²×C₈₃	—	8	1	no	—
212	C₂²×C₈₃	—	8	1	no	—
213	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
214	C₂²×C₈₃	C₂×#124	1	1	yes	characteristic
215	C₂²×C₈₃	#532	1	1	yes	characteristic
216	C₂²×C₈₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
217	C₂²×C₈₃	C₂×#137	1	1	yes	characteristic
218	C₂²×C₈₃	#575	1	1	yes	characteristic
219	C₂²×C₈₃	#575	1	1	yes	characteristic
220	C₄×C₈₃	—	2	2	no	—
221	C₄×C₈₃	—	2	2	no	—
222	C₄×C₈₃	—	2	2	no	—
223	C₄×C₈₃	—	2	2	no	—
224	C₄×C₈₃	—	2	2	no	—
225	C₄×C₈₃	—	2	2	no	—
226	C₄×C₈₃	—	4	4	no	—
227	C₄×C₈₃	—	4	2	no	—
228	C₄×C₈₃	—	8	1	no	—
229	C₄×C₈₃	—	8	1	no	—
230	C₄×C₈₃	—	8	2	no	—
231	C₄×C₈₃	C₄×#41	1	2	yes	—
232	C₄×C₈₃	#529	1	2	yes	—
233	#21655	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂×C₈₃	—	8	2	no	—
235	C₂×C₈₃	C₄×#124	1	1	yes	characteristic
236	C₂×C₈₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
237	C₂×C₈₃	C₄×#137	1	1	yes	characteristic
238	C₂×C₈₃	#3140	1	1	yes	characteristic
239	C₂×C₈₃	#3141	1	1	yes	characteristic
240	C₂×C₈₃	#3180	1	1	yes	characteristic
241	C₂×C₈₃	#3181	1	1	yes	characteristic
242	C₂×#489	C₂×C₈₃	1	1	yes	characteristic
243	C₄×C₄⋊Q₈	C₂×C₈₃	1	1	yes	characteristic, complemented
244	C₄×#124	C₂×C₈₃	1	1	yes	characteristic
245	#1993	C₂×C₈₃	1	1	yes	characteristic, complemented
246	#1959	C₂×C₈₃	1	1	yes	characteristic
247	#1934	C₂×C₈₃	1	2	yes	—
248	#1933	C₂×C₈₃	1	2	yes	complemented
249	#1836	C₂×C₈₃	1	1	yes	characteristic, complemented
250	#1763	C₂×C₈₃	1	2	yes	complemented
251	#1762	C₂×C₈₃	1	2	yes	—
252	C₄×#97	C₂×C₈₃	1	1	yes	characteristic, complemented
253	C₈₃	#21655	1	1	yes	characteristic, direct product factor, Sylow
254	C₂×C₄⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
255	C₂×#124	C₂²×C₈₃	1	1	yes	characteristic
256	C₂×C₄×Q₈	—	2	1	no	—
257	C₂×C₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
258	C₂×C₄×D₄	C₂²×C₈₃	1	1	yes	characteristic
259	#489	C₄×C₈₃	1	8	yes	complemented
260	C₂×#103	C₂²×C₈₃	1	2	yes	—
261	C₂×#103	C₂²×C₈₃	1	2	yes	—
262	C₂×#102	C₂²×C₈₃	1	2	yes	—
263	C₂×#102	C₂²×C₈₃	1	2	yes	—
264	C₂×#97	C₂²×C₈₃	1	1	yes	characteristic
265	C₂×#97	C₂²×C₈₃	1	2	yes	—
266	C₂×#97	C₂²×C₈₃	1	1	yes	characteristic
267	C₂×C₄×C₈	C₂²×C₈₃	1	2	yes	—
268	#391	—	2	1	no	—
269	#391	C₂²×C₈₃	1	1	yes	characteristic
270	#390	C₂²×C₈₃	1	1	yes	characteristic
271	#389	—	2	1	no	—
272	#389	C₂²×C₈₃	1	2	yes	—
273	#388	—	2	1	no	—
274	#388	—	2	1	no	—
275	#384	C₂²×C₈₃	1	1	yes	characteristic
276	#382	C₂²×C₈₃	1	1	yes	characteristic
277	C₄×C₄⋊C₄	—	2	1	no	—
278	C₄×C₄⋊C₄	C₂²×C₈₃	1	2	yes	—
279	C₄×C₂²⋊C₄	—	2	1	no	—
280	C₄×C₂²⋊C₄	—	2	1	no	—
281	C₄³	C₂²×C₈₃	1	1	yes	characteristic
282	#340	C₂²×C₈₃	1	2	yes	—
283	#340	C₂²×C₈₃	1	2	yes	—
284	#340	C₂²×C₈₃	1	2	yes	—
285	#340	C₂²×C₈₃	1	2	yes	—
286	C₂²×Q₈	—	2	1	no	—
287	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
288	C₂²×D₄	C₂³×C₈₃	1	1	yes	characteristic
289	C₂³×C₄	—	2	1	no	—
290	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
291	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
292	C₄⋊Q₈	—	2	2	no	—
293	C₄⋊Q₈	C₂×C₄×C₈₃	1	4	yes	complemented
294	#124	—	2	2	no	—
295	#124	C₂×C₄×C₈₃	1	4	yes	—
296	C₄×Q₈	—	2	4	no	—
297	C₄×Q₈	—	4	4	no	—
298	C₄×D₄	—	2	4	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
307	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₄²	—	2	2	no	—
314	C₂×C₄²	—	2	1	no	—
315	C₂×C₄²	D₄×C₈₃	1	1	yes	characteristic
316	C₂×C₄²	D₄×C₈₃	1	1	yes	characteristic
317	C₂×C₄²	D₄×C₈₃	1	1	yes	characteristic
318	C₂×C₄²	D₄×C₈₃	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
320	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
322	#103	—	2	4	no	—
323	#103	C₂×C₄×C₈₃	1	8	yes	complemented
324	#102	—	2	4	no	—
325	#102	C₂×C₄×C₈₃	1	8	yes	—
326	#97	—	2	2	no	—
327	#97	—	2	4	no	—
328	#97	C₂×C₄×C₈₃	1	4	yes	complemented
329	C₄×C₈	—	2	4	no	—
330	#95	—	2	1	no	—
331	#95	—	2	1	no	—
332	#95	—	2	1	no	—
333	#95	—	2	1	no	—
334	#95	—	2	2	no	—
335	#95	—	2	2	no	—
336	C₂⁴	—	2	1	no	—
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	4	2	no	—
342	C₂×Q₈	—	4	2	no	—
343	C₂×Q₈	C₂²×C₄×C₈₃	1	2	yes	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	C₂²×C₄×C₈₃	1	2	yes	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	C₂²×C₄×C₈₃	1	4	yes	—
368	C₂×C₈	#41×C₈₃	1	4	yes	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₄⋊C₄	—	4	4	no	—
379	C₄⋊C₄	C₂²×C₄×C₈₃	1	4	yes	—
380	C₂²⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	4	2	no	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₂²⋊C₄	—	4	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	4	1	no	—
389	C₄²	—	4	1	no	—
390	C₄²	—	4	4	no	—
391	C₄²	—	4	2	no	—
392	C₄²	C₂²×C₄×C₈₃	1	2	yes	—
393	C₄²	#41×C₈₃	1	2	yes	—
394	C₄²	#41×C₈₃	1	4	yes	—
395	C₂³	—	2	2	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	4	1	no	—
402	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
403	Q₈	—	2	4	no	—
404	Q₈	—	4	8	no	—
405	Q₈	—	4	2	no	—
406	D₄	—	2	4	no	—
407	D₄	—	4	2	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	8	4	no	—
436	C₂×C₄	C₄×D₄×C₈₃	1	2	yes	—
437	C₂×C₄	C₄×D₄×C₈₃	1	2	yes	—
438	C₂×C₄	#124×C₈₃	1	2	yes	—
439	C₂×C₄	#124×C₈₃	1	2	yes	—
440	C₂×C₄	AGL(1,ℤ/8)×C₈₃	1	2	yes	—
441	C₂×C₄	#137×C₈₃	1	2	yes	—
442	C₂×C₄	C₂³×C₄×C₈₃	1	1	yes	characteristic
443	C₂×C₄	C₂×#41×C₈₃	1	2	yes	—
444	C₂×C₄	C₂×#41×C₈₃	1	2	yes	—
445	C₂×C₄	C₂×#41×C₈₃	1	1	yes	characteristic
446	C₈	—	2	4	no	—
447	C₈	—	2	4	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	1	no	—
453	C₂²	—	8	1	no	—
454	C₂²	—	8	1	no	—
455	C₂²	C₂×C₄×D₄×C₈₃	1	1	yes	characteristic
456	C₂²	C₂×#124×C₈₃	1	1	yes	characteristic
457	C₂²	#532×C₈₃	1	1	yes	characteristic
458	C₂²	C₂×AGL(1,ℤ/8)×C₈₃	1	1	yes	characteristic
459	C₂²	C₂×#137×C₈₃	1	1	yes	characteristic
460	C₂²	#575×C₈₃	1	1	yes	characteristic
461	C₂²	#575×C₈₃	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	2	2	no	—
467	C₄	—	2	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	4	no	—
470	C₄	—	8	1	no	—
471	C₄	—	8	1	no	—
472	C₄	—	8	2	no	—
473	C₄	C₄×#41×C₈₃	1	2	yes	—
474	C₄	#529×C₈₃	1	2	yes	—
475	C₂	—	8	2	no	—
476	C₂	C₄×#124×C₈₃	1	1	yes	characteristic
477	C₂	C₄×AGL(1,ℤ/8)×C₈₃	1	1	yes	characteristic
478	C₂	C₄×#137×C₈₃	1	1	yes	characteristic
479	C₂	C₈₃×#3140	1	1	yes	characteristic
480	C₂	C₈₃×#3141	1	1	yes	characteristic
481	C₂	C₈₃×#3180	1	1	yes	characteristic
482	C₂	C₈₃×#3181	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₈₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₃
prime radical	C₂²×D₄×C₈₃	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₃ ◁ C₄³×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₄⋊Q₈×C₈₃	C₂	semidirect
4. C₈₃×#1993	C₂	semidirect
7. C₈₃×#1933	C₂	semidirect
8. C₈₃×#1836	C₂	semidirect
9. C₈₃×#1763	C₂	semidirect
11. C₄×#97×C₈₃	C₂	semidirect
17. #489×C₈₃	C₄	semidirect
51. C₄⋊Q₈×C₈₃	C₂×C₄	semidirect
81. #103×C₈₃	C₂×C₄	semidirect
86. #97×C₈₃	C₂×C₄	semidirect
233. #21655	C₈₃	direct (N × H)
243. C₄×C₄⋊Q₈	C₂×C₈₃	semidirect
245. #1993	C₂×C₈₃	semidirect
248. #1933	C₂×C₈₃	semidirect
249. #1836	C₂×C₈₃	semidirect
250. #1763	C₂×C₈₃	semidirect
252. C₄×#97	C₂×C₈₃	semidirect
253. C₈₃	#21655	direct (N × H)
259. #489	C₄×C₈₃	semidirect
293. C₄⋊Q₈	C₂×C₄×C₈₃	semidirect
323. #103	C₂×C₄×C₈₃	semidirect
328. #97	C₂×C₄×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#489×C₈₃	2
C₄×C₄⋊Q₈×C₈₃	2
C₄×#124×C₈₃	2
C₈₃×#1993	2
C₈₃×#1959	2
C₈₃×#1934	2
C₈₃×#1933	2
C₈₃×#1836	2
C₈₃×#1763	2
C₈₃×#1762	2
C₄×#97×C₈₃	2
#21655	83

Subgroups — C83×#21655 #35249479

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#21655 #35249479