Subgroups — #1591×D₈₃ #35374142

Order 21248.

670 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#446×D₈₃	C₂	1	2	yes	maximal
2	C₄×Q₁₆×D₈₃	C₂	1	1	yes	maximal, characteristic
3	#24906361	C₂	1	1	yes	maximal, characteristic, complemented
4	#24906360	C₂	1	1	yes	maximal, characteristic, complemented
5	#24906359	C₂	1	1	yes	maximal, characteristic, complemented
6	#24906358	C₂	1	2	yes	maximal, complemented
7	#24906357	C₂	1	2	yes	maximal, complemented
8	#335×D₈₃	C₂	1	1	yes	maximal, characteristic
9	Q₈⋊C₈×D₈₃	C₂	1	2	yes	maximal
10	C₈²×D₈₃	C₂	1	1	yes	maximal, characteristic
11	C₈₃×#1591	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₈₃	C₄	1	1	yes	characteristic
13	C₄×Q₈×D₈₃	C₂²	1	2	yes	—
14	#19127832	C₂²	1	2	yes	—
15	#19127831	C₂²	1	2	yes	—
16	#19127830	—	2	2	no	—
17	#19127829	—	2	2	no	—
18	#19127828	C₂²	1	2	yes	—
19	C₄×Dic₃₃₂	C₂²	1	1	yes	characteristic
20	Q₁₆×Dic₈₃	C₄	1	1	yes	characteristic
21	#19127795	C₄	1	1	yes	characteristic
22	C₄×#13050580	C₂²	1	2	yes	—
23	#19127793	C₄	1	2	yes	—
24	#107×D₈₃	C₄	1	1	yes	characteristic
25	C₄⋊C₈×D₈₃	—	2	2	no	—
26	C₄⋊C₈×D₈₃	C₂²	1	2	yes	—
27	#103×D₈₃	C₄	1	2	yes	—
28	#97×D₈₃	—	2	2	no	—
29	C₄×C₈×D₈₃	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₈₃	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₈₃	C₂²	1	1	yes	characteristic
32	#19127454	C₂²	1	1	yes	characteristic
33	#19127453	C₂²	1	2	yes	—
34	#19127433	C₂²	1	2	yes	—
35	Q₈⋊(C₈₃⋊C₈)	C₂²	1	2	yes	—
36	#19127431	C₂²	1	2	yes	—
37	C₈×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
38	C₈×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
39	C₈×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
40	#446×C₈₃	C₂²	1	2	yes	—
41	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
42	#335×C₈₃	C₂²	1	1	yes	characteristic
43	Q₈⋊C₈×C₈₃	C₂²	1	2	yes	—
44	C₈²×C₈₃	C₂²	1	1	yes	characteristic
45	C₂×Q₈×D₈₃	C₂×C₄	1	2	yes	—
46	C₂×Dic₃₃₂	C₂×C₄	1	1	yes	characteristic
47	C₂×#13050580	C₂×C₄	1	2	yes	—
48	Q₁₆×D₈₃	—	2	4	no	—
49	C₂×C₈×D₈₃	—	2	1	no	—
50	C₂×C₈×D₈₃	—	2	2	no	—
51	C₂×C₈×D₈₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₈₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₈₃	D₄	1	1	yes	characteristic
54	C₂×C₈×D₈₃	D₄	1	1	yes	characteristic
55	Q₈×Dic₈₃	C₂×C₄	1	2	yes	—
56	C₄×Dic₁₆₆	—	2	2	no	—
57	C₄×Dic₁₆₆	C₂³	1	2	yes	—
58	#14581757	—	2	2	no	—
59	#14581757	C₂×C₄	1	2	yes	—
60	C₄⋊C₄×D₈₃	—	2	2	no	—
61	C₄⋊C₄×D₈₃	C₂×C₄	1	2	yes	—
62	C₄²×D₈₃	—	2	2	no	—
63	C₄²×D₈₃	C₂³	1	1	yes	characteristic
64	#14581726	C₂×C₄	1	1	yes	characteristic
65	#14581725	C₂×C₄	1	2	yes	—
66	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
67	C₄⋊(C₈₃⋊C₈)	C₂³	1	2	yes	—
68	Dic₈₃⋊C₈	—	2	2	no	—
69	Dic₈₃⋊C₈	—	2	2	no	—
70	Dic₈₃⋊C₈	—	2	2	no	—
71	#14581717	C₂×C₄	1	2	yes	—
72	#14581716	C₂×C₄	1	2	yes	—
73	#14581715	C₂×C₄	1	2	yes	—
74	#14581703	—	2	2	no	—
75	#14581702	—	2	2	no	—
76	#14581702	—	2	2	no	—
77	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
78	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
79	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
80	C₈×Dic₈₃	—	2	1	no	—
81	C₈×Dic₈₃	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₈₃	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₈₃	D₄	1	1	yes	characteristic
84	C₈×Dic₈₃	D₄	1	1	yes	characteristic
85	C₂×Q₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
87	#107×C₈₃	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₈×C₈₃	—	2	2	no	—
89	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
90	#103×C₈₃	C₂×C₄	1	2	yes	—
91	#97×C₈₃	—	2	2	no	—
92	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
95	C₂×Dic₁₆₆	—	2	2	no	—
96	C₂×Dic₁₆₆	C₂²×C₄	1	2	yes	—
97	Q₈×D₈₃	—	2	4	no	—
98	Q₈×D₈₃	—	2	4	no	—
99	C₂×C₄×D₈₃	—	2	2	no	—
100	C₂×C₄×D₈₃	—	2	2	no	—
101	C₂×C₄×D₈₃	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄×D₈₃	C₂×D₄	1	1	yes	characteristic
103	C₂×C₄×D₈₃	#41	1	1	yes	characteristic
104	Dic₃₃₂	—	2	2	no	—
105	#13050580	—	2	4	no	—
106	C₂×C₈₃⋊C₈	—	2	1	no	—
107	C₂×C₈₃⋊C₈	—	2	2	no	—
108	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
112	C₈×D₈₃	—	2	4	no	—
113	C₈×D₈₃	—	2	2	no	—
114	C₈×D₈₃	—	2	2	no	—
115	C₈×D₈₃	—	4	4	no	—
116	C₈×D₈₃	M₁₆	1	4	yes	—
117	C₈×D₈₃	Q₁₆	1	4	yes	complemented
118	C₄⋊Dic₈₃	—	2	2	no	—
119	C₄⋊Dic₈₃	C₂²×C₄	1	2	yes	—
120	Dic₈₃⋊C₄	—	2	2	no	—
121	Dic₈₃⋊C₄	—	2	2	no	—
122	Dic₈₃⋊C₄	—	2	2	no	—
123	C₄×Dic₈₃	—	2	2	no	—
124	C₄×Dic₈₃	—	2	2	no	—
125	C₄×Dic₈₃	—	2	2	no	—
126	C₄×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
128	C₄×Dic₈₃	#41	1	1	yes	characteristic
129	C₂×Q₈×C₈₃	C₂²×C₄	1	2	yes	—
130	Q₁₆×C₈₃	—	2	2	no	—
131	C₂×C₈×C₈₃	—	2	1	no	—
132	C₂×C₈×C₈₃	—	2	2	no	—
133	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
137	C₄⋊C₄×C₈₃	—	2	2	no	—
138	C₄⋊C₄×C₈₃	C₂²×C₄	1	2	yes	—
139	C₄²×C₈₃	—	2	2	no	—
140	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
141	C₂²×D₈₃	C₄×D₄	1	1	yes	characteristic
142	Q₈×C₈₃	—	2	2	no	—
143	Q₈×C₈₃	—	2	2	no	—
144	C₂×C₄×C₈₃	—	2	2	no	—
145	C₂×C₄×C₈₃	—	2	2	no	—
146	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
149	C₂×Dic₈₃	—	2	2	no	—
150	C₂×Dic₈₃	—	2	2	no	—
151	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
152	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
153	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
154	C₄×D₈₃	—	2	2	no	—
155	C₄×D₈₃	—	4	4	no	—
156	C₄×D₈₃	—	4	4	no	—
157	C₄×D₈₃	C₂×M₁₆	1	2	yes	—
158	C₄×D₈₃	#131	1	2	yes	—
159	C₄×D₈₃	C₂×Q₁₆	1	2	yes	—
160	C₄×D₈₃	#135	1	2	yes	—
161	Dic₁₆₆	—	2	2	no	—
162	Dic₁₆₆	—	2	2	no	—
163	Dic₁₆₆	—	4	4	no	—
164	C₈×C₈₃	—	2	2	no	—
165	C₈×C₈₃	—	2	1	no	—
166	C₈×C₈₃	—	2	1	no	—
167	C₈×C₈₃	—	4	2	no	—
168	C₈×C₈₃	C₂×M₁₆	1	2	yes	—
169	C₈×C₈₃	C₂×Q₁₆	1	2	yes	complemented
170	C₈₃⋊C₈	—	2	2	no	—
171	C₈₃⋊C₈	—	2	1	no	—
172	C₈₃⋊C₈	—	2	1	no	—
173	C₈₃⋊C₈	—	4	2	no	—
174	C₈₃⋊C₈	C₂×M₁₆	1	2	yes	—
175	C₈₃⋊C₈	C₂×Q₁₆	1	2	yes	complemented
176	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
177	C₂×D₈₃	#436	1	2	yes	—
178	C₂×D₈₃	C₄×Q₁₆	1	2	yes	—
179	C₂×D₈₃	#443	1	2	yes	—
180	C₄×C₈₃	—	2	1	no	—
181	C₄×C₈₃	—	4	2	no	—
182	C₄×C₈₃	—	4	2	no	—
183	C₄×C₈₃	C₂²×M₁₆	1	1	yes	characteristic
184	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
185	C₄×C₈₃	C₂²×Q₁₆	1	1	yes	characteristic
186	C₄×C₈₃	C₂×#135	1	1	yes	characteristic
187	Dic₈₃	—	2	1	no	—
188	Dic₈₃	—	4	2	no	—
189	Dic₈₃	—	4	2	no	—
190	Dic₈₃	#436	1	2	yes	—
191	Dic₈₃	C₄×Q₁₆	1	2	yes	—
192	C₂×#1591	—	83	1	no	maximal, Sylow
193	C₂×C₈₃	C₂×#436	1	1	yes	characteristic
194	C₂×C₈₃	C₂×C₄×Q₁₆	1	1	yes	characteristic
195	C₂×C₈₃	C₂×#443	1	1	yes	characteristic
196	D₈₃	#1591	1	4	yes	direct product factor
197	C₂×#446	—	83	2	no	—
198	C₂×C₄×Q₁₆	—	83	1	no	—
199	#1591	—	83	2	no	—
200	#1591	—	83	1	no	—
201	#1591	—	83	1	no	—
202	#1591	—	83	2	no	—
203	#1591	—	83	1	no	—
204	#1591	D₈₃	1	1	yes	characteristic, direct product factor
205	C₂×#335	—	83	1	no	—
206	C₂×Q₈⋊C₈	—	83	2	no	—
207	C₂×C₈²	—	83	1	no	—
208	C₈₃	C₂×#1591	1	1	yes	characteristic, complemented, Sylow
209	C₂²×Q₁₆	—	83	1	no	—
210	C₂×C₄×Q₈	—	83	2	no	—
211	#446	—	83	2	no	—
212	#446	—	83	2	no	—
213	#446	—	83	2	no	—
214	#446	—	166	2	no	—
215	#446	—	166	2	no	—
216	#446	C₂×D₈₃	1	2	yes	—
217	C₄×Q₁₆	—	83	1	no	—
218	C₄×Q₁₆	—	83	2	no	—
219	C₄×Q₁₆	—	83	1	no	—
220	C₄×Q₁₆	—	83	2	no	—
221	C₄×Q₁₆	—	83	1	no	—
222	C₄×Q₁₆	C₂×D₈₃	1	1	yes	characteristic
223	C₂×#107	—	83	1	no	—
224	C₂×C₄⋊C₈	—	83	2	no	—
225	C₂×C₄⋊C₈	—	166	2	no	—
226	C₂×#103	—	83	2	no	—
227	C₂×#97	—	166	2	no	—
228	C₂×C₄×C₈	—	83	1	no	—
229	C₂×C₄×C₈	—	83	1	no	—
230	C₂×C₄×C₈	—	83	1	no	—
231	#335	—	83	2	no	—
232	#335	—	83	1	no	—
233	#335	C₂×D₈₃	1	1	yes	characteristic
234	Q₈⋊C₈	—	83	2	no	—
235	Q₈⋊C₈	—	83	2	no	—
236	Q₈⋊C₈	—	83	2	no	—
237	Q₈⋊C₈	C₂×D₈₃	1	2	yes	—
238	C₈²	—	83	1	no	—
239	C₈²	—	83	1	no	—
240	C₈²	—	83	1	no	—
241	C₈²	C₂×D₈₃	1	1	yes	characteristic
242	C₂²×Q₈	—	83	2	no	—
243	C₂×Q₁₆	—	83	2	no	—
244	C₂×Q₁₆	—	83	1	no	—
245	C₂×Q₁₆	—	166	4	no	—
246	C₂×Q₁₆	C₄×D₈₃	1	1	yes	characteristic
247	C₂²×C₈	—	83	1	no	—
248	C₂²×C₈	—	83	1	no	—
249	C₂²×C₈	—	83	1	no	—
250	C₂²×C₈	—	83	1	no	—
251	C₂²×C₈	—	166	2	no	—
252	C₂²×C₈	—	166	1	no	—
253	C₄×Q₈	—	83	2	no	—
254	C₄×Q₈	—	83	2	no	—
255	C₄×Q₈	—	83	2	no	—
256	C₄×Q₈	—	166	2	no	—
257	C₄×Q₈	—	166	2	no	—
258	C₄×Q₈	C₂²×D₈₃	1	2	yes	—
259	C₂×C₄⋊C₄	—	83	2	no	—
260	C₂×C₄⋊C₄	—	166	2	no	—
261	C₂×C₄²	—	83	1	no	—
262	C₂×C₄²	—	166	2	no	—
263	#107	—	83	1	no	—
264	#107	—	83	2	no	—
265	#107	C₄×D₈₃	1	1	yes	characteristic
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	—	83	2	no	—
268	C₄⋊C₈	—	166	2	no	—
269	C₄⋊C₈	—	166	2	no	—
270	C₄⋊C₈	—	166	2	no	—
271	C₄⋊C₈	—	166	2	no	—
272	C₄⋊C₈	C₂²×D₈₃	1	2	yes	—
273	#103	—	83	2	no	—
274	#103	—	83	2	no	—
275	#103	—	83	2	no	—
276	#103	C₄×D₈₃	1	2	yes	—
277	#97	—	2	2	no	—
278	#97	—	166	2	no	—
279	#97	—	166	2	no	—
280	#97	—	166	2	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	—	83	1	no	—
286	C₄×C₈	—	83	1	no	—
287	C₄×C₈	—	83	1	no	—
288	C₄×C₈	—	166	1	no	—
289	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
290	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
291	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
292	C₂×Q₈	—	83	2	no	—
293	C₂×Q₈	—	166	2	no	—
294	C₂×Q₈	—	166	4	no	—
295	C₂×Q₈	—	166	4	no	—
296	C₂×Q₈	C₂×C₄×D₈₃	1	2	yes	—
297	C₂²×C₄	—	83	1	no	—
298	C₂²×C₄	—	83	1	no	—
299	C₂²×C₄	—	83	1	no	—
300	C₂²×C₄	—	166	2	no	—
301	C₂²×C₄	—	166	2	no	—
302	Q₁₆	—	2	2	no	—
303	Q₁₆	—	166	4	no	—
304	Q₁₆	—	166	2	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	332	4	no	—
308	C₂×C₈	—	83	1	no	—
309	C₂×C₈	—	83	1	no	—
310	C₂×C₈	—	83	4	no	—
311	C₂×C₈	—	83	4	no	—
312	C₂×C₈	—	83	1	no	—
313	C₂×C₈	—	83	1	no	—
314	C₂×C₈	—	166	2	no	—
315	C₂×C₈	—	166	2	no	—
316	C₂×C₈	—	166	4	no	—
317	C₂×C₈	—	166	2	no	—
318	C₂×C₈	—	166	1	no	—
319	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
320	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
321	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
322	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	83	2	no	—
325	C₄⋊C₄	—	166	2	no	—
326	C₄⋊C₄	—	166	2	no	—
327	C₄⋊C₄	—	166	2	no	—
328	C₄⋊C₄	—	166	2	no	—
329	C₄⋊C₄	C₂×C₄×D₈₃	1	2	yes	—
330	C₄²	—	2	2	no	—
331	C₄²	—	83	1	no	—
332	C₄²	—	83	1	no	—
333	C₄²	—	83	1	no	—
334	C₄²	—	166	2	no	—
335	C₄²	—	166	2	no	—
336	C₄²	—	166	2	no	—
337	C₄²	C₂³×D₈₃	1	1	yes	characteristic
338	C₂³	—	83	1	no	—
339	Q₈	—	2	2	no	—
340	Q₈	—	2	2	no	—
341	Q₈	—	332	4	no	—
342	Q₈	—	166	2	no	—
343	Q₈	—	166	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	332	4	no	—
347	C₂×C₄	—	332	4	no	—
348	C₂×C₄	—	83	1	no	—
349	C₂×C₄	—	83	1	no	—
350	C₂×C₄	—	83	2	no	—
351	C₂×C₄	—	83	2	no	—
352	C₂×C₄	—	83	2	no	—
353	C₂×C₄	—	83	2	no	—
354	C₂×C₄	—	83	1	no	—
355	C₂×C₄	—	166	2	no	—
356	C₂×C₄	—	166	2	no	—
357	C₂×C₄	—	166	2	no	—
358	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
359	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
360	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
361	C₈	—	2	2	no	—
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	4	2	no	—
365	C₈	—	332	2	no	—
366	C₈	—	83	2	no	—
367	C₈	—	83	2	no	—
368	C₈	—	166	2	no	—
369	C₈	—	166	1	no	—
370	C₈	—	166	1	no	—
371	C₈	M₁₆×D₈₃	1	2	yes	—
372	C₈	Q₁₆×D₈₃	1	2	yes	complemented
373	C₂²	—	83	2	no	—
374	C₂²	—	83	2	no	—
375	C₂²	—	83	2	no	—
376	C₂²	C₄×D₄×D₈₃	1	1	yes	characteristic
377	C₄	—	2	1	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	2	no	—
380	C₄	—	332	2	no	—
381	C₄	—	332	2	no	—
382	C₄	—	83	2	no	—
383	C₄	—	83	2	no	—
384	C₄	—	166	1	no	—
385	C₄	C₂×M₁₆×D₈₃	1	1	yes	characteristic
386	C₄	#131×D₈₃	1	1	yes	characteristic
387	C₄	C₂×Q₁₆×D₈₃	1	1	yes	characteristic
388	C₄	#135×D₈₃	1	1	yes	characteristic
389	C₂	—	83	4	no	—
390	C₂	#436×D₈₃	1	1	yes	characteristic
391	C₂	C₄×Q₁₆×D₈₃	1	1	yes	characteristic
392	C₂	#443×D₈₃	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×#1591	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	C₂²×D₈₃	C₄×D₄
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	#1591	D₈₃
hypocenter	C₈₃	C₂×#1591
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1591

Complements

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

N	H ≅ G/N	type
3. #24906361	C₂	semidirect
4. #24906360	C₂	semidirect
5. #24906359	C₂	semidirect
6. #24906358	C₂	semidirect
7. #24906357	C₂	semidirect
11. C₈₃×#1591	C₂	semidirect
117. C₈×D₈₃	Q₁₆	semidirect
169. C₈×C₈₃	C₂×Q₁₆	semidirect
175. C₈₃⋊C₈	C₂×Q₁₆	semidirect
196. D₈₃	#1591	direct (N × H)
204. #1591	D₈₃	direct (N × H)
208. C₈₃	C₂×#1591	semidirect
372. C₈	Q₁₆×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
#446×D₈₃	2
C₄×Q₁₆×D₈₃	2
#24906361	2
#24906360	2
#24906359	2
#24906358	2
#24906357	2
#335×D₈₃	2
Q₈⋊C₈×D₈₃	2
C₈²×D₈₃	2
C₈₃×#1591	2
C₂×#1591	83

Subgroups — #1591×D83 #35374142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1591×D₈₃ #35374142