Subgroups — C₈₃×#34367 #35262191

Order 21248.

2510 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₈₃	C₂	1	1	yes	maximal, characteristic
2	C₈₃×#2377	C₂	1	4	yes	maximal, complemented
3	C₈₃×#2363	C₂	1	4	yes	maximal, complemented
4	C₈₃×#2354	C₂	1	2	yes	maximal, complemented
5	C₈₃×#2352	C₂	1	4	yes	maximal, complemented
6	D₄×C₄⋊C₄×C₈₃	C₂	1	2	yes	maximal, complemented
7	C₈₃×#2337	C₂	1	4	yes	maximal, complemented
8	C₈₃×#2331	C₂	1	2	yes	maximal, complemented
9	C₈₃×#2328	C₂	1	2	yes	maximal, complemented
10	C₈₃×#2311	C₂	1	4	yes	maximal, complemented
11	C₈₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₈₃	C₂²	1	2	yes	—
14	#532×C₈₃	C₄	1	16	yes	complemented
15	C₂×C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
16	C₂×#127×C₈₃	C₂²	1	1	yes	characteristic
17	C₂×#124×C₈₃	C₂²	1	2	yes	—
18	C₂×#121×C₈₃	C₂²	1	2	yes	—
19	C₂×#121×C₈₃	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₈₃	C₂²	1	4	yes	—
21	C₂×C₄×D₄×C₈₃	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₈₃	C₂²	1	2	yes	—
23	C₂×#117×C₈₃	C₂²	1	2	yes	—
24	C₂×#117×C₈₃	C₂²	1	4	yes	—
25	C₂²×C₄⋊C₄×C₈₃	C₂²	1	4	yes	—
26	C₂²×C₄²×C₈₃	C₂²	1	1	yes	characteristic
27	#391×C₈₃	C₂²	1	8	yes	—
28	#390×C₈₃	C₂²	1	8	yes	—
29	#390×C₈₃	C₂²	1	4	yes	—
30	#389×C₈₃	C₂²	1	4	yes	—
31	#388×C₈₃	C₂²	1	8	yes	—
32	#388×C₈₃	C₂²	1	8	yes	—
33	#387×C₈₃	C₂²	1	8	yes	—
34	#386×C₈₃	C₂²	1	8	yes	—
35	#386×C₈₃	C₂²	1	8	yes	—
36	#386×C₈₃	C₂²	1	8	yes	—
37	#385×C₈₃	C₂²	1	8	yes	—
38	#384×C₈₃	C₂²	1	2	yes	—
39	#383×C₈₃	C₂²	1	2	yes	—
40	#382×C₈₃	C₂²	1	2	yes	—
41	#382×C₈₃	C₂²	1	2	yes	—
42	#381×C₈₃	C₂²	1	2	yes	—
43	#380×C₈₃	C₂²	1	2	yes	—
44	#380×C₈₃	C₂²	1	2	yes	—
45	#380×C₈₃	C₂²	1	2	yes	—
46	#380×C₈₃	C₂²	1	4	yes	—
47	#380×C₈₃	C₂²	1	4	yes	—
48	C₄×C₄⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
49	C₄×C₄⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
50	C₄×C₄⋊C₄×C₈₃	C₂²	1	2	yes	—
51	C₄×C₄⋊C₄×C₈₃	C₂²	1	2	yes	—
52	C₄×C₄⋊C₄×C₈₃	C₂²	1	4	yes	—
53	C₄×C₂²⋊C₄×C₈₃	C₂²	1	2	yes	—
54	C₄×C₂²⋊C₄×C₈₃	C₂²	1	8	yes	—
55	#376×C₈₃	C₂²	1	2	yes	—
56	C₂×#41×C₈₃	—	4	8	no	—
57	C₂×#41×C₈₃	C₂×C₄	1	16	yes	complemented
58	C₂²×Q₈×C₈₃	C₂³	1	2	yes	—
59	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
60	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
61	C₂²×D₄×C₈₃	C₂³	1	4	yes	—
62	C₂²×D₄×C₈₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₈₃	C₂³	1	4	yes	—
66	C₂³×C₄×C₈₃	C₂³	1	8	yes	—
67	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
68	C₄⋊Q₈×C₈₃	C₂×C₄	1	8	yes	complemented
69	#127×C₈₃	C₂×C₄	1	8	yes	—
70	#124×C₈₃	C₂×C₄	1	16	yes	complemented
71	#121×C₈₃	C₂×C₄	1	16	yes	complemented
72	#121×C₈₃	C₂×C₄	1	16	yes	complemented
73	C₄×D₄×C₈₃	—	4	8	no	—
74	C₄×D₄×C₈₃	C₂×C₄	1	16	yes	complemented
75	C₄×D₄×C₈₃	C₂×C₄	1	16	yes	complemented
76	#117×C₈₃	—	4	8	no	—
77	#117×C₈₃	—	4	4	no	—
78	C₂×C₄⋊C₄×C₈₃	—	4	8	no	—
79	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₈₃	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₈₃	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₈₃	C₂³	1	8	yes	—
84	C₂×C₄⋊C₄×C₈₃	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
87	C₂×C₂²⋊C₄×C₈₃	C₂³	1	4	yes	—
88	C₂×C₂²⋊C₄×C₈₃	C₂³	1	8	yes	—
89	C₂×C₂²⋊C₄×C₈₃	C₂³	1	8	yes	—
90	C₂×C₂²⋊C₄×C₈₃	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₈₃	C₂³	1	8	yes	—
92	C₂×C₂²⋊C₄×C₈₃	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₈₃	C₂³	1	4	yes	—
94	C₂×C₄²×C₈₃	C₂×C₄	1	8	yes	complemented
95	C₂×C₄²×C₈₃	C₂³	1	2	yes	—
96	C₂×C₄²×C₈₃	C₂³	1	2	yes	—
97	C₂×C₄²×C₈₃	C₂³	1	4	yes	—
98	C₂×C₄²×C₈₃	C₂³	1	8	yes	—
99	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
103	#95×C₈₃	C₂³	1	4	yes	—
104	#95×C₈₃	C₂³	1	4	yes	—
105	#95×C₈₃	C₂³	1	4	yes	—
106	#95×C₈₃	C₂³	1	8	yes	—
107	#95×C₈₃	C₂³	1	4	yes	—
108	#95×C₈₃	C₂³	1	4	yes	—
109	#95×C₈₃	C₂³	1	8	yes	—
110	#95×C₈₃	C₂³	1	2	yes	—
111	#95×C₈₃	C₂³	1	2	yes	—
112	C₂⁴×C₈₃	C₂⁴	1	1	yes	characteristic
113	C₂⁴×C₈₃	C₂⁴	1	4	yes	—
114	#41×C₈₃	—	4	32	no	—
115	C₂×Q₈×C₈₃	—	4	4	no	—
116	C₂×Q₈×C₈₃	C₂²×C₄	1	8	yes	—
117	C₂×D₄×C₈₃	—	2	4	no	—
118	C₂×D₄×C₈₃	—	2	4	no	—
119	C₂×D₄×C₈₃	—	4	4	no	—
120	C₂×D₄×C₈₃	—	4	4	no	—
121	C₂×D₄×C₈₃	—	4	4	no	—
122	C₂×D₄×C₈₃	—	4	4	no	—
123	C₂×D₄×C₈₃	C₂²×C₄	1	8	yes	—
124	C₂×D₄×C₈₃	C₂²×C₄	1	8	yes	—
125	C₂×D₄×C₈₃	C₂²×C₄	1	16	yes	—
126	C₂×D₄×C₈₃	C₂²×C₄	1	8	yes	—
127	C₂²×C₄×C₈₃	—	2	8	no	—
128	C₂²×C₄×C₈₃	—	2	2	no	—
129	C₂²×C₄×C₈₃	—	2	8	no	—
130	C₂²×C₄×C₈₃	—	2	4	no	—
131	C₂²×C₄×C₈₃	—	2	2	no	—
132	C₂²×C₄×C₈₃	—	4	2	no	—
133	C₂²×C₄×C₈₃	—	4	8	no	—
134	C₂²×C₄×C₈₃	—	4	8	no	—
135	C₂²×C₄×C₈₃	—	4	8	no	—
136	C₂²×C₄×C₈₃	C₂²×C₄	1	4	yes	—
137	C₂²×C₄×C₈₃	C₂²×C₄	1	4	yes	—
138	C₂²×C₄×C₈₃	C₂²×C₄	1	16	yes	—
139	C₂²×C₄×C₈₃	C₂²×C₄	1	4	yes	—
140	C₂²×C₄×C₈₃	C₂⁴	1	4	yes	—
141	C₂²×C₄×C₈₃	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₈₃	C₂⁴	1	8	yes	—
143	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
144	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
145	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
146	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
147	C₂²×C₄×C₈₃	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
149	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
150	C₄⋊C₄×C₈₃	—	2	4	no	—
151	C₄⋊C₄×C₈₃	—	2	8	no	—
152	C₄⋊C₄×C₈₃	—	2	4	no	—
153	C₄⋊C₄×C₈₃	—	2	8	no	—
154	C₄⋊C₄×C₈₃	—	4	8	no	—
155	C₄⋊C₄×C₈₃	—	4	4	no	—
156	C₄⋊C₄×C₈₃	C₂²×C₄	1	8	yes	—
157	C₄⋊C₄×C₈₃	C₂²×C₄	1	8	yes	—
158	C₂²⋊C₄×C₈₃	—	4	8	no	—
159	C₂²⋊C₄×C₈₃	—	4	4	no	—
160	C₂²⋊C₄×C₈₃	—	4	8	no	—
161	C₂²⋊C₄×C₈₃	—	4	4	no	—
162	C₂²⋊C₄×C₈₃	—	4	8	no	—
163	C₂²⋊C₄×C₈₃	C₂²×C₄	1	16	yes	—
164	C₂²⋊C₄×C₈₃	C₂²×C₄	1	16	yes	—
165	C₄²×C₈₃	—	2	4	no	—
166	C₄²×C₈₃	—	2	4	no	—
167	C₄²×C₈₃	—	4	4	no	—
168	C₄²×C₈₃	—	4	8	no	—
169	C₄²×C₈₃	C₂²×C₄	1	4	yes	—
170	C₄²×C₈₃	C₂²×C₄	1	4	yes	—
171	C₄²×C₈₃	C₂²×C₄	1	4	yes	—
172	C₄²×C₈₃	C₂²×C₄	1	4	yes	—
173	C₂³×C₈₃	—	2	1	no	—
174	C₂³×C₈₃	—	2	4	no	—
175	C₂³×C₈₃	—	2	4	no	—
176	C₂³×C₈₃	—	2	4	no	—
177	C₂³×C₈₃	—	2	2	no	—
178	C₂³×C₈₃	—	2	1	no	—
179	C₂³×C₈₃	—	2	4	no	—
180	C₂³×C₈₃	—	2	2	no	—
181	C₂³×C₈₃	—	2	4	no	—
182	C₂³×C₈₃	—	2	4	no	—
183	C₂³×C₈₃	C₂³×C₄	1	8	yes	—
184	C₂³×C₈₃	C₂³×C₄	1	2	yes	—
185	C₂³×C₈₃	C₂⁵	1	1	yes	characteristic
186	Q₈×C₈₃	—	4	8	no	—
187	D₄×C₈₃	—	2	16	no	—
188	D₄×C₈₃	—	4	8	no	—
189	D₄×C₈₃	—	4	8	no	—
190	D₄×C₈₃	—	4	16	no	—
191	C₂×C₄×C₈₃	—	2	1	no	—
192	C₂×C₄×C₈₃	—	2	4	no	—
193	C₂×C₄×C₈₃	—	2	4	no	—
194	C₂×C₄×C₈₃	—	2	2	no	—
195	C₂×C₄×C₈₃	—	2	1	no	—
196	C₂×C₄×C₈₃	—	2	2	no	—
197	C₂×C₄×C₈₃	—	2	2	no	—
198	C₂×C₄×C₈₃	—	2	32	no	—
199	C₂×C₄×C₈₃	—	2	8	no	—
200	C₂×C₄×C₈₃	—	2	8	no	—
201	C₂×C₄×C₈₃	—	2	4	no	—
202	C₂×C₄×C₈₃	—	2	4	no	—
203	C₂×C₄×C₈₃	—	2	8	no	—
204	C₂×C₄×C₈₃	—	2	8	no	—
205	C₂×C₄×C₈₃	—	2	4	no	—
206	C₂×C₄×C₈₃	—	2	4	no	—
207	C₂×C₄×C₈₃	—	2	4	no	—
208	C₂×C₄×C₈₃	—	2	8	no	—
209	C₂×C₄×C₈₃	—	2	4	no	—
210	C₂×C₄×C₈₃	—	4	4	no	—
211	C₂×C₄×C₈₃	—	8	16	no	—
212	C₂×C₄×C₈₃	C₂³×C₄	1	2	yes	—
213	C₂×C₄×C₈₃	C₂³×C₄	1	2	yes	—
214	C₂×C₄×C₈₃	C₂³×C₄	1	2	yes	—
215	C₂×C₄×C₈₃	C₂³×C₄	1	2	yes	—
216	C₂×C₄×C₈₃	C₂³×C₄	1	8	yes	—
217	C₂×C₄×C₈₃	C₂³×C₄	1	2	yes	—
218	C₂×C₄×C₈₃	C₂³×C₄	1	2	yes	—
219	C₂×C₄×C₈₃	H(5,𝔽₂)	1	4	yes	—
220	C₂×C₄×C₈₃	H(5,𝔽₂)	1	2	yes	—
221	C₂×C₄×C₈₃	2₋¹⁺⁴	1	2	yes	—
222	C₂²×C₈₃	—	2	2	no	—
223	C₂²×C₈₃	—	2	8	no	—
224	C₂²×C₈₃	—	2	2	no	—
225	C₂²×C₈₃	—	2	8	no	—
226	C₂²×C₈₃	—	2	2	no	—
227	C₂²×C₈₃	—	2	8	no	—
228	C₂²×C₈₃	—	4	4	no	—
229	C₂²×C₈₃	—	4	2	no	—
230	C₂²×C₈₃	—	4	4	no	—
231	C₂²×C₈₃	—	4	4	no	—
232	C₂²×C₈₃	—	4	4	no	—
233	C₂²×C₈₃	—	4	2	no	—
234	C₂²×C₈₃	C₂⁴×C₄	1	1	yes	characteristic
235	C₂²×C₈₃	C₂×H(5,𝔽₂)	1	2	yes	—
236	C₂²×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
237	C₂²×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
238	C₂²×C₈₃	#585	1	2	yes	—
239	C₄×C₈₃	—	2	2	no	—
240	C₄×C₈₃	—	2	8	no	—
241	C₄×C₈₃	—	2	2	no	—
242	C₄×C₈₃	—	2	2	no	—
243	C₄×C₈₃	—	2	2	no	—
244	C₄×C₈₃	—	4	8	no	—
245	C₄×C₈₃	—	4	4	no	—
246	C₄×C₈₃	—	4	4	no	—
247	C₄×C₈₃	#518	1	4	yes	—
248	C₄×C₈₃	#520	1	4	yes	—
249	#34367	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂×C₈₃	—	4	2	no	—
251	C₂×C₈₃	—	4	8	no	—
252	C₂×C₈₃	C₂×#518	1	1	yes	characteristic
253	C₂×C₈₃	C₂×#520	1	1	yes	characteristic
254	C₂×C₈₃	#3428	1	1	yes	characteristic
255	C₂×C₈₃	#3546	1	2	yes	—
256	C₂×C₈₃	#3547	1	2	yes	—
257	C₂×#532	C₂×C₈₃	1	1	yes	characteristic
258	#2377	C₂×C₈₃	1	4	yes	complemented
259	#2363	C₂×C₈₃	1	4	yes	complemented
260	#2354	C₂×C₈₃	1	2	yes	complemented
261	#2352	C₂×C₈₃	1	4	yes	complemented
262	D₄×C₄⋊C₄	C₂×C₈₃	1	2	yes	complemented
263	#2337	C₂×C₈₃	1	4	yes	complemented
264	#2331	C₂×C₈₃	1	2	yes	complemented
265	#2328	C₂×C₈₃	1	2	yes	complemented
266	#2311	C₂×C₈₃	1	4	yes	complemented
267	#2285	C₂×C₈₃	1	1	yes	characteristic, complemented
268	#2283	C₂×C₈₃	1	1	yes	characteristic, complemented
269	C₈₃	#34367	1	1	yes	characteristic, direct product factor, Sylow
270	C₂²×#41	C₂²×C₈₃	1	2	yes	—
271	#532	C₄×C₈₃	1	16	yes	complemented
272	C₂×C₄⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic
273	C₂×#127	C₂²×C₈₃	1	1	yes	characteristic
274	C₂×#124	C₂²×C₈₃	1	2	yes	—
275	C₂×#121	C₂²×C₈₃	1	2	yes	—
276	C₂×#121	C₂²×C₈₃	1	2	yes	—
277	C₂×C₄×D₄	C₂²×C₈₃	1	4	yes	—
278	C₂×C₄×D₄	C₂²×C₈₃	1	2	yes	—
279	C₂×C₄×D₄	C₂²×C₈₃	1	2	yes	—
280	C₂×#117	C₂²×C₈₃	1	4	yes	—
281	C₂×#117	C₂²×C₈₃	1	2	yes	—
282	C₂²×C₄⋊C₄	C₂²×C₈₃	1	4	yes	—
283	C₂²×C₄²	C₂²×C₈₃	1	1	yes	characteristic
284	#391	C₂²×C₈₃	1	8	yes	—
285	#390	C₂²×C₈₃	1	8	yes	—
286	#390	C₂²×C₈₃	1	4	yes	—
287	#389	C₂²×C₈₃	1	4	yes	—
288	#388	C₂²×C₈₃	1	8	yes	—
289	#388	C₂²×C₈₃	1	8	yes	—
290	#387	C₂²×C₈₃	1	8	yes	—
291	#386	C₂²×C₈₃	1	8	yes	—
292	#386	C₂²×C₈₃	1	8	yes	—
293	#386	C₂²×C₈₃	1	8	yes	—
294	#385	C₂²×C₈₃	1	8	yes	—
295	#384	C₂²×C₈₃	1	2	yes	—
296	#383	C₂²×C₈₃	1	2	yes	—
297	#382	C₂²×C₈₃	1	2	yes	—
298	#382	C₂²×C₈₃	1	2	yes	—
299	#381	C₂²×C₈₃	1	2	yes	—
300	#380	C₂²×C₈₃	1	2	yes	—
301	#380	C₂²×C₈₃	1	2	yes	—
302	#380	C₂²×C₈₃	1	4	yes	—
303	#380	C₂²×C₈₃	1	4	yes	—
304	#380	C₂²×C₈₃	1	2	yes	—
305	C₄×C₄⋊C₄	C₂²×C₈₃	1	4	yes	—
306	C₄×C₄⋊C₄	C₂²×C₈₃	1	2	yes	—
307	C₄×C₄⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
308	C₄×C₄⋊C₄	C₂²×C₈₃	1	2	yes	—
309	C₄×C₄⋊C₄	C₂²×C₈₃	1	1	yes	characteristic
310	C₄×C₂²⋊C₄	C₂²×C₈₃	1	8	yes	—
311	C₄×C₂²⋊C₄	C₂²×C₈₃	1	2	yes	—
312	#376	C₂²×C₈₃	1	2	yes	—
313	C₂×#41	—	4	8	no	—
314	C₂×#41	C₂×C₄×C₈₃	1	16	yes	complemented
315	C₂²×Q₈	C₂³×C₈₃	1	2	yes	—
316	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
317	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
318	C₂²×D₄	C₂³×C₈₃	1	4	yes	—
319	C₂²×D₄	C₂³×C₈₃	1	2	yes	—
320	C₂³×C₄	C₂³×C₈₃	1	4	yes	—
321	C₂³×C₄	C₂³×C₈₃	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₈₃	1	1	yes	characteristic
323	C₂³×C₄	C₂³×C₈₃	1	8	yes	—
324	C₂³×C₄	C₂³×C₈₃	1	1	yes	characteristic
325	C₄⋊Q₈	C₂×C₄×C₈₃	1	8	yes	complemented
326	#127	C₂×C₄×C₈₃	1	8	yes	—
327	#124	C₂×C₄×C₈₃	1	16	yes	complemented
328	#121	C₂×C₄×C₈₃	1	16	yes	complemented
329	#121	C₂×C₄×C₈₃	1	16	yes	complemented
330	C₄×D₄	—	4	8	no	—
331	C₄×D₄	C₂×C₄×C₈₃	1	16	yes	complemented
332	C₄×D₄	C₂×C₄×C₈₃	1	16	yes	complemented
333	#117	—	4	8	no	—
334	#117	—	4	4	no	—
335	C₂×C₄⋊C₄	—	4	8	no	—
336	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
337	C₂×C₄⋊C₄	C₂³×C₈₃	1	4	yes	—
338	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
339	C₂×C₄⋊C₄	C₂³×C₈₃	1	4	yes	—
340	C₂×C₄⋊C₄	C₂³×C₈₃	1	8	yes	—
341	C₂×C₄⋊C₄	C₂³×C₈₃	1	4	yes	—
342	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
343	C₂×C₄⋊C₄	C₂³×C₈₃	1	2	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₈₃	1	4	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₈₃	1	8	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₈₃	1	8	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₈₃	1	4	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₈₃	1	8	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₈₃	1	4	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₈₃	1	4	yes	—
351	C₂×C₄²	C₂×C₄×C₈₃	1	8	yes	complemented
352	C₂×C₄²	C₂³×C₈₃	1	2	yes	—
353	C₂×C₄²	C₂³×C₈₃	1	2	yes	—
354	C₂×C₄²	C₂³×C₈₃	1	4	yes	—
355	C₂×C₄²	C₂³×C₈₃	1	8	yes	—
356	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
359	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
360	#95	C₂³×C₈₃	1	4	yes	—
361	#95	C₂³×C₈₃	1	4	yes	—
362	#95	C₂³×C₈₃	1	4	yes	—
363	#95	C₂³×C₈₃	1	8	yes	—
364	#95	C₂³×C₈₃	1	4	yes	—
365	#95	C₂³×C₈₃	1	4	yes	—
366	#95	C₂³×C₈₃	1	8	yes	—
367	#95	C₂³×C₈₃	1	2	yes	—
368	#95	C₂³×C₈₃	1	2	yes	—
369	C₂⁴	C₂⁴×C₈₃	1	1	yes	characteristic
370	C₂⁴	C₂⁴×C₈₃	1	4	yes	—
371	#41	—	4	32	no	—
372	C₂×Q₈	—	4	4	no	—
373	C₂×Q₈	C₂²×C₄×C₈₃	1	8	yes	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	4	4	no	—
377	C₂×D₄	—	4	4	no	—
378	C₂×D₄	—	4	4	no	—
379	C₂×D₄	—	4	4	no	—
380	C₂×D₄	C₂²×C₄×C₈₃	1	8	yes	—
381	C₂×D₄	C₂²×C₄×C₈₃	1	8	yes	—
382	C₂×D₄	C₂²×C₄×C₈₃	1	16	yes	—
383	C₂×D₄	C₂²×C₄×C₈₃	1	8	yes	—
384	C₂²×C₄	—	2	8	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	8	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	—	4	8	no	—
391	C₂²×C₄	—	4	8	no	—
392	C₂²×C₄	—	4	8	no	—
393	C₂²×C₄	C₂²×C₄×C₈₃	1	4	yes	—
394	C₂²×C₄	C₂²×C₄×C₈₃	1	4	yes	—
395	C₂²×C₄	C₂²×C₄×C₈₃	1	16	yes	—
396	C₂²×C₄	C₂²×C₄×C₈₃	1	4	yes	—
397	C₂²×C₄	C₂⁴×C₈₃	1	4	yes	—
398	C₂²×C₄	C₂⁴×C₈₃	1	4	yes	—
399	C₂²×C₄	C₂⁴×C₈₃	1	8	yes	—
400	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
401	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
402	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
403	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
404	C₂²×C₄	C₂⁴×C₈₃	1	4	yes	—
405	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
406	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	8	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	8	no	—
411	C₄⋊C₄	—	4	8	no	—
412	C₄⋊C₄	—	4	4	no	—
413	C₄⋊C₄	C₂²×C₄×C₈₃	1	8	yes	—
414	C₄⋊C₄	C₂²×C₄×C₈₃	1	8	yes	—
415	C₂²⋊C₄	—	4	8	no	—
416	C₂²⋊C₄	—	4	4	no	—
417	C₂²⋊C₄	—	4	8	no	—
418	C₂²⋊C₄	—	4	8	no	—
419	C₂²⋊C₄	—	4	4	no	—
420	C₂²⋊C₄	C₂²×C₄×C₈₃	1	16	yes	—
421	C₂²⋊C₄	C₂²×C₄×C₈₃	1	16	yes	—
422	C₄²	—	2	4	no	—
423	C₄²	—	2	4	no	—
424	C₄²	—	4	4	no	—
425	C₄²	—	4	8	no	—
426	C₄²	C₂²×C₄×C₈₃	1	4	yes	—
427	C₄²	C₂²×C₄×C₈₃	1	4	yes	—
428	C₄²	C₂²×C₄×C₈₃	1	4	yes	—
429	C₄²	C₂²×C₄×C₈₃	1	4	yes	—
430	C₂³	—	2	1	no	—
431	C₂³	—	2	4	no	—
432	C₂³	—	2	4	no	—
433	C₂³	—	2	4	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	4	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	4	no	—
440	C₂³	C₂³×C₄×C₈₃	1	8	yes	—
441	C₂³	C₂³×C₄×C₈₃	1	2	yes	—
442	C₂³	C₂⁵×C₈₃	1	1	yes	characteristic
443	Q₈	—	4	8	no	—
444	D₄	—	2	16	no	—
445	D₄	—	4	8	no	—
446	D₄	—	4	16	no	—
447	D₄	—	4	8	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	8	no	—
456	C₂×C₄	—	2	32	no	—
457	C₂×C₄	—	2	8	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	8	no	—
461	C₂×C₄	—	2	8	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	8	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	8	16	no	—
469	C₂×C₄	C₂³×C₄×C₈₃	1	2	yes	—
470	C₂×C₄	C₂³×C₄×C₈₃	1	2	yes	—
471	C₂×C₄	C₂³×C₄×C₈₃	1	2	yes	—
472	C₂×C₄	C₂³×C₄×C₈₃	1	2	yes	—
473	C₂×C₄	C₂³×C₄×C₈₃	1	8	yes	—
474	C₂×C₄	C₂³×C₄×C₈₃	1	2	yes	—
475	C₂×C₄	C₂³×C₄×C₈₃	1	2	yes	—
476	C₂×C₄	H(5,𝔽₂)×C₈₃	1	4	yes	—
477	C₂×C₄	H(5,𝔽₂)×C₈₃	1	2	yes	—
478	C₂×C₄	2₋¹⁺⁴×C₈₃	1	2	yes	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	8	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	8	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	8	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	4	2	no	—
491	C₂²	C₂⁴×C₄×C₈₃	1	1	yes	characteristic
492	C₂²	C₂×H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
493	C₂²	C₂×H(5,𝔽₂)×C₈₃	1	2	yes	—
494	C₂²	C₂×2₋¹⁺⁴×C₈₃	1	1	yes	characteristic
495	C₂²	#585×C₈₃	1	2	yes	—
496	C₄	—	2	2	no	—
497	C₄	—	2	8	no	—
498	C₄	—	2	2	no	—
499	C₄	—	2	2	no	—
500	C₄	—	2	2	no	—
501	C₄	—	4	4	no	—
502	C₄	—	4	8	no	—
503	C₄	—	4	4	no	—
504	C₄	#518×C₈₃	1	4	yes	—
505	C₄	#520×C₈₃	1	4	yes	—
506	C₂	—	4	2	no	—
507	C₂	—	4	8	no	—
508	C₂	C₂×#518×C₈₃	1	1	yes	characteristic
509	C₂	C₂×#520×C₈₃	1	1	yes	characteristic
510	C₂	C₈₃×#3428	1	1	yes	characteristic
511	C₂	C₈₃×#3546	1	2	yes	—
512	C₂	C₈₃×#3547	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₈₃
Frattini, cosocle	C₂³	C₂⁵×C₈₃
prime radical	C₂×#532×C₈₃	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₃×#2377	C₂	semidirect
3. C₈₃×#2363	C₂	semidirect
4. C₈₃×#2354	C₂	semidirect
5. C₈₃×#2352	C₂	semidirect
6. D₄×C₄⋊C₄×C₈₃	C₂	semidirect
7. C₈₃×#2337	C₂	semidirect
8. C₈₃×#2331	C₂	semidirect
9. C₈₃×#2328	C₂	semidirect
10. C₈₃×#2311	C₂	semidirect
11. C₈₃×#2285	C₂	semidirect
12. C₈₃×#2283	C₂	semidirect
14. #532×C₈₃	C₄	semidirect
57. C₂×#41×C₈₃	C₂×C₄	semidirect
68. C₄⋊Q₈×C₈₃	C₂×C₄	semidirect
70. #124×C₈₃	C₂×C₄	semidirect
71. #121×C₈₃	C₂×C₄	semidirect
72. #121×C₈₃	C₂×C₄	semidirect
74. C₄×D₄×C₈₃	C₂×C₄	semidirect
75. C₄×D₄×C₈₃	C₂×C₄	semidirect
94. C₂×C₄²×C₈₃	C₂×C₄	semidirect
249. #34367	C₈₃	direct (N × H)
258. #2377	C₂×C₈₃	semidirect
259. #2363	C₂×C₈₃	semidirect
260. #2354	C₂×C₈₃	semidirect
261. #2352	C₂×C₈₃	semidirect
262. D₄×C₄⋊C₄	C₂×C₈₃	semidirect
263. #2337	C₂×C₈₃	semidirect
264. #2331	C₂×C₈₃	semidirect
265. #2328	C₂×C₈₃	semidirect
266. #2311	C₂×C₈₃	semidirect
267. #2285	C₂×C₈₃	semidirect
268. #2283	C₂×C₈₃	semidirect
269. C₈₃	#34367	direct (N × H)
271. #532	C₄×C₈₃	semidirect
314. C₂×#41	C₂×C₄×C₈₃	semidirect
325. C₄⋊Q₈	C₂×C₄×C₈₃	semidirect
327. #124	C₂×C₄×C₈₃	semidirect
328. #121	C₂×C₄×C₈₃	semidirect
329. #121	C₂×C₄×C₈₃	semidirect
331. C₄×D₄	C₂×C₄×C₈₃	semidirect
332. C₄×D₄	C₂×C₄×C₈₃	semidirect
351. C₂×C₄²	C₂×C₄×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#532×C₈₃	2
C₈₃×#2377	2
C₈₃×#2363	2
C₈₃×#2354	2
C₈₃×#2352	2
D₄×C₄⋊C₄×C₈₃	2
C₈₃×#2337	2
C₈₃×#2331	2
C₈₃×#2328	2
C₈₃×#2311	2
C₈₃×#2285	2
C₈₃×#2283	2
#34367	83

Subgroups — C83×#34367 #35262191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#34367 #35262191