Subgroups — C₈₃×#9173 #35236997

Order 21248.

562 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3038	C₂	1	1	yes	maximal, characteristic
2	C₈₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₃×#1545	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#331×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₃×#1477	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₃×#1301	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₃×#1292	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×AGL(1,ℤ/8)×C₈₃	—	2	1	no	—
9	C₂×#131×C₈₃	—	2	1	no	—
10	C₂×#127×C₈₃	C₂²	1	1	yes	characteristic
11	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
12	#460×C₈₃	—	2	1	no	—
13	#460×C₈₃	C₄	1	2	yes	—
14	#459×C₈₃	—	2	1	no	—
15	#459×C₈₃	C₄	1	2	yes	—
16	#431×C₈₃	C₂²	1	1	yes	characteristic
17	#424×C₈₃	—	2	1	no	—
18	#424×C₈₃	—	2	2	no	—
19	#423×C₈₃	—	2	1	no	—
20	#423×C₈₃	C₂²	1	1	yes	characteristic
21	#423×C₈₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₈₃	—	2	1	no	—
23	C₂×C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
25	#418×C₈₃	—	2	1	no	—
26	#331×C₈₃	—	2	1	no	—
27	#331×C₈₃	—	2	1	no	—
28	#331×C₈₃	—	2	2	no	—
29	Q₈⋊C₈×C₈₃	—	2	1	no	—
30	D₄⋊C₈×C₈₃	—	2	1	no	—
31	C₂×#41×C₈₃	D₄	1	1	yes	characteristic
32	C₂²×D₄×C₈₃	—	2	1	no	—
33	C₂²×D₄×C₈₃	—	2	1	no	—
34	C₂²×D₄×C₈₃	—	2	1	no	—
35	AGL(1,ℤ/8)×C₈₃	—	4	2	no	—
36	AGL(1,ℤ/8)×C₈₃	—	4	2	no	—
37	C₂×SD₁₆×C₈₃	—	2	2	no	—
38	C₂×D₈×C₈₃	—	2	2	no	—
39	#131×C₈₃	—	4	2	no	—
40	#131×C₈₃	—	4	2	no	—
41	C₂×M₁₆×C₈₃	—	2	2	no	—
42	C₂×M₁₆×C₈₃	—	2	1	no	—
43	C₂×M₁₆×C₈₃	—	2	1	no	—
44	C₂²×C₈×C₈₃	—	2	2	no	—
45	C₂²×C₈×C₈₃	—	2	1	no	—
46	C₂²×C₈×C₈₃	—	2	1	no	—
47	#127×C₈₃	—	2	1	no	—
48	#127×C₈₃	—	2	1	no	—
49	#127×C₈₃	—	2	1	no	—
50	#127×C₈₃	C₂×C₄	1	2	yes	—
51	C₄×Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
52	C₄×Q₈×C₈₃	D₄	1	1	yes	characteristic
53	C₄×D₄×C₈₃	—	2	1	no	—
54	C₄×D₄×C₈₃	—	2	1	no	—
55	C₄×D₄×C₈₃	C₂×C₄	1	1	yes	characteristic
56	C₄×D₄×C₈₃	D₄	1	1	yes	characteristic
57	#117×C₈₃	—	2	1	no	—
58	#117×C₈₃	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₈₃	—	2	1	no	—
60	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
61	C₄⋊C₈×C₈₃	—	2	2	no	—
62	C₄⋊C₈×C₈₃	—	2	2	no	—
63	C₄⋊C₈×C₈₃	—	2	1	no	—
64	C₄⋊C₈×C₈₃	—	2	1	no	—
65	C₄⋊C₈×C₈₃	—	2	1	no	—
66	C₄⋊C₈×C₈₃	—	2	1	no	—
67	C₄⋊C₈×C₈₃	—	2	1	no	—
68	C₄⋊C₈×C₈₃	—	2	1	no	—
69	C₄⋊C₈×C₈₃	C₂×C₄	1	2	yes	—
70	C₄⋊C₈×C₈₃	D₄	1	1	yes	characteristic
71	C₄⋊C₈×C₈₃	D₄	1	1	yes	characteristic
72	C₄⋊C₈×C₈₃	D₄	1	2	yes	—
73	#102×C₈₃	—	2	2	no	—
74	#102×C₈₃	—	2	2	no	—
75	C₂²⋊C₈×C₈₃	—	2	1	no	—
76	C₄×C₈×C₈₃	—	2	1	no	—
77	C₂⁴×C₈₃	—	4	1	no	—
78	#41×C₈₃	—	2	1	no	—
79	#41×C₈₃	—	2	1	no	—
80	#41×C₈₃	D₈	1	2	yes	—
81	#41×C₈₃	SD₁₆	1	2	yes	—
82	C₂×Q₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
83	C₂×D₄×C₈₃	—	2	1	no	—
84	C₂×D₄×C₈₃	—	2	2	no	—
85	C₂×D₄×C₈₃	—	2	2	no	—
86	C₂×D₄×C₈₃	—	2	2	no	—
87	C₂×D₄×C₈₃	—	4	1	no	—
88	C₂×D₄×C₈₃	—	4	1	no	—
89	C₂×D₄×C₈₃	—	4	1	no	—
90	C₂×D₄×C₈₃	—	4	1	no	—
91	C₂×D₄×C₈₃	—	4	1	no	—
92	C₂×D₄×C₈₃	—	4	1	no	—
93	C₂×D₄×C₈₃	—	4	1	no	—
94	C₂×D₄×C₈₃	—	8	1	no	—
95	C₂×D₄×C₈₃	—	8	1	no	—
96	C₂×D₄×C₈₃	—	8	2	no	—
97	C₂×D₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₈₃	—	2	1	no	—
99	C₂²×C₄×C₈₃	—	2	1	no	—
100	C₂²×C₄×C₈₃	—	2	1	no	—
101	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
103	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
104	SD₁₆×C₈₃	—	4	4	no	—
105	D₈×C₈₃	—	4	4	no	—
106	M₁₆×C₈₃	—	4	4	no	—
107	M₁₆×C₈₃	—	4	1	no	—
108	M₁₆×C₈₃	—	4	1	no	—
109	M₁₆×C₈₃	—	4	1	no	—
110	M₁₆×C₈₃	—	4	1	no	—
111	C₂×C₈×C₈₃	—	2	2	no	—
112	C₂×C₈×C₈₃	—	2	1	no	—
113	C₂×C₈×C₈₃	—	2	2	no	—
114	C₂×C₈×C₈₃	—	2	1	no	—
115	C₂×C₈×C₈₃	—	4	4	no	—
116	C₂×C₈×C₈₃	—	4	1	no	—
117	C₂×C₈×C₈₃	—	4	1	no	—
118	C₂×C₈×C₈₃	—	4	1	no	—
119	C₂×C₈×C₈₃	—	4	1	no	—
120	C₂×C₈×C₈₃	—	8	1	no	—
121	C₄⋊C₄×C₈₃	—	2	1	no	—
122	C₄⋊C₄×C₈₃	—	2	1	no	—
123	C₄⋊C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₄⋊C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²⋊C₄×C₈₃	—	2	1	no	—
126	C₂²⋊C₄×C₈₃	—	2	1	no	—
127	C₂²⋊C₄×C₈₃	—	2	1	no	—
128	C₄²×C₈₃	—	2	1	no	—
129	C₄²×C₈₃	—	2	1	no	—
130	C₄²×C₈₃	—	2	1	no	—
131	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
135	C₂³×C₈₃	—	2	1	no	—
136	C₂³×C₈₃	—	4	2	no	—
137	C₂³×C₈₃	—	8	2	no	—
138	C₂³×C₈₃	—	8	2	no	—
139	C₂³×C₈₃	—	8	1	no	—
140	C₂³×C₈₃	—	8	1	no	—
141	C₂³×C₈₃	#123	1	1	yes	characteristic
142	Q₈×C₈₃	—	2	1	no	—
143	Q₈×C₈₃	#102	1	2	yes	—
144	D₄×C₈₃	—	2	2	no	—
145	D₄×C₈₃	—	2	2	no	—
146	D₄×C₈₃	—	2	1	no	—
147	D₄×C₈₃	—	4	2	no	—
148	D₄×C₈₃	—	4	2	no	—
149	D₄×C₈₃	—	8	2	no	—
150	D₄×C₈₃	—	8	2	no	—
151	D₄×C₈₃	—	8	2	no	—
152	D₄×C₈₃	—	8	1	no	—
153	D₄×C₈₃	—	8	1	no	—
154	D₄×C₈₃	—	8	1	no	—
155	D₄×C₈₃	—	8	1	no	—
156	D₄×C₈₃	#102	1	2	yes	—
157	C₂×C₄×C₈₃	—	2	1	no	—
158	C₂×C₄×C₈₃	—	2	2	no	—
159	C₂×C₄×C₈₃	—	2	2	no	—
160	C₂×C₄×C₈₃	—	2	1	no	—
161	C₂×C₄×C₈₃	—	2	1	no	—
162	C₂×C₄×C₈₃	—	2	1	no	—
163	C₂×C₄×C₈₃	—	2	1	no	—
164	C₂×C₄×C₈₃	—	4	1	no	—
165	C₂×C₄×C₈₃	—	4	1	no	—
166	C₂×C₄×C₈₃	—	4	1	no	—
167	C₂×C₄×C₈₃	—	8	1	no	—
168	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₈₃	#120	1	1	yes	characteristic
172	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
173	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
174	C₂×C₄×C₈₃	C₂×D₈	1	1	yes	characteristic
175	C₂×C₄×C₈₃	C₂×SD₁₆	1	1	yes	characteristic
176	C₂×C₄×C₈₃	AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₂×C₄×C₈₃	#137	1	1	yes	characteristic
178	C₈×C₈₃	—	4	2	no	—
179	C₈×C₈₃	—	4	1	no	—
180	C₈×C₈₃	—	4	2	no	—
181	C₈×C₈₃	—	4	1	no	—
182	C₈×C₈₃	—	8	1	no	—
183	C₈×C₈₃	—	8	1	no	—
184	C₂²×C₈₃	—	2	1	no	—
185	C₂²×C₈₃	—	2	1	no	—
186	C₂²×C₈₃	—	2	2	no	—
187	C₂²×C₈₃	—	4	1	no	—
188	C₂²×C₈₃	—	4	1	no	—
189	C₂²×C₈₃	—	8	2	no	—
190	C₂²×C₈₃	—	8	2	no	—
191	C₂²×C₈₃	—	8	2	no	—
192	C₂²×C₈₃	—	16	2	no	—
193	C₂²×C₈₃	—	16	2	no	—
194	C₂²×C₈₃	#386	1	1	yes	characteristic
195	C₂²×C₈₃	#480	1	1	yes	characteristic
196	C₂²×C₈₃	#481	1	1	yes	characteristic
197	C₄×C₈₃	—	2	2	no	—
198	C₄×C₈₃	—	2	1	no	—
199	C₄×C₈₃	—	2	1	no	—
200	C₄×C₈₃	—	2	1	no	—
201	C₄×C₈₃	—	4	1	no	—
202	C₄×C₈₃	—	4	1	no	—
203	C₄×C₈₃	C₂×#102	1	1	yes	characteristic
204	C₄×C₈₃	#417	1	1	yes	characteristic
205	C₄×C₈₃	#447	1	1	yes	characteristic
206	C₄×C₈₃	#448	1	1	yes	characteristic
207	C₄×C₈₃	#471	1	1	yes	characteristic
208	C₄×C₈₃	#472	1	1	yes	characteristic
209	#9173	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂×C₈₃	—	2	1	no	—
211	C₂×C₈₃	—	2	1	no	—
212	C₂×C₈₃	—	4	2	no	—
213	C₂×C₈₃	—	16	2	no	—
214	C₂×C₈₃	#1874	1	1	yes	characteristic
215	C₂×C₈₃	#1903	1	1	yes	characteristic
216	C₂×C₈₃	#1907	1	1	yes	characteristic
217	#3038	C₂×C₈₃	1	1	yes	characteristic
218	#2906	C₂×C₈₃	1	1	yes	characteristic, complemented
219	#1545	C₂×C₈₃	1	1	yes	characteristic, complemented
220	C₂×#331	C₂×C₈₃	1	1	yes	characteristic, complemented
221	#1477	C₂×C₈₃	1	1	yes	characteristic, complemented
222	#1301	C₂×C₈₃	1	1	yes	characteristic, complemented
223	#1292	C₂×C₈₃	1	1	yes	characteristic, complemented
224	C₈₃	#9173	1	1	yes	characteristic, direct product factor, Sylow
225	C₂×AGL(1,ℤ/8)	—	2	1	no	—
226	C₂×#131	—	2	1	no	—
227	C₂×#127	C₂²×C₈₃	1	1	yes	characteristic
228	C₄×#41	C₂²×C₈₃	1	1	yes	characteristic
229	#460	—	2	1	no	—
230	#460	C₄×C₈₃	1	2	yes	—
231	#459	—	2	1	no	—
232	#459	C₄×C₈₃	1	2	yes	—
233	#431	C₂²×C₈₃	1	1	yes	characteristic
234	#424	—	2	1	no	—
235	#424	—	2	2	no	—
236	#423	—	2	1	no	—
237	#423	C₂²×C₈₃	1	1	yes	characteristic
238	#423	C₂²×C₈₃	1	1	yes	characteristic
239	C₂×C₄⋊C₈	—	2	1	no	—
240	C₂×C₄⋊C₈	C₂²×C₈₃	1	1	yes	characteristic
241	C₂×C₄⋊C₈	C₂²×C₈₃	1	1	yes	characteristic
242	#418	—	2	1	no	—
243	#331	—	2	1	no	—
244	#331	—	2	1	no	—
245	#331	—	2	2	no	—
246	Q₈⋊C₈	—	2	1	no	—
247	D₄⋊C₈	—	2	1	no	—
248	C₂×#41	D₄×C₈₃	1	1	yes	characteristic
249	C₂²×D₄	—	2	1	no	—
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	—	2	1	no	—
252	AGL(1,ℤ/8)	—	4	2	no	—
253	AGL(1,ℤ/8)	—	4	2	no	—
254	C₂×SD₁₆	—	2	2	no	—
255	C₂×D₈	—	2	2	no	—
256	#131	—	4	2	no	—
257	#131	—	4	2	no	—
258	C₂×M₁₆	—	2	2	no	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	—	2	1	no	—
264	#127	—	2	1	no	—
265	#127	—	2	1	no	—
266	#127	—	2	1	no	—
267	#127	C₂×C₄×C₈₃	1	2	yes	—
268	C₄×Q₈	C₂×C₄×C₈₃	1	1	yes	characteristic
269	C₄×Q₈	D₄×C₈₃	1	1	yes	characteristic
270	C₄×D₄	—	2	1	no	—
271	C₄×D₄	—	2	1	no	—
272	C₄×D₄	C₂×C₄×C₈₃	1	1	yes	characteristic
273	C₄×D₄	D₄×C₈₃	1	1	yes	characteristic
274	#117	—	2	1	no	—
275	#117	D₄×C₈₃	1	1	yes	characteristic
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
278	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	—	2	2	no	—
280	C₄⋊C₈	—	2	1	no	—
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	—	2	1	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	C₂×C₄×C₈₃	1	2	yes	—
287	C₄⋊C₈	D₄×C₈₃	1	1	yes	characteristic
288	C₄⋊C₈	D₄×C₈₃	1	1	yes	characteristic
289	C₄⋊C₈	D₄×C₈₃	1	2	yes	—
290	#102	—	2	2	no	—
291	#102	—	2	2	no	—
292	C₂²⋊C₈	—	2	1	no	—
293	C₄×C₈	—	2	1	no	—
294	C₂⁴	—	4	1	no	—
295	#41	—	2	1	no	—
296	#41	—	2	1	no	—
297	#41	D₈×C₈₃	1	2	yes	—
298	#41	SD₁₆×C₈₃	1	2	yes	—
299	C₂×Q₈	C₂²⋊C₄×C₈₃	1	1	yes	characteristic
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	8	1	no	—
312	C₂×D₄	—	8	1	no	—
313	C₂×D₄	—	8	2	no	—
314	C₂×D₄	C₂²⋊C₄×C₈₃	1	1	yes	characteristic
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
319	C₂²×C₄	#41×C₈₃	1	1	yes	characteristic
320	C₂²×C₄	#41×C₈₃	1	1	yes	characteristic
321	SD₁₆	—	4	4	no	—
322	D₈	—	4	4	no	—
323	M₁₆	—	4	4	no	—
324	M₁₆	—	4	1	no	—
325	M₁₆	—	4	1	no	—
326	M₁₆	—	4	1	no	—
327	M₁₆	—	4	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	4	4	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	8	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	C₂²⋊C₄×C₈₃	1	1	yes	characteristic
341	C₄⋊C₄	C₂²⋊C₄×C₈₃	1	1	yes	characteristic
342	C₂²⋊C₄	—	2	1	no	—
343	C₂²⋊C₄	—	2	1	no	—
344	C₂²⋊C₄	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	1	no	—
348	C₄²	C₂²×C₄×C₈₃	1	1	yes	characteristic
349	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
350	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
351	C₄²	C₂×D₄×C₈₃	1	1	yes	characteristic
352	C₂³	—	2	1	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	8	2	no	—
355	C₂³	—	8	2	no	—
356	C₂³	—	8	1	no	—
357	C₂³	—	8	1	no	—
358	C₂³	#123×C₈₃	1	1	yes	characteristic
359	Q₈	—	2	1	no	—
360	Q₈	#102×C₈₃	1	2	yes	—
361	D₄	—	2	2	no	—
362	D₄	—	2	2	no	—
363	D₄	—	2	1	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	2	no	—
366	D₄	—	8	2	no	—
367	D₄	—	8	2	no	—
368	D₄	—	8	2	no	—
369	D₄	—	8	1	no	—
370	D₄	—	8	1	no	—
371	D₄	—	8	1	no	—
372	D₄	—	8	1	no	—
373	D₄	#102×C₈₃	1	2	yes	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	8	1	no	—
385	C₂×C₄	C₂×C₂²⋊C₄×C₈₃	1	1	yes	characteristic
386	C₂×C₄	C₄×D₄×C₈₃	1	1	yes	characteristic
387	C₂×C₄	C₄×D₄×C₈₃	1	1	yes	characteristic
388	C₂×C₄	#120×C₈₃	1	1	yes	characteristic
389	C₂×C₄	#121×C₈₃	1	1	yes	characteristic
390	C₂×C₄	#121×C₈₃	1	1	yes	characteristic
391	C₂×C₄	C₂×D₈×C₈₃	1	1	yes	characteristic
392	C₂×C₄	C₂×SD₁₆×C₈₃	1	1	yes	characteristic
393	C₂×C₄	AGL(1,ℤ/8)×C₈₃	1	1	yes	characteristic
394	C₂×C₄	#137×C₈₃	1	1	yes	characteristic
395	C₈	—	4	2	no	—
396	C₈	—	4	1	no	—
397	C₈	—	4	2	no	—
398	C₈	—	4	1	no	—
399	C₈	—	8	1	no	—
400	C₈	—	8	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	2	no	—
409	C₂²	—	16	2	no	—
410	C₂²	—	16	2	no	—
411	C₂²	#386×C₈₃	1	1	yes	characteristic
412	C₂²	#480×C₈₃	1	1	yes	characteristic
413	C₂²	#481×C₈₃	1	1	yes	characteristic
414	C₄	—	2	2	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	1	no	—
420	C₄	C₂×#102×C₈₃	1	1	yes	characteristic
421	C₄	#417×C₈₃	1	1	yes	characteristic
422	C₄	#447×C₈₃	1	1	yes	characteristic
423	C₄	#448×C₈₃	1	1	yes	characteristic
424	C₄	#471×C₈₃	1	1	yes	characteristic
425	C₄	#472×C₈₃	1	1	yes	characteristic
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	4	2	no	—
429	C₂	—	16	2	no	—
430	C₂	C₈₃×#1874	1	1	yes	characteristic
431	C₂	C₈₃×#1903	1	1	yes	characteristic
432	C₂	C₈₃×#1907	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₃	#386
commutator	C₄²	C₂²×C₄×C₈₃
Frattini, cosocle	C₂×C₄²	C₂³×C₈₃
prime radical	C₈₃×#3038	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ C₂×C₄²×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₃×#2906	C₂	semidirect
3. C₈₃×#1545	C₂	semidirect
4. C₂×#331×C₈₃	C₂	semidirect
5. C₈₃×#1477	C₂	semidirect
6. C₈₃×#1301	C₂	semidirect
7. C₈₃×#1292	C₂	semidirect
209. #9173	C₈₃	direct (N × H)
218. #2906	C₂×C₈₃	semidirect
219. #1545	C₂×C₈₃	semidirect
220. C₂×#331	C₂×C₈₃	semidirect
221. #1477	C₂×C₈₃	semidirect
222. #1301	C₂×C₈₃	semidirect
223. #1292	C₂×C₈₃	semidirect
224. C₈₃	#9173	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×#3038	2
C₈₃×#2906	2
C₈₃×#1545	2
C₂×#331×C₈₃	2
C₈₃×#1477	2
C₈₃×#1301	2
C₈₃×#1292	2
#9173	83

Subgroups — C83×#9173 #35236997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#9173 #35236997