Subgroups — C₈₃×#61111 #35288935

Order 21248.

2600 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3586	C₂	1	4	yes	maximal, complemented
2	C₈₃×#3293	C₂	1	4	yes	maximal, complemented
3	C₈₃×#3291	C₂	1	4	yes	maximal, complemented
4	C₈₃×#3289	C₂	1	8	yes	maximal, complemented
5	C₈₃×#3152	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₃×#3069	C₂	1	4	yes	maximal, complemented
7	C₈₃×#3018	C₂	1	2	yes	maximal, complemented
8	C₂×#456×C₈₃	C₂	1	2	yes	maximal, complemented
9	C₈₃×#2956	C₂	1	2	yes	maximal, complemented
10	#585×C₈₃	C₂²	1	2	yes	complemented
11	C₂×2₋¹⁺⁴×C₈₃	C₂²	1	2	yes	—
12	#578×C₈₃	—	2	8	no	—
13	#578×C₈₃	C₂²	1	16	yes	complemented
14	#577×C₈₃	—	2	8	no	—
15	#577×C₈₃	C₂²	1	16	yes	complemented
16	#575×C₈₃	—	2	8	no	—
17	#575×C₈₃	C₂²	1	4	yes	—
18	#575×C₈₃	C₂²	1	2	yes	—
19	C₂×#137×C₈₃	—	2	8	no	—
20	C₂×#137×C₈₃	C₂²	1	4	yes	complemented
21	C₂×#137×C₈₃	C₂²	1	4	yes	complemented
22	#568×C₈₃	C₂²	1	4	yes	complemented
23	#532×C₈₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
25	#497×C₈₃	C₂²	1	4	yes	complemented
26	#494×C₈₃	C₂²	1	2	yes	complemented
27	#492×C₈₃	C₂²	1	2	yes	complemented
28	#473×C₈₃	C₂²	1	16	yes	complemented
29	#471×C₈₃	C₂²	1	16	yes	complemented
30	#456×C₈₃	C₂²	1	8	yes	complemented
31	#456×C₈₃	C₂²	1	8	yes	complemented
32	#456×C₈₃	C₂²	1	4	yes	complemented
33	#455×C₈₃	C₂²	1	4	yes	complemented
34	#454×C₈₃	C₂²	1	4	yes	complemented
35	#453×C₈₃	C₂²	1	4	yes	complemented
36	#444×C₈₃	C₂²	1	8	yes	complemented
37	#443×C₈₃	C₂²	1	8	yes	complemented
38	#430×C₈₃	C₂²	1	2	yes	complemented
39	C₂×#104×C₈₃	C₂²	1	4	yes	complemented
40	#413×C₈₃	C₂²	1	2	yes	complemented
41	C₂×#101×C₈₃	C₂²	1	2	yes	complemented
42	C₄×M₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
43	2₋¹⁺⁴×C₈₃	—	2	8	no	—
44	2₋¹⁺⁴×C₈₃	—	2	4	no	—
45	2₋¹⁺⁴×C₈₃	—	4	2	no	—
46	2₋¹⁺⁴×C₈₃	C₂³	1	8	yes	—
47	2₋¹⁺⁴×C₈₃	C₂³	1	4	yes	—
48	H(5,𝔽₂)×C₈₃	—	2	4	no	—
49	H(5,𝔽₂)×C₈₃	—	4	2	no	—
50	H(5,𝔽₂)×C₈₃	C₂³	1	4	yes	—
51	C₂×#41×C₈₃	—	2	8	no	—
52	C₂×#41×C₈₃	—	2	4	no	—
53	C₂×#41×C₈₃	—	4	2	no	—
54	C₂×#41×C₈₃	—	4	2	no	—
55	C₂×#41×C₈₃	C₂³	1	4	yes	—
56	C₂×#41×C₈₃	C₂³	1	2	yes	—
57	C₂²×Q₈×C₈₃	—	2	4	no	—
58	C₂²×Q₈×C₈₃	C₂³	1	2	yes	—
59	#137×C₈₃	—	2	8	no	—
60	#137×C₈₃	—	2	4	no	—
61	#137×C₈₃	—	2	16	no	—
62	#137×C₈₃	—	2	16	no	—
63	#137×C₈₃	—	2	16	no	—
64	#137×C₈₃	—	2	8	no	—
65	#137×C₈₃	—	2	8	no	—
66	#137×C₈₃	D₄	1	8	yes	complemented
67	#137×C₈₃	C₂³	1	16	yes	—
68	#137×C₈₃	C₂³	1	8	yes	—
69	AGL(1,ℤ/8)×C₈₃	—	2	4	no	—
70	AGL(1,ℤ/8)×C₈₃	—	2	16	no	—
71	AGL(1,ℤ/8)×C₈₃	D₄	1	8	yes	complemented
72	AGL(1,ℤ/8)×C₈₃	C₂³	1	8	yes	—
73	#135×C₈₃	—	2	8	no	—
74	#135×C₈₃	—	2	16	no	—
75	#135×C₈₃	—	2	16	no	—
76	#135×C₈₃	C₂³	1	8	yes	—
77	C₂×Q₁₆×C₈₃	—	2	4	no	—
78	C₂×Q₁₆×C₈₃	—	2	16	no	—
79	C₂×Q₁₆×C₈₃	C₂³	1	8	yes	—
80	C₂×SD₁₆×C₈₃	—	2	4	no	—
81	C₂×SD₁₆×C₈₃	—	2	16	no	—
82	C₂×SD₁₆×C₈₃	C₂³	1	8	yes	—
83	#131×C₈₃	—	2	8	no	—
84	#131×C₈₃	C₂³	1	16	yes	—
85	C₂×M₁₆×C₈₃	—	2	8	no	—
86	C₂×M₁₆×C₈₃	C₂³	1	4	yes	—
87	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
88	C₄⋊Q₈×C₈₃	—	4	1	no	—
89	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
90	C₄⋊Q₈×C₈₃	C₂³	1	1	yes	characteristic
91	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
92	#127×C₈₃	C₂³	1	1	yes	characteristic
93	#124×C₈₃	C₂³	1	2	yes	—
94	#121×C₈₃	—	4	1	no	—
95	C₄×D₄×C₈₃	—	4	1	no	—
96	C₂×C₄⋊C₄×C₈₃	—	4	1	no	—
97	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
98	#108×C₈₃	C₂³	1	8	yes	—
99	#104×C₈₃	C₂³	1	8	yes	—
100	#104×C₈₃	C₂³	1	8	yes	—
101	#101×C₈₃	C₂³	1	8	yes	—
102	#101×C₈₃	C₂³	1	4	yes	—
103	#100×C₈₃	C₂³	1	4	yes	—
104	#97×C₈₃	C₂³	1	2	yes	—
105	C₄×C₈×C₈₃	C₂³	1	2	yes	—
106	#41×C₈₃	—	2	4	no	—
107	#41×C₈₃	—	2	4	no	—
108	#41×C₈₃	—	2	8	no	—
109	#41×C₈₃	—	2	16	no	—
110	#41×C₈₃	—	2	8	no	—
111	#41×C₈₃	—	2	4	no	—
112	#41×C₈₃	—	2	4	no	—
113	#41×C₈₃	—	4	4	no	—
114	#41×C₈₃	—	4	4	no	—
115	#41×C₈₃	—	4	8	no	—
116	#41×C₈₃	—	4	8	no	—
117	#41×C₈₃	—	4	8	no	—
118	#41×C₈₃	—	4	8	no	—
119	#41×C₈₃	—	4	4	no	—
120	#41×C₈₃	C₂×D₄	1	8	yes	—
121	#41×C₈₃	C₂⁴	1	8	yes	—
122	C₂×Q₈×C₈₃	—	2	2	no	—
123	C₂×Q₈×C₈₃	—	2	16	no	—
124	C₂×Q₈×C₈₃	—	2	8	no	—
125	C₂×Q₈×C₈₃	—	2	4	no	—
126	C₂×Q₈×C₈₃	—	2	4	no	—
127	C₂×Q₈×C₈₃	—	4	2	no	—
128	C₂×Q₈×C₈₃	—	4	8	no	—
129	C₂×Q₈×C₈₃	—	4	2	no	—
130	C₂×Q₈×C₈₃	C₂×D₄	1	4	yes	—
131	C₂×Q₈×C₈₃	C₂⁴	1	2	yes	—
132	C₂×Q₈×C₈₃	C₂⁴	1	4	yes	—
133	C₂×D₄×C₈₃	—	2	4	no	—
134	C₂×D₄×C₈₃	—	2	8	no	—
135	C₂×D₄×C₈₃	—	2	2	no	—
136	C₂×D₄×C₈₃	—	4	1	no	—
137	C₂×D₄×C₈₃	—	4	4	no	—
138	C₂×D₄×C₈₃	—	4	2	no	—
139	C₂×D₄×C₈₃	—	4	8	no	—
140	C₂×D₄×C₈₃	—	4	2	no	—
141	C₂×D₄×C₈₃	C₂×D₄	1	4	yes	—
142	C₂×D₄×C₈₃	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₈₃	—	2	4	no	—
144	C₂²×C₄×C₈₃	—	2	1	no	—
145	C₂²×C₄×C₈₃	—	2	2	no	—
146	C₂²×C₄×C₈₃	—	2	2	no	—
147	C₂²×C₄×C₈₃	—	4	4	no	—
148	C₂²×C₄×C₈₃	—	4	4	no	—
149	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
150	Q₁₆×C₈₃	—	2	16	no	—
151	Q₁₆×C₈₃	—	2	8	no	—
152	Q₁₆×C₈₃	—	2	16	no	—
153	Q₁₆×C₈₃	C₂×D₄	1	8	yes	—
154	SD₁₆×C₈₃	—	2	8	no	—
155	SD₁₆×C₈₃	—	2	16	no	—
156	SD₁₆×C₈₃	—	2	8	no	—
157	SD₁₆×C₈₃	—	2	16	no	—
158	SD₁₆×C₈₃	C₂×D₄	1	16	yes	—
159	D₈×C₈₃	—	2	8	no	—
160	D₈×C₈₃	C₂×D₄	1	8	yes	—
161	M₁₆×C₈₃	—	2	4	no	—
162	M₁₆×C₈₃	—	2	16	no	—
163	M₁₆×C₈₃	C₂×D₄	1	8	yes	—
164	M₁₆×C₈₃	C₂⁴	1	8	yes	—
165	C₂×C₈×C₈₃	—	2	4	no	—
166	C₂×C₈×C₈₃	—	2	16	no	—
167	C₂×C₈×C₈₃	C₂⁴	1	4	yes	—
168	C₄⋊C₄×C₈₃	—	4	2	no	—
169	C₄⋊C₄×C₈₃	—	4	2	no	—
170	C₄⋊C₄×C₈₃	—	4	1	no	—
171	C₂²⋊C₄×C₈₃	—	4	2	no	—
172	C₄²×C₈₃	—	2	1	no	—
173	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
174	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
175	C₂³×C₈₃	—	2	4	no	—
176	C₂³×C₈₃	—	2	2	no	—
177	C₂³×C₈₃	—	4	4	no	—
178	C₂³×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
179	Q₈×C₈₃	—	2	4	no	—
180	Q₈×C₈₃	—	2	8	no	—
181	Q₈×C₈₃	—	2	4	no	—
182	Q₈×C₈₃	—	4	8	no	—
183	Q₈×C₈₃	—	4	4	no	—
184	Q₈×C₈₃	—	4	4	no	—
185	Q₈×C₈₃	C₂²×D₄	1	8	yes	—
186	D₄×C₈₃	—	2	8	no	—
187	D₄×C₈₃	—	2	8	no	—
188	D₄×C₈₃	—	2	4	no	—
189	D₄×C₈₃	—	2	4	no	—
190	D₄×C₈₃	—	4	8	no	—
191	D₄×C₈₃	—	4	4	no	—
192	D₄×C₈₃	—	4	8	no	—
193	D₄×C₈₃	—	4	4	no	—
194	D₄×C₈₃	—	8	2	no	—
195	D₄×C₈₃	C₂²×D₄	1	8	yes	—
196	C₂×C₄×C₈₃	—	2	4	no	—
197	C₂×C₄×C₈₃	—	2	1	no	—
198	C₂×C₄×C₈₃	—	2	8	no	—
199	C₂×C₄×C₈₃	—	2	8	no	—
200	C₂×C₄×C₈₃	—	2	1	no	—
201	C₂×C₄×C₈₃	—	2	2	no	—
202	C₂×C₄×C₈₃	—	2	4	no	—
203	C₂×C₄×C₈₃	—	4	4	no	—
204	C₂×C₄×C₈₃	—	4	8	no	—
205	C₂×C₄×C₈₃	—	4	16	no	—
206	C₂×C₄×C₈₃	—	4	2	no	—
207	C₂×C₄×C₈₃	—	4	2	no	—
208	C₂×C₄×C₈₃	—	4	2	no	—
209	C₂×C₄×C₈₃	—	4	2	no	—
210	C₂×C₄×C₈₃	—	4	2	no	—
211	C₂×C₄×C₈₃	C₂²×D₄	1	4	yes	—
212	C₂×C₄×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
213	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
214	C₈×C₈₃	—	2	8	no	—
215	C₈×C₈₃	C₂²×D₄	1	8	yes	—
216	C₂²×C₈₃	—	2	8	no	—
217	C₂²×C₈₃	—	4	1	no	—
218	C₂²×C₈₃	—	4	2	no	—
219	C₂²×C₈₃	—	8	4	no	—
220	C₂²×C₈₃	—	8	2	no	—
221	C₂²×C₈₃	—	16	4	no	—
222	C₂²×C₈₃	D₄²	1	2	yes	—
223	C₂²×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
224	C₄×C₈₃	—	2	2	no	—
225	C₄×C₈₃	—	2	8	no	—
226	C₄×C₈₃	—	4	1	no	—
227	C₄×C₈₃	—	4	2	no	—
228	C₄×C₈₃	—	4	4	no	—
229	C₄×C₈₃	D₄²	1	2	yes	—
230	C₄×C₈₃	C₂³×D₄	1	2	yes	—
231	#61111	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂×C₈₃	—	2	1	no	—
233	C₂×C₈₃	—	2	2	no	—
234	C₂×C₈₃	—	4	8	no	—
235	C₂×C₈₃	—	8	2	no	—
236	C₂×C₈₃	C₂×D₄²	1	1	yes	characteristic
237	#3586	C₂×C₈₃	1	4	yes	complemented
238	#3293	C₂×C₈₃	1	4	yes	complemented
239	#3291	C₂×C₈₃	1	4	yes	complemented
240	#3289	C₂×C₈₃	1	8	yes	complemented
241	#3152	C₂×C₈₃	1	1	yes	characteristic, complemented
242	#3069	C₂×C₈₃	1	4	yes	complemented
243	#3018	C₂×C₈₃	1	2	yes	complemented
244	C₂×#456	C₂×C₈₃	1	2	yes	complemented
245	#2956	C₂×C₈₃	1	2	yes	complemented
246	C₈₃	#61111	1	1	yes	characteristic, direct product factor, Sylow
247	#585	C₂²×C₈₃	1	2	yes	complemented
248	C₂×2₋¹⁺⁴	C₂²×C₈₃	1	2	yes	—
249	#578	—	2	8	no	—
250	#578	C₂²×C₈₃	1	16	yes	complemented
251	#577	—	2	8	no	—
252	#577	C₂²×C₈₃	1	16	yes	complemented
253	#575	—	2	8	no	—
254	#575	C₂²×C₈₃	1	4	yes	—
255	#575	C₂²×C₈₃	1	2	yes	—
256	C₂×#137	—	2	8	no	—
257	C₂×#137	C₂²×C₈₃	1	4	yes	complemented
258	C₂×#137	C₂²×C₈₃	1	4	yes	complemented
259	#568	C₂²×C₈₃	1	4	yes	complemented
260	#532	C₂²×C₈₃	1	1	yes	characteristic
261	C₂×C₄⋊Q₈	C₂²×C₈₃	1	1	yes	characteristic, complemented
262	#497	C₂²×C₈₃	1	4	yes	complemented
263	#494	C₂²×C₈₃	1	2	yes	complemented
264	#492	C₂²×C₈₃	1	2	yes	complemented
265	#473	C₂²×C₈₃	1	16	yes	complemented
266	#471	C₂²×C₈₃	1	16	yes	complemented
267	#456	C₂²×C₈₃	1	8	yes	complemented
268	#456	C₂²×C₈₃	1	8	yes	complemented
269	#456	C₂²×C₈₃	1	4	yes	complemented
270	#455	C₂²×C₈₃	1	4	yes	complemented
271	#454	C₂²×C₈₃	1	4	yes	complemented
272	#453	C₂²×C₈₃	1	4	yes	complemented
273	#444	C₂²×C₈₃	1	8	yes	complemented
274	#443	C₂²×C₈₃	1	8	yes	complemented
275	#430	C₂²×C₈₃	1	2	yes	complemented
276	C₂×#104	C₂²×C₈₃	1	4	yes	complemented
277	#413	C₂²×C₈₃	1	2	yes	complemented
278	C₂×#101	C₂²×C₈₃	1	2	yes	complemented
279	C₄×M₁₆	C₂²×C₈₃	1	1	yes	characteristic, complemented
280	2₋¹⁺⁴	—	2	8	no	—
281	2₋¹⁺⁴	—	2	4	no	—
282	2₋¹⁺⁴	—	4	2	no	—
283	2₋¹⁺⁴	C₂³×C₈₃	1	8	yes	—
284	2₋¹⁺⁴	C₂³×C₈₃	1	4	yes	—
285	H(5,𝔽₂)	—	2	4	no	—
286	H(5,𝔽₂)	—	4	2	no	—
287	H(5,𝔽₂)	C₂³×C₈₃	1	4	yes	—
288	C₂×#41	—	2	8	no	—
289	C₂×#41	—	2	4	no	—
290	C₂×#41	—	4	2	no	—
291	C₂×#41	—	4	2	no	—
292	C₂×#41	C₂³×C₈₃	1	4	yes	—
293	C₂×#41	C₂³×C₈₃	1	2	yes	—
294	C₂²×Q₈	—	2	4	no	—
295	C₂²×Q₈	C₂³×C₈₃	1	2	yes	—
296	#137	—	2	8	no	—
297	#137	—	2	4	no	—
298	#137	—	2	16	no	—
299	#137	—	2	16	no	—
300	#137	—	2	16	no	—
301	#137	—	2	8	no	—
302	#137	—	2	8	no	—
303	#137	D₄×C₈₃	1	8	yes	complemented
304	#137	C₂³×C₈₃	1	16	yes	—
305	#137	C₂³×C₈₃	1	8	yes	—
306	AGL(1,ℤ/8)	—	2	4	no	—
307	AGL(1,ℤ/8)	—	2	16	no	—
308	AGL(1,ℤ/8)	D₄×C₈₃	1	8	yes	complemented
309	AGL(1,ℤ/8)	C₂³×C₈₃	1	8	yes	—
310	#135	—	2	8	no	—
311	#135	—	2	16	no	—
312	#135	—	2	16	no	—
313	#135	C₂³×C₈₃	1	8	yes	—
314	C₂×Q₁₆	—	2	4	no	—
315	C₂×Q₁₆	—	2	16	no	—
316	C₂×Q₁₆	C₂³×C₈₃	1	8	yes	—
317	C₂×SD₁₆	—	2	4	no	—
318	C₂×SD₁₆	—	2	16	no	—
319	C₂×SD₁₆	C₂³×C₈₃	1	8	yes	—
320	#131	—	2	8	no	—
321	#131	C₂³×C₈₃	1	16	yes	—
322	C₂×M₁₆	—	2	8	no	—
323	C₂×M₁₆	C₂³×C₈₃	1	4	yes	—
324	C₂×M₁₆	C₂³×C₈₃	1	2	yes	—
325	C₄⋊Q₈	—	4	1	no	—
326	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
327	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
328	C₄⋊Q₈	C₂³×C₈₃	1	1	yes	characteristic
329	#127	C₂³×C₈₃	1	1	yes	characteristic
330	#124	C₂³×C₈₃	1	2	yes	—
331	#121	—	4	1	no	—
332	C₄×D₄	—	4	1	no	—
333	C₂×C₄⋊C₄	—	4	1	no	—
334	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
335	#108	C₂³×C₈₃	1	8	yes	—
336	#104	C₂³×C₈₃	1	8	yes	—
337	#104	C₂³×C₈₃	1	8	yes	—
338	#101	C₂³×C₈₃	1	8	yes	—
339	#101	C₂³×C₈₃	1	4	yes	—
340	#100	C₂³×C₈₃	1	4	yes	—
341	#97	C₂³×C₈₃	1	2	yes	—
342	C₄×C₈	C₂³×C₈₃	1	2	yes	—
343	#41	—	2	4	no	—
344	#41	—	2	4	no	—
345	#41	—	2	8	no	—
346	#41	—	2	16	no	—
347	#41	—	2	8	no	—
348	#41	—	2	4	no	—
349	#41	—	2	4	no	—
350	#41	—	4	4	no	—
351	#41	—	4	4	no	—
352	#41	—	4	8	no	—
353	#41	—	4	8	no	—
354	#41	—	4	8	no	—
355	#41	—	4	8	no	—
356	#41	—	4	4	no	—
357	#41	C₂×D₄×C₈₃	1	8	yes	—
358	#41	C₂⁴×C₈₃	1	8	yes	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	16	no	—
361	C₂×Q₈	—	2	8	no	—
362	C₂×Q₈	—	2	4	no	—
363	C₂×Q₈	—	2	4	no	—
364	C₂×Q₈	—	4	2	no	—
365	C₂×Q₈	—	4	8	no	—
366	C₂×Q₈	—	4	2	no	—
367	C₂×Q₈	C₂×D₄×C₈₃	1	4	yes	—
368	C₂×Q₈	C₂⁴×C₈₃	1	2	yes	—
369	C₂×Q₈	C₂⁴×C₈₃	1	4	yes	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	2	8	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	4	1	no	—
374	C₂×D₄	—	4	4	no	—
375	C₂×D₄	—	4	2	no	—
376	C₂×D₄	—	4	8	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	C₂×D₄×C₈₃	1	4	yes	—
379	C₂×D₄	C₂⁴×C₈₃	1	2	yes	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	—	4	4	no	—
386	C₂²×C₄	C₂⁴×C₈₃	1	1	yes	characteristic
387	Q₁₆	—	2	16	no	—
388	Q₁₆	—	2	8	no	—
389	Q₁₆	—	2	16	no	—
390	Q₁₆	C₂×D₄×C₈₃	1	8	yes	—
391	SD₁₆	—	2	8	no	—
392	SD₁₆	—	2	16	no	—
393	SD₁₆	—	2	8	no	—
394	SD₁₆	—	2	16	no	—
395	SD₁₆	C₂×D₄×C₈₃	1	16	yes	—
396	D₈	—	2	8	no	—
397	D₈	C₂×D₄×C₈₃	1	8	yes	—
398	M₁₆	—	2	4	no	—
399	M₁₆	—	2	16	no	—
400	M₁₆	C₂×D₄×C₈₃	1	8	yes	—
401	M₁₆	C₂⁴×C₈₃	1	8	yes	—
402	C₂×C₈	—	2	4	no	—
403	C₂×C₈	—	2	16	no	—
404	C₂×C₈	C₂⁴×C₈₃	1	4	yes	—
405	C₄⋊C₄	—	4	2	no	—
406	C₄⋊C₄	—	4	2	no	—
407	C₄⋊C₄	—	4	1	no	—
408	C₂²⋊C₄	—	4	2	no	—
409	C₄²	—	2	1	no	—
410	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
411	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
412	C₂³	—	2	4	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	4	4	no	—
415	C₂³	H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
416	Q₈	—	2	4	no	—
417	Q₈	—	2	8	no	—
418	Q₈	—	2	4	no	—
419	Q₈	—	4	8	no	—
420	Q₈	—	4	4	no	—
421	Q₈	—	4	4	no	—
422	Q₈	C₂²×D₄×C₈₃	1	8	yes	—
423	D₄	—	2	8	no	—
424	D₄	—	2	8	no	—
425	D₄	—	2	4	no	—
426	D₄	—	2	4	no	—
427	D₄	—	4	8	no	—
428	D₄	—	4	4	no	—
429	D₄	—	4	8	no	—
430	D₄	—	4	4	no	—
431	D₄	—	8	2	no	—
432	D₄	C₂²×D₄×C₈₃	1	8	yes	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	8	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	8	no	—
442	C₂×C₄	—	4	16	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	C₂²×D₄×C₈₃	1	4	yes	—
449	C₂×C₄	H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
450	C₂×C₄	C₂⁵×C₈₃	1	1	yes	characteristic
451	C₈	—	2	8	no	—
452	C₈	C₂²×D₄×C₈₃	1	8	yes	—
453	C₂²	—	2	8	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	8	4	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	16	4	no	—
459	C₂²	D₄²×C₈₃	1	2	yes	—
460	C₂²	C₂×H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
461	C₄	—	2	2	no	—
462	C₄	—	2	8	no	—
463	C₄	—	4	1	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	4	no	—
466	C₄	D₄²×C₈₃	1	2	yes	—
467	C₄	C₂³×D₄×C₈₃	1	2	yes	—
468	C₂	—	2	1	no	—
469	C₂	—	2	2	no	—
470	C₂	—	4	8	no	—
471	C₂	—	8	2	no	—
472	C₂	C₂×D₄²×C₈₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₈₃	C₂×D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈₃ ◁ C₂²×C₄×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3586	C₂	semidirect
2. C₈₃×#3293	C₂	semidirect
3. C₈₃×#3291	C₂	semidirect
4. C₈₃×#3289	C₂	semidirect
5. C₈₃×#3152	C₂	semidirect
6. C₈₃×#3069	C₂	semidirect
7. C₈₃×#3018	C₂	semidirect
8. C₂×#456×C₈₃	C₂	semidirect
9. C₈₃×#2956	C₂	semidirect
10. #585×C₈₃	C₂²	semidirect
13. #578×C₈₃	C₂²	semidirect
15. #577×C₈₃	C₂²	semidirect
20. C₂×#137×C₈₃	C₂²	semidirect
21. C₂×#137×C₈₃	C₂²	semidirect
22. #568×C₈₃	C₂²	semidirect
24. C₂×C₄⋊Q₈×C₈₃	C₂²	semidirect
25. #497×C₈₃	C₂²	semidirect
26. #494×C₈₃	C₂²	semidirect
27. #492×C₈₃	C₂²	semidirect
28. #473×C₈₃	C₂²	semidirect
29. #471×C₈₃	C₂²	semidirect
30. #456×C₈₃	C₂²	semidirect
31. #456×C₈₃	C₂²	semidirect
32. #456×C₈₃	C₂²	semidirect
33. #455×C₈₃	C₂²	semidirect
34. #454×C₈₃	C₂²	semidirect
35. #453×C₈₃	C₂²	semidirect
36. #444×C₈₃	C₂²	semidirect
37. #443×C₈₃	C₂²	semidirect
38. #430×C₈₃	C₂²	semidirect
39. C₂×#104×C₈₃	C₂²	semidirect
40. #413×C₈₃	C₂²	semidirect
41. C₂×#101×C₈₃	C₂²	semidirect
42. C₄×M₁₆×C₈₃	C₂²	semidirect
66. #137×C₈₃	D₄	semidirect
71. AGL(1,ℤ/8)×C₈₃	D₄	semidirect
231. #61111	C₈₃	direct (N × H)
237. #3586	C₂×C₈₃	semidirect
238. #3293	C₂×C₈₃	semidirect
239. #3291	C₂×C₈₃	semidirect
240. #3289	C₂×C₈₃	semidirect
241. #3152	C₂×C₈₃	semidirect
242. #3069	C₂×C₈₃	semidirect
243. #3018	C₂×C₈₃	semidirect
244. C₂×#456	C₂×C₈₃	semidirect
245. #2956	C₂×C₈₃	semidirect
246. C₈₃	#61111	direct (N × H)
247. #585	C₂²×C₈₃	semidirect
250. #578	C₂²×C₈₃	semidirect
252. #577	C₂²×C₈₃	semidirect
257. C₂×#137	C₂²×C₈₃	semidirect
258. C₂×#137	C₂²×C₈₃	semidirect
259. #568	C₂²×C₈₃	semidirect
261. C₂×C₄⋊Q₈	C₂²×C₈₃	semidirect
262. #497	C₂²×C₈₃	semidirect
263. #494	C₂²×C₈₃	semidirect
264. #492	C₂²×C₈₃	semidirect
265. #473	C₂²×C₈₃	semidirect
266. #471	C₂²×C₈₃	semidirect
267. #456	C₂²×C₈₃	semidirect
268. #456	C₂²×C₈₃	semidirect
269. #456	C₂²×C₈₃	semidirect
270. #455	C₂²×C₈₃	semidirect
271. #454	C₂²×C₈₃	semidirect
272. #453	C₂²×C₈₃	semidirect
273. #444	C₂²×C₈₃	semidirect
274. #443	C₂²×C₈₃	semidirect
275. #430	C₂²×C₈₃	semidirect
276. C₂×#104	C₂²×C₈₃	semidirect
277. #413	C₂²×C₈₃	semidirect
278. C₂×#101	C₂²×C₈₃	semidirect
279. C₄×M₁₆	C₂²×C₈₃	semidirect
303. #137	D₄×C₈₃	semidirect
308. AGL(1,ℤ/8)	D₄×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₈₃×#3586	2
C₈₃×#3293	2
C₈₃×#3291	2
C₈₃×#3289	2
C₈₃×#3152	2
C₈₃×#3069	2
C₈₃×#3018	2
C₂×#456×C₈₃	2
C₈₃×#2956	2
#61111	83

Subgroups — C83×#61111 #35288935

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#61111 #35288935