Subgroups — C₈₃×#17849 #35245673

Order 21248.

734 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#41×C₈₃	C₂	1	2	yes	maximal, complemented
2	C₄×#135×C₈₃	C₂	1	1	yes	maximal, characteristic
3	C₈₃×#1580	C₂	1	2	yes	maximal, complemented
4	C₈₃×#1579	C₂	1	2	yes	maximal, complemented
5	C₈₃×SD₁₆⋊C₈	C₂	1	4	yes	maximal, complemented
6	C₈₃×#1564	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₃×#1476	C₂	1	2	yes	maximal, complemented
8	C₂×#322×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#135×C₈₃	C₄	1	1	yes	characteristic
10	C₄×#41×C₈₃	C₂²	1	2	yes	—
11	C₈×Q₈×C₈₃	C₂²	1	4	yes	—
12	C₄×Q₁₆×C₈₃	C₄	1	1	yes	characteristic
13	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
14	C₄×SD₁₆×C₈₃	C₄	1	2	yes	—
15	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	—
16	C₄×D₈×C₈₃	C₄	1	1	yes	characteristic
17	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic
18	C₈×D₄×C₈₃	—	2	4	no	—
19	C₈×D₄×C₈₃	C₂²	1	4	yes	—
20	#431×C₈₃	—	2	2	no	—
21	#431×C₈₃	C₂²	1	2	yes	—
22	#427×C₈₃	C₄	1	1	yes	characteristic
23	#416×C₈₃	C₄	1	2	yes	—
24	C₂×C₄×C₈×C₈₃	—	2	2	no	—
25	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
28	#335×C₈₃	C₂²	1	2	yes	—
29	#334×C₈₃	C₂²	1	2	yes	—
30	Q₈⋊C₈×C₈₃	C₂²	1	4	yes	—
31	D₄⋊C₈×C₈₃	C₂²	1	4	yes	—
32	#322×C₈₃	C₂²	1	2	yes	—
33	#322×C₈₃	C₂²	1	2	yes	—
34	C₂×#41×C₈₃	C₂×C₄	1	2	yes	—
35	#135×C₈₃	C₈	1	8	yes	complemented
36	C₂×Q₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic
37	C₂×SD₁₆×C₈₃	C₂×C₄	1	2	yes	—
38	C₂×D₈×C₈₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₈₃	—	2	1	no	—
40	C₂²×C₈×C₈₃	—	2	4	no	—
41	C₂²×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₈×C₈₃	D₄	1	2	yes	—
44	C₄×Q₈×C₈₃	C₂×C₄	1	2	yes	—
45	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
46	C₄×D₄×C₈₃	—	2	2	no	—
47	C₄×D₄×C₈₃	—	2	2	no	—
48	C₄×D₄×C₈₃	C₂×C₄	1	2	yes	—
49	C₄×D₄×C₈₃	C₂³	1	2	yes	—
50	#117×C₈₃	—	2	2	no	—
51	#117×C₈₃	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₈₃	—	2	2	no	—
53	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
54	#107×C₈₃	C₂×C₄	1	1	yes	characteristic
55	#107×C₈₃	C₂×C₄	1	1	yes	characteristic
56	#106×C₈₃	C₂×C₄	1	2	yes	—
57	C₄⋊C₈×C₈₃	—	2	4	no	—
58	C₄⋊C₈×C₈₃	C₂³	1	4	yes	—
59	#103×C₈₃	C₂×C₄	1	2	yes	—
60	#103×C₈₃	C₂×C₄	1	2	yes	—
61	#102×C₈₃	C₂×C₄	1	2	yes	—
62	#102×C₈₃	C₂×C₄	1	2	yes	—
63	C₂²⋊C₈×C₈₃	—	2	2	no	—
64	C₂²⋊C₈×C₈₃	—	2	4	no	—
65	C₄×C₈×C₈₃	—	2	4	no	—
66	C₄×C₈×C₈₃	—	2	2	no	—
67	C₄×C₈×C₈₃	—	2	1	no	—
68	C₄×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
69	C₄×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
70	C₄×C₈×C₈₃	D₄	1	2	yes	—
71	C₄×C₈×C₈₃	C₂³	1	2	yes	—
72	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
73	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₈₃	C₂³	1	2	yes	—
75	#41×C₈₃	—	2	4	no	—
76	#41×C₈₃	C₂×C₈	1	8	yes	complemented
77	C₂×Q₈×C₈₃	C₂²×C₄	1	2	yes	—
78	C₂×D₄×C₈₃	—	2	2	no	—
79	C₂×D₄×C₈₃	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₈₃	—	2	2	no	—
81	C₂²×C₄×C₈₃	—	2	2	no	—
82	C₂²×C₄×C₈₃	—	2	2	no	—
83	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
86	Q₁₆×C₈₃	C₂×C₈	1	4	yes	complemented
87	SD₁₆×C₈₃	C₂×C₈	1	8	yes	complemented
88	D₈×C₈₃	C₂×C₈	1	4	yes	complemented
89	C₂×C₈×C₈₃	—	2	2	no	—
90	C₂×C₈×C₈₃	—	2	4	no	—
91	C₂×C₈×C₈₃	—	2	2	no	—
92	C₂×C₈×C₈₃	—	4	2	no	—
93	C₂×C₈×C₈₃	—	4	8	no	—
94	C₂×C₈×C₈₃	—	4	2	no	—
95	C₂×C₈×C₈₃	C₂×C₈	1	4	yes	complemented
96	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₈₃	C₂×D₄	1	4	yes	—
101	C₄⋊C₄×C₈₃	—	2	2	no	—
102	C₄⋊C₄×C₈₃	—	2	2	no	—
103	C₄⋊C₄×C₈₃	C₂²×C₄	1	2	yes	—
104	C₄⋊C₄×C₈₃	C₂²×C₄	1	2	yes	—
105	C₂²⋊C₄×C₈₃	—	2	2	no	—
106	C₂²⋊C₄×C₈₃	—	2	2	no	—
107	C₂²⋊C₄×C₈₃	—	2	2	no	—
108	C₄²×C₈₃	—	2	2	no	—
109	C₄²×C₈₃	—	2	2	no	—
110	C₄²×C₈₃	—	2	2	no	—
111	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₈₃	#41	1	1	yes	characteristic
114	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
115	C₂³×C₈₃	—	2	2	no	—
116	C₂³×C₈₃	C₄×D₄	1	1	yes	characteristic
117	Q₈×C₈₃	—	2	2	no	—
118	Q₈×C₈₃	C₂²×C₈	1	4	yes	—
119	D₄×C₈₃	—	2	8	no	—
120	D₄×C₈₃	—	2	2	no	—
121	D₄×C₈₃	C₂²×C₈	1	4	yes	—
122	C₂×C₄×C₈₃	—	2	2	no	—
123	C₂×C₄×C₈₃	—	2	2	no	—
124	C₂×C₄×C₈₃	—	2	8	no	—
125	C₂×C₄×C₈₃	—	2	2	no	—
126	C₂×C₄×C₈₃	—	2	2	no	—
127	C₂×C₄×C₈₃	—	2	2	no	—
128	C₂×C₄×C₈₃	—	4	4	no	—
129	C₂×C₄×C₈₃	—	4	4	no	—
130	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
131	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
132	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
133	C₂×C₄×C₈₃	C₂²×C₈	1	2	yes	—
134	C₂×C₄×C₈₃	#131	1	2	yes	—
135	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
136	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
137	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
138	C₈×C₈₃	—	2	1	no	—
139	C₈×C₈₃	—	2	1	no	—
140	C₈×C₈₃	—	2	4	no	—
141	C₈×C₈₃	—	4	2	no	—
142	C₈×C₈₃	—	4	4	no	—
143	C₈×C₈₃	C₂²×C₈	1	2	yes	—
144	C₈×C₈₃	C₂²×C₈	1	2	yes	—
145	C₂²×C₈₃	—	2	1	no	—
146	C₂²×C₈₃	—	2	1	no	—
147	C₂²×C₈₃	—	2	4	no	—
148	C₂²×C₈₃	—	4	2	no	—
149	C₂²×C₈₃	—	4	2	no	—
150	C₂²×C₈₃	C₈×D₄	1	2	yes	—
151	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
152	C₄×C₈₃	—	2	4	no	—
153	C₄×C₈₃	—	2	1	no	—
154	C₄×C₈₃	—	2	1	no	—
155	C₄×C₈₃	—	4	2	no	—
156	C₄×C₈₃	—	4	2	no	—
157	C₄×C₈₃	C₈×D₄	1	2	yes	—
158	C₄×C₈₃	#444	1	2	yes	—
159	C₄×C₈₃	C₂³×C₈	1	1	yes	characteristic
160	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
161	C₄×C₈₃	#575	1	2	yes	—
162	#17849	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂×C₈₃	—	2	2	no	—
164	C₂×C₈₃	—	4	4	no	—
165	C₂×C₈₃	C₂×C₈×D₄	1	1	yes	characteristic
166	C₂×C₈₃	#2943	1	1	yes	characteristic
167	C₂×C₈₃	C₂×#444	1	1	yes	characteristic
168	C₈×#41	C₂×C₈₃	1	2	yes	complemented
169	C₄×#135	C₂×C₈₃	1	1	yes	characteristic
170	#1580	C₂×C₈₃	1	2	yes	complemented
171	#1579	C₂×C₈₃	1	2	yes	complemented
172	SD₁₆⋊C₈	C₂×C₈₃	1	4	yes	complemented
173	#1564	C₂×C₈₃	1	1	yes	characteristic, complemented
174	#1476	C₂×C₈₃	1	2	yes	complemented
175	C₂×#322	C₂×C₈₃	1	1	yes	characteristic, complemented
176	C₈₃	#17849	1	1	yes	characteristic, direct product factor, Sylow
177	C₂×#135	C₄×C₈₃	1	1	yes	characteristic
178	C₄×#41	C₂²×C₈₃	1	2	yes	—
179	C₈×Q₈	C₂²×C₈₃	1	4	yes	—
180	C₄×Q₁₆	C₄×C₈₃	1	1	yes	characteristic
181	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic
182	C₄×SD₁₆	C₄×C₈₃	1	2	yes	—
183	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	—
184	C₄×D₈	C₄×C₈₃	1	1	yes	characteristic
185	C₄×D₈	C₂²×C₈₃	1	1	yes	characteristic
186	C₈×D₄	—	2	4	no	—
187	C₈×D₄	C₂²×C₈₃	1	4	yes	—
188	#431	—	2	2	no	—
189	#431	C₂²×C₈₃	1	2	yes	—
190	#427	C₄×C₈₃	1	1	yes	characteristic
191	#416	C₄×C₈₃	1	2	yes	—
192	C₂×C₄×C₈	—	2	2	no	—
193	C₂×C₄×C₈	C₂²×C₈₃	1	1	yes	characteristic
194	C₂×C₄×C₈	C₂²×C₈₃	1	1	yes	characteristic
195	C₂×C₄×C₈	C₂²×C₈₃	1	1	yes	characteristic
196	#335	C₂²×C₈₃	1	2	yes	—
197	#334	C₂²×C₈₃	1	2	yes	—
198	Q₈⋊C₈	C₂²×C₈₃	1	4	yes	—
199	D₄⋊C₈	C₂²×C₈₃	1	4	yes	—
200	#322	C₂²×C₈₃	1	2	yes	—
201	#322	C₂²×C₈₃	1	2	yes	—
202	C₂×#41	C₂×C₄×C₈₃	1	2	yes	—
203	#135	C₈×C₈₃	1	8	yes	complemented
204	C₂×Q₁₆	C₂×C₄×C₈₃	1	1	yes	characteristic
205	C₂×SD₁₆	C₂×C₄×C₈₃	1	2	yes	—
206	C₂×D₈	C₂×C₄×C₈₃	1	1	yes	characteristic
207	C₂²×C₈	—	2	1	no	—
208	C₂²×C₈	—	2	4	no	—
209	C₂²×C₈	C₂×C₄×C₈₃	1	1	yes	characteristic
210	C₂²×C₈	C₂×C₄×C₈₃	1	1	yes	characteristic
211	C₂²×C₈	D₄×C₈₃	1	2	yes	—
212	C₄×Q₈	C₂×C₄×C₈₃	1	2	yes	—
213	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
214	C₄×D₄	—	2	2	no	—
215	C₄×D₄	—	2	2	no	—
216	C₄×D₄	C₂×C₄×C₈₃	1	2	yes	—
217	C₄×D₄	C₂³×C₈₃	1	2	yes	—
218	#117	—	2	2	no	—
219	#117	C₂×C₄×C₈₃	1	2	yes	—
220	C₂×C₄²	—	2	2	no	—
221	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
222	#107	C₂×C₄×C₈₃	1	1	yes	characteristic
223	#107	C₂×C₄×C₈₃	1	1	yes	characteristic
224	#106	C₂×C₄×C₈₃	1	2	yes	—
225	C₄⋊C₈	—	2	4	no	—
226	C₄⋊C₈	C₂³×C₈₃	1	4	yes	—
227	#103	C₂×C₄×C₈₃	1	2	yes	—
228	#103	C₂×C₄×C₈₃	1	2	yes	—
229	#102	C₂×C₄×C₈₃	1	2	yes	—
230	#102	C₂×C₄×C₈₃	1	2	yes	—
231	C₂²⋊C₈	—	2	2	no	—
232	C₂²⋊C₈	—	2	4	no	—
233	C₄×C₈	—	2	4	no	—
234	C₄×C₈	—	2	2	no	—
235	C₄×C₈	—	2	1	no	—
236	C₄×C₈	C₂×C₄×C₈₃	1	1	yes	characteristic
237	C₄×C₈	C₂×C₄×C₈₃	1	1	yes	characteristic
238	C₄×C₈	D₄×C₈₃	1	2	yes	—
239	C₄×C₈	C₂³×C₈₃	1	2	yes	—
240	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
241	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
242	C₄×C₈	C₂³×C₈₃	1	2	yes	—
243	#41	—	2	4	no	—
244	#41	C₂×C₈×C₈₃	1	8	yes	complemented
245	C₂×Q₈	C₂²×C₄×C₈₃	1	2	yes	—
246	C₂×D₄	—	2	2	no	—
247	C₂×D₄	C₂²×C₄×C₈₃	1	2	yes	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	C₂²×C₄×C₈₃	1	1	yes	characteristic
252	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
253	C₂²×C₄	#41×C₈₃	1	1	yes	characteristic
254	Q₁₆	C₂×C₈×C₈₃	1	4	yes	complemented
255	SD₁₆	C₂×C₈×C₈₃	1	8	yes	complemented
256	D₈	C₂×C₈×C₈₃	1	4	yes	complemented
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	4	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	4	2	no	—
261	C₂×C₈	—	4	8	no	—
262	C₂×C₈	—	4	2	no	—
263	C₂×C₈	C₂×C₈×C₈₃	1	4	yes	complemented
264	C₂×C₈	C₂²×C₄×C₈₃	1	1	yes	characteristic
265	C₂×C₈	C₂²×C₄×C₈₃	1	1	yes	characteristic
266	C₂×C₈	C₂²×C₄×C₈₃	1	1	yes	characteristic
267	C₂×C₈	C₂²×C₄×C₈₃	1	1	yes	characteristic
268	C₂×C₈	C₂×D₄×C₈₃	1	4	yes	—
269	C₄⋊C₄	—	2	2	no	—
270	C₄⋊C₄	—	2	2	no	—
271	C₄⋊C₄	C₂²×C₄×C₈₃	1	2	yes	—
272	C₄⋊C₄	C₂²×C₄×C₈₃	1	2	yes	—
273	C₂²⋊C₄	—	2	2	no	—
274	C₂²⋊C₄	—	2	2	no	—
275	C₂²⋊C₄	—	2	2	no	—
276	C₄²	—	2	2	no	—
277	C₄²	—	2	2	no	—
278	C₄²	—	2	2	no	—
279	C₄²	C₂²×C₄×C₈₃	1	1	yes	characteristic
280	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
281	C₄²	#41×C₈₃	1	1	yes	characteristic
282	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
283	C₂³	—	2	2	no	—
284	C₂³	C₄×D₄×C₈₃	1	1	yes	characteristic
285	Q₈	—	2	2	no	—
286	Q₈	C₂²×C₈×C₈₃	1	4	yes	—
287	D₄	—	2	8	no	—
288	D₄	—	2	2	no	—
289	D₄	C₂²×C₈×C₈₃	1	4	yes	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	8	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	4	4	no	—
297	C₂×C₄	—	4	4	no	—
298	C₂×C₄	C₄×D₄×C₈₃	1	1	yes	characteristic
299	C₂×C₄	C₄×D₄×C₈₃	1	1	yes	characteristic
300	C₂×C₄	C₄×D₄×C₈₃	1	1	yes	characteristic
301	C₂×C₄	C₂²×C₈×C₈₃	1	2	yes	—
302	C₂×C₄	#131×C₈₃	1	2	yes	—
303	C₂×C₄	C₂³×C₄×C₈₃	1	1	yes	characteristic
304	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
305	C₂×C₄	C₂×#41×C₈₃	1	1	yes	characteristic
306	C₈	—	2	1	no	—
307	C₈	—	2	1	no	—
308	C₈	—	2	4	no	—
309	C₈	—	4	2	no	—
310	C₈	—	4	4	no	—
311	C₈	C₂²×C₈×C₈₃	1	2	yes	—
312	C₈	C₂²×C₈×C₈₃	1	2	yes	—
313	C₂²	—	2	1	no	—
314	C₂²	—	2	1	no	—
315	C₂²	—	2	4	no	—
316	C₂²	—	4	2	no	—
317	C₂²	—	4	2	no	—
318	C₂²	C₈×D₄×C₈₃	1	2	yes	—
319	C₂²	C₂×C₄×D₄×C₈₃	1	1	yes	characteristic
320	C₄	—	2	4	no	—
321	C₄	—	2	1	no	—
322	C₄	—	2	1	no	—
323	C₄	—	4	2	no	—
324	C₄	—	4	2	no	—
325	C₄	C₈×D₄×C₈₃	1	2	yes	—
326	C₄	#444×C₈₃	1	2	yes	—
327	C₄	C₂³×C₈×C₈₃	1	1	yes	characteristic
328	C₄	C₂×#131×C₈₃	1	1	yes	characteristic
329	C₄	#575×C₈₃	1	2	yes	—
330	C₂	—	2	2	no	—
331	C₂	—	4	4	no	—
332	C₂	C₂×C₈×D₄×C₈₃	1	1	yes	characteristic
333	C₂	C₈₃×#2943	1	1	yes	characteristic
334	C₂	C₂×#444×C₈₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₈₃	C₂×D₄
commutator	C₄	C₂³×C₈×C₈₃
Frattini, cosocle	C₄²	C₂⁴×C₈₃
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	C₂×#135×C₈₃	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₈₃ ◁ C₂×C₄×C₈×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈×#41×C₈₃	C₂	semidirect
3. C₈₃×#1580	C₂	semidirect
4. C₈₃×#1579	C₂	semidirect
5. C₈₃×SD₁₆⋊C₈	C₂	semidirect
6. C₈₃×#1564	C₂	semidirect
7. C₈₃×#1476	C₂	semidirect
8. C₂×#322×C₈₃	C₂	semidirect
35. #135×C₈₃	C₈	semidirect
76. #41×C₈₃	C₂×C₈	semidirect
86. Q₁₆×C₈₃	C₂×C₈	semidirect
87. SD₁₆×C₈₃	C₂×C₈	semidirect
88. D₈×C₈₃	C₂×C₈	semidirect
95. C₂×C₈×C₈₃	C₂×C₈	semidirect
162. #17849	C₈₃	direct (N × H)
168. C₈×#41	C₂×C₈₃	semidirect
170. #1580	C₂×C₈₃	semidirect
171. #1579	C₂×C₈₃	semidirect
172. SD₁₆⋊C₈	C₂×C₈₃	semidirect
173. #1564	C₂×C₈₃	semidirect
174. #1476	C₂×C₈₃	semidirect
175. C₂×#322	C₂×C₈₃	semidirect
176. C₈₃	#17849	direct (N × H)
203. #135	C₈×C₈₃	semidirect
244. #41	C₂×C₈×C₈₃	semidirect
254. Q₁₆	C₂×C₈×C₈₃	semidirect
255. SD₁₆	C₂×C₈×C₈₃	semidirect
256. D₈	C₂×C₈×C₈₃	semidirect
263. C₂×C₈	C₂×C₈×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₈×#41×C₈₃	2
C₄×#135×C₈₃	2
C₈₃×#1580	2
C₈₃×#1579	2
C₈₃×SD₁₆⋊C₈	2
C₈₃×#1564	2
C₈₃×#1476	2
C₂×#322×C₈₃	2
#17849	83

Subgroups — C83×#17849 #35245673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#17849 #35245673