Subgroups — C₈₃×#61907 #35289731

Order 21248.

2092 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3522	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#550×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3399	C₂	1	6	yes	maximal, complemented
4	C₈₃×#3391	C₂	1	2	yes	maximal, complemented
5	C₈₃×#3366	C₂	1	6	yes	maximal, complemented
6	C₈₃×#3362	C₂	1	2	yes	maximal, complemented
7	C₈₃×#3217	C₂	1	3	yes	maximal, complemented
8	C₈₃×#3205	C₂	1	3	yes	maximal, complemented
9	C₈₃×#3109	C₂	1	3	yes	maximal, complemented
10	C₈₃×#3105	C₂	1	3	yes	maximal, complemented
11	C₈₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₈₃	—	2	1	no	—
13	#559×C₈₃	C₂²	1	3	yes	complemented
14	Q₈²×C₈₃	C₂²	1	1	yes	characteristic, complemented
15	#554×C₈₃	C₂²	1	3	yes	complemented
16	#550×C₈₃	—	2	1	no	—
17	#550×C₈₃	—	2	3	no	—
18	#550×C₈₃	C₂²	1	2	yes	—
19	#550×C₈₃	C₂²	1	6	yes	—
20	#550×C₈₃	C₂²	1	1	yes	characteristic, complemented
21	#548×C₈₃	—	2	1	no	—
22	#547×C₈₃	—	2	3	no	—
23	#542×C₈₃	—	2	3	no	—
24	#532×C₈₃	C₂²	1	3	yes	—
25	C₂×#127×C₈₃	C₂²	1	3	yes	—
26	#529×C₈₃	C₂²	1	3	yes	—
27	C₂×#121×C₈₃	—	2	3	no	—
28	#520×C₈₃	—	2	1	no	—
29	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₈₃	C₂²	1	3	yes	—
31	#496×C₈₃	C₂²	1	6	yes	complemented
32	#493×C₈₃	C₂²	1	6	yes	complemented
33	#490×C₈₃	C₂²	1	6	yes	complemented
34	#486×C₈₃	C₂²	1	6	yes	complemented
35	#484×C₈₃	C₂²	1	1	yes	characteristic
36	#481×C₈₃	C₂²	1	3	yes	—
37	#478×C₈₃	C₂²	1	6	yes	complemented
38	#476×C₈₃	C₂²	1	6	yes	complemented
39	#463×C₈₃	C₂²	1	6	yes	complemented
40	#460×C₈₃	C₂²	1	6	yes	complemented
41	#459×C₈₃	C₂²	1	6	yes	complemented
42	#459×C₈₃	C₂²	1	6	yes	complemented
43	#459×C₈₃	C₂²	1	12	yes	complemented
44	#450×C₈₃	C₂²	1	3	yes	—
45	#447×C₈₃	C₂²	1	3	yes	—
46	#447×C₈₃	C₂²	1	6	yes	—
47	#446×C₈₃	C₂²	1	6	yes	complemented
48	C₈×Q₈×C₈₃	C₂²	1	2	yes	complemented
49	#442×C₈₃	C₂²	1	12	yes	complemented
50	C₄×SD₁₆×C₈₃	C₂²	1	6	yes	complemented
51	C₄×D₈×C₈₃	C₂²	1	6	yes	complemented
52	#432×C₈₃	C₂²	1	3	yes	—
53	#431×C₈₃	C₂²	1	3	yes	—
54	C₂×#41×C₈₃	—	2	1	no	—
55	C₂×#41×C₈₃	—	2	6	no	—
56	C₂×#41×C₈₃	—	2	2	no	—
57	C₂×#41×C₈₃	—	2	3	no	—
58	C₂×#41×C₈₃	—	4	8	no	—
59	C₂²×Q₈×C₈₃	D₄	1	1	yes	characteristic
60	C₂²×D₄×C₈₃	—	2	3	no	—
61	C₂²×D₄×C₈₃	—	2	3	no	—
62	C₂²×D₄×C₈₃	C₂³	1	3	yes	—
63	C₂³×C₄×C₈₃	—	2	3	no	—
64	C₂×SD₁₆×C₈₃	C₂³	1	6	yes	—
65	C₂×D₈×C₈₃	C₂³	1	6	yes	—
66	C₂×D₈×C₈₃	C₂³	1	12	yes	—
67	C₄⋊Q₈×C₈₃	—	2	3	no	—
68	C₄⋊Q₈×C₈₃	C₂³	1	3	yes	—
69	#127×C₈₃	—	2	3	no	—
70	#127×C₈₃	—	2	3	no	—
71	#127×C₈₃	C₂³	1	6	yes	—
72	#127×C₈₃	C₂³	1	6	yes	—
73	#127×C₈₃	C₂³	1	3	yes	—
74	#126×C₈₃	—	2	3	no	—
75	#125×C₈₃	C₂³	1	3	yes	—
76	#124×C₈₃	—	2	3	no	—
77	#124×C₈₃	—	2	3	no	—
78	#124×C₈₃	C₂³	1	3	yes	—
79	#123×C₈₃	—	2	3	no	—
80	#123×C₈₃	—	2	6	no	—
81	C₂²⋊Q₈×C₈₃	—	2	3	no	—
82	C₂²⋊Q₈×C₈₃	—	2	6	no	—
83	C₂²⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
84	#121×C₈₃	—	2	3	no	—
85	#121×C₈₃	—	2	6	no	—
86	#121×C₈₃	—	2	6	no	—
87	#121×C₈₃	—	2	12	no	—
88	#121×C₈₃	—	2	3	no	—
89	#121×C₈₃	C₂³	1	3	yes	—
90	C₄×Q₈×C₈₃	—	2	1	no	—
91	C₄×Q₈×C₈₃	D₄	1	1	yes	characteristic
92	C₄×Q₈×C₈₃	D₄	1	3	yes	—
93	C₄×Q₈×C₈₃	C₂³	1	3	yes	—
94	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
95	C₄×Q₈×C₈₃	C₂³	1	3	yes	—
96	C₄×D₄×C₈₃	—	2	3	no	—
97	C₄×D₄×C₈₃	—	2	3	no	—
98	C₄×D₄×C₈₃	—	2	3	no	—
99	C₄×D₄×C₈₃	—	2	3	no	—
100	C₄×D₄×C₈₃	—	2	3	no	—
101	C₄×D₄×C₈₃	C₂³	1	6	yes	—
102	C₄×D₄×C₈₃	C₂³	1	6	yes	—
103	C₄×D₄×C₈₃	C₂³	1	3	yes	—
104	C₄×D₄×C₈₃	C₂³	1	6	yes	—
105	#117×C₈₃	—	2	3	no	—
106	C₂×C₄⋊C₄×C₈₃	—	2	3	no	—
107	C₂×C₄⋊C₄×C₈₃	D₄	1	3	yes	—
108	C₂×C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₈₃	—	2	3	no	—
110	C₂×C₄²×C₈₃	C₂³	1	3	yes	—
111	#107×C₈₃	C₂³	1	2	yes	—
112	#106×C₈₃	C₂³	1	6	yes	—
113	C₄⋊C₈×C₈₃	C₂³	1	6	yes	—
114	C₄⋊C₈×C₈₃	C₂³	1	6	yes	—
115	#103×C₈₃	C₂³	1	2	yes	—
116	#102×C₈₃	C₂³	1	6	yes	—
117	#102×C₈₃	C₂³	1	12	yes	—
118	#102×C₈₃	C₂³	1	6	yes	—
119	#102×C₈₃	C₂³	1	6	yes	—
120	C₂²⋊C₈×C₈₃	C₂³	1	3	yes	—
121	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
122	#97×C₈₃	C₂³	1	6	yes	—
123	C₄×C₈×C₈₃	C₂³	1	6	yes	—
124	C₂⁴×C₈₃	—	2	3	no	—
125	#41×C₈₃	—	4	24	no	—
126	#41×C₈₃	—	4	4	no	—
127	#41×C₈₃	—	4	8	no	—
128	#41×C₈₃	—	8	6	no	—
129	C₂×Q₈×C₈₃	—	2	4	no	—
130	C₂×Q₈×C₈₃	—	2	3	no	—
131	C₂×Q₈×C₈₃	C₂×D₄	1	3	yes	—
132	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
133	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
134	C₂×D₄×C₈₃	—	2	3	no	—
135	C₂×D₄×C₈₃	—	2	3	no	—
136	C₂×D₄×C₈₃	—	2	3	no	—
137	C₂×D₄×C₈₃	—	2	6	no	—
138	C₂×D₄×C₈₃	—	2	6	no	—
139	C₂×D₄×C₈₃	—	2	6	no	—
140	C₂×D₄×C₈₃	—	2	6	no	—
141	C₂×D₄×C₈₃	—	2	3	no	—
142	C₂×D₄×C₈₃	—	4	6	no	—
143	C₂×D₄×C₈₃	—	4	12	no	—
144	C₂×D₄×C₈₃	—	8	6	no	—
145	C₂×D₄×C₈₃	C₂⁴	1	6	yes	—
146	C₂×D₄×C₈₃	C₂⁴	1	3	yes	—
147	C₂²×C₄×C₈₃	—	2	1	no	—
148	C₂²×C₄×C₈₃	—	2	3	no	—
149	C₂²×C₄×C₈₃	—	2	6	no	—
150	C₂²×C₄×C₈₃	—	2	6	no	—
151	C₂²×C₄×C₈₃	—	2	6	no	—
152	C₂²×C₄×C₈₃	—	4	12	no	—
153	C₂²×C₄×C₈₃	C₂×D₄	1	3	yes	—
154	C₂²×C₄×C₈₃	C₂×D₄	1	3	yes	—
155	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
156	SD₁₆×C₈₃	—	4	6	no	—
157	D₈×C₈₃	—	4	6	no	—
158	D₈×C₈₃	—	4	12	no	—
159	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
160	C₂×C₈×C₈₃	C₂⁴	1	6	yes	—
161	C₄⋊C₄×C₈₃	—	2	3	no	—
162	C₄⋊C₄×C₈₃	—	2	3	no	—
163	C₄⋊C₄×C₈₃	—	2	1	no	—
164	C₄⋊C₄×C₈₃	—	2	1	no	—
165	C₄⋊C₄×C₈₃	—	2	3	no	—
166	C₄⋊C₄×C₈₃	—	2	3	no	—
167	C₄⋊C₄×C₈₃	C₂×D₄	1	3	yes	—
168	C₄⋊C₄×C₈₃	C₂×D₄	1	3	yes	—
169	C₄⋊C₄×C₈₃	C₂×D₄	1	6	yes	—
170	C₄⋊C₄×C₈₃	C₂⁴	1	3	yes	—
171	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
172	C₄⋊C₄×C₈₃	C₂⁴	1	2	yes	—
173	C₂²⋊C₄×C₈₃	—	2	1	no	—
174	C₂²⋊C₄×C₈₃	—	2	6	no	—
175	C₂²⋊C₄×C₈₃	—	2	6	no	—
176	C₂²⋊C₄×C₈₃	—	2	3	no	—
177	C₂²⋊C₄×C₈₃	—	2	3	no	—
178	C₂²⋊C₄×C₈₃	—	2	3	no	—
179	C₂²⋊C₄×C₈₃	—	2	3	no	—
180	C₂²⋊C₄×C₈₃	—	2	6	no	—
181	C₄²×C₈₃	—	2	3	no	—
182	C₄²×C₈₃	C₂×D₄	1	3	yes	—
183	C₄²×C₈₃	C₂×D₄	1	3	yes	—
184	C₄²×C₈₃	C₂⁴	1	3	yes	—
185	C₄²×C₈₃	C₂⁴	1	3	yes	—
186	C₂³×C₈₃	—	2	3	no	—
187	C₂³×C₈₃	—	2	6	no	—
188	C₂³×C₈₃	—	4	6	no	—
189	C₂³×C₈₃	—	4	6	no	—
190	C₂³×C₈₃	—	4	6	no	—
191	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
192	Q₈×C₈₃	—	2	6	no	—
193	Q₈×C₈₃	—	2	2	no	—
194	Q₈×C₈₃	—	8	3	no	—
195	Q₈×C₈₃	AGL(1,ℤ/8)	1	4	yes	—
196	D₄×C₈₃	—	2	6	no	—
197	D₄×C₈₃	—	2	6	no	—
198	D₄×C₈₃	—	2	6	no	—
199	D₄×C₈₃	—	4	6	no	—
200	D₄×C₈₃	—	4	12	no	—
201	D₄×C₈₃	—	4	6	no	—
202	D₄×C₈₃	—	4	12	no	—
203	D₄×C₈₃	—	4	6	no	—
204	D₄×C₈₃	—	8	6	no	—
205	D₄×C₈₃	—	8	6	no	—
206	D₄×C₈₃	—	8	3	no	—
207	C₂×C₄×C₈₃	—	2	6	no	—
208	C₂×C₄×C₈₃	—	2	6	no	—
209	C₂×C₄×C₈₃	—	2	2	no	—
210	C₂×C₄×C₈₃	—	2	1	no	—
211	C₂×C₄×C₈₃	—	2	3	no	—
212	C₂×C₄×C₈₃	—	2	2	no	—
213	C₂×C₄×C₈₃	—	2	1	no	—
214	C₂×C₄×C₈₃	—	4	12	no	—
215	C₂×C₄×C₈₃	—	4	2	no	—
216	C₂×C₄×C₈₃	—	4	12	no	—
217	C₂×C₄×C₈₃	—	4	6	no	—
218	C₂×C₄×C₈₃	—	8	6	no	—
219	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₈₃	C₂²×D₄	1	3	yes	—
221	C₂×C₄×C₈₃	C₂²×D₄	1	3	yes	—
222	C₂×C₄×C₈₃	C₂²×D₄	1	3	yes	—
223	C₂×C₄×C₈₃	C₂²×D₄	1	3	yes	—
224	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
225	C₈×C₈₃	—	2	2	no	—
226	C₈×C₈₃	—	2	6	no	—
227	C₂²×C₈₃	—	2	1	no	—
228	C₂²×C₈₃	—	2	1	no	—
229	C₂²×C₈₃	—	4	6	no	—
230	C₂²×C₈₃	—	4	3	no	—
231	C₂²×C₈₃	—	4	6	no	—
232	C₂²×C₈₃	—	4	3	no	—
233	C₂²×C₈₃	—	4	3	no	—
234	C₂²×C₈₃	—	4	6	no	—
235	C₂²×C₈₃	—	8	12	no	—
236	C₂²×C₈₃	#576	1	2	yes	—
237	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
238	C₄×C₈₃	—	2	1	no	—
239	C₄×C₈₃	—	2	3	no	—
240	C₄×C₈₃	—	2	3	no	—
241	C₄×C₈₃	—	2	3	no	—
242	C₄×C₈₃	—	4	1	no	—
243	C₄×C₈₃	—	4	1	no	—
244	C₄×C₈₃	—	4	2	no	—
245	C₄×C₈₃	—	4	3	no	—
246	C₄×C₈₃	C₂×AGL(1,ℤ/8)	1	6	yes	—
247	C₄×C₈₃	#585	1	2	yes	—
248	#61907	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
249	C₂×C₈₃	—	2	2	no	—
250	C₂×C₈₃	—	8	3	no	—
251	C₂×C₈₃	—	8	6	no	—
252	C₂×C₈₃	#3487	1	1	yes	characteristic
253	C₂×C₈₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
254	C₂×C₈₃	C₂×#576	1	1	yes	characteristic
255	#3522	C₂×C₈₃	1	1	yes	characteristic, complemented
256	C₂×#550	C₂×C₈₃	1	1	yes	characteristic, complemented
257	#3399	C₂×C₈₃	1	6	yes	complemented
258	#3391	C₂×C₈₃	1	2	yes	complemented
259	#3366	C₂×C₈₃	1	6	yes	complemented
260	#3362	C₂×C₈₃	1	2	yes	complemented
261	#3217	C₂×C₈₃	1	3	yes	complemented
262	#3205	C₂×C₈₃	1	3	yes	complemented
263	#3109	C₂×C₈₃	1	3	yes	complemented
264	#3105	C₂×C₈₃	1	3	yes	complemented
265	#2984	C₂×C₈₃	1	1	yes	characteristic, complemented
266	C₈₃	#61907	1	1	yes	characteristic, direct product factor, Sylow
267	C₂²×#41	—	2	1	no	—
268	#559	C₂²×C₈₃	1	3	yes	complemented
269	Q₈²	C₂²×C₈₃	1	1	yes	characteristic, complemented
270	#554	C₂²×C₈₃	1	3	yes	complemented
271	#550	—	2	1	no	—
272	#550	—	2	3	no	—
273	#550	C₂²×C₈₃	1	2	yes	—
274	#550	C₂²×C₈₃	1	6	yes	—
275	#550	C₂²×C₈₃	1	1	yes	characteristic, complemented
276	#548	—	2	1	no	—
277	#547	—	2	3	no	—
278	#542	—	2	3	no	—
279	#532	C₂²×C₈₃	1	3	yes	—
280	C₂×#127	C₂²×C₈₃	1	3	yes	—
281	#529	C₂²×C₈₃	1	3	yes	—
282	C₂×#121	—	2	3	no	—
283	#520	—	2	1	no	—
284	C₂×C₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
285	C₂×C₄×D₄	C₂²×C₈₃	1	3	yes	—
286	#496	C₂²×C₈₃	1	6	yes	complemented
287	#493	C₂²×C₈₃	1	6	yes	complemented
288	#490	C₂²×C₈₃	1	6	yes	complemented
289	#486	C₂²×C₈₃	1	6	yes	complemented
290	#484	C₂²×C₈₃	1	1	yes	characteristic
291	#481	C₂²×C₈₃	1	3	yes	—
292	#478	C₂²×C₈₃	1	6	yes	complemented
293	#476	C₂²×C₈₃	1	6	yes	complemented
294	#463	C₂²×C₈₃	1	6	yes	complemented
295	#460	C₂²×C₈₃	1	6	yes	complemented
296	#459	C₂²×C₈₃	1	6	yes	complemented
297	#459	C₂²×C₈₃	1	6	yes	complemented
298	#459	C₂²×C₈₃	1	12	yes	complemented
299	#450	C₂²×C₈₃	1	3	yes	—
300	#447	C₂²×C₈₃	1	3	yes	—
301	#447	C₂²×C₈₃	1	6	yes	—
302	#446	C₂²×C₈₃	1	6	yes	complemented
303	C₈×Q₈	C₂²×C₈₃	1	2	yes	complemented
304	#442	C₂²×C₈₃	1	12	yes	complemented
305	C₄×SD₁₆	C₂²×C₈₃	1	6	yes	complemented
306	C₄×D₈	C₂²×C₈₃	1	6	yes	complemented
307	#432	C₂²×C₈₃	1	3	yes	—
308	#431	C₂²×C₈₃	1	3	yes	—
309	C₂×#41	—	2	1	no	—
310	C₂×#41	—	2	6	no	—
311	C₂×#41	—	2	2	no	—
312	C₂×#41	—	2	3	no	—
313	C₂×#41	—	4	8	no	—
314	C₂²×Q₈	D₄×C₈₃	1	1	yes	characteristic
315	C₂²×D₄	—	2	3	no	—
316	C₂²×D₄	—	2	3	no	—
317	C₂²×D₄	C₂³×C₈₃	1	3	yes	—
318	C₂³×C₄	—	2	3	no	—
319	C₂×SD₁₆	C₂³×C₈₃	1	6	yes	—
320	C₂×D₈	C₂³×C₈₃	1	6	yes	—
321	C₂×D₈	C₂³×C₈₃	1	12	yes	—
322	C₄⋊Q₈	—	2	3	no	—
323	C₄⋊Q₈	C₂³×C₈₃	1	3	yes	—
324	#127	—	2	3	no	—
325	#127	—	2	3	no	—
326	#127	C₂³×C₈₃	1	6	yes	—
327	#127	C₂³×C₈₃	1	6	yes	—
328	#127	C₂³×C₈₃	1	3	yes	—
329	#126	—	2	3	no	—
330	#125	C₂³×C₈₃	1	3	yes	—
331	#124	—	2	3	no	—
332	#124	—	2	3	no	—
333	#124	C₂³×C₈₃	1	3	yes	—
334	#123	—	2	3	no	—
335	#123	—	2	6	no	—
336	C₂²⋊Q₈	—	2	3	no	—
337	C₂²⋊Q₈	—	2	6	no	—
338	C₂²⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
339	#121	—	2	3	no	—
340	#121	—	2	6	no	—
341	#121	—	2	6	no	—
342	#121	—	2	12	no	—
343	#121	—	2	3	no	—
344	#121	C₂³×C₈₃	1	3	yes	—
345	C₄×Q₈	—	2	1	no	—
346	C₄×Q₈	D₄×C₈₃	1	1	yes	characteristic
347	C₄×Q₈	D₄×C₈₃	1	3	yes	—
348	C₄×Q₈	C₂³×C₈₃	1	3	yes	—
349	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
350	C₄×Q₈	C₂³×C₈₃	1	3	yes	—
351	C₄×D₄	—	2	3	no	—
352	C₄×D₄	—	2	3	no	—
353	C₄×D₄	—	2	3	no	—
354	C₄×D₄	—	2	3	no	—
355	C₄×D₄	—	2	3	no	—
356	C₄×D₄	C₂³×C₈₃	1	6	yes	—
357	C₄×D₄	C₂³×C₈₃	1	6	yes	—
358	C₄×D₄	C₂³×C₈₃	1	3	yes	—
359	C₄×D₄	C₂³×C₈₃	1	6	yes	—
360	#117	—	2	3	no	—
361	C₂×C₄⋊C₄	—	2	3	no	—
362	C₂×C₄⋊C₄	D₄×C₈₃	1	3	yes	—
363	C₂×C₄⋊C₄	C₂³×C₈₃	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	—	2	3	no	—
365	C₂×C₄²	C₂³×C₈₃	1	3	yes	—
366	#107	C₂³×C₈₃	1	2	yes	—
367	#106	C₂³×C₈₃	1	6	yes	—
368	C₄⋊C₈	C₂³×C₈₃	1	6	yes	—
369	C₄⋊C₈	C₂³×C₈₃	1	6	yes	—
370	#103	C₂³×C₈₃	1	2	yes	—
371	#102	C₂³×C₈₃	1	6	yes	—
372	#102	C₂³×C₈₃	1	6	yes	—
373	#102	C₂³×C₈₃	1	6	yes	—
374	#102	C₂³×C₈₃	1	12	yes	—
375	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
376	C₂²⋊C₈	C₂³×C₈₃	1	3	yes	—
377	#97	C₂³×C₈₃	1	6	yes	—
378	C₄×C₈	C₂³×C₈₃	1	6	yes	—
379	C₂⁴	—	2	3	no	—
380	#41	—	4	24	no	—
381	#41	—	4	8	no	—
382	#41	—	4	4	no	—
383	#41	—	8	6	no	—
384	C₂×Q₈	—	2	4	no	—
385	C₂×Q₈	—	2	3	no	—
386	C₂×Q₈	C₂×D₄×C₈₃	1	3	yes	—
387	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
388	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
389	C₂×D₄	—	2	3	no	—
390	C₂×D₄	—	2	3	no	—
391	C₂×D₄	—	2	3	no	—
392	C₂×D₄	—	2	6	no	—
393	C₂×D₄	—	2	6	no	—
394	C₂×D₄	—	2	6	no	—
395	C₂×D₄	—	2	6	no	—
396	C₂×D₄	—	2	3	no	—
397	C₂×D₄	—	4	6	no	—
398	C₂×D₄	—	4	12	no	—
399	C₂×D₄	—	8	6	no	—
400	C₂×D₄	C₂⁴×C₈₃	1	6	yes	—
401	C₂×D₄	C₂⁴×C₈₃	1	3	yes	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	3	no	—
404	C₂²×C₄	—	2	6	no	—
405	C₂²×C₄	—	2	6	no	—
406	C₂²×C₄	—	2	6	no	—
407	C₂²×C₄	—	4	12	no	—
408	C₂²×C₄	C₂×D₄×C₈₃	1	3	yes	—
409	C₂²×C₄	C₂×D₄×C₈₃	1	3	yes	—
410	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
411	SD₁₆	—	4	6	no	—
412	D₈	—	4	6	no	—
413	D₈	—	4	12	no	—
414	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
415	C₂×C₈	C₂⁴×C₈₃	1	6	yes	—
416	C₄⋊C₄	—	2	3	no	—
417	C₄⋊C₄	—	2	3	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	3	no	—
421	C₄⋊C₄	—	2	3	no	—
422	C₄⋊C₄	C₂×D₄×C₈₃	1	3	yes	—
423	C₄⋊C₄	C₂×D₄×C₈₃	1	3	yes	—
424	C₄⋊C₄	C₂×D₄×C₈₃	1	6	yes	—
425	C₄⋊C₄	C₂⁴×C₈₃	1	3	yes	—
426	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
427	C₄⋊C₄	C₂⁴×C₈₃	1	2	yes	—
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	6	no	—
430	C₂²⋊C₄	—	2	6	no	—
431	C₂²⋊C₄	—	2	3	no	—
432	C₂²⋊C₄	—	2	3	no	—
433	C₂²⋊C₄	—	2	3	no	—
434	C₂²⋊C₄	—	2	3	no	—
435	C₂²⋊C₄	—	2	6	no	—
436	C₄²	—	2	3	no	—
437	C₄²	C₂×D₄×C₈₃	1	3	yes	—
438	C₄²	C₂×D₄×C₈₃	1	3	yes	—
439	C₄²	C₂⁴×C₈₃	1	3	yes	—
440	C₄²	C₂⁴×C₈₃	1	3	yes	—
441	C₂³	—	2	3	no	—
442	C₂³	—	2	6	no	—
443	C₂³	—	4	6	no	—
444	C₂³	—	4	6	no	—
445	C₂³	—	4	6	no	—
446	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
447	Q₈	—	2	6	no	—
448	Q₈	—	2	2	no	—
449	Q₈	—	8	3	no	—
450	Q₈	AGL(1,ℤ/8)×C₈₃	1	4	yes	—
451	D₄	—	2	6	no	—
452	D₄	—	2	6	no	—
453	D₄	—	2	6	no	—
454	D₄	—	4	12	no	—
455	D₄	—	4	6	no	—
456	D₄	—	4	6	no	—
457	D₄	—	4	12	no	—
458	D₄	—	4	6	no	—
459	D₄	—	8	6	no	—
460	D₄	—	8	6	no	—
461	D₄	—	8	3	no	—
462	C₂×C₄	—	2	6	no	—
463	C₂×C₄	—	2	6	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	3	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	4	12	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	12	no	—
472	C₂×C₄	—	4	6	no	—
473	C₂×C₄	—	8	6	no	—
474	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
475	C₂×C₄	C₂²×D₄×C₈₃	1	3	yes	—
476	C₂×C₄	C₂²×D₄×C₈₃	1	3	yes	—
477	C₂×C₄	C₂²×D₄×C₈₃	1	3	yes	—
478	C₂×C₄	C₂²×D₄×C₈₃	1	3	yes	—
479	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
480	C₈	—	2	2	no	—
481	C₈	—	2	6	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	4	6	no	—
485	C₂²	—	4	3	no	—
486	C₂²	—	4	3	no	—
487	C₂²	—	4	6	no	—
488	C₂²	—	4	6	no	—
489	C₂²	—	4	3	no	—
490	C₂²	—	8	12	no	—
491	C₂²	#576×C₈₃	1	2	yes	—
492	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
493	C₄	—	2	3	no	—
494	C₄	—	2	3	no	—
495	C₄	—	2	3	no	—
496	C₄	—	2	1	no	—
497	C₄	—	4	2	no	—
498	C₄	—	4	1	no	—
499	C₄	—	4	3	no	—
500	C₄	—	4	1	no	—
501	C₄	C₂×AGL(1,ℤ/8)×C₈₃	1	6	yes	—
502	C₄	#585×C₈₃	1	2	yes	—
503	C₂	—	2	2	no	—
504	C₂	—	8	6	no	—
505	C₂	—	8	3	no	—
506	C₂	C₈₃×#3487	1	1	yes	characteristic
507	C₂	C₂²×AGL(1,ℤ/8)×C₈₃	1	1	yes	characteristic
508	C₂	C₂×#576×C₈₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ C₂×C₄×Q₈×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3522	C₂	semidirect
2. C₂×#550×C₈₃	C₂	semidirect
3. C₈₃×#3399	C₂	semidirect
4. C₈₃×#3391	C₂	semidirect
5. C₈₃×#3366	C₂	semidirect
6. C₈₃×#3362	C₂	semidirect
7. C₈₃×#3217	C₂	semidirect
8. C₈₃×#3205	C₂	semidirect
9. C₈₃×#3109	C₂	semidirect
10. C₈₃×#3105	C₂	semidirect
11. C₈₃×#2984	C₂	semidirect
13. #559×C₈₃	C₂²	semidirect
14. Q₈²×C₈₃	C₂²	semidirect
15. #554×C₈₃	C₂²	semidirect
20. #550×C₈₃	C₂²	semidirect
31. #496×C₈₃	C₂²	semidirect
32. #493×C₈₃	C₂²	semidirect
33. #490×C₈₃	C₂²	semidirect
34. #486×C₈₃	C₂²	semidirect
37. #478×C₈₃	C₂²	semidirect
38. #476×C₈₃	C₂²	semidirect
39. #463×C₈₃	C₂²	semidirect
40. #460×C₈₃	C₂²	semidirect
41. #459×C₈₃	C₂²	semidirect
42. #459×C₈₃	C₂²	semidirect
43. #459×C₈₃	C₂²	semidirect
47. #446×C₈₃	C₂²	semidirect
48. C₈×Q₈×C₈₃	C₂²	semidirect
49. #442×C₈₃	C₂²	semidirect
50. C₄×SD₁₆×C₈₃	C₂²	semidirect
51. C₄×D₈×C₈₃	C₂²	semidirect
248. #61907	C₈₃	direct (N × H)
255. #3522	C₂×C₈₃	semidirect
256. C₂×#550	C₂×C₈₃	semidirect
257. #3399	C₂×C₈₃	semidirect
258. #3391	C₂×C₈₃	semidirect
259. #3366	C₂×C₈₃	semidirect
260. #3362	C₂×C₈₃	semidirect
261. #3217	C₂×C₈₃	semidirect
262. #3205	C₂×C₈₃	semidirect
263. #3109	C₂×C₈₃	semidirect
264. #3105	C₂×C₈₃	semidirect
265. #2984	C₂×C₈₃	semidirect
266. C₈₃	#61907	direct (N × H)
268. #559	C₂²×C₈₃	semidirect
269. Q₈²	C₂²×C₈₃	semidirect
270. #554	C₂²×C₈₃	semidirect
275. #550	C₂²×C₈₃	semidirect
286. #496	C₂²×C₈₃	semidirect
287. #493	C₂²×C₈₃	semidirect
288. #490	C₂²×C₈₃	semidirect
289. #486	C₂²×C₈₃	semidirect
292. #478	C₂²×C₈₃	semidirect
293. #476	C₂²×C₈₃	semidirect
294. #463	C₂²×C₈₃	semidirect
295. #460	C₂²×C₈₃	semidirect
296. #459	C₂²×C₈₃	semidirect
297. #459	C₂²×C₈₃	semidirect
298. #459	C₂²×C₈₃	semidirect
302. #446	C₂²×C₈₃	semidirect
303. C₈×Q₈	C₂²×C₈₃	semidirect
304. #442	C₂²×C₈₃	semidirect
305. C₄×SD₁₆	C₂²×C₈₃	semidirect
306. C₄×D₈	C₂²×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₈₃×#3522	2
C₂×#550×C₈₃	2
C₈₃×#3399	2
C₈₃×#3391	2
C₈₃×#3366	2
C₈₃×#3362	2
C₈₃×#3217	2
C₈₃×#3205	2
C₈₃×#3109	2
C₈₃×#3105	2
C₈₃×#2984	2
#61907	83

Subgroups — C83×#61907 #35289731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61907 #35289731