Subgroups — #2165×D₈₃ #35557522

Order 21248.

570 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×M₁₆×D₈₃	C₂	1	1	yes	maximal, characteristic
2	#24909275	C₂	1	1	yes	maximal, characteristic, complemented
3	#24909274	C₂	1	2	yes	maximal, complemented
4	#24909273	C₂	1	2	yes	maximal, complemented
5	#24909272	C₂	1	2	yes	maximal, complemented
6	#364×D₈₃	C₂	1	2	yes	maximal, complemented
7	#349×D₈₃	C₂	1	2	yes	maximal
8	#347×D₈₃	C₂	1	2	yes	maximal, complemented
9	C₈₃×#2165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×M₁₆×D₈₃	C₄	1	1	yes	characteristic
11	C₂×M₁₆×D₈₃	C₂²	1	1	yes	characteristic
12	C₂×C₄²×D₈₃	C₄	1	1	yes	characteristic
13	M₃₂×D₈₃	C₂²	1	4	yes	—
14	C₄×#13050574	C₄	1	1	yes	characteristic
15	#19127653	C₄	1	1	yes	characteristic
16	#19127653	C₂²	1	1	yes	characteristic
17	M₁₆×Dic₈₃	C₄	1	1	yes	characteristic
18	M₁₆×Dic₈₃	C₂²	1	1	yes	characteristic
19	C₄×#13050573	C₄	1	1	yes	characteristic
20	C₄×#13050573	C₂²	1	1	yes	characteristic
21	#97×D₈₃	C₄	1	1	yes	characteristic
22	#97×D₈₃	C₂²	1	1	yes	characteristic
23	C₄×C₈×D₈₃	C₄	1	1	yes	characteristic
24	C₄×C₈×D₈₃	C₂²	1	1	yes	characteristic
25	#19127522	C₂²	1	2	yes	complemented
26	#19127521	C₂²	1	4	yes	complemented
27	#19127483	C₂²	1	2	yes	—
28	#19127482	C₂²	1	4	yes	—
29	#19127479	C₂²	1	2	yes	complemented
30	#19127478	C₂²	1	4	yes	complemented
31	C₄×M₁₆×C₈₃	C₂²	1	1	yes	characteristic
32	#364×C₈₃	C₂²	1	2	yes	complemented
33	#349×C₈₃	C₂²	1	2	yes	—
34	#347×C₈₃	C₂²	1	2	yes	complemented
35	C₂²×C₄×D₈₃	—	2	1	no	—
36	C₂²×C₄×D₈₃	C₂×C₄	1	1	yes	characteristic
37	C₂×#13050574	C₂×C₄	1	1	yes	characteristic
38	C₂×#13050574	C₂×C₄	1	1	yes	characteristic
39	C₂×#13050573	C₂×C₄	1	1	yes	characteristic
40	C₂×#13050573	C₂×C₄	1	1	yes	characteristic
41	C₂×#13050573	C₂×C₄	1	1	yes	characteristic
42	C₂×#13050573	C₂³	1	1	yes	characteristic
43	M₁₆×D₈₃	—	2	2	no	—
44	M₁₆×D₈₃	—	2	2	no	—
45	M₁₆×D₈₃	—	2	2	no	—
46	M₁₆×D₈₃	—	2	2	no	—
47	C₂×C₈×D₈₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₈₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₈₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₈₃	C₂³	1	1	yes	characteristic
51	C₂×C₄×Dic₈₃	—	2	1	no	—
52	C₂×C₄×Dic₈₃	C₂×C₄	1	1	yes	characteristic
53	C₄²×D₈₃	—	2	1	no	—
54	C₄²×D₈₃	—	2	1	no	—
55	C₄²×D₈₃	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₈₃	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₈₃	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₈₃	C₂×C₄	1	1	yes	characteristic
59	#14581732	C₂³	1	4	yes	—
60	#14581731	—	2	4	no	—
61	C₁₆×D₈₃	—	2	4	no	—
62	#14581703	C₂×C₄	1	1	yes	characteristic
63	#14581703	C₂×C₄	1	1	yes	characteristic
64	#14581702	C₂×C₄	1	1	yes	characteristic
65	#14581702	C₂×C₄	1	1	yes	characteristic
66	#14581702	C₂×C₄	1	1	yes	characteristic
67	#14581702	C₂³	1	1	yes	characteristic
68	C₄×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
69	C₄×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
70	C₈×Dic₈₃	C₂×C₄	1	1	yes	characteristic
71	C₈×Dic₈₃	C₂×C₄	1	1	yes	characteristic
72	C₈×Dic₈₃	C₂×C₄	1	1	yes	characteristic
73	C₈×Dic₈₃	C₂³	1	1	yes	characteristic
74	C₂×M₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic
75	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
77	M₃₂×C₈₃	C₂³	1	4	yes	—
78	#97×C₈₃	C₂×C₄	1	1	yes	characteristic
79	#97×C₈₃	C₂³	1	1	yes	characteristic
80	C₄×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
82	C₂³×D₈₃	M₁₆	1	1	yes	characteristic
83	C₂²×Dic₈₃	—	2	1	no	—
84	C₂²×Dic₈₃	M₁₆	1	1	yes	characteristic
85	C₂×C₄×D₈₃	—	2	1	no	—
86	C₂×C₄×D₈₃	—	2	1	no	—
87	C₂×C₄×D₈₃	—	2	1	no	—
88	C₂×C₄×D₈₃	—	2	1	no	—
89	C₂×C₄×D₈₃	—	2	1	no	—
90	C₂×C₄×D₈₃	—	2	1	no	—
91	C₂×C₄×D₈₃	—	2	1	no	—
92	C₂×C₄×D₈₃	—	2	1	no	—
93	C₂×C₄×D₈₃	—	4	4	no	—
94	C₂×C₄×D₈₃	M₁₆	1	1	yes	characteristic
95	C₂×C₄×D₈₃	M₁₆	1	1	yes	characteristic
96	C₂×C₄×D₈₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₄×D₈₃	C₂²×C₄	1	1	yes	characteristic
98	#13050574	—	2	2	no	—
99	#13050574	—	2	2	no	—
100	#13050573	—	2	2	no	—
101	#13050573	—	2	2	no	—
102	#13050573	—	2	2	no	—
103	#13050573	—	2	2	no	—
104	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
108	C₈×D₈₃	—	2	1	no	—
109	C₈×D₈₃	—	2	1	no	—
110	C₈×D₈₃	—	2	1	no	—
111	C₈×D₈₃	—	2	1	no	—
112	C₈×D₈₃	M₁₆	1	2	yes	—
113	C₈×D₈₃	M₁₆	1	2	yes	—
114	C₈×D₈₃	#41	1	2	yes	—
115	C₈×D₈₃	#41	1	2	yes	—
116	C₄×Dic₈₃	—	2	1	no	—
117	C₄×Dic₈₃	—	2	1	no	—
118	C₄×Dic₈₃	—	2	1	no	—
119	C₄×Dic₈₃	—	2	1	no	—
120	C₄×Dic₈₃	—	2	1	no	—
121	C₄×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
122	C₄×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
123	C₈₃⋊C₁₆	—	2	4	no	—
124	C₂²×C₄×C₈₃	—	2	1	no	—
125	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
126	M₁₆×C₈₃	—	2	2	no	—
127	M₁₆×C₈₃	—	2	2	no	—
128	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
132	C₄²×C₈₃	—	2	1	no	—
133	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
135	C₁₆×C₈₃	—	2	4	no	—
136	C₂³×C₈₃	C₂×M₁₆	1	1	yes	characteristic
137	C₂²×D₈₃	—	2	1	no	—
138	C₂²×D₈₃	—	2	1	no	—
139	C₂²×D₈₃	—	4	2	no	—
140	C₂²×D₈₃	C₂×M₁₆	1	1	yes	characteristic
141	C₂²×D₈₃	C₂×M₁₆	1	1	yes	characteristic
142	C₂×C₄×C₈₃	—	2	1	no	—
143	C₂×C₄×C₈₃	—	2	1	no	—
144	C₂×C₄×C₈₃	—	2	1	no	—
145	C₂×C₄×C₈₃	—	2	1	no	—
146	C₂×C₄×C₈₃	—	4	2	no	—
147	C₂×C₄×C₈₃	C₂×M₁₆	1	1	yes	characteristic
148	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
149	C₂×Dic₈₃	—	2	1	no	—
150	C₂×Dic₈₃	—	2	1	no	—
151	C₂×Dic₈₃	—	2	1	no	—
152	C₂×Dic₈₃	—	2	1	no	—
153	C₂×Dic₈₃	—	4	2	no	—
154	C₂×Dic₈₃	C₂×M₁₆	1	1	yes	characteristic
155	C₂×Dic₈₃	C₂×M₁₆	1	1	yes	characteristic
156	C₄×D₈₃	—	2	4	no	—
157	C₄×D₈₃	—	2	1	no	—
158	C₄×D₈₃	—	2	1	no	—
159	C₄×D₈₃	—	2	1	no	—
160	C₄×D₈₃	—	2	1	no	—
161	C₄×D₈₃	—	2	1	no	—
162	C₄×D₈₃	—	2	1	no	—
163	C₄×D₈₃	—	4	2	no	—
164	C₄×D₈₃	—	4	2	no	—
165	C₄×D₈₃	—	4	2	no	—
166	C₄×D₈₃	#117	1	1	yes	characteristic
167	C₄×D₈₃	#117	1	1	yes	characteristic
168	C₄×D₈₃	C₂×M₁₆	1	1	yes	characteristic
169	C₄×D₈₃	C₂×M₁₆	1	1	yes	characteristic
170	C₈×C₈₃	—	2	1	no	—
171	C₈×C₈₃	—	2	1	no	—
172	C₈×C₈₃	C₂×M₁₆	1	2	yes	—
173	C₈×C₈₃	C₂×#41	1	2	yes	—
174	C₈₃⋊C₈	—	2	1	no	—
175	C₈₃⋊C₈	—	2	1	no	—
176	C₈₃⋊C₈	#117	1	2	yes	—
177	C₈₃⋊C₈	C₂×M₁₆	1	2	yes	—
178	C₂²×C₈₃	—	2	1	no	—
179	C₂²×C₈₃	—	4	1	no	—
180	C₂²×C₈₃	C₂²×M₁₆	1	1	yes	characteristic
181	C₂×D₈₃	—	2	2	no	—
182	C₂×D₈₃	—	2	1	no	—
183	C₂×D₈₃	—	4	2	no	—
184	C₂×D₈₃	—	4	2	no	—
185	C₂×D₈₃	—	4	1	no	—
186	C₂×D₈₃	#432	1	1	yes	characteristic
187	C₂×D₈₃	#432	1	1	yes	characteristic
188	C₄×C₈₃	—	2	2	no	—
189	C₄×C₈₃	—	2	1	no	—
190	C₄×C₈₃	—	4	1	no	—
191	C₄×C₈₃	C₂×#117	1	1	yes	characteristic
192	C₄×C₈₃	C₂²×M₁₆	1	1	yes	characteristic
193	Dic₈₃	—	2	2	no	—
194	Dic₈₃	—	2	1	no	—
195	Dic₈₃	—	4	1	no	—
196	Dic₈₃	#432	1	1	yes	characteristic
197	Dic₈₃	#432	1	1	yes	characteristic
198	C₂×#2165	—	83	1	no	maximal, Sylow
199	C₂×C₈₃	—	2	1	no	—
200	C₂×C₈₃	—	4	1	no	—
201	C₂×C₈₃	C₂×#432	1	1	yes	characteristic
202	D₈₃	—	2	1	no	—
203	D₈₃	—	4	1	no	—
204	D₈₃	#2165	1	2	yes	direct product factor
205	C₂×C₄×M₁₆	—	83	1	no	—
206	#2165	—	83	1	no	—
207	#2165	—	83	2	no	—
208	#2165	—	83	2	no	—
209	#2165	—	83	2	no	—
210	#2165	D₈₃	1	1	yes	characteristic, direct product factor
211	C₂×#364	—	83	2	no	—
212	C₂×#349	—	83	2	no	—
213	C₂×#347	—	83	2	no	—
214	C₈₃	C₂×#2165	1	1	yes	characteristic, complemented, Sylow
215	C₂²×M₁₆	—	83	1	no	—
216	C₂²×M₁₆	—	83	1	no	—
217	C₂²×C₄²	—	83	1	no	—
218	C₂×M₃₂	—	83	4	no	—
219	C₄×M₁₆	—	83	1	no	—
220	C₄×M₁₆	—	83	1	no	—
221	C₄×M₁₆	—	83	1	no	—
222	C₄×M₁₆	—	83	1	no	—
223	C₄×M₁₆	—	83	1	no	—
224	C₄×M₁₆	—	83	1	no	—
225	C₄×M₁₆	—	83	1	no	—
226	C₄×M₁₆	C₂×D₈₃	1	1	yes	characteristic
227	C₂×#97	—	83	1	no	—
228	C₂×#97	—	83	1	no	—
229	C₂×C₄×C₈	—	83	1	no	—
230	C₂×C₄×C₈	—	83	1	no	—
231	#364	—	83	4	no	—
232	#364	—	83	2	no	—
233	#364	C₂×D₈₃	1	2	yes	complemented
234	#349	—	83	2	no	—
235	#349	—	83	4	no	—
236	#349	C₂×D₈₃	1	2	yes	—
237	#347	—	83	4	no	—
238	#347	—	83	2	no	—
239	#347	C₂×D₈₃	1	2	yes	complemented
240	C₂³×C₄	—	83	1	no	—
241	C₂³×C₄	—	166	1	no	—
242	C₂×M₁₆	—	83	1	no	—
243	C₂×M₁₆	—	83	1	no	—
244	C₂×M₁₆	—	83	1	no	—
245	C₂×M₁₆	—	83	1	no	—
246	C₂×M₁₆	—	83	1	no	—
247	C₂×M₁₆	—	83	1	no	—
248	C₂×M₁₆	—	166	2	no	—
249	C₂×M₁₆	—	166	2	no	—
250	C₂×M₁₆	—	166	2	no	—
251	C₂×M₁₆	—	166	2	no	—
252	C₂×M₁₆	C₄×D₈₃	1	1	yes	characteristic
253	C₂×M₁₆	C₂²×D₈₃	1	1	yes	characteristic
254	C₂²×C₈	—	83	1	no	—
255	C₂²×C₈	—	83	1	no	—
256	C₂²×C₈	—	83	1	no	—
257	C₂²×C₈	—	83	1	no	—
258	C₂×C₄²	—	83	1	no	—
259	C₂×C₄²	—	83	1	no	—
260	C₂×C₄²	—	83	1	no	—
261	C₂×C₄²	—	83	1	no	—
262	C₂×C₄²	—	83	1	no	—
263	C₂×C₄²	—	166	1	no	—
264	C₂×C₄²	—	166	1	no	—
265	C₂×C₄²	—	166	1	no	—
266	C₂×C₄²	C₄×D₈₃	1	1	yes	characteristic
267	M₃₂	—	83	4	no	—
268	M₃₂	—	166	4	no	—
269	M₃₂	C₂²×D₈₃	1	4	yes	—
270	C₂×C₁₆	—	166	4	no	—
271	#97	—	83	1	no	—
272	#97	—	83	1	no	—
273	#97	—	83	1	no	—
274	#97	—	83	1	no	—
275	#97	—	83	1	no	—
276	#97	—	83	1	no	—
277	#97	C₄×D₈₃	1	1	yes	characteristic
278	#97	C₂²×D₈₃	1	1	yes	characteristic
279	C₄×C₈	—	83	1	no	—
280	C₄×C₈	—	83	1	no	—
281	C₄×C₈	—	83	1	no	—
282	C₄×C₈	—	83	1	no	—
283	C₄×C₈	—	83	1	no	—
284	C₄×C₈	—	83	1	no	—
285	C₄×C₈	C₄×D₈₃	1	1	yes	characteristic
286	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
287	C₂⁴	—	83	1	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	332	4	no	—
290	C₂²×C₄	—	83	1	no	—
291	C₂²×C₄	—	83	1	no	—
292	C₂²×C₄	—	83	1	no	—
293	C₂²×C₄	—	83	1	no	—
294	C₂²×C₄	—	83	1	no	—
295	C₂²×C₄	—	166	1	no	—
296	C₂²×C₄	—	166	1	no	—
297	C₂²×C₄	—	166	1	no	—
298	C₂²×C₄	—	166	1	no	—
299	C₂²×C₄	—	166	1	no	—
300	C₂²×C₄	—	166	1	no	—
301	C₂²×C₄	—	166	1	no	—
302	C₂²×C₄	—	166	1	no	—
303	C₂²×C₄	—	166	1	no	—
304	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
305	M₁₆	—	2	2	no	—
306	M₁₆	—	2	2	no	—
307	M₁₆	—	166	2	no	—
308	M₁₆	—	166	2	no	—
309	M₁₆	—	166	2	no	—
310	M₁₆	—	166	2	no	—
311	M₁₆	—	166	2	no	—
312	M₁₆	—	166	2	no	—
313	C₂×C₈	—	83	1	no	—
314	C₂×C₈	—	83	1	no	—
315	C₂×C₈	—	83	2	no	—
316	C₂×C₈	—	83	2	no	—
317	C₂×C₈	—	83	2	no	—
318	C₂×C₈	—	83	2	no	—
319	C₂×C₈	—	83	1	no	—
320	C₂×C₈	—	83	1	no	—
321	C₂×C₈	—	166	1	no	—
322	C₂×C₈	—	166	1	no	—
323	C₂×C₈	—	166	1	no	—
324	C₂×C₈	—	166	1	no	—
325	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
326	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
327	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
328	C₂×C₈	C₂³×D₈₃	1	1	yes	characteristic
329	C₄²	—	2	1	no	—
330	C₄²	—	83	1	no	—
331	C₄²	—	83	1	no	—
332	C₄²	—	166	1	no	—
333	C₄²	—	166	1	no	—
334	C₄²	—	166	1	no	—
335	C₄²	—	166	1	no	—
336	C₄²	—	166	1	no	—
337	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
338	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
339	C₁₆	—	2	4	no	—
340	C₁₆	—	166	4	no	—
341	C₂³	—	332	2	no	—
342	C₂³	—	83	1	no	—
343	C₂³	—	83	1	no	—
344	C₂³	—	166	1	no	—
345	C₂³	—	166	1	no	—
346	C₂³	M₁₆×D₈₃	1	1	yes	characteristic
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	332	2	no	—
353	C₂×C₄	—	332	2	no	—
354	C₂×C₄	—	332	2	no	—
355	C₂×C₄	—	332	2	no	—
356	C₂×C₄	—	83	1	no	—
357	C₂×C₄	—	83	1	no	—
358	C₂×C₄	—	83	1	no	—
359	C₂×C₄	—	83	1	no	—
360	C₂×C₄	—	83	1	no	—
361	C₂×C₄	—	83	1	no	—
362	C₂×C₄	—	166	1	no	—
363	C₂×C₄	—	166	1	no	—
364	C₂×C₄	—	166	1	no	—
365	C₂×C₄	—	166	1	no	—
366	C₂×C₄	—	166	4	no	—
367	C₂×C₄	—	166	1	no	—
368	C₂×C₄	—	166	1	no	—
369	C₂×C₄	—	166	1	no	—
370	C₂×C₄	—	166	1	no	—
371	C₂×C₄	—	166	1	no	—
372	C₂×C₄	—	166	1	no	—
373	C₂×C₄	M₁₆×D₈₃	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	83	2	no	—
378	C₈	—	83	2	no	—
379	C₈	—	166	1	no	—
380	C₈	—	166	1	no	—
381	C₈	M₁₆×D₈₃	1	2	yes	—
382	C₈	#41×D₈₃	1	2	yes	—
383	C₂²	—	2	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	332	1	no	—
386	C₂²	—	332	2	no	—
387	C₂²	—	332	2	no	—
388	C₂²	—	83	1	no	—
389	C₂²	—	83	1	no	—
390	C₂²	—	166	2	no	—
391	C₂²	—	166	1	no	—
392	C₂²	C₂×M₁₆×D₈₃	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	2	1	no	—
395	C₄	—	4	1	no	—
396	C₄	—	332	1	no	—
397	C₄	—	83	1	no	—
398	C₄	—	83	1	no	—
399	C₄	—	166	2	no	—
400	C₄	—	166	1	no	—
401	C₄	#117×D₈₃	1	1	yes	characteristic
402	C₄	C₂×M₁₆×D₈₃	1	1	yes	characteristic
403	C₂	—	2	1	no	—
404	C₂	—	4	1	no	—
405	C₂	—	332	1	no	—
406	C₂	—	83	2	no	—
407	C₂	—	166	1	no	—
408	C₂	#432×D₈₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#117×D₈₃
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₈₃
Fitting	C₈₃×#2165	C₂
socle	C₂×C₈₃	C₂×#432
prime radical	C₂³×D₈₃	M₁₆
cosocle	C₂×C₈×C₈₃	C₂⁴
hypercenter	#2165	D₈₃
hypocenter	C₈₃	C₂×#2165
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₄ ◁ #97 ◁ #2165

Complements

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

N	H ≅ G/N	type
2. #24909275	C₂	semidirect
3. #24909274	C₂	semidirect
4. #24909273	C₂	semidirect
5. #24909272	C₂	semidirect
6. #364×D₈₃	C₂	semidirect
8. #347×D₈₃	C₂	semidirect
9. C₈₃×#2165	C₂	semidirect
25. #19127522	C₂²	semidirect
26. #19127521	C₂²	semidirect
29. #19127479	C₂²	semidirect
30. #19127478	C₂²	semidirect
32. #364×C₈₃	C₂²	semidirect
34. #347×C₈₃	C₂²	semidirect
204. D₈₃	#2165	direct (N × H)
210. #2165	D₈₃	direct (N × H)
214. C₈₃	C₂×#2165	semidirect
233. #364	C₂×D₈₃	semidirect
239. #347	C₂×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×M₁₆×D₈₃	2
#24909275	2
#24909274	2
#24909273	2
#24909272	2
#364×D₈₃	2
#349×D₈₃	2
#347×D₈₃	2
C₈₃×#2165	2
C₂×#2165	83

Subgroups — #2165×D83 #35557522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2165×D₈₃ #35557522