Subgroups — C₈₃×#17873 #35245697

Order 21248.

700 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×AGL(1,ℤ/8)×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₈₃×#1586	C₂	1	2	yes	maximal, complemented
5	C₈₃×#1585	C₂	1	2	yes	maximal, complemented
6	C₈₃×#1582	C₂	1	2	yes	maximal, complemented
7	C₈₃×#1581	C₂	1	2	yes	maximal, complemented
8	C₈₃×#1565	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×D₄⋊C₈×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₈₃	C₄	1	1	yes	characteristic
13	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
15	#446×C₈₃	C₂²	1	2	yes	complemented
16	#442×C₈₃	C₄	1	2	yes	—
17	#440×C₈₃	C₄	1	2	yes	—
18	C₄×SD₁₆×C₈₃	C₂²	1	2	yes	—
19	C₄×D₈×C₈₃	C₂²	1	2	yes	—
20	#436×C₈₃	C₂²	1	2	yes	complemented
21	#435×C₈₃	—	2	2	no	—
22	C₈×D₄×C₈₃	—	2	1	no	—
23	C₈×D₄×C₈₃	—	2	1	no	—
24	C₈×D₄×C₈₃	C₂²	1	2	yes	—
25	C₈×D₄×C₈₃	C₂²	1	2	yes	—
26	#432×C₈₃	—	2	1	no	—
27	#431×C₈₃	C₂²	1	1	yes	characteristic
28	#431×C₈₃	C₂²	1	1	yes	characteristic
29	#428×C₈₃	C₄	1	1	yes	characteristic
30	#423×C₈₃	—	2	1	no	—
31	C₂×C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
32	#418×C₈₃	C₄	1	1	yes	characteristic
33	#417×C₈₃	C₄	1	1	yes	characteristic
34	C₂×C₂²⋊C₈×C₈₃	—	2	2	no	—
35	C₄×M₁₆×C₈₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
37	#335×C₈₃	C₂²	1	2	yes	complemented
38	#334×C₈₃	C₂²	1	2	yes	complemented
39	Q₈⋊C₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
40	Q₈⋊C₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
41	D₄⋊C₈×C₈₃	C₂²	1	2	yes	—
42	D₄⋊C₈×C₈₃	C₂²	1	2	yes	—
43	D₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
44	D₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
45	#322×C₈₃	C₂²	1	2	yes	complemented
46	#322×C₈₃	C₂²	1	2	yes	complemented
47	C₂×#41×C₈₃	C₂×C₄	1	1	yes	characteristic
48	C₂²×D₄×C₈₃	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₈₃	—	2	1	no	—
50	AGL(1,ℤ/8)×C₈₃	—	2	4	no	—
51	C₂×SD₁₆×C₈₃	C₂×C₄	1	2	yes	—
52	C₂×D₈×C₈₃	C₂×C₄	1	2	yes	—
53	C₂×M₁₆×C₈₃	—	2	2	no	—
54	C₂×M₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic
55	C₂×M₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₈×C₈₃	—	2	1	no	—
57	C₂²×C₈×C₈₃	—	2	1	no	—
58	C₂²×C₈×C₈₃	—	2	2	no	—
59	C₂²×C₈×C₈₃	—	2	2	no	—
60	C₄×Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
61	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
62	C₄×D₄×C₈₃	—	2	1	no	—
63	C₄×D₄×C₈₃	—	2	1	no	—
64	C₄×D₄×C₈₃	—	2	1	no	—
65	C₄×D₄×C₈₃	—	2	1	no	—
66	C₄×D₄×C₈₃	C₂×C₄	1	2	yes	—
67	C₄×D₄×C₈₃	C₂×C₄	1	1	yes	characteristic
68	C₄×D₄×C₈₃	C₂³	1	2	yes	—
69	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
70	#117×C₈₃	—	2	1	no	—
71	#117×C₈₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
74	C₂×C₄²×C₈₃	—	2	1	no	—
75	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
76	#107×C₈₃	C₂×C₄	1	2	yes	—
77	#106×C₈₃	C₂×C₄	1	2	yes	—
78	C₄⋊C₈×C₈₃	—	2	2	no	—
79	C₄⋊C₈×C₈₃	—	2	1	no	—
80	C₄⋊C₈×C₈₃	D₄	1	1	yes	characteristic
81	C₄⋊C₈×C₈₃	D₄	1	1	yes	characteristic
82	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
83	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
85	#103×C₈₃	C₂×C₄	1	2	yes	—
86	#102×C₈₃	C₂×C₄	1	2	yes	—
87	#102×C₈₃	C₂×C₄	1	2	yes	—
88	#102×C₈₃	C₂×C₄	1	2	yes	—
89	C₂²⋊C₈×C₈₃	—	2	1	no	—
90	C₂²⋊C₈×C₈₃	—	2	2	no	—
91	C₂²⋊C₈×C₈₃	—	2	2	no	—
92	C₂²⋊C₈×C₈₃	—	2	2	no	—
93	C₂²⋊C₈×C₈₃	D₄	1	2	yes	—
94	#97×C₈₃	—	2	2	no	—
95	#97×C₈₃	C₂×C₄	1	2	yes	—
96	C₄×C₈×C₈₃	—	2	1	no	—
97	C₄×C₈×C₈₃	—	2	1	no	—
98	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₈₃	C₂³	1	2	yes	—
101	C₄×C₈×C₈₃	C₂³	1	2	yes	—
102	C₂⁴×C₈₃	—	2	1	no	—
103	#41×C₈₃	—	2	2	no	—
104	#41×C₈₃	—	2	2	no	—
105	C₂×Q₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×D₄×C₈₃	—	2	1	no	—
107	C₂×D₄×C₈₃	—	2	1	no	—
108	C₂×D₄×C₈₃	—	2	2	no	—
109	C₂×D₄×C₈₃	M₁₆	1	4	yes	complemented
110	C₂×D₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×D₄×C₈₃	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₈₃	—	2	1	no	—
113	C₂²×C₄×C₈₃	—	2	1	no	—
114	C₂²×C₄×C₈₃	—	2	1	no	—
115	C₂²×C₄×C₈₃	—	2	2	no	—
116	C₂²×C₄×C₈₃	—	2	1	no	—
117	C₂²×C₄×C₈₃	—	2	2	no	—
118	C₂²×C₄×C₈₃	—	8	1	no	—
119	C₂²×C₄×C₈₃	—	8	1	no	—
120	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
123	SD₁₆×C₈₃	—	2	4	no	—
124	D₈×C₈₃	—	2	4	no	—
125	M₁₆×C₈₃	—	2	2	no	—
126	M₁₆×C₈₃	—	2	2	no	—
127	M₁₆×C₈₃	—	8	2	no	—
128	C₂×C₈×C₈₃	—	2	1	no	—
129	C₂×C₈×C₈₃	—	2	1	no	—
130	C₂×C₈×C₈₃	—	2	1	no	—
131	C₂×C₈×C₈₃	—	2	2	no	—
132	C₂×C₈×C₈₃	—	2	1	no	—
133	C₂×C₈×C₈₃	—	4	2	no	—
134	C₂×C₈×C₈₃	—	8	2	no	—
135	C₂×C₈×C₈₃	—	8	2	no	—
136	C₂×C₈×C₈₃	—	8	1	no	—
137	C₂×C₈×C₈₃	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₈₃	C₂²×C₄	1	2	yes	—
139	C₂×C₈×C₈₃	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₈₃	C₂×D₄	1	2	yes	—
141	C₄⋊C₄×C₈₃	—	2	1	no	—
142	C₄⋊C₄×C₈₃	—	2	1	no	—
143	C₄⋊C₄×C₈₃	—	2	1	no	—
144	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
145	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
146	C₄⋊C₄×C₈₃	C₂²×C₄	1	2	yes	—
147	C₂²⋊C₄×C₈₃	—	2	1	no	—
148	C₂²⋊C₄×C₈₃	—	2	2	no	—
149	C₂²⋊C₄×C₈₃	—	2	1	no	—
150	C₂²⋊C₄×C₈₃	—	2	2	no	—
151	C₂²⋊C₄×C₈₃	—	2	1	no	—
152	C₄²×C₈₃	—	2	1	no	—
153	C₄²×C₈₃	—	2	1	no	—
154	C₄²×C₈₃	—	2	1	no	—
155	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₈₃	#41	1	1	yes	characteristic
158	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
159	C₂³×C₈₃	—	2	2	no	—
160	C₂³×C₈₃	—	2	4	no	—
161	C₂³×C₈₃	—	2	1	no	—
162	C₂³×C₈₃	—	8	1	no	—
163	C₂³×C₈₃	—	8	1	no	—
164	C₂³×C₈₃	C₄×D₄	1	1	yes	characteristic
165	Q₈×C₈₃	—	2	1	no	—
166	Q₈×C₈₃	—	2	1	no	—
167	D₄×C₈₃	—	2	1	no	—
168	D₄×C₈₃	—	2	2	no	—
169	D₄×C₈₃	—	2	1	no	—
170	D₄×C₈₃	—	2	4	no	—
171	D₄×C₈₃	—	4	2	no	—
172	D₄×C₈₃	C₂×M₁₆	1	4	yes	—
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	—	4	1	no	—
180	C₂×C₄×C₈₃	—	4	2	no	—
181	C₂×C₄×C₈₃	—	4	1	no	—
182	C₂×C₄×C₈₃	—	4	2	no	—
183	C₂×C₄×C₈₃	—	4	1	no	—
184	C₂×C₄×C₈₃	—	4	2	no	—
185	C₂×C₄×C₈₃	—	8	1	no	—
186	C₂×C₄×C₈₃	—	8	2	no	—
187	C₂×C₄×C₈₃	—	8	1	no	—
188	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₈₃	C₂×M₁₆	1	2	yes	—
192	C₂×C₄×C₈₃	#131	1	2	yes	—
193	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
196	C₈×C₈₃	—	2	2	no	—
197	C₈×C₈₃	—	2	2	no	—
198	C₈×C₈₃	—	2	2	no	—
199	C₈×C₈₃	—	2	2	no	—
200	C₈×C₈₃	—	2	2	no	—
201	C₈×C₈₃	—	4	1	no	—
202	C₈×C₈₃	—	4	1	no	—
203	C₈×C₈₃	—	4	2	no	—
204	C₈×C₈₃	—	4	1	no	—
205	C₂²×C₈₃	—	2	1	no	—
206	C₂²×C₈₃	—	2	1	no	—
207	C₂²×C₈₃	—	2	4	no	—
208	C₂²×C₈₃	—	4	2	no	—
209	C₂²×C₈₃	—	4	2	no	—
210	C₂²×C₈₃	—	4	1	no	—
211	C₂²×C₈₃	—	4	1	no	—
212	C₂²×C₈₃	—	4	1	no	—
213	C₂²×C₈₃	—	8	4	no	—
214	C₂²×C₈₃	#435	1	2	yes	—
215	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
216	C₄×C₈₃	—	2	1	no	—
217	C₄×C₈₃	—	2	1	no	—
218	C₄×C₈₃	—	2	1	no	—
219	C₄×C₈₃	—	4	1	no	—
220	C₄×C₈₃	—	4	1	no	—
221	C₄×C₈₃	—	4	2	no	—
222	C₄×C₈₃	—	4	1	no	—
223	C₄×C₈₃	#435	1	2	yes	—
224	C₄×C₈₃	C₂²×M₁₆	1	1	yes	characteristic
225	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
226	C₄×C₈₃	#576	1	1	yes	characteristic
227	C₄×C₈₃	#577	1	1	yes	characteristic
228	#17873	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂×C₈₃	—	2	2	no	—
230	C₂×C₈₃	—	4	4	no	—
231	C₂×C₈₃	—	8	1	no	—
232	C₂×C₈₃	C₂×#435	1	1	yes	characteristic
233	C₂×C₈₃	#2946	1	1	yes	characteristic
234	C₂×C₈₃	#2956	1	1	yes	characteristic
235	#2989	C₂×C₈₃	1	1	yes	characteristic, complemented
236	#2972	C₂×C₈₃	1	1	yes	characteristic, complemented
237	C₄×AGL(1,ℤ/8)	C₂×C₈₃	1	1	yes	characteristic
238	#1586	C₂×C₈₃	1	2	yes	complemented
239	#1585	C₂×C₈₃	1	2	yes	complemented
240	#1582	C₂×C₈₃	1	2	yes	complemented
241	#1581	C₂×C₈₃	1	2	yes	complemented
242	#1565	C₂×C₈₃	1	1	yes	characteristic, complemented
243	#1476	C₂×C₈₃	1	1	yes	characteristic, complemented
244	C₂×D₄⋊C₈	C₂×C₈₃	1	1	yes	characteristic, complemented
245	#1451	C₂×C₈₃	1	1	yes	characteristic, complemented
246	C₈₃	#17873	1	1	yes	characteristic, direct product factor, Sylow
247	C₂×AGL(1,ℤ/8)	C₄×C₈₃	1	1	yes	characteristic
248	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic
249	C₂×C₄×D₄	C₂²×C₈₃	1	1	yes	characteristic
250	#446	C₂²×C₈₃	1	2	yes	complemented
251	#442	C₄×C₈₃	1	2	yes	—
252	#440	C₄×C₈₃	1	2	yes	—
253	C₄×SD₁₆	C₂²×C₈₃	1	2	yes	—
254	C₄×D₈	C₂²×C₈₃	1	2	yes	—
255	#436	C₂²×C₈₃	1	2	yes	complemented
256	#435	—	2	2	no	—
257	C₈×D₄	—	2	1	no	—
258	C₈×D₄	—	2	1	no	—
259	C₈×D₄	C₂²×C₈₃	1	2	yes	—
260	C₈×D₄	C₂²×C₈₃	1	2	yes	—
261	#432	—	2	1	no	—
262	#431	C₂²×C₈₃	1	1	yes	characteristic
263	#431	C₂²×C₈₃	1	1	yes	characteristic
264	#428	C₄×C₈₃	1	1	yes	characteristic
265	#423	—	2	1	no	—
266	C₂×C₄⋊C₈	C₂²×C₈₃	1	1	yes	characteristic
267	#418	C₄×C₈₃	1	1	yes	characteristic
268	#417	C₄×C₈₃	1	1	yes	characteristic
269	C₂×C₂²⋊C₈	—	2	2	no	—
270	C₄×M₁₆	C₂²×C₈₃	1	1	yes	characteristic
271	C₂×C₄×C₈	C₂²×C₈₃	1	1	yes	characteristic
272	#335	C₂²×C₈₃	1	2	yes	complemented
273	#334	C₂²×C₈₃	1	2	yes	complemented
274	Q₈⋊C₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
275	Q₈⋊C₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
276	D₄⋊C₈	C₂²×C₈₃	1	2	yes	—
277	D₄⋊C₈	C₂²×C₈₃	1	2	yes	—
278	D₄⋊C₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
279	D₄⋊C₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
280	#322	C₂²×C₈₃	1	2	yes	complemented
281	#322	C₂²×C₈₃	1	2	yes	complemented
282	C₂×#41	C₂×C₄×C₈₃	1	1	yes	characteristic
283	C₂²×D₄	C₂×C₄×C₈₃	1	1	yes	characteristic
284	C₂³×C₄	—	2	1	no	—
285	AGL(1,ℤ/8)	—	2	4	no	—
286	C₂×SD₁₆	C₂×C₄×C₈₃	1	2	yes	—
287	C₂×D₈	C₂×C₄×C₈₃	1	2	yes	—
288	C₂×M₁₆	—	2	2	no	—
289	C₂×M₁₆	C₂×C₄×C₈₃	1	1	yes	characteristic
290	C₂×M₁₆	C₂×C₄×C₈₃	1	1	yes	characteristic
291	C₂²×C₈	—	2	1	no	—
292	C₂²×C₈	—	2	1	no	—
293	C₂²×C₈	—	2	2	no	—
294	C₂²×C₈	—	2	2	no	—
295	C₄×Q₈	C₂×C₄×C₈₃	1	1	yes	characteristic
296	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	C₂×C₄×C₈₃	1	2	yes	—
302	C₄×D₄	C₂×C₄×C₈₃	1	1	yes	characteristic
303	C₄×D₄	C₂³×C₈₃	1	2	yes	—
304	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
305	#117	—	2	1	no	—
306	#117	C₂×C₄×C₈₃	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂×C₄×C₈₃	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
311	#107	C₂×C₄×C₈₃	1	2	yes	—
312	#106	C₂×C₄×C₈₃	1	2	yes	—
313	C₄⋊C₈	—	2	2	no	—
314	C₄⋊C₈	—	2	1	no	—
315	C₄⋊C₈	D₄×C₈₃	1	1	yes	characteristic
316	C₄⋊C₈	D₄×C₈₃	1	1	yes	characteristic
317	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
318	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
319	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
320	#103	C₂×C₄×C₈₃	1	2	yes	—
321	#102	C₂×C₄×C₈₃	1	2	yes	—
322	#102	C₂×C₄×C₈₃	1	2	yes	—
323	#102	C₂×C₄×C₈₃	1	2	yes	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	C₂²⋊C₈	—	2	2	no	—
328	C₂²⋊C₈	D₄×C₈₃	1	2	yes	—
329	#97	—	2	2	no	—
330	#97	C₂×C₄×C₈₃	1	2	yes	—
331	C₄×C₈	—	2	1	no	—
332	C₄×C₈	—	2	1	no	—
333	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
334	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
335	C₄×C₈	C₂³×C₈₃	1	2	yes	—
336	C₄×C₈	C₂³×C₈₃	1	2	yes	—
337	C₂⁴	—	2	1	no	—
338	#41	—	2	2	no	—
339	#41	—	2	2	no	—
340	C₂×Q₈	C₂²×C₄×C₈₃	1	1	yes	characteristic
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	M₁₆×C₈₃	1	4	yes	complemented
345	C₂×D₄	C₂²×C₄×C₈₃	1	1	yes	characteristic
346	C₂×D₄	C₂²×C₄×C₈₃	1	2	yes	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	8	1	no	—
354	C₂²×C₄	—	8	1	no	—
355	C₂²×C₄	C₂²×C₄×C₈₃	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
357	C₂²×C₄	#41×C₈₃	1	1	yes	characteristic
358	SD₁₆	—	2	4	no	—
359	D₈	—	2	4	no	—
360	M₁₆	—	2	2	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	8	2	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	4	2	no	—
369	C₂×C₈	—	8	2	no	—
370	C₂×C₈	—	8	2	no	—
371	C₂×C₈	—	8	1	no	—
372	C₂×C₈	C₂²×C₄×C₈₃	1	2	yes	—
373	C₂×C₈	C₂²×C₄×C₈₃	1	2	yes	—
374	C₂×C₈	C₂×D₄×C₈₃	1	2	yes	—
375	C₂×C₈	C₂×D₄×C₈₃	1	2	yes	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	C₂²×C₄×C₈₃	1	1	yes	characteristic
380	C₄⋊C₄	C₂²×C₄×C₈₃	1	1	yes	characteristic
381	C₄⋊C₄	C₂²×C₄×C₈₃	1	2	yes	—
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	C₂²×C₄×C₈₃	1	1	yes	characteristic
391	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
392	C₄²	#41×C₈₃	1	1	yes	characteristic
393	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
394	C₂³	—	2	2	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	2	1	no	—
397	C₂³	—	8	1	no	—
398	C₂³	—	8	1	no	—
399	C₂³	C₄×D₄×C₈₃	1	1	yes	characteristic
400	Q₈	—	2	1	no	—
401	Q₈	—	2	1	no	—
402	D₄	—	2	1	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	1	no	—
405	D₄	—	2	4	no	—
406	D₄	—	4	2	no	—
407	D₄	C₂×M₁₆×C₈₃	1	4	yes	—
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	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	8	2	no	—
421	C₂×C₄	—	8	1	no	—
422	C₂×C₄	—	8	1	no	—
423	C₂×C₄	C₄×D₄×C₈₃	1	1	yes	characteristic
424	C₂×C₄	C₄×D₄×C₈₃	1	1	yes	characteristic
425	C₂×C₄	C₄×D₄×C₈₃	1	1	yes	characteristic
426	C₂×C₄	C₂×M₁₆×C₈₃	1	2	yes	—
427	C₂×C₄	#131×C₈₃	1	2	yes	—
428	C₂×C₄	C₂³×C₄×C₈₃	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
430	C₂×C₄	C₂×#41×C₈₃	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	2	2	no	—
434	C₈	—	2	2	no	—
435	C₈	—	2	2	no	—
436	C₈	—	4	1	no	—
437	C₈	—	4	1	no	—
438	C₈	—	4	2	no	—
439	C₈	—	4	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	8	4	no	—
449	C₂²	#435×C₈₃	1	2	yes	—
450	C₂²	C₂×C₄×D₄×C₈₃	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	4	1	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	1	no	—
457	C₄	—	4	1	no	—
458	C₄	#435×C₈₃	1	2	yes	—
459	C₄	C₂²×M₁₆×C₈₃	1	1	yes	characteristic
460	C₄	C₂×#131×C₈₃	1	1	yes	characteristic
461	C₄	#576×C₈₃	1	1	yes	characteristic
462	C₄	#577×C₈₃	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	4	4	no	—
465	C₂	—	8	1	no	—
466	C₂	C₂×#435×C₈₃	1	1	yes	characteristic
467	C₂	C₈₃×#2946	1	1	yes	characteristic
468	C₂	C₈₃×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₈₃
Frattini, cosocle	C₄²	C₂⁴×C₈₃
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	C₂×AGL(1,ℤ/8)×C₈₃	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₃ ◁ #431×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#2989	C₂	semidirect
2. C₈₃×#2972	C₂	semidirect
4. C₈₃×#1586	C₂	semidirect
5. C₈₃×#1585	C₂	semidirect
6. C₈₃×#1582	C₂	semidirect
7. C₈₃×#1581	C₂	semidirect
8. C₈₃×#1565	C₂	semidirect
9. C₈₃×#1476	C₂	semidirect
10. C₂×D₄⋊C₈×C₈₃	C₂	semidirect
11. C₈₃×#1451	C₂	semidirect
15. #446×C₈₃	C₂²	semidirect
20. #436×C₈₃	C₂²	semidirect
37. #335×C₈₃	C₂²	semidirect
38. #334×C₈₃	C₂²	semidirect
39. Q₈⋊C₈×C₈₃	C₂²	semidirect
40. Q₈⋊C₈×C₈₃	C₂²	semidirect
43. D₄⋊C₈×C₈₃	C₂²	semidirect
44. D₄⋊C₈×C₈₃	C₂²	semidirect
45. #322×C₈₃	C₂²	semidirect
46. #322×C₈₃	C₂²	semidirect
109. C₂×D₄×C₈₃	M₁₆	semidirect
228. #17873	C₈₃	direct (N × H)
235. #2989	C₂×C₈₃	semidirect
236. #2972	C₂×C₈₃	semidirect
238. #1586	C₂×C₈₃	semidirect
239. #1585	C₂×C₈₃	semidirect
240. #1582	C₂×C₈₃	semidirect
241. #1581	C₂×C₈₃	semidirect
242. #1565	C₂×C₈₃	semidirect
243. #1476	C₂×C₈₃	semidirect
244. C₂×D₄⋊C₈	C₂×C₈₃	semidirect
245. #1451	C₂×C₈₃	semidirect
246. C₈₃	#17873	direct (N × H)
250. #446	C₂²×C₈₃	semidirect
255. #436	C₂²×C₈₃	semidirect
272. #335	C₂²×C₈₃	semidirect
273. #334	C₂²×C₈₃	semidirect
274. Q₈⋊C₈	C₂²×C₈₃	semidirect
275. Q₈⋊C₈	C₂²×C₈₃	semidirect
278. D₄⋊C₈	C₂²×C₈₃	semidirect
279. D₄⋊C₈	C₂²×C₈₃	semidirect
280. #322	C₂²×C₈₃	semidirect
281. #322	C₂²×C₈₃	semidirect
344. C₂×D₄	M₁₆×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₈₃×#2989	2
C₈₃×#2972	2
C₄×AGL(1,ℤ/8)×C₈₃	2
C₈₃×#1586	2
C₈₃×#1585	2
C₈₃×#1582	2
C₈₃×#1581	2
C₈₃×#1565	2
C₈₃×#1476	2
C₂×D₄⋊C₈×C₈₃	2
C₈₃×#1451	2
#17873	83

Subgroups — C83×#17873 #35245697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#17873 #35245697