Subgroups — C₈₃×#29514 #35257338

Order 21248.

734 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#2860	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊Q₈×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#2099	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₃×#2093	C₂	1	1	yes	maximal, characteristic
5	C₈₃×#2057	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₃×#2023	C₂	1	1	yes	maximal, characteristic
7	C₈₃×#1942	C₂	1	2	yes	maximal, complemented
8	C₈₃×#1934	C₂	1	2	yes	maximal
9	C₈₃×#1925	C₂	1	2	yes	maximal
10	C₈₃×#1918	C₂	1	2	yes	maximal, complemented
11	C₈₃×#1744	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
13	C₂×#126×C₈₃	—	2	1	no	—
14	C₂×C₄×Q₈×C₈₃	—	2	1	no	—
15	C₂×#107×C₈₃	C₂²	1	2	yes	—
16	C₂×#107×C₈₃	C₂²	1	2	yes	—
17	C₂×#102×C₈₃	C₂²	1	2	yes	—
18	C₂×#102×C₈₃	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₈₃	C₂²	1	2	yes	—
20	#391×C₈₃	—	2	1	no	—
21	#390×C₈₃	C₂²	1	1	yes	characteristic
22	#390×C₈₃	C₂²	1	1	yes	characteristic
23	#390×C₈₃	C₂²	1	1	yes	characteristic
24	#389×C₈₃	—	2	1	no	—
25	#389×C₈₃	C₂²	1	2	yes	—
26	#389×C₈₃	C₂²	1	1	yes	characteristic
27	#389×C₈₃	C₂²	1	1	yes	characteristic
28	#389×C₈₃	C₂²	1	1	yes	characteristic
29	#388×C₈₃	—	2	1	no	—
30	#388×C₈₃	—	2	1	no	—
31	#388×C₈₃	—	2	1	no	—
32	#384×C₈₃	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₈₃	—	2	1	no	—
34	C₄×C₄⋊C₄×C₈₃	C₂²	1	2	yes	—
35	C₄³×C₈₃	C₂²	1	1	yes	characteristic
36	#340×C₈₃	C₂²	1	2	yes	—
37	#340×C₈₃	C₂²	1	2	yes	—
38	#340×C₈₃	C₂²	1	2	yes	—
39	#340×C₈₃	C₂²	1	2	yes	—
40	#336×C₈₃	C₂²	1	1	yes	characteristic
41	#336×C₈₃	C₂²	1	1	yes	characteristic
42	#336×C₈₃	C₂²	1	2	yes	—
43	C₂²×Q₈×C₈₃	—	2	1	no	—
44	C₂²×D₄×C₈₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₈₃	C₂³	1	2	yes	—
47	C₄⋊Q₈×C₈₃	—	2	4	no	—
48	#126×C₈₃	—	4	4	no	—
49	C₄×Q₈×C₈₃	—	4	4	no	—
50	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
51	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
52	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
53	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
54	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
55	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
56	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
57	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
68	C₂×C₄²×C₈₃	—	2	2	no	—
69	C₂×C₄²×C₈₃	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₈₃	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₈₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₈₃	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
76	#107×C₈₃	—	2	4	no	—
77	#107×C₈₃	—	2	4	no	—
78	#102×C₈₃	—	2	4	no	—
79	#102×C₈₃	—	2	4	no	—
80	C₄×C₈×C₈₃	—	2	4	no	—
81	#95×C₈₃	—	2	2	no	—
82	#95×C₈₃	—	2	2	no	—
83	#95×C₈₃	—	2	1	no	—
84	#95×C₈₃	—	2	1	no	—
85	#95×C₈₃	—	2	1	no	—
86	C₂⁴×C₈₃	—	2	1	no	—
87	C₂×Q₈×C₈₃	—	2	4	no	—
88	C₂×Q₈×C₈₃	—	4	2	no	—
89	C₂×Q₈×C₈₃	—	4	2	no	—
90	C₂×D₄×C₈₃	—	2	2	no	—
91	C₂×D₄×C₈₃	—	2	2	no	—
92	C₂×D₄×C₈₃	—	2	1	no	—
93	C₂×D₄×C₈₃	—	2	1	no	—
94	C₂²×C₄×C₈₃	—	2	2	no	—
95	C₂²×C₄×C₈₃	—	2	2	no	—
96	C₂²×C₄×C₈₃	—	2	1	no	—
97	C₂²×C₄×C₈₃	—	2	1	no	—
98	C₂²×C₄×C₈₃	—	2	1	no	—
99	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
106	C₂×C₈×C₈₃	—	2	2	no	—
107	C₂×C₈×C₈₃	—	2	2	no	—
108	C₂×C₈×C₈₃	—	2	2	no	—
109	C₂×C₈×C₈₃	—	2	2	no	—
110	C₂×C₈×C₈₃	—	2	2	no	—
111	C₂×C₈×C₈₃	#41	1	4	yes	—
112	C₄⋊C₄×C₈₃	—	2	4	no	—
113	C₄⋊C₄×C₈₃	—	2	2	no	—
114	C₄⋊C₄×C₈₃	—	2	2	no	—
115	C₄⋊C₄×C₈₃	—	2	2	no	—
116	C₄⋊C₄×C₈₃	—	2	2	no	—
117	C₄⋊C₄×C₈₃	—	2	2	no	—
118	C₄⋊C₄×C₈₃	—	2	1	no	—
119	C₄⋊C₄×C₈₃	—	2	1	no	—
120	C₄⋊C₄×C₈₃	—	4	4	no	—
121	C₄⋊C₄×C₈₃	—	4	2	no	—
122	C₄⋊C₄×C₈₃	—	4	2	no	—
123	C₄⋊C₄×C₈₃	—	4	2	no	—
124	C₄⋊C₄×C₈₃	—	4	2	no	—
125	C₄⋊C₄×C₈₃	—	4	2	no	—
126	C₄⋊C₄×C₈₃	#41	1	4	yes	—
127	C₂²⋊C₄×C₈₃	—	4	2	no	—
128	C₂²⋊C₄×C₈₃	—	4	2	no	—
129	C₂²⋊C₄×C₈₃	—	4	2	no	—
130	C₂²⋊C₄×C₈₃	—	4	2	no	—
131	C₂²⋊C₄×C₈₃	—	4	2	no	—
132	C₂²⋊C₄×C₈₃	—	4	2	no	—
133	C₄²×C₈₃	—	2	2	no	—
134	C₄²×C₈₃	—	2	2	no	—
135	C₄²×C₈₃	—	2	2	no	—
136	C₄²×C₈₃	—	2	2	no	—
137	C₄²×C₈₃	—	2	1	no	—
138	C₄²×C₈₃	—	2	1	no	—
139	C₄²×C₈₃	—	4	1	no	—
140	C₄²×C₈₃	—	4	4	no	—
141	C₄²×C₈₃	D₈	1	4	yes	—
142	C₂³×C₈₃	—	4	1	no	—
143	C₂³×C₈₃	—	4	1	no	—
144	C₂³×C₈₃	—	4	1	no	—
145	C₂³×C₈₃	—	4	1	no	—
146	C₂³×C₈₃	—	4	1	no	—
147	C₂³×C₈₃	—	4	1	no	—
148	C₂³×C₈₃	—	4	1	no	—
149	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₈₃	—	4	8	no	—
151	D₄×C₈₃	—	4	2	no	—
152	D₄×C₈₃	—	4	2	no	—
153	C₂×C₄×C₈₃	—	2	1	no	—
154	C₂×C₄×C₈₃	—	2	1	no	—
155	C₂×C₄×C₈₃	—	2	1	no	—
156	C₂×C₄×C₈₃	—	2	1	no	—
157	C₂×C₄×C₈₃	—	2	1	no	—
158	C₂×C₄×C₈₃	—	2	1	no	—
159	C₂×C₄×C₈₃	—	2	1	no	—
160	C₂×C₄×C₈₃	—	2	1	no	—
161	C₂×C₄×C₈₃	—	2	1	no	—
162	C₂×C₄×C₈₃	—	2	1	no	—
163	C₂×C₄×C₈₃	—	2	4	no	—
164	C₂×C₄×C₈₃	—	2	1	no	—
165	C₂×C₄×C₈₃	—	2	1	no	—
166	C₂×C₄×C₈₃	—	2	1	no	—
167	C₂×C₄×C₈₃	—	4	2	no	—
168	C₂×C₄×C₈₃	—	4	2	no	—
169	C₂×C₄×C₈₃	—	4	1	no	—
170	C₂×C₄×C₈₃	—	4	2	no	—
171	C₂×C₄×C₈₃	—	4	1	no	—
172	C₂×C₄×C₈₃	—	4	1	no	—
173	C₂×C₄×C₈₃	—	4	2	no	—
174	C₂×C₄×C₈₃	—	4	1	no	—
175	C₂×C₄×C₈₃	—	4	1	no	—
176	C₂×C₄×C₈₃	—	4	1	no	—
177	C₂×C₄×C₈₃	—	4	1	no	—
178	C₂×C₄×C₈₃	—	4	2	no	—
179	C₂×C₄×C₈₃	—	4	1	no	—
180	C₂×C₄×C₈₃	—	4	1	no	—
181	C₂×C₄×C₈₃	C₂×D₈	1	2	yes	—
182	C₂×C₄×C₈₃	C₂×D₈	1	2	yes	—
183	C₂×C₄×C₈₃	C₂×D₈	1	2	yes	—
184	C₂×C₄×C₈₃	#135	1	2	yes	—
185	C₂×C₄×C₈₃	#137	1	2	yes	—
186	C₂×C₄×C₈₃	C₂×#41	1	2	yes	—
187	C₂×C₄×C₈₃	C₂×#41	1	2	yes	—
188	C₂×C₄×C₈₃	2₋¹⁺⁴	1	1	yes	characteristic
189	C₂×C₄×C₈₃	2₋¹⁺⁴	1	1	yes	characteristic
190	C₈×C₈₃	—	2	4	no	—
191	C₈×C₈₃	—	4	2	no	—
192	C₂²×C₈₃	—	8	1	no	—
193	C₂²×C₈₃	—	8	1	no	—
194	C₂²×C₈₃	—	8	1	no	—
195	C₂²×C₈₃	—	8	1	no	—
196	C₂²×C₈₃	—	8	1	no	—
197	C₂²×C₈₃	—	8	1	no	—
198	C₂²×C₈₃	—	8	1	no	—
199	C₂²×C₈₃	#525	1	1	yes	characteristic
200	C₂²×C₈₃	#532	1	1	yes	characteristic
201	C₂²×C₈₃	#536	1	1	yes	characteristic
202	C₂²×C₈₃	C₂²×D₈	1	1	yes	characteristic
203	C₂²×C₈₃	C₂×#135	1	1	yes	characteristic
204	C₂²×C₈₃	C₂×#137	1	1	yes	characteristic
205	C₂²×C₈₃	#575	1	1	yes	characteristic
206	C₄×C₈₃	—	2	2	no	—
207	C₄×C₈₃	—	2	2	no	—
208	C₄×C₈₃	—	2	2	no	—
209	C₄×C₈₃	—	2	2	no	—
210	C₄×C₈₃	—	2	2	no	—
211	C₄×C₈₃	—	4	4	no	—
212	C₄×C₈₃	—	4	1	no	—
213	C₄×C₈₃	—	8	1	no	—
214	C₄×C₈₃	—	8	2	no	—
215	C₄×C₈₃	—	8	1	no	—
216	C₄×C₈₃	—	8	1	no	—
217	C₄×C₈₃	#552	1	2	yes	—
218	C₄×C₈₃	#556	1	2	yes	—
219	#29514	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂×C₈₃	—	16	1	no	—
221	C₂×C₈₃	#2604	1	1	yes	characteristic
222	C₂×C₈₃	#3100	1	1	yes	characteristic
223	C₂×C₈₃	#3108	1	1	yes	characteristic
224	C₂×C₈₃	#3169	1	1	yes	characteristic
225	C₂×C₈₃	#3181	1	1	yes	characteristic
226	C₂×C₈₃	#3226	1	1	yes	characteristic
227	C₂×C₈₃	#3233	1	1	yes	characteristic
228	#2860	C₂×C₈₃	1	1	yes	characteristic
229	C₄×C₄⋊Q₈	C₂×C₈₃	1	1	yes	characteristic, complemented
230	#2099	C₂×C₈₃	1	1	yes	characteristic, complemented
231	#2093	C₂×C₈₃	1	1	yes	characteristic
232	#2057	C₂×C₈₃	1	1	yes	characteristic, complemented
233	#2023	C₂×C₈₃	1	1	yes	characteristic
234	#1942	C₂×C₈₃	1	2	yes	complemented
235	#1934	C₂×C₈₃	1	2	yes	—
236	#1925	C₂×C₈₃	1	2	yes	—
237	#1918	C₂×C₈₃	1	2	yes	complemented
238	#1744	C₂×C₈₃	1	1	yes	characteristic, complemented
239	C₈₃	#29514	1	1	yes	characteristic, direct product factor, Sylow
240	C₂×C₄⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
241	C₂×#126	—	2	1	no	—
242	C₂×C₄×Q₈	—	2	1	no	—
243	C₂×#107	C₂²×C₈₃	1	2	yes	—
244	C₂×#107	C₂²×C₈₃	1	2	yes	—
245	C₂×#102	C₂²×C₈₃	1	2	yes	—
246	C₂×#102	C₂²×C₈₃	1	2	yes	—
247	C₂×C₄×C₈	C₂²×C₈₃	1	2	yes	—
248	#391	—	2	1	no	—
249	#390	C₂²×C₈₃	1	1	yes	characteristic
250	#390	C₂²×C₈₃	1	1	yes	characteristic
251	#390	C₂²×C₈₃	1	1	yes	characteristic
252	#389	—	2	1	no	—
253	#389	C₂²×C₈₃	1	2	yes	—
254	#389	C₂²×C₈₃	1	1	yes	characteristic
255	#389	C₂²×C₈₃	1	1	yes	characteristic
256	#389	C₂²×C₈₃	1	1	yes	characteristic
257	#388	—	2	1	no	—
258	#388	—	2	1	no	—
259	#388	—	2	1	no	—
260	#384	C₂²×C₈₃	1	1	yes	characteristic
261	C₄×C₄⋊C₄	—	2	1	no	—
262	C₄×C₄⋊C₄	C₂²×C₈₃	1	2	yes	—
263	C₄³	C₂²×C₈₃	1	1	yes	characteristic
264	#340	C₂²×C₈₃	1	2	yes	—
265	#340	C₂²×C₈₃	1	2	yes	—
266	#340	C₂²×C₈₃	1	2	yes	—
267	#340	C₂²×C₈₃	1	2	yes	—
268	#336	C₂²×C₈₃	1	1	yes	characteristic
269	#336	C₂²×C₈₃	1	1	yes	characteristic
270	#336	C₂²×C₈₃	1	2	yes	—
271	C₂²×Q₈	—	2	1	no	—
272	C₂²×D₄	C₂³×C₈₃	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
274	C₂²×C₈	C₂³×C₈₃	1	2	yes	—
275	C₄⋊Q₈	—	2	4	no	—
276	#126	—	4	4	no	—
277	C₄×Q₈	—	4	4	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	D₄×C₈₃	1	1	yes	characteristic
298	C₂×C₄²	D₄×C₈₃	1	1	yes	characteristic
299	C₂×C₄²	D₄×C₈₃	1	1	yes	characteristic
300	C₂×C₄²	D₄×C₈₃	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
304	#107	—	2	4	no	—
305	#107	—	2	4	no	—
306	#102	—	2	4	no	—
307	#102	—	2	4	no	—
308	C₄×C₈	—	2	4	no	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	—	2	1	no	—
312	#95	—	2	1	no	—
313	#95	—	2	1	no	—
314	C₂⁴	—	2	1	no	—
315	C₂×Q₈	—	2	4	no	—
316	C₂×Q₈	—	4	2	no	—
317	C₂×Q₈	—	4	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
333	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	#41×C₈₃	1	4	yes	—
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	4	4	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	#41×C₈₃	1	4	yes	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₂²⋊C₄	—	4	2	no	—
358	C₂²⋊C₄	—	4	2	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₂²⋊C₄	—	4	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	4	1	no	—
368	C₄²	—	4	4	no	—
369	C₄²	D₈×C₈₃	1	4	yes	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
378	Q₈	—	4	8	no	—
379	D₄	—	4	2	no	—
380	D₄	—	4	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	C₂×D₈×C₈₃	1	2	yes	—
410	C₂×C₄	C₂×D₈×C₈₃	1	2	yes	—
411	C₂×C₄	C₂×D₈×C₈₃	1	2	yes	—
412	C₂×C₄	#135×C₈₃	1	2	yes	—
413	C₂×C₄	#137×C₈₃	1	2	yes	—
414	C₂×C₄	C₂×#41×C₈₃	1	2	yes	—
415	C₂×C₄	C₂×#41×C₈₃	1	2	yes	—
416	C₂×C₄	2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
417	C₂×C₄	2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
418	C₈	—	2	4	no	—
419	C₈	—	4	2	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	1	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	#525×C₈₃	1	1	yes	characteristic
428	C₂²	#532×C₈₃	1	1	yes	characteristic
429	C₂²	#536×C₈₃	1	1	yes	characteristic
430	C₂²	C₂²×D₈×C₈₃	1	1	yes	characteristic
431	C₂²	C₂×#135×C₈₃	1	1	yes	characteristic
432	C₂²	C₂×#137×C₈₃	1	1	yes	characteristic
433	C₂²	#575×C₈₃	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	4	4	no	—
440	C₄	—	4	1	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	2	no	—
443	C₄	—	8	1	no	—
444	C₄	—	8	1	no	—
445	C₄	#552×C₈₃	1	2	yes	—
446	C₄	#556×C₈₃	1	2	yes	—
447	C₂	—	16	1	no	—
448	C₂	C₈₃×#2604	1	1	yes	characteristic
449	C₂	C₈₃×#3100	1	1	yes	characteristic
450	C₂	C₈₃×#3108	1	1	yes	characteristic
451	C₂	C₈₃×#3169	1	1	yes	characteristic
452	C₂	C₈₃×#3181	1	1	yes	characteristic
453	C₂	C₈₃×#3226	1	1	yes	characteristic
454	C₂	C₈₃×#3233	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₃
prime radical	C₂²×D₄×C₈₃	C₂³
LCS	G ▷ C₂²×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
3. C₈₃×#2099	C₂	semidirect
5. C₈₃×#2057	C₂	semidirect
7. C₈₃×#1942	C₂	semidirect
10. C₈₃×#1918	C₂	semidirect
11. C₈₃×#1744	C₂	semidirect
219. #29514	C₈₃	direct (N × H)
229. C₄×C₄⋊Q₈	C₂×C₈₃	semidirect
230. #2099	C₂×C₈₃	semidirect
232. #2057	C₂×C₈₃	semidirect
234. #1942	C₂×C₈₃	semidirect
237. #1918	C₂×C₈₃	semidirect
238. #1744	C₂×C₈₃	semidirect
239. C₈₃	#29514	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₃×#2860	2
C₄×C₄⋊Q₈×C₈₃	2
C₈₃×#2099	2
C₈₃×#2093	2
C₈₃×#2057	2
C₈₃×#2023	2
C₈₃×#1942	2
C₈₃×#1934	2
C₈₃×#1925	2
C₈₃×#1918	2
C₈₃×#1744	2
#29514	83

Subgroups — C83×#29514 #35257338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#29514 #35257338