Subgroups — C₈₃×#61843 #35289667

Order 21248.

1984 conjugacy classes of subgroups.

The subgroup lattice has 502 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×D₄×Q₈×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#3384	C₂	1	6	yes	maximal, complemented
4	Q₈×SD₁₆×C₈₃	C₂	1	2	yes	maximal, complemented
5	C₈₃×#3373	C₂	1	6	yes	maximal, complemented
6	C₈₃×#3358	C₂	1	2	yes	maximal, complemented
7	C₈₃×#3239	C₂	1	3	yes	maximal, complemented
8	C₈₃×#3227	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	C₂³×Q₈×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	C₂²	1	1	yes	characteristic, complemented
17	D₄×Q₈×C₈₃	—	2	1	no	—
18	D₄×Q₈×C₈₃	—	2	3	no	—
19	D₄×Q₈×C₈₃	C₂²	1	2	yes	—
20	D₄×Q₈×C₈₃	C₂²	1	6	yes	—
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×C₄⋊Q₈×C₈₃	C₂²	1	3	yes	—
26	#529×C₈₃	C₂²	1	3	yes	—
27	C₂×C₂²⋊Q₈×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	#501×C₈₃	C₂²	1	6	yes	complemented
32	#498×C₈₃	C₂²	1	6	yes	complemented
33	#489×C₈₃	C₂²	1	6	yes	complemented
34	#486×C₈₃	C₂²	1	6	yes	complemented
35	#484×C₈₃	C₂²	1	3	yes	—
36	#481×C₈₃	C₂²	1	3	yes	—
37	#481×C₈₃	C₂²	1	6	yes	—
38	#478×C₈₃	C₂²	1	6	yes	—
39	#476×C₈₃	C₂²	1	6	yes	—
40	#476×C₈₃	C₂²	1	12	yes	complemented
41	#475×C₈₃	C₂²	1	6	yes	complemented
42	#474×C₈₃	C₂²	1	6	yes	complemented
43	#463×C₈₃	C₂²	1	6	yes	—
44	#459×C₈₃	C₂²	1	6	yes	—
45	#450×C₈₃	C₂²	1	1	yes	characteristic
46	#447×C₈₃	C₂²	1	3	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	—
50	C₄×SD₁₆×C₈₃	C₂²	1	6	yes	—
51	C₄×D₈×C₈₃	C₂²	1	6	yes	—
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	3	no	—
56	C₂²×Q₈×C₈₃	—	2	6	no	—
57	C₂²×Q₈×C₈₃	—	2	2	no	—
58	C₂²×Q₈×C₈₃	—	2	3	no	—
59	C₂²×Q₈×C₈₃	—	4	8	no	—
60	C₂²×Q₈×C₈₃	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₈₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₈₃	—	2	3	no	—
63	C₂×SD₁₆×C₈₃	C₂³	1	2	yes	—
64	C₂×D₈×C₈₃	C₂³	1	6	yes	—
65	C₄⋊Q₈×C₈₃	—	2	3	no	—
66	C₄⋊Q₈×C₈₃	—	2	3	no	—
67	C₄⋊Q₈×C₈₃	—	2	3	no	—
68	C₄⋊Q₈×C₈₃	C₂³	1	6	yes	—
69	C₄⋊Q₈×C₈₃	C₂³	1	3	yes	—
70	C₄⋊Q₈×C₈₃	C₂³	1	6	yes	—
71	#127×C₈₃	C₂³	1	3	yes	—
72	#126×C₈₃	—	2	3	no	—
73	#125×C₈₃	C₂³	1	3	yes	—
74	#124×C₈₃	—	2	3	no	—
75	#124×C₈₃	—	2	3	no	—
76	#124×C₈₃	C₂³	1	3	yes	—
77	#123×C₈₃	—	2	3	no	—
78	#123×C₈₃	—	2	6	no	—
79	C₂²⋊Q₈×C₈₃	—	2	3	no	—
80	C₂²⋊Q₈×C₈₃	—	2	6	no	—
81	C₂²⋊Q₈×C₈₃	—	2	6	no	—
82	C₂²⋊Q₈×C₈₃	—	2	12	no	—
83	C₂²⋊Q₈×C₈₃	—	2	6	no	—
84	C₂²⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
85	#121×C₈₃	—	2	3	no	—
86	#121×C₈₃	—	2	3	no	—
87	#121×C₈₃	C₂³	1	3	yes	—
88	C₄×Q₈×C₈₃	—	2	1	no	—
89	C₄×Q₈×C₈₃	D₄	1	1	yes	characteristic
90	C₄×Q₈×C₈₃	D₄	1	3	yes	—
91	C₄×Q₈×C₈₃	C₂³	1	3	yes	—
92	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
93	C₄×Q₈×C₈₃	C₂³	1	3	yes	—
94	C₄×D₄×C₈₃	—	2	3	no	—
95	C₄×D₄×C₈₃	—	2	3	no	—
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	C₂³	1	6	yes	—
100	C₄×D₄×C₈₃	C₂³	1	3	yes	—
101	C₄×D₄×C₈₃	C₂³	1	6	yes	—
102	C₄×D₄×C₈₃	C₂³	1	6	yes	—
103	#117×C₈₃	—	2	3	no	—
104	C₂×C₄⋊C₄×C₈₃	—	2	3	no	—
105	C₂×C₄⋊C₄×C₈₃	—	2	3	no	—
106	C₂×C₄⋊C₄×C₈₃	D₄	1	3	yes	—
107	C₂×C₄⋊C₄×C₈₃	C₂³	1	3	yes	—
108	C₂×C₂²⋊C₄×C₈₃	—	2	3	no	—
109	C₂×C₄²×C₈₃	C₂³	1	3	yes	—
110	#107×C₈₃	C₂³	1	6	yes	—
111	#106×C₈₃	C₂³	1	12	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	6	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	2	yes	—
120	C₂²⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
121	C₂²⋊C₈×C₈₃	C₂³	1	3	yes	—
122	#97×C₈₃	C₂³	1	6	yes	—
123	C₄×C₈×C₈₃	C₂³	1	6	yes	—
124	C₂⁴×C₈₃	—	2	1	no	—
125	#41×C₈₃	—	4	4	no	—
126	#41×C₈₃	—	8	6	no	—
127	C₂×Q₈×C₈₃	—	2	4	no	—
128	C₂×Q₈×C₈₃	—	2	6	no	—
129	C₂×Q₈×C₈₃	—	2	6	no	—
130	C₂×Q₈×C₈₃	—	2	3	no	—
131	C₂×Q₈×C₈₃	—	4	12	no	—
132	C₂×Q₈×C₈₃	—	4	24	no	—
133	C₂×Q₈×C₈₃	—	4	8	no	—
134	C₂×Q₈×C₈₃	C₂×D₄	1	3	yes	—
135	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
136	C₂×Q₈×C₈₃	C₂⁴	1	1	yes	characteristic
137	C₂×D₄×C₈₃	—	2	4	no	—
138	C₂×D₄×C₈₃	—	2	3	no	—
139	C₂×D₄×C₈₃	—	2	1	no	—
140	C₂×D₄×C₈₃	—	2	3	no	—
141	C₂×D₄×C₈₃	—	2	3	no	—
142	C₂×D₄×C₈₃	C₂⁴	1	3	yes	—
143	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₈₃	—	2	3	no	—
145	C₂²×C₄×C₈₃	—	2	3	no	—
146	C₂²×C₄×C₈₃	—	2	6	no	—
147	C₂²×C₄×C₈₃	—	2	6	no	—
148	C₂²×C₄×C₈₃	—	2	6	no	—
149	C₂²×C₄×C₈₃	—	4	12	no	—
150	C₂²×C₄×C₈₃	C₂×D₄	1	3	yes	—
151	C₂²×C₄×C₈₃	C₂×D₄	1	3	yes	—
152	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
153	SD₁₆×C₈₃	—	2	4	no	—
154	D₈×C₈₃	—	2	12	no	—
155	C₂×C₈×C₈₃	C₂⁴	1	2	yes	—
156	C₂×C₈×C₈₃	C₂⁴	1	6	yes	—
157	C₄⋊C₄×C₈₃	—	2	3	no	—
158	C₄⋊C₄×C₈₃	—	2	3	no	—
159	C₄⋊C₄×C₈₃	—	2	6	no	—
160	C₄⋊C₄×C₈₃	—	2	6	no	—
161	C₄⋊C₄×C₈₃	—	2	3	no	—
162	C₄⋊C₄×C₈₃	—	2	1	no	—
163	C₄⋊C₄×C₈₃	—	2	3	no	—
164	C₄⋊C₄×C₈₃	—	2	3	no	—
165	C₄⋊C₄×C₈₃	C₂×D₄	1	3	yes	—
166	C₄⋊C₄×C₈₃	C₂×D₄	1	3	yes	—
167	C₄⋊C₄×C₈₃	C₂×D₄	1	6	yes	—
168	C₄⋊C₄×C₈₃	C₂⁴	1	6	yes	—
169	C₄⋊C₄×C₈₃	C₂⁴	1	3	yes	—
170	C₄⋊C₄×C₈₃	C₂⁴	1	1	yes	characteristic
171	C₂²⋊C₄×C₈₃	—	2	1	no	—
172	C₂²⋊C₄×C₈₃	—	2	6	no	—
173	C₂²⋊C₄×C₈₃	—	2	6	no	—
174	C₂²⋊C₄×C₈₃	—	2	3	no	—
175	C₂²⋊C₄×C₈₃	—	2	3	no	—
176	C₂²⋊C₄×C₈₃	—	2	3	no	—
177	C₂²⋊C₄×C₈₃	—	2	3	no	—
178	C₂²⋊C₄×C₈₃	—	2	6	no	—
179	C₄²×C₈₃	—	2	3	no	—
180	C₄²×C₈₃	C₂×D₄	1	3	yes	—
181	C₄²×C₈₃	C₂×D₄	1	3	yes	—
182	C₄²×C₈₃	C₂⁴	1	3	yes	—
183	C₄²×C₈₃	C₂⁴	1	3	yes	—
184	C₂³×C₈₃	—	2	4	no	—
185	C₂³×C₈₃	—	2	2	no	—
186	C₂³×C₈₃	—	2	3	no	—
187	C₂³×C₈₃	—	4	2	no	—
188	C₂³×C₈₃	—	4	2	no	—
189	C₂³×C₈₃	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₈₃	—	2	6	no	—
191	Q₈×C₈₃	—	2	2	no	—
192	Q₈×C₈₃	—	4	12	no	—
193	Q₈×C₈₃	—	4	12	no	—
194	Q₈×C₈₃	—	8	3	no	—
195	Q₈×C₈₃	AGL(1,ℤ/8)	1	4	yes	—
196	D₄×C₈₃	—	2	4	no	—
197	D₄×C₈₃	—	2	2	no	—
198	D₄×C₈₃	—	2	6	no	—
199	D₄×C₈₃	—	4	6	no	—
200	D₄×C₈₃	—	4	6	no	—
201	D₄×C₈₃	—	8	3	no	—
202	D₄×C₈₃	2₋¹⁺⁴	1	4	yes	—
203	C₂×C₄×C₈₃	—	2	6	no	—
204	C₂×C₄×C₈₃	—	2	6	no	—
205	C₂×C₄×C₈₃	—	2	2	no	—
206	C₂×C₄×C₈₃	—	2	1	no	—
207	C₂×C₄×C₈₃	—	2	3	no	—
208	C₂×C₄×C₈₃	—	2	1	no	—
209	C₂×C₄×C₈₃	—	2	6	no	—
210	C₂×C₄×C₈₃	—	4	12	no	—
211	C₂×C₄×C₈₃	—	4	6	no	—
212	C₂×C₄×C₈₃	—	4	12	no	—
213	C₂×C₄×C₈₃	—	4	6	no	—
214	C₂×C₄×C₈₃	—	8	6	no	—
215	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₈₃	C₂²×D₄	1	3	yes	—
217	C₂×C₄×C₈₃	C₂²×D₄	1	3	yes	—
218	C₂×C₄×C₈₃	C₂²×D₄	1	3	yes	—
219	C₂×C₄×C₈₃	C₂²×D₄	1	3	yes	—
220	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
221	C₈×C₈₃	—	2	6	no	—
222	C₈×C₈₃	—	2	2	no	—
223	C₂²×C₈₃	—	2	1	no	—
224	C₂²×C₈₃	—	2	1	no	—
225	C₂²×C₈₃	—	2	4	no	—
226	C₂²×C₈₃	—	4	8	no	—
227	C₂²×C₈₃	—	4	2	no	—
228	C₂²×C₈₃	—	4	2	no	—
229	C₂²×C₈₃	—	4	3	no	—
230	C₂²×C₈₃	—	4	3	no	—
231	C₂²×C₈₃	—	4	3	no	—
232	C₂²×C₈₃	#577	1	2	yes	—
233	C₂²×C₈₃	C₂³×D₄	1	1	yes	characteristic
234	C₄×C₈₃	—	2	1	no	—
235	C₄×C₈₃	—	2	3	no	—
236	C₄×C₈₃	—	2	3	no	—
237	C₄×C₈₃	—	2	3	no	—
238	C₄×C₈₃	—	4	1	no	—
239	C₄×C₈₃	—	4	1	no	—
240	C₄×C₈₃	—	4	6	no	—
241	C₄×C₈₃	—	4	3	no	—
242	C₄×C₈₃	C₂×AGL(1,ℤ/8)	1	6	yes	—
243	C₄×C₈₃	C₂×2₋¹⁺⁴	1	2	yes	—
244	#61843	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
245	C₂×C₈₃	—	2	2	no	—
246	C₂×C₈₃	—	4	4	no	—
247	C₂×C₈₃	—	8	3	no	—
248	C₂×C₈₃	#3486	1	1	yes	characteristic
249	C₂×C₈₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
250	C₂×C₈₃	C₂×#577	1	1	yes	characteristic
251	#3522	C₂×C₈₃	1	1	yes	characteristic, complemented
252	C₂×D₄×Q₈	C₂×C₈₃	1	1	yes	characteristic, complemented
253	#3384	C₂×C₈₃	1	6	yes	complemented
254	Q₈×SD₁₆	C₂×C₈₃	1	2	yes	complemented
255	#3373	C₂×C₈₃	1	6	yes	complemented
256	#3358	C₂×C₈₃	1	2	yes	complemented
257	#3239	C₂×C₈₃	1	3	yes	complemented
258	#3227	C₂×C₈₃	1	3	yes	complemented
259	#3109	C₂×C₈₃	1	3	yes	complemented
260	#3105	C₂×C₈₃	1	3	yes	complemented
261	#2984	C₂×C₈₃	1	1	yes	characteristic, complemented
262	C₈₃	#61843	1	1	yes	characteristic, direct product factor, Sylow
263	C₂³×Q₈	—	2	1	no	—
264	#559	C₂²×C₈₃	1	3	yes	complemented
265	Q₈²	C₂²×C₈₃	1	1	yes	characteristic, complemented
266	#554	C₂²×C₈₃	1	3	yes	complemented
267	#550	C₂²×C₈₃	1	1	yes	characteristic, complemented
268	D₄×Q₈	—	2	1	no	—
269	D₄×Q₈	—	2	3	no	—
270	D₄×Q₈	C₂²×C₈₃	1	2	yes	—
271	D₄×Q₈	C₂²×C₈₃	1	6	yes	—
272	#548	—	2	1	no	—
273	#547	—	2	3	no	—
274	#542	—	2	3	no	—
275	#532	C₂²×C₈₃	1	3	yes	—
276	C₂×C₄⋊Q₈	C₂²×C₈₃	1	3	yes	—
277	#529	C₂²×C₈₃	1	3	yes	—
278	C₂×C₂²⋊Q₈	—	2	3	no	—
279	#520	—	2	1	no	—
280	C₂×C₄×Q₈	C₂²×C₈₃	1	1	yes	characteristic
281	C₂×C₄×D₄	C₂²×C₈₃	1	3	yes	—
282	#501	C₂²×C₈₃	1	6	yes	complemented
283	#498	C₂²×C₈₃	1	6	yes	complemented
284	#489	C₂²×C₈₃	1	6	yes	complemented
285	#486	C₂²×C₈₃	1	6	yes	complemented
286	#484	C₂²×C₈₃	1	3	yes	—
287	#481	C₂²×C₈₃	1	3	yes	—
288	#481	C₂²×C₈₃	1	6	yes	—
289	#478	C₂²×C₈₃	1	6	yes	—
290	#476	C₂²×C₈₃	1	6	yes	—
291	#476	C₂²×C₈₃	1	12	yes	complemented
292	#475	C₂²×C₈₃	1	6	yes	complemented
293	#474	C₂²×C₈₃	1	6	yes	complemented
294	#463	C₂²×C₈₃	1	6	yes	—
295	#459	C₂²×C₈₃	1	6	yes	—
296	#450	C₂²×C₈₃	1	1	yes	characteristic
297	#447	C₂²×C₈₃	1	3	yes	—
298	#446	C₂²×C₈₃	1	6	yes	complemented
299	C₈×Q₈	C₂²×C₈₃	1	2	yes	complemented
300	#442	C₂²×C₈₃	1	12	yes	—
301	C₄×SD₁₆	C₂²×C₈₃	1	6	yes	—
302	C₄×D₈	C₂²×C₈₃	1	6	yes	—
303	#432	C₂²×C₈₃	1	3	yes	—
304	#431	C₂²×C₈₃	1	3	yes	—
305	C₂×#41	—	2	1	no	—
306	C₂×#41	—	2	3	no	—
307	C₂²×Q₈	—	2	6	no	—
308	C₂²×Q₈	—	2	2	no	—
309	C₂²×Q₈	—	2	3	no	—
310	C₂²×Q₈	—	4	8	no	—
311	C₂²×Q₈	D₄×C₈₃	1	1	yes	characteristic
312	C₂²×D₄	C₂³×C₈₃	1	1	yes	characteristic
313	C₂³×C₄	—	2	3	no	—
314	C₂×SD₁₆	C₂³×C₈₃	1	2	yes	—
315	C₂×D₈	C₂³×C₈₃	1	6	yes	—
316	C₄⋊Q₈	—	2	3	no	—
317	C₄⋊Q₈	—	2	3	no	—
318	C₄⋊Q₈	—	2	3	no	—
319	C₄⋊Q₈	C₂³×C₈₃	1	6	yes	—
320	C₄⋊Q₈	C₂³×C₈₃	1	6	yes	—
321	C₄⋊Q₈	C₂³×C₈₃	1	3	yes	—
322	#127	C₂³×C₈₃	1	3	yes	—
323	#126	—	2	3	no	—
324	#125	C₂³×C₈₃	1	3	yes	—
325	#124	—	2	3	no	—
326	#124	—	2	3	no	—
327	#124	C₂³×C₈₃	1	3	yes	—
328	#123	—	2	3	no	—
329	#123	—	2	6	no	—
330	C₂²⋊Q₈	—	2	3	no	—
331	C₂²⋊Q₈	—	2	6	no	—
332	C₂²⋊Q₈	—	2	6	no	—
333	C₂²⋊Q₈	—	2	12	no	—
334	C₂²⋊Q₈	—	2	6	no	—
335	C₂²⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
336	#121	—	2	3	no	—
337	#121	—	2	3	no	—
338	#121	C₂³×C₈₃	1	3	yes	—
339	C₄×Q₈	—	2	1	no	—
340	C₄×Q₈	D₄×C₈₃	1	1	yes	characteristic
341	C₄×Q₈	D₄×C₈₃	1	3	yes	—
342	C₄×Q₈	C₂³×C₈₃	1	3	yes	—
343	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
344	C₄×Q₈	C₂³×C₈₃	1	3	yes	—
345	C₄×D₄	—	2	3	no	—
346	C₄×D₄	—	2	3	no	—
347	C₄×D₄	—	2	3	no	—
348	C₄×D₄	—	2	3	no	—
349	C₄×D₄	—	2	3	no	—
350	C₄×D₄	C₂³×C₈₃	1	6	yes	—
351	C₄×D₄	C₂³×C₈₃	1	6	yes	—
352	C₄×D₄	C₂³×C₈₃	1	3	yes	—
353	C₄×D₄	C₂³×C₈₃	1	6	yes	—
354	#117	—	2	3	no	—
355	C₂×C₄⋊C₄	—	2	3	no	—
356	C₂×C₄⋊C₄	—	2	3	no	—
357	C₂×C₄⋊C₄	D₄×C₈₃	1	3	yes	—
358	C₂×C₄⋊C₄	C₂³×C₈₃	1	3	yes	—
359	C₂×C₂²⋊C₄	—	2	3	no	—
360	C₂×C₄²	C₂³×C₈₃	1	3	yes	—
361	#107	C₂³×C₈₃	1	6	yes	—
362	#106	C₂³×C₈₃	1	6	yes	—
363	#106	C₂³×C₈₃	1	12	yes	—
364	C₄⋊C₈	C₂³×C₈₃	1	6	yes	—
365	C₄⋊C₈	C₂³×C₈₃	1	6	yes	—
366	#103	C₂³×C₈₃	1	6	yes	—
367	#102	C₂³×C₈₃	1	2	yes	—
368	#102	C₂³×C₈₃	1	6	yes	—
369	#102	C₂³×C₈₃	1	6	yes	—
370	#102	C₂³×C₈₃	1	12	yes	—
371	C₂²⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
372	C₂²⋊C₈	C₂³×C₈₃	1	3	yes	—
373	#97	C₂³×C₈₃	1	6	yes	—
374	C₄×C₈	C₂³×C₈₃	1	6	yes	—
375	C₂⁴	—	2	1	no	—
376	#41	—	4	4	no	—
377	#41	—	8	6	no	—
378	C₂×Q₈	—	2	4	no	—
379	C₂×Q₈	—	2	6	no	—
380	C₂×Q₈	—	2	6	no	—
381	C₂×Q₈	—	2	3	no	—
382	C₂×Q₈	—	4	12	no	—
383	C₂×Q₈	—	4	24	no	—
384	C₂×Q₈	—	4	8	no	—
385	C₂×Q₈	C₂×D₄×C₈₃	1	3	yes	—
386	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
387	C₂×Q₈	C₂⁴×C₈₃	1	1	yes	characteristic
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	3	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	3	no	—
392	C₂×D₄	—	2	3	no	—
393	C₂×D₄	C₂⁴×C₈₃	1	3	yes	—
394	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
395	C₂²×C₄	—	2	3	no	—
396	C₂²×C₄	—	2	3	no	—
397	C₂²×C₄	—	2	6	no	—
398	C₂²×C₄	—	2	6	no	—
399	C₂²×C₄	—	2	6	no	—
400	C₂²×C₄	—	4	12	no	—
401	C₂²×C₄	C₂×D₄×C₈₃	1	3	yes	—
402	C₂²×C₄	C₂×D₄×C₈₃	1	3	yes	—
403	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
404	SD₁₆	—	2	4	no	—
405	D₈	—	2	12	no	—
406	C₂×C₈	C₂⁴×C₈₃	1	2	yes	—
407	C₂×C₈	C₂⁴×C₈₃	1	6	yes	—
408	C₄⋊C₄	—	2	3	no	—
409	C₄⋊C₄	—	2	3	no	—
410	C₄⋊C₄	—	2	6	no	—
411	C₄⋊C₄	—	2	6	no	—
412	C₄⋊C₄	—	2	3	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	3	no	—
415	C₄⋊C₄	—	2	3	no	—
416	C₄⋊C₄	C₂×D₄×C₈₃	1	3	yes	—
417	C₄⋊C₄	C₂×D₄×C₈₃	1	3	yes	—
418	C₄⋊C₄	C₂×D₄×C₈₃	1	6	yes	—
419	C₄⋊C₄	C₂⁴×C₈₃	1	6	yes	—
420	C₄⋊C₄	C₂⁴×C₈₃	1	3	yes	—
421	C₄⋊C₄	C₂⁴×C₈₃	1	1	yes	characteristic
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	6	no	—
424	C₂²⋊C₄	—	2	6	no	—
425	C₂²⋊C₄	—	2	3	no	—
426	C₂²⋊C₄	—	2	3	no	—
427	C₂²⋊C₄	—	2	3	no	—
428	C₂²⋊C₄	—	2	3	no	—
429	C₂²⋊C₄	—	2	6	no	—
430	C₄²	—	2	3	no	—
431	C₄²	C₂×D₄×C₈₃	1	3	yes	—
432	C₄²	C₂×D₄×C₈₃	1	3	yes	—
433	C₄²	C₂⁴×C₈₃	1	3	yes	—
434	C₄²	C₂⁴×C₈₃	1	3	yes	—
435	C₂³	—	2	4	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	3	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	C₂²×D₄×C₈₃	1	1	yes	characteristic
441	Q₈	—	2	6	no	—
442	Q₈	—	2	2	no	—
443	Q₈	—	4	12	no	—
444	Q₈	—	4	12	no	—
445	Q₈	—	8	3	no	—
446	Q₈	AGL(1,ℤ/8)×C₈₃	1	4	yes	—
447	D₄	—	2	4	no	—
448	D₄	—	2	2	no	—
449	D₄	—	2	6	no	—
450	D₄	—	4	6	no	—
451	D₄	—	4	6	no	—
452	D₄	—	8	3	no	—
453	D₄	2₋¹⁺⁴×C₈₃	1	4	yes	—
454	C₂×C₄	—	2	6	no	—
455	C₂×C₄	—	2	6	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	3	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	6	no	—
461	C₂×C₄	—	4	12	no	—
462	C₂×C₄	—	4	6	no	—
463	C₂×C₄	—	4	12	no	—
464	C₂×C₄	—	4	6	no	—
465	C₂×C₄	—	8	6	no	—
466	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
467	C₂×C₄	C₂²×D₄×C₈₃	1	3	yes	—
468	C₂×C₄	C₂²×D₄×C₈₃	1	3	yes	—
469	C₂×C₄	C₂²×D₄×C₈₃	1	3	yes	—
470	C₂×C₄	C₂²×D₄×C₈₃	1	3	yes	—
471	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
472	C₈	—	2	6	no	—
473	C₈	—	2	2	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	4	no	—
477	C₂²	—	4	8	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	3	no	—
481	C₂²	—	4	3	no	—
482	C₂²	—	4	3	no	—
483	C₂²	#577×C₈₃	1	2	yes	—
484	C₂²	C₂³×D₄×C₈₃	1	1	yes	characteristic
485	C₄	—	2	3	no	—
486	C₄	—	2	3	no	—
487	C₄	—	2	3	no	—
488	C₄	—	2	1	no	—
489	C₄	—	4	6	no	—
490	C₄	—	4	1	no	—
491	C₄	—	4	3	no	—
492	C₄	—	4	1	no	—
493	C₄	C₂×AGL(1,ℤ/8)×C₈₃	1	6	yes	—
494	C₄	C₂×2₋¹⁺⁴×C₈₃	1	2	yes	—
495	C₂	—	2	2	no	—
496	C₂	—	4	4	no	—
497	C₂	—	8	3	no	—
498	C₂	C₈₃×#3486	1	1	yes	characteristic
499	C₂	C₂²×AGL(1,ℤ/8)×C₈₃	1	1	yes	characteristic
500	C₂	C₂×#577×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×D₄×Q₈×C₈₃	C₂	semidirect
3. C₈₃×#3384	C₂	semidirect
4. Q₈×SD₁₆×C₈₃	C₂	semidirect
5. C₈₃×#3373	C₂	semidirect
6. C₈₃×#3358	C₂	semidirect
7. C₈₃×#3239	C₂	semidirect
8. C₈₃×#3227	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
16. #550×C₈₃	C₂²	semidirect
31. #501×C₈₃	C₂²	semidirect
32. #498×C₈₃	C₂²	semidirect
33. #489×C₈₃	C₂²	semidirect
34. #486×C₈₃	C₂²	semidirect
40. #476×C₈₃	C₂²	semidirect
41. #475×C₈₃	C₂²	semidirect
42. #474×C₈₃	C₂²	semidirect
47. #446×C₈₃	C₂²	semidirect
48. C₈×Q₈×C₈₃	C₂²	semidirect
244. #61843	C₈₃	direct (N × H)
251. #3522	C₂×C₈₃	semidirect
252. C₂×D₄×Q₈	C₂×C₈₃	semidirect
253. #3384	C₂×C₈₃	semidirect
254. Q₈×SD₁₆	C₂×C₈₃	semidirect
255. #3373	C₂×C₈₃	semidirect
256. #3358	C₂×C₈₃	semidirect
257. #3239	C₂×C₈₃	semidirect
258. #3227	C₂×C₈₃	semidirect
259. #3109	C₂×C₈₃	semidirect
260. #3105	C₂×C₈₃	semidirect
261. #2984	C₂×C₈₃	semidirect
262. C₈₃	#61843	direct (N × H)
264. #559	C₂²×C₈₃	semidirect
265. Q₈²	C₂²×C₈₃	semidirect
266. #554	C₂²×C₈₃	semidirect
267. #550	C₂²×C₈₃	semidirect
282. #501	C₂²×C₈₃	semidirect
283. #498	C₂²×C₈₃	semidirect
284. #489	C₂²×C₈₃	semidirect
285. #486	C₂²×C₈₃	semidirect
291. #476	C₂²×C₈₃	semidirect
292. #475	C₂²×C₈₃	semidirect
293. #474	C₂²×C₈₃	semidirect
298. #446	C₂²×C₈₃	semidirect
299. C₈×Q₈	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×D₄×Q₈×C₈₃	2
C₈₃×#3384	2
Q₈×SD₁₆×C₈₃	2
C₈₃×#3373	2
C₈₃×#3358	2
C₈₃×#3239	2
C₈₃×#3227	2
C₈₃×#3109	2
C₈₃×#3105	2
C₈₃×#2984	2
#61843	83

Subgroups — C83×#61843 #35289667

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61843 #35289667