Subgroups — C₈₃×#61917 #35289741

Order 21248.

1696 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3402	C₂	1	4	yes	maximal, complemented
4	C₈₃×#3400	C₂	1	2	yes	maximal, complemented
5	C₈₃×#3396	C₂	1	2	yes	maximal, complemented
6	C₈₃×#3375	C₂	1	2	yes	maximal, complemented
7	C₈₃×#3367	C₂	1	4	yes	maximal, complemented
8	C₈₃×#3363	C₂	1	2	yes	maximal, complemented
9	C₈₃×#3225	C₂	1	4	yes	maximal, complemented
10	C₈₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#3207	C₂	1	1	yes	maximal, characteristic
12	C₈₃×#3124	C₂	1	4	yes	maximal, complemented
13	C₈₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#2985	C₂	1	1	yes	maximal, characteristic, complemented
16	#563×C₈₃	—	2	2	no	—
17	#559×C₈₃	C₂²	1	2	yes	—
18	#559×C₈₃	C₂²	1	2	yes	—
19	Q₈²×C₈₃	C₂²	1	2	yes	—
20	#557×C₈₃	C₂²	1	2	yes	—
21	#556×C₈₃	—	2	1	no	—
22	#556×C₈₃	—	2	1	no	—
23	#556×C₈₃	C₂²	1	2	yes	—
24	#556×C₈₃	C₂²	1	4	yes	—
25	#554×C₈₃	—	2	1	no	—
26	#552×C₈₃	—	2	2	no	—
27	D₄×Q₈×C₈₃	—	2	1	no	—
28	D₄×Q₈×C₈₃	C₂²	1	2	yes	—
29	#542×C₈₃	—	2	2	no	—
30	#542×C₈₃	C₂²	1	4	yes	—
31	#539×C₈₃	—	2	2	no	—
32	#536×C₈₃	—	2	2	no	—
33	#536×C₈₃	C₂²	1	2	yes	—
34	#533×C₈₃	C₂²	1	1	yes	characteristic
35	#533×C₈₃	C₂²	1	1	yes	characteristic
36	#532×C₈₃	C₂²	1	1	yes	characteristic
37	#532×C₈₃	C₂²	1	1	yes	characteristic
38	#529×C₈₃	—	2	2	no	—
39	#520×C₈₃	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
41	#497×C₈₃	C₂²	1	4	yes	—
42	#497×C₈₃	C₂²	1	2	yes	—
43	#495×C₈₃	C₂²	1	4	yes	—
44	#493×C₈₃	C₂²	1	1	yes	characteristic
45	#492×C₈₃	C₂²	1	1	yes	characteristic
46	#489×C₈₃	C₂²	1	2	yes	—
47	#489×C₈₃	C₂²	1	4	yes	—
48	#487×C₈₃	C₂²	1	1	yes	characteristic
49	#487×C₈₃	C₂²	1	4	yes	—
50	#486×C₈₃	C₂²	1	1	yes	characteristic
51	#484×C₈₃	C₂²	1	2	yes	—
52	#480×C₈₃	C₂²	1	2	yes	—
53	#477×C₈₃	C₂²	1	2	yes	—
54	#477×C₈₃	C₂²	1	4	yes	—
55	#477×C₈₃	C₂²	1	2	yes	—
56	#474×C₈₃	C₂²	1	4	yes	—
57	#464×C₈₃	C₂²	1	4	yes	—
58	#464×C₈₃	C₂²	1	4	yes	—
59	#463×C₈₃	C₂²	1	4	yes	—
60	#463×C₈₃	C₂²	1	4	yes	—
61	#463×C₈₃	C₂²	1	4	yes	—
62	#462×C₈₃	C₂²	1	2	yes	—
63	#462×C₈₃	C₂²	1	2	yes	—
64	#462×C₈₃	C₂²	1	4	yes	—
65	#461×C₈₃	C₂²	1	4	yes	—
66	#460×C₈₃	C₂²	1	2	yes	—
67	#460×C₈₃	C₂²	1	2	yes	—
68	#452×C₈₃	C₂²	1	4	yes	—
69	#451×C₈₃	C₂²	1	2	yes	—
70	#449×C₈₃	C₂²	1	4	yes	—
71	#448×C₈₃	C₂²	1	2	yes	—
72	#446×C₈₃	C₂²	1	4	yes	—
73	#446×C₈₃	C₂²	1	2	yes	—
74	C₈×Q₈×C₈₃	C₂²	1	2	yes	—
75	#440×C₈₃	C₂²	1	4	yes	—
76	#440×C₈₃	C₂²	1	4	yes	—
77	#440×C₈₃	C₂²	1	4	yes	—
78	C₄×Q₁₆×C₈₃	C₂²	1	2	yes	—
79	C₄×Q₁₆×C₈₃	C₂²	1	2	yes	—
80	C₄×Q₁₆×C₈₃	C₂²	1	4	yes	—
81	C₄×D₈×C₈₃	C₂²	1	4	yes	—
82	#433×C₈₃	C₂²	1	4	yes	—
83	#432×C₈₃	C₂²	1	1	yes	characteristic
84	#431×C₈₃	C₂²	1	1	yes	characteristic
85	C₂×#41×C₈₃	—	2	1	no	—
86	C₂×#41×C₈₃	C₂³	1	2	yes	—
87	C₂²×Q₈×C₈₃	—	2	2	no	—
88	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
89	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
90	C₂×Q₁₆×C₈₃	C₂³	1	4	yes	—
91	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
92	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
93	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
94	C₂×SD₁₆×C₈₃	C₂³	1	4	yes	—
95	C₂×D₈×C₈₃	C₂³	1	4	yes	—
96	C₄⋊Q₈×C₈₃	—	2	4	no	—
97	C₄⋊Q₈×C₈₃	—	2	2	no	—
98	C₄⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
99	C₄⋊Q₈×C₈₃	D₄	1	1	yes	characteristic
100	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
101	C₄⋊Q₈×C₈₃	C₂³	1	4	yes	—
102	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
103	C₄⋊Q₈×C₈₃	C₂³	1	4	yes	—
104	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
105	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
106	#127×C₈₃	C₂³	1	1	yes	characteristic
107	#127×C₈₃	C₂³	1	1	yes	characteristic
108	#126×C₈₃	—	2	4	no	—
109	#126×C₈₃	—	2	4	no	—
110	#126×C₈₃	—	2	4	no	—
111	#126×C₈₃	—	2	4	no	—
112	#125×C₈₃	—	2	2	no	—
113	#125×C₈₃	—	2	4	no	—
114	#125×C₈₃	—	2	1	no	—
115	#125×C₈₃	D₄	1	2	yes	—
116	#124×C₈₃	—	2	2	no	—
117	#124×C₈₃	—	2	2	no	—
118	#124×C₈₃	—	2	4	no	—
119	#124×C₈₃	—	2	1	no	—
120	#124×C₈₃	C₂³	1	2	yes	—
121	#124×C₈₃	C₂³	1	4	yes	—
122	#124×C₈₃	C₂³	1	4	yes	—
123	#123×C₈₃	—	2	4	no	—
124	#123×C₈₃	—	2	4	no	—
125	#123×C₈₃	—	2	4	no	—
126	#123×C₈₃	—	2	4	no	—
127	C₂²⋊Q₈×C₈₃	—	2	2	no	—
128	C₂²⋊Q₈×C₈₃	—	2	4	no	—
129	C₂²⋊Q₈×C₈₃	—	2	1	no	—
130	C₂²⋊Q₈×C₈₃	—	2	2	no	—
131	C₂²⋊Q₈×C₈₃	—	2	2	no	—
132	C₂²⋊Q₈×C₈₃	—	2	2	no	—
133	C₂²⋊Q₈×C₈₃	—	2	4	no	—
134	C₂²⋊Q₈×C₈₃	—	2	4	no	—
135	C₂²⋊Q₈×C₈₃	D₄	1	2	yes	—
136	C₂²⋊Q₈×C₈₃	D₄	1	2	yes	—
137	C₂²⋊Q₈×C₈₃	C₂³	1	2	yes	—
138	#121×C₈₃	—	2	1	no	—
139	#121×C₈₃	—	2	1	no	—
140	#121×C₈₃	—	2	1	no	—
141	#121×C₈₃	C₂³	1	2	yes	—
142	C₄×Q₈×C₈₃	—	2	2	no	—
143	C₄×Q₈×C₈₃	—	2	2	no	—
144	C₄×Q₈×C₈₃	—	2	1	no	—
145	C₄×Q₈×C₈₃	—	2	1	no	—
146	C₄×Q₈×C₈₃	—	2	1	no	—
147	C₄×Q₈×C₈₃	C₂³	1	4	yes	—
148	C₄×Q₈×C₈₃	C₂³	1	4	yes	—
149	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
150	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
151	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
152	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
153	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
154	C₄×D₄×C₈₃	—	2	2	no	—
155	C₄×D₄×C₈₃	—	2	2	no	—
156	C₄×D₄×C₈₃	—	2	4	no	—
157	C₄×D₄×C₈₃	—	2	1	no	—
158	C₄×D₄×C₈₃	—	2	1	no	—
159	C₄×D₄×C₈₃	—	2	1	no	—
160	C₄×D₄×C₈₃	C₂³	1	2	yes	—
161	C₄×D₄×C₈₃	C₂³	1	4	yes	—
162	C₄×D₄×C₈₃	C₂³	1	4	yes	—
163	#117×C₈₃	—	2	1	no	—
164	#117×C₈₃	—	2	2	no	—
165	#117×C₈₃	—	2	4	no	—
166	#117×C₈₃	—	2	2	no	—
167	#117×C₈₃	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
169	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
170	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₈₃	—	2	1	no	—
172	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
173	#107×C₈₃	C₂³	1	2	yes	—
174	#107×C₈₃	C₂³	1	4	yes	—
175	#107×C₈₃	C₂³	1	2	yes	—
176	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
177	C₄⋊C₈×C₈₃	C₂³	1	4	yes	—
178	C₄⋊C₈×C₈₃	C₂³	1	4	yes	—
179	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
180	#103×C₈₃	C₂³	1	2	yes	—
181	#103×C₈₃	C₂³	1	2	yes	—
182	#103×C₈₃	C₂³	1	4	yes	—
183	#103×C₈₃	C₂³	1	2	yes	—
184	#103×C₈₃	C₂³	1	4	yes	—
185	#103×C₈₃	C₂³	1	4	yes	—
186	#103×C₈₃	C₂³	1	2	yes	—
187	#102×C₈₃	C₂³	1	4	yes	—
188	#102×C₈₃	C₂³	1	4	yes	—
189	#102×C₈₃	C₂³	1	4	yes	—
190	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
191	C₂²⋊C₈×C₈₃	C₂³	1	2	yes	—
192	#97×C₈₃	C₂³	1	2	yes	—
193	#97×C₈₃	C₂³	1	4	yes	—
194	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₈₃	C₂³	1	4	yes	—
197	#41×C₈₃	—	4	4	no	—
198	#41×C₈₃	—	8	2	no	—
199	C₂×Q₈×C₈₃	—	2	1	no	—
200	C₂×Q₈×C₈₃	—	2	1	no	—
201	C₂×Q₈×C₈₃	—	2	4	no	—
202	C₂×Q₈×C₈₃	—	2	1	no	—
203	C₂×Q₈×C₈₃	—	4	2	no	—
204	C₂×Q₈×C₈₃	—	8	4	no	—
205	C₂×Q₈×C₈₃	C₂×D₄	1	2	yes	—
206	C₂×Q₈×C₈₃	C₂×D₄	1	2	yes	—
207	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
208	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
209	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
210	C₂×D₄×C₈₃	—	2	2	no	—
211	C₂×D₄×C₈₃	—	2	2	no	—
212	C₂×D₄×C₈₃	—	2	1	no	—
213	C₂×D₄×C₈₃	—	2	1	no	—
214	C₂×D₄×C₈₃	—	2	1	no	—
215	C₂×D₄×C₈₃	—	2	1	no	—
216	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
217	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₈₃	—	2	1	no	—
219	C₂²×C₄×C₈₃	—	2	1	no	—
220	C₂²×C₄×C₈₃	—	2	2	no	—
221	C₂²×C₄×C₈₃	—	2	2	no	—
222	C₂²×C₄×C₈₃	—	2	4	no	—
223	C₂²×C₄×C₈₃	—	2	4	no	—
224	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
227	Q₁₆×C₈₃	—	4	2	no	—
228	Q₁₆×C₈₃	—	4	2	no	—
229	Q₁₆×C₈₃	—	4	4	no	—
230	SD₁₆×C₈₃	—	4	4	no	—
231	SD₁₆×C₈₃	—	4	4	no	—
232	SD₁₆×C₈₃	—	4	4	no	—
233	D₈×C₈₃	—	4	4	no	—
234	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
235	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
236	C₂×C₈×C₈₃	C₂⁴	1	4	yes	—
237	C₄⋊C₄×C₈₃	—	2	1	no	—
238	C₄⋊C₄×C₈₃	—	2	4	no	—
239	C₄⋊C₄×C₈₃	—	2	2	no	—
240	C₄⋊C₄×C₈₃	—	2	2	no	—
241	C₄⋊C₄×C₈₃	—	2	1	no	—
242	C₄⋊C₄×C₈₃	—	2	1	no	—
243	C₄⋊C₄×C₈₃	—	2	4	no	—
244	C₄⋊C₄×C₈₃	—	2	1	no	—
245	C₄⋊C₄×C₈₃	—	2	1	no	—
246	C₄⋊C₄×C₈₃	—	2	1	no	—
247	C₄⋊C₄×C₈₃	—	2	1	no	—
248	C₄⋊C₄×C₈₃	—	2	2	no	—
249	C₄⋊C₄×C₈₃	—	2	4	no	—
250	C₄⋊C₄×C₈₃	—	2	4	no	—
251	C₄⋊C₄×C₈₃	—	2	4	no	—
252	C₄⋊C₄×C₈₃	—	2	2	no	—
253	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
254	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
255	C₄⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
256	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
259	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
262	C₂²⋊C₄×C₈₃	—	2	2	no	—
263	C₂²⋊C₄×C₈₃	—	2	2	no	—
264	C₂²⋊C₄×C₈₃	—	2	4	no	—
265	C₂²⋊C₄×C₈₃	—	2	4	no	—
266	C₂²⋊C₄×C₈₃	—	2	4	no	—
267	C₂²⋊C₄×C₈₃	—	2	2	no	—
268	C₂²⋊C₄×C₈₃	—	2	2	no	—
269	C₂²⋊C₄×C₈₃	—	2	4	no	—
270	C₂²⋊C₄×C₈₃	—	2	4	no	—
271	C₂²⋊C₄×C₈₃	—	2	2	no	—
272	C₂²⋊C₄×C₈₃	—	2	4	no	—
273	C₂²⋊C₄×C₈₃	C₂×D₄	1	4	yes	—
274	C₄²×C₈₃	—	2	2	no	—
275	C₄²×C₈₃	—	2	2	no	—
276	C₄²×C₈₃	—	2	4	no	—
277	C₄²×C₈₃	—	2	2	no	—
278	C₄²×C₈₃	—	2	4	no	—
279	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
282	C₄²×C₈₃	C₂⁴	1	4	yes	—
283	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
284	C₂³×C₈₃	—	2	2	no	—
285	C₂³×C₈₃	—	2	2	no	—
286	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
287	Q₈×C₈₃	—	2	4	no	—
288	Q₈×C₈₃	—	2	2	no	—
289	Q₈×C₈₃	—	2	2	no	—
290	Q₈×C₈₃	—	2	4	no	—
291	Q₈×C₈₃	—	2	2	no	—
292	Q₈×C₈₃	—	2	2	no	—
293	Q₈×C₈₃	—	4	2	no	—
294	Q₈×C₈₃	—	4	2	no	—
295	Q₈×C₈₃	—	4	2	no	—
296	Q₈×C₈₃	—	8	4	no	—
297	Q₈×C₈₃	—	8	1	no	—
298	D₄×C₈₃	—	2	4	no	—
299	D₄×C₈₃	—	2	4	no	—
300	D₄×C₈₃	—	4	4	no	—
301	D₄×C₈₃	—	4	2	no	—
302	D₄×C₈₃	—	4	2	no	—
303	D₄×C₈₃	—	8	1	no	—
304	D₄×C₈₃	—	8	1	no	—
305	D₄×C₈₃	—	8	2	no	—
306	C₂×C₄×C₈₃	—	2	2	no	—
307	C₂×C₄×C₈₃	—	2	2	no	—
308	C₂×C₄×C₈₃	—	2	2	no	—
309	C₂×C₄×C₈₃	—	2	2	no	—
310	C₂×C₄×C₈₃	—	2	2	no	—
311	C₂×C₄×C₈₃	—	2	2	no	—
312	C₂×C₄×C₈₃	—	2	2	no	—
313	C₂×C₄×C₈₃	—	2	2	no	—
314	C₂×C₄×C₈₃	—	4	1	no	—
315	C₂×C₄×C₈₃	—	4	4	no	—
316	C₂×C₄×C₈₃	—	4	4	no	—
317	C₂×C₄×C₈₃	—	4	2	no	—
318	C₂×C₄×C₈₃	—	8	4	no	—
319	C₂×C₄×C₈₃	—	8	4	no	—
320	C₂×C₄×C₈₃	—	8	1	no	—
321	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₈₃	C₂²×D₄	1	4	yes	—
323	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₈₃	C₂²×D₄	1	4	yes	—
327	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
329	C₈×C₈₃	—	2	2	no	—
330	C₈×C₈₃	—	2	2	no	—
331	C₈×C₈₃	—	2	4	no	—
332	C₂²×C₈₃	—	2	1	no	—
333	C₂²×C₈₃	—	2	1	no	—
334	C₂²×C₈₃	—	2	1	no	—
335	C₂²×C₈₃	—	4	2	no	—
336	C₂²×C₈₃	—	4	2	no	—
337	C₂²×C₈₃	—	4	2	no	—
338	C₂²×C₈₃	—	4	2	no	—
339	C₂²×C₈₃	—	4	2	no	—
340	C₂²×C₈₃	—	4	2	no	—
341	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
342	C₄×C₈₃	—	2	1	no	—
343	C₄×C₈₃	—	2	1	no	—
344	C₄×C₈₃	—	2	4	no	—
345	C₄×C₈₃	—	2	1	no	—
346	C₄×C₈₃	—	2	1	no	—
347	C₄×C₈₃	—	2	4	no	—
348	C₄×C₈₃	—	4	2	no	—
349	C₄×C₈₃	—	4	2	no	—
350	C₄×C₈₃	—	4	2	no	—
351	C₄×C₈₃	—	4	2	no	—
352	C₄×C₈₃	—	4	2	no	—
353	C₄×C₈₃	—	4	2	no	—
354	C₄×C₈₃	#578	1	2	yes	—
355	C₄×C₈₃	#585	1	2	yes	—
356	#61917	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
357	C₂×C₈₃	—	4	1	no	—
358	C₂×C₈₃	—	8	2	no	—
359	C₂×C₈₃	—	8	2	no	—
360	C₂×C₈₃	#3487	1	1	yes	characteristic
361	C₂×C₈₃	C₂×#578	1	1	yes	characteristic
362	C₂×C₈₃	#3585	1	1	yes	characteristic
363	#3550	C₂×C₈₃	1	1	yes	characteristic, complemented
364	#3507	C₂×C₈₃	1	1	yes	characteristic, complemented
365	#3402	C₂×C₈₃	1	4	yes	complemented
366	#3400	C₂×C₈₃	1	2	yes	complemented
367	#3396	C₂×C₈₃	1	2	yes	complemented
368	#3375	C₂×C₈₃	1	2	yes	complemented
369	#3367	C₂×C₈₃	1	4	yes	complemented
370	#3363	C₂×C₈₃	1	2	yes	complemented
371	#3225	C₂×C₈₃	1	4	yes	complemented
372	#3216	C₂×C₈₃	1	1	yes	characteristic, complemented
373	#3207	C₂×C₈₃	1	1	yes	characteristic
374	#3124	C₂×C₈₃	1	4	yes	complemented
375	#3112	C₂×C₈₃	1	1	yes	characteristic, complemented
376	#3104	C₂×C₈₃	1	1	yes	characteristic, complemented
377	#2985	C₂×C₈₃	1	1	yes	characteristic, complemented
378	C₈₃	#61917	1	1	yes	characteristic, direct product factor, Sylow
379	#563	—	2	2	no	—
380	#559	C₂²×C₈₃	1	2	yes	—
381	#559	C₂²×C₈₃	1	2	yes	—
382	Q₈²	C₂²×C₈₃	1	2	yes	—
383	#557	C₂²×C₈₃	1	2	yes	—
384	#556	—	2	1	no	—
385	#556	—	2	1	no	—
386	#556	C₂²×C₈₃	1	4	yes	—
387	#556	C₂²×C₈₃	1	2	yes	—
388	#554	—	2	1	no	—
389	#552	—	2	2	no	—
390	D₄×Q₈	—	2	1	no	—
391	D₄×Q₈	C₂²×C₈₃	1	2	yes	—
392	#542	—	2	2	no	—
393	#542	C₂²×C₈₃	1	4	yes	—
394	#539	—	2	2	no	—
395	#536	—	2	2	no	—
396	#536	C₂²×C₈₃	1	2	yes	—
397	#533	C₂²×C₈₃	1	1	yes	characteristic
398	#533	C₂²×C₈₃	1	1	yes	characteristic
399	#532	C₂²×C₈₃	1	1	yes	characteristic
400	#532	C₂²×C₈₃	1	1	yes	characteristic
401	#529	—	2	2	no	—
402	#520	C₂²×C₈₃	1	2	yes	—
403	C₂×C₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
404	#497	C₂²×C₈₃	1	4	yes	—
405	#497	C₂²×C₈₃	1	2	yes	—
406	#495	C₂²×C₈₃	1	4	yes	—
407	#493	C₂²×C₈₃	1	1	yes	characteristic
408	#492	C₂²×C₈₃	1	1	yes	characteristic
409	#489	C₂²×C₈₃	1	2	yes	—
410	#489	C₂²×C₈₃	1	4	yes	—
411	#487	C₂²×C₈₃	1	1	yes	characteristic
412	#487	C₂²×C₈₃	1	4	yes	—
413	#486	C₂²×C₈₃	1	1	yes	characteristic
414	#484	C₂²×C₈₃	1	2	yes	—
415	#480	C₂²×C₈₃	1	2	yes	—
416	#477	C₂²×C₈₃	1	2	yes	—
417	#477	C₂²×C₈₃	1	4	yes	—
418	#477	C₂²×C₈₃	1	2	yes	—
419	#474	C₂²×C₈₃	1	4	yes	—
420	#464	C₂²×C₈₃	1	4	yes	—
421	#464	C₂²×C₈₃	1	4	yes	—
422	#463	C₂²×C₈₃	1	4	yes	—
423	#463	C₂²×C₈₃	1	4	yes	—
424	#463	C₂²×C₈₃	1	4	yes	—
425	#462	C₂²×C₈₃	1	2	yes	—
426	#462	C₂²×C₈₃	1	2	yes	—
427	#462	C₂²×C₈₃	1	4	yes	—
428	#461	C₂²×C₈₃	1	4	yes	—
429	#460	C₂²×C₈₃	1	2	yes	—
430	#460	C₂²×C₈₃	1	2	yes	—
431	#452	C₂²×C₈₃	1	4	yes	—
432	#451	C₂²×C₈₃	1	2	yes	—
433	#449	C₂²×C₈₃	1	4	yes	—
434	#448	C₂²×C₈₃	1	2	yes	—
435	#446	C₂²×C₈₃	1	4	yes	—
436	#446	C₂²×C₈₃	1	2	yes	—
437	C₈×Q₈	C₂²×C₈₃	1	2	yes	—
438	#440	C₂²×C₈₃	1	4	yes	—
439	#440	C₂²×C₈₃	1	4	yes	—
440	#440	C₂²×C₈₃	1	4	yes	—
441	C₄×Q₁₆	C₂²×C₈₃	1	2	yes	—
442	C₄×Q₁₆	C₂²×C₈₃	1	2	yes	—
443	C₄×Q₁₆	C₂²×C₈₃	1	4	yes	—
444	C₄×D₈	C₂²×C₈₃	1	4	yes	—
445	#433	C₂²×C₈₃	1	4	yes	—
446	#432	C₂²×C₈₃	1	1	yes	characteristic
447	#431	C₂²×C₈₃	1	1	yes	characteristic
448	C₂×#41	—	2	1	no	—
449	C₂×#41	C₂³×C₈₃	1	2	yes	—
450	C₂²×Q₈	—	2	2	no	—
451	C₂²×Q₈	C₂³×C₈₃	1	1	yes	characteristic
452	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
453	C₂×Q₁₆	C₂³×C₈₃	1	2	yes	—
454	C₂×Q₁₆	C₂³×C₈₃	1	4	yes	—
455	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
456	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
457	C₂×SD₁₆	C₂³×C₈₃	1	4	yes	—
458	C₂×D₈	C₂³×C₈₃	1	4	yes	—
459	C₄⋊Q₈	—	2	4	no	—
460	C₄⋊Q₈	—	2	2	no	—
461	C₄⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
462	C₄⋊Q₈	D₄×C₈₃	1	1	yes	characteristic
463	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
464	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
465	C₄⋊Q₈	C₂³×C₈₃	1	4	yes	—
466	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
467	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
468	C₄⋊Q₈	C₂³×C₈₃	1	4	yes	—
469	#127	C₂³×C₈₃	1	1	yes	characteristic
470	#127	C₂³×C₈₃	1	1	yes	characteristic
471	#126	—	2	4	no	—
472	#126	—	2	4	no	—
473	#126	—	2	4	no	—
474	#126	—	2	4	no	—
475	#125	—	2	2	no	—
476	#125	—	2	4	no	—
477	#125	—	2	1	no	—
478	#125	D₄×C₈₃	1	2	yes	—
479	#124	—	2	2	no	—
480	#124	—	2	2	no	—
481	#124	—	2	4	no	—
482	#124	—	2	1	no	—
483	#124	C₂³×C₈₃	1	2	yes	—
484	#124	C₂³×C₈₃	1	4	yes	—
485	#124	C₂³×C₈₃	1	4	yes	—
486	#123	—	2	4	no	—
487	#123	—	2	4	no	—
488	#123	—	2	4	no	—
489	#123	—	2	4	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	4	no	—
492	C₂²⋊Q₈	—	2	1	no	—
493	C₂²⋊Q₈	—	2	2	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	—	2	2	no	—
496	C₂²⋊Q₈	—	2	4	no	—
497	C₂²⋊Q₈	—	2	4	no	—
498	C₂²⋊Q₈	D₄×C₈₃	1	2	yes	—
499	C₂²⋊Q₈	D₄×C₈₃	1	2	yes	—
500	C₂²⋊Q₈	C₂³×C₈₃	1	2	yes	—
501	#121	—	2	1	no	—
502	#121	—	2	1	no	—
503	#121	—	2	1	no	—
504	#121	C₂³×C₈₃	1	2	yes	—
505	C₄×Q₈	—	2	2	no	—
506	C₄×Q₈	—	2	2	no	—
507	C₄×Q₈	—	2	1	no	—
508	C₄×Q₈	—	2	1	no	—
509	C₄×Q₈	—	2	1	no	—
510	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
511	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
512	C₄×Q₈	C₂³×C₈₃	1	4	yes	—
513	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
514	C₄×Q₈	C₂³×C₈₃	1	4	yes	—
515	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
516	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	4	no	—
520	C₄×D₄	—	2	1	no	—
521	C₄×D₄	—	2	1	no	—
522	C₄×D₄	—	2	1	no	—
523	C₄×D₄	C₂³×C₈₃	1	4	yes	—
524	C₄×D₄	C₂³×C₈₃	1	2	yes	—
525	C₄×D₄	C₂³×C₈₃	1	4	yes	—
526	#117	—	2	1	no	—
527	#117	—	2	2	no	—
528	#117	—	2	4	no	—
529	#117	—	2	2	no	—
530	#117	C₂³×C₈₃	1	2	yes	—
531	C₂×C₄⋊C₄	—	2	1	no	—
532	C₂×C₄⋊C₄	—	2	2	no	—
533	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
534	C₂×C₄²	—	2	1	no	—
535	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
536	#107	C₂³×C₈₃	1	2	yes	—
537	#107	C₂³×C₈₃	1	2	yes	—
538	#107	C₂³×C₈₃	1	4	yes	—
539	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
540	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
541	C₄⋊C₈	C₂³×C₈₃	1	4	yes	—
542	C₄⋊C₈	C₂³×C₈₃	1	4	yes	—
543	#103	C₂³×C₈₃	1	2	yes	—
544	#103	C₂³×C₈₃	1	2	yes	—
545	#103	C₂³×C₈₃	1	4	yes	—
546	#103	C₂³×C₈₃	1	2	yes	—
547	#103	C₂³×C₈₃	1	2	yes	—
548	#103	C₂³×C₈₃	1	4	yes	—
549	#103	C₂³×C₈₃	1	4	yes	—
550	#102	C₂³×C₈₃	1	4	yes	—
551	#102	C₂³×C₈₃	1	4	yes	—
552	#102	C₂³×C₈₃	1	4	yes	—
553	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
554	C₂²⋊C₈	C₂³×C₈₃	1	2	yes	—
555	#97	C₂³×C₈₃	1	2	yes	—
556	#97	C₂³×C₈₃	1	4	yes	—
557	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
558	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
559	C₄×C₈	C₂³×C₈₃	1	4	yes	—
560	#41	—	4	4	no	—
561	#41	—	8	2	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	4	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	4	2	no	—
567	C₂×Q₈	—	8	4	no	—
568	C₂×Q₈	C₂×D₄×C₈₃	1	2	yes	—
569	C₂×Q₈	C₂×D₄×C₈₃	1	2	yes	—
570	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
571	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
572	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
580	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
588	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
590	Q₁₆	—	4	2	no	—
591	Q₁₆	—	4	2	no	—
592	Q₁₆	—	4	4	no	—
593	SD₁₆	—	4	4	no	—
594	SD₁₆	—	4	4	no	—
595	SD₁₆	—	4	4	no	—
596	D₈	—	4	4	no	—
597	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
598	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
599	C₂×C₈	C₂⁴×C₈₃	1	4	yes	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
617	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
618	C₄⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
619	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
620	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
621	C₄⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
622	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
623	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
624	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	—	2	2	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	C₂×D₄×C₈₃	1	4	yes	—
637	C₄²	—	2	2	no	—
638	C₄²	—	2	2	no	—
639	C₄²	—	2	4	no	—
640	C₄²	—	2	2	no	—
641	C₄²	—	2	4	no	—
642	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
643	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
644	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
645	C₄²	C₂⁴×C₈₃	1	4	yes	—
646	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
650	Q₈	—	2	4	no	—
651	Q₈	—	2	2	no	—
652	Q₈	—	2	2	no	—
653	Q₈	—	2	4	no	—
654	Q₈	—	2	2	no	—
655	Q₈	—	2	2	no	—
656	Q₈	—	4	2	no	—
657	Q₈	—	4	2	no	—
658	Q₈	—	4	2	no	—
659	Q₈	—	8	4	no	—
660	Q₈	—	8	1	no	—
661	D₄	—	2	4	no	—
662	D₄	—	2	4	no	—
663	D₄	—	4	4	no	—
664	D₄	—	4	2	no	—
665	D₄	—	4	2	no	—
666	D₄	—	8	1	no	—
667	D₄	—	8	1	no	—
668	D₄	—	8	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	4	no	—
679	C₂×C₄	—	4	4	no	—
680	C₂×C₄	—	4	2	no	—
681	C₂×C₄	—	8	4	no	—
682	C₂×C₄	—	8	4	no	—
683	C₂×C₄	—	8	1	no	—
684	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
685	C₂×C₄	C₂²×D₄×C₈₃	1	4	yes	—
686	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
687	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
688	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
689	C₂×C₄	C₂²×D₄×C₈₃	1	4	yes	—
690	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
691	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
692	C₈	—	2	2	no	—
693	C₈	—	2	2	no	—
694	C₈	—	2	4	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	2	1	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
705	C₄	—	2	1	no	—
706	C₄	—	2	4	no	—
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	2	4	no	—
710	C₄	—	2	1	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	2	no	—
717	C₄	#578×C₈₃	1	2	yes	—
718	C₄	#585×C₈₃	1	2	yes	—
719	C₂	—	4	1	no	—
720	C₂	—	8	2	no	—
721	C₂	—	8	2	no	—
722	C₂	C₈₃×#3487	1	1	yes	characteristic
723	C₂	C₂×#578×C₈₃	1	1	yes	characteristic
724	C₂	C₈₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
prime radical	C₈₃×#3207	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ #533×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3550	C₂	semidirect
2. C₈₃×#3507	C₂	semidirect
3. C₈₃×#3402	C₂	semidirect
4. C₈₃×#3400	C₂	semidirect
5. C₈₃×#3396	C₂	semidirect
6. C₈₃×#3375	C₂	semidirect
7. C₈₃×#3367	C₂	semidirect
8. C₈₃×#3363	C₂	semidirect
9. C₈₃×#3225	C₂	semidirect
10. C₈₃×#3216	C₂	semidirect
12. C₈₃×#3124	C₂	semidirect
13. C₈₃×#3112	C₂	semidirect
14. C₈₃×#3104	C₂	semidirect
15. C₈₃×#2985	C₂	semidirect
356. #61917	C₈₃	direct (N × H)
363. #3550	C₂×C₈₃	semidirect
364. #3507	C₂×C₈₃	semidirect
365. #3402	C₂×C₈₃	semidirect
366. #3400	C₂×C₈₃	semidirect
367. #3396	C₂×C₈₃	semidirect
368. #3375	C₂×C₈₃	semidirect
369. #3367	C₂×C₈₃	semidirect
370. #3363	C₂×C₈₃	semidirect
371. #3225	C₂×C₈₃	semidirect
372. #3216	C₂×C₈₃	semidirect
374. #3124	C₂×C₈₃	semidirect
375. #3112	C₂×C₈₃	semidirect
376. #3104	C₂×C₈₃	semidirect
377. #2985	C₂×C₈₃	semidirect
378. C₈₃	#61917	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×#3550	2
C₈₃×#3507	2
C₈₃×#3402	2
C₈₃×#3400	2
C₈₃×#3396	2
C₈₃×#3375	2
C₈₃×#3367	2
C₈₃×#3363	2
C₈₃×#3225	2
C₈₃×#3216	2
C₈₃×#3207	2
C₈₃×#3124	2
C₈₃×#3112	2
C₈₃×#3104	2
C₈₃×#2985	2
#61917	83

Subgroups — C83×#61917 #35289741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61917 #35289741