Subgroups — #35375007

Order 21248.

662 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24918056	C₂	1	1	yes	maximal, characteristic
2	#24916441	C₂	1	1	yes	maximal, characteristic, complemented
3	#24916172	C₂	1	1	yes	maximal, characteristic, complemented
4	#24906355	C₂	1	1	yes	maximal, characteristic, complemented
5	#24906351	C₂	1	1	yes	maximal, characteristic, complemented
6	#24906346	C₂	1	1	yes	maximal, characteristic, complemented
7	#24906287	C₂	1	1	yes	maximal, characteristic, complemented
8	#24906284	C₂	1	1	yes	maximal, characteristic, complemented
9	#24906274	C₂	1	1	yes	maximal, characteristic, complemented
10	#24906272	C₂	1	1	yes	maximal, characteristic, complemented
11	#24906229	C₂	1	1	yes	maximal, characteristic, complemented
12	#24905930	C₂	1	1	yes	maximal, characteristic, complemented
13	#24905925	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#13050573	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#1589	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14581800	—	2	1	no	—
17	#19128248	C₂²	1	1	yes	characteristic
18	#19128233	C₂²	1	1	yes	characteristic
19	#19128109	C₄	1	1	yes	characteristic
20	#19128089	C₄	1	1	yes	characteristic
21	#19128064	C₄	1	1	yes	characteristic
22	#19128059	C₄	1	1	yes	characteristic
23	#19127953	C₄	1	1	yes	characteristic
24	#19127951	C₄	1	1	yes	characteristic
25	#19127948	C₄	1	1	yes	characteristic
26	#19127946	C₄	1	1	yes	characteristic
27	#19127831	C₂²	1	1	yes	characteristic
28	#19127825	C₂²	1	1	yes	characteristic
29	C₄×#13050579	C₂²	1	1	yes	characteristic
30	C₄×#13050578	C₂²	1	1	yes	characteristic
31	C₄×#13050575	C₂²	1	1	yes	characteristic
32	#19127780	C₂²	1	1	yes	characteristic
33	#19127777	—	2	1	no	—
34	#19127770	—	2	1	no	—
35	D₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
36	D₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
37	#19127766	C₂²	1	1	yes	characteristic
38	(C₂²⋊D₈₃)⋊C₈	—	2	1	no	—
39	(C₂²⋊D₈₃)⋊C₈	—	2	1	no	—
40	#19127759	—	2	1	no	—
41	#19127757	C₂²	1	1	yes	characteristic
42	#19127752	C₂²	1	1	yes	characteristic
43	#19127723	C₂²	1	1	yes	characteristic
44	#19127666	—	2	1	no	—
45	#19127659	—	2	1	no	—
46	C₄×#13050573	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₈₃	C₂²	1	1	yes	characteristic
48	#19127453	C₂²	1	1	yes	characteristic
49	#19127452	C₂²	1	1	yes	characteristic
50	#19127451	C₂²	1	1	yes	characteristic
51	#19127433	C₂²	1	1	yes	characteristic
52	#19127431	C₂²	1	1	yes	characteristic
53	#19127430	C₂²	1	1	yes	characteristic
54	D₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
55	D₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
56	#19127428	C₂²	1	1	yes	characteristic
57	#19127423	C₂²	1	1	yes	characteristic
58	#19127422	C₂²	1	1	yes	characteristic
59	C₈×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
60	C₄×D₈×C₈₃	C₂²	1	1	yes	characteristic
61	#436×C₈₃	C₂²	1	1	yes	characteristic
62	#436×C₈₃	C₂²	1	1	yes	characteristic
63	#335×C₈₃	C₂²	1	1	yes	characteristic
64	D₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
65	D₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
66	C₈²×C₈₃	C₂²	1	1	yes	characteristic
67	C₂×#13050590	—	2	1	no	—
68	C₂×#13050579	C₂×C₄	1	1	yes	characteristic
69	C₂×#13050578	C₂×C₄	1	1	yes	characteristic
70	C₂×#13050575	C₂×C₄	1	1	yes	characteristic
71	#14581800	—	4	4	no	—
72	C₂×#13050573	—	2	1	no	—
73	C₂×#13050573	—	2	1	no	—
74	C₂×#13050573	C₂×C₄	1	1	yes	characteristic
75	C₂×#13050573	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₈₃⋊C₈	—	2	1	no	—
77	C₂²×C₈₃⋊C₈	—	2	1	no	—
78	C₂×C₈×D₈₃	—	2	1	no	—
79	C₂×C₈×D₈₃	D₄	1	1	yes	characteristic
80	C₂×C₈×D₈₃	D₄	1	1	yes	characteristic
81	#14581791	C₂×C₄	1	1	yes	characteristic
82	#14581788	C₂×C₄	1	1	yes	characteristic
83	#14581785	—	2	1	no	—
84	#14581783	C₂×C₄	1	1	yes	characteristic
85	#14581779	C₂×C₄	1	1	yes	characteristic
86	#14581778	—	2	1	no	—
87	#14581774	—	2	1	no	—
88	#14581772	C₂×C₄	1	1	yes	characteristic
89	#14581767	C₂×C₄	1	1	yes	characteristic
90	#14581765	—	2	1	no	—
91	#14581763	C₂×C₄	1	1	yes	characteristic
92	#14581763	C₂×C₄	1	1	yes	characteristic
93	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
94	C₄×D₃₃₂	C₂³	1	1	yes	characteristic
95	C₄×C₂²⋊D₈₃	—	2	1	no	—
96	C₄×C₂²⋊D₈₃	—	2	1	no	—
97	#14581751	—	2	1	no	—
98	C₄²×D₈₃	C₂³	1	1	yes	characteristic
99	#14581725	C₂×C₄	1	1	yes	characteristic
100	#14581724	C₂×C₄	1	1	yes	characteristic
101	#14581723	C₂×C₄	1	1	yes	characteristic
102	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
103	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
104	Dic₈₃⋊C₈	—	2	1	no	—
105	Dic₈₃⋊C₈	—	2	1	no	—
106	Dic₈₃⋊C₈	—	2	1	no	—
107	Dic₈₃⋊C₈	—	2	1	no	—
108	#14581717	C₂×C₄	1	1	yes	characteristic
109	#14581715	C₂×C₄	1	1	yes	characteristic
110	#14581714	C₂×C₄	1	1	yes	characteristic
111	#14581713	C₂×C₄	1	1	yes	characteristic
112	#14581713	C₂×C₄	1	1	yes	characteristic
113	#14581712	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
115	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
116	(C₂×D₈₃)⋊C₈	—	2	1	no	—
117	(C₂×D₈₃)⋊C₈	—	2	1	no	—
118	(C₂×D₈₃)⋊C₈	—	2	1	no	—
119	(C₂×D₈₃)⋊C₈	—	2	1	no	—
120	#14581702	—	2	1	no	—
121	#14581702	—	2	1	no	—
122	#14581702	C₂×C₄	1	1	yes	characteristic
123	#14581702	C₂×C₄	1	1	yes	characteristic
124	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
125	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
126	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
127	C₈×Dic₈₃	—	2	1	no	—
128	C₈×Dic₈₃	D₄	1	1	yes	characteristic
129	C₈×Dic₈₃	D₄	1	1	yes	characteristic
130	C₂×D₈×C₈₃	C₂×C₄	1	1	yes	characteristic
131	C₂×M₁₆×C₈₃	—	2	1	no	—
132	C₂×M₁₆×C₈₃	—	2	1	no	—
133	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
134	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
135	#107×C₈₃	C₂×C₄	1	1	yes	characteristic
136	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
138	#102×C₈₃	C₂×C₄	1	1	yes	characteristic
139	#102×C₈₃	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₈₃	—	2	1	no	—
141	C₂²⋊C₈×C₈₃	—	2	1	no	—
142	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
145	#13050590	—	4	2	no	—
146	#13050590	—	4	2	no	—
147	C₂×Dic₁₆₆	—	2	1	no	—
148	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
149	C₂×D₃₃₂	—	2	1	no	—
150	C₂×D₃₃₂	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₂²⋊D₈₃	—	2	1	no	—
152	C₂×C₂²⋊D₈₃	—	2	1	no	—
153	C₂×C₂²⋊D₈₃	—	2	1	no	—
154	C₂×C₂²⋊D₈₃	—	2	1	no	—
155	C₂×C₄×D₈₃	—	2	1	no	—
156	C₂×C₄×D₈₃	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₄×D₈₃	C₂×D₄	1	1	yes	characteristic
158	C₂×C₄×D₈₃	#41	1	1	yes	characteristic
159	#13050579	—	2	2	no	—
160	#13050578	—	2	2	no	—
161	#13050575	—	2	2	no	—
162	#13050573	—	2	2	no	—
163	#13050573	—	2	2	no	—
164	#13050573	—	4	2	no	—
165	#13050573	—	4	2	no	—
166	C₂×C₈₃⋊C₈	—	2	1	no	—
167	C₂×C₈₃⋊C₈	—	2	1	no	—
168	C₂×C₈₃⋊C₈	—	2	1	no	—
169	C₂×C₈₃⋊C₈	—	4	2	no	—
170	C₂×C₈₃⋊C₈	—	4	2	no	—
171	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
175	C₈×D₈₃	—	2	2	no	—
176	C₈×D₈₃	—	4	1	no	—
177	C₈×D₈₃	—	4	2	no	—
178	C₄⋊Dic₈₃	—	2	1	no	—
179	C₄⋊Dic₈₃	—	2	1	no	—
180	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
181	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
182	Dic₈₃⋊C₄	—	2	1	no	—
183	Dic₈₃⋊C₄	—	2	1	no	—
184	Dic₈₃⋊C₄	—	2	1	no	—
185	C₂²⋊Dic₈₃	—	2	1	no	—
186	C₂²⋊Dic₈₃	—	2	1	no	—
187	C₂²⋊Dic₈₃	—	2	1	no	—
188	C₂²⋊Dic₈₃	—	2	1	no	—
189	(C₂×D₈₃)⋊C₄	—	2	1	no	—
190	(C₂×D₈₃)⋊C₄	—	2	1	no	—
191	(C₂×D₈₃)⋊C₄	—	2	1	no	—
192	C₄×Dic₈₃	—	2	1	no	—
193	C₄×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
194	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
195	C₄×Dic₈₃	#41	1	1	yes	characteristic
196	C₂×D₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
197	C₂×D₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₈₃	—	2	1	no	—
199	C₂²×C₄×C₈₃	—	2	1	no	—
200	D₈×C₈₃	—	2	2	no	—
201	M₁₆×C₈₃	—	4	2	no	—
202	M₁₆×C₈₃	—	4	2	no	—
203	C₂×C₈×C₈₃	—	2	1	no	—
204	C₂×C₈×C₈₃	—	2	1	no	—
205	C₂×C₈×C₈₃	—	2	1	no	—
206	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
207	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
208	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
209	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
210	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
211	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
212	C₂²⋊C₄×C₈₃	—	2	1	no	—
213	C₂²⋊C₄×C₈₃	—	2	1	no	—
214	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
215	C₂³×C₈₃	—	2	1	no	—
216	C₂³×C₈₃	—	2	1	no	—
217	C₂²×D₈₃	—	2	1	no	—
218	C₂²×D₈₃	C₄×D₄	1	1	yes	characteristic
219	D₄×C₈₃	—	2	1	no	—
220	D₄×C₈₃	—	2	1	no	—
221	D₄×C₈₃	—	2	1	no	—
222	D₄×C₈₃	—	2	1	no	—
223	C₂×C₄×C₈₃	—	2	1	no	—
224	C₂×C₄×C₈₃	—	2	1	no	—
225	C₂×C₄×C₈₃	—	4	1	no	—
226	C₂×C₄×C₈₃	—	4	1	no	—
227	C₂×C₄×C₈₃	—	4	1	no	—
228	C₂×C₄×C₈₃	—	4	1	no	—
229	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
230	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
232	C₂²⋊D₈₃	—	4	2	no	—
233	C₂²⋊D₈₃	—	4	2	no	—
234	C₂²⋊D₈₃	—	4	2	no	—
235	C₂²⋊D₈₃	—	4	2	no	—
236	C₂×Dic₈₃	—	2	1	no	—
237	C₂×Dic₈₃	—	2	1	no	—
238	C₂×Dic₈₃	—	2	1	no	—
239	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
240	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
241	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
242	D₃₃₂	—	2	1	no	—
243	D₃₃₂	—	2	1	no	—
244	D₃₃₂	—	4	2	no	—
245	C₄×D₈₃	—	2	1	no	—
246	C₄×D₈₃	—	2	1	no	—
247	C₄×D₈₃	—	2	1	no	—
248	C₄×D₈₃	—	2	1	no	—
249	C₄×D₈₃	—	4	1	no	—
250	C₄×D₈₃	—	4	1	no	—
251	C₄×D₈₃	—	4	1	no	—
252	Dic₁₆₆	—	2	1	no	—
253	Dic₁₆₆	—	2	1	no	—
254	Dic₁₆₆	—	4	2	no	—
255	C₈×C₈₃	—	2	1	no	—
256	C₈×C₈₃	—	2	1	no	—
257	C₈×C₈₃	—	4	1	no	—
258	C₈×C₈₃	—	4	1	no	—
259	C₈×C₈₃	—	4	1	no	—
260	C₈×C₈₃	#131	1	2	yes	complemented
261	C₈×C₈₃	AGL(1,ℤ/8)	1	2	yes	—
262	C₈₃⋊C₈	—	2	1	no	—
263	C₈₃⋊C₈	—	2	1	no	—
264	C₈₃⋊C₈	—	2	1	no	—
265	C₈₃⋊C₈	—	4	1	no	—
266	C₈₃⋊C₈	—	4	1	no	—
267	C₈₃⋊C₈	—	4	1	no	—
268	C₈₃⋊C₈	#131	1	2	yes	complemented
269	C₂²×C₈₃	—	4	1	no	—
270	C₂²×C₈₃	—	4	1	no	—
271	C₂²×C₈₃	—	4	1	no	—
272	C₂²×C₈₃	—	4	1	no	—
273	C₂²×C₈₃	—	4	1	no	—
274	C₂²×C₈₃	—	4	1	no	—
275	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
276	C₂×D₈₃	—	2	1	no	—
277	C₂×D₈₃	—	2	1	no	—
278	C₂×D₈₃	—	2	1	no	—
279	C₂×D₈₃	—	4	1	no	—
280	C₂×D₈₃	—	4	1	no	—
281	C₂×D₈₃	—	4	1	no	—
282	C₄×C₈₃	—	2	1	no	—
283	C₄×C₈₃	—	4	1	no	—
284	C₄×C₈₃	—	4	1	no	—
285	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
286	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
287	C₄×C₈₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
288	C₄×C₈₃	#575	1	1	yes	characteristic
289	Dic₈₃	—	2	1	no	—
290	Dic₈₃	—	2	1	no	—
291	Dic₈₃	—	2	1	no	—
292	Dic₈₃	—	4	1	no	—
293	Dic₈₃	—	4	1	no	—
294	Dic₈₃	—	4	1	no	—
295	#17966	—	83	1	no	maximal, Sylow
296	C₂×C₈₃	—	8	1	no	—
297	C₂×C₈₃	—	8	1	no	—
298	C₂×C₈₃	#2931	1	1	yes	characteristic
299	C₂×C₈₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
300	C₂×C₈₃	#2955	1	1	yes	characteristic
301	D₈₃	—	4	1	no	—
302	D₈₃	—	8	1	no	—
303	#3171	—	83	1	no	—
304	#2966	—	83	1	no	—
305	#2931	—	83	1	no	—
306	#1590	—	83	1	no	—
307	#1590	—	83	1	no	—
308	#1589	—	83	1	no	—
309	#1589	D₈₃	1	1	yes	characteristic, complemented
310	#1580	—	83	1	no	—
311	#1580	—	83	1	no	—
312	SD₁₆⋊C₈	—	83	1	no	—
313	SD₁₆⋊C₈	—	83	1	no	—
314	#1569	—	83	1	no	—
315	#1496	—	83	1	no	—
316	#1495	—	83	1	no	—
317	C₈×M₁₆	—	83	1	no	—
318	C₈₃	#17966	1	1	yes	characteristic, complemented, Sylow
319	C₂×#131	—	166	1	no	—
320	#532	—	83	1	no	—
321	#529	—	83	1	no	—
322	#501	—	83	1	no	—
323	#496	—	83	1	no	—
324	#490	—	83	1	no	—
325	#489	—	83	1	no	—
326	#469	—	83	1	no	—
327	#469	—	83	1	no	—
328	#468	—	83	1	no	—
329	#468	—	83	1	no	—
330	#446	—	83	1	no	—
331	C₈×Q₈	—	83	1	no	—
332	C₄×SD₁₆	—	83	1	no	—
333	C₄×SD₁₆	—	83	1	no	—
334	C₄×D₈	—	83	1	no	—
335	C₄×D₈	C₂×D₈₃	1	1	yes	characteristic
336	#436	—	83	1	no	—
337	#436	—	166	1	no	—
338	#436	C₂×D₈₃	1	1	yes	characteristic
339	#436	C₂×D₈₃	1	1	yes	characteristic
340	#435	—	166	1	no	—
341	C₈×D₄	—	83	1	no	—
342	C₈×D₄	—	83	1	no	—
343	C₈×D₄	—	83	1	no	—
344	C₈×D₄	—	166	1	no	—
345	C₈×D₄	—	166	1	no	—
346	#433	—	166	1	no	—
347	#432	—	83	1	no	—
348	#431	—	83	1	no	—
349	#423	—	83	1	no	—
350	#408	—	166	1	no	—
351	#405	—	166	1	no	—
352	C₄×M₁₆	—	83	1	no	—
353	C₂×C₄×C₈	—	83	1	no	—
354	#335	—	83	1	no	—
355	#335	C₂×D₈₃	1	1	yes	characteristic
356	#334	—	83	1	no	—
357	#334	—	83	1	no	—
358	Q₈⋊C₈	—	83	1	no	—
359	Q₈⋊C₈	—	83	1	no	—
360	D₄⋊C₈	—	83	1	no	—
361	D₄⋊C₈	—	83	1	no	—
362	D₄⋊C₈	—	83	1	no	—
363	D₄⋊C₈	—	83	1	no	—
364	D₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic
365	D₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic
366	#322	—	83	1	no	—
367	#322	—	83	1	no	—
368	C₈²	—	83	1	no	—
369	C₈²	C₂×D₈₃	1	1	yes	characteristic
370	C₂×#41	—	166	1	no	—
371	C₂×SD₁₆	—	83	1	no	—
372	C₂×SD₁₆	—	83	1	no	—
373	C₂×D₈	—	83	1	no	—
374	C₂×D₈	C₄×D₈₃	1	1	yes	characteristic
375	#131	—	332	4	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	—	83	1	no	—
379	C₂×M₁₆	—	83	1	no	—
380	C₂×M₁₆	—	166	1	no	—
381	C₂×M₁₆	—	166	1	no	—
382	C₂²×C₈	—	83	1	no	—
383	C₂²×C₈	—	83	1	no	—
384	C₂²×C₈	—	166	1	no	—
385	C₂²×C₈	—	166	1	no	—
386	C₂²×C₈	—	166	1	no	—
387	C₄⋊Q₈	—	83	1	no	—
388	#127	—	83	1	no	—
389	#126	—	166	1	no	—
390	#125	—	83	1	no	—
391	#124	—	83	1	no	—
392	#124	—	166	1	no	—
393	#123	—	166	1	no	—
394	C₂²⋊Q₈	—	83	1	no	—
395	#121	—	83	1	no	—
396	#121	—	83	1	no	—
397	#121	—	83	1	no	—
398	#121	—	166	1	no	—
399	C₄×Q₈	—	83	1	no	—
400	C₄×D₄	—	83	1	no	—
401	C₄×D₄	—	166	1	no	—
402	C₄×D₄	—	166	1	no	—
403	C₄×D₄	C₂²×D₈₃	1	1	yes	characteristic
404	C₄×D₄	C₂²×D₈₃	1	1	yes	characteristic
405	#117	—	166	1	no	—
406	C₂×C₄²	—	83	1	no	—
407	#107	—	83	1	no	—
408	#107	C₄×D₈₃	1	1	yes	characteristic
409	#106	—	83	1	no	—
410	#106	—	83	1	no	—
411	C₄⋊C₈	—	83	1	no	—
412	C₄⋊C₈	—	83	1	no	—
413	C₄⋊C₈	—	166	1	no	—
414	C₄⋊C₈	—	166	1	no	—
415	C₄⋊C₈	—	166	1	no	—
416	C₄⋊C₈	—	166	1	no	—
417	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
418	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
419	#103	—	83	1	no	—
420	#103	—	83	1	no	—
421	#102	—	83	1	no	—
422	#102	—	83	1	no	—
423	#102	—	83	1	no	—
424	#102	—	83	1	no	—
425	#102	C₄×D₈₃	1	1	yes	characteristic
426	#102	C₄×D₈₃	1	1	yes	characteristic
427	C₂²⋊C₈	—	2	1	no	—
428	C₂²⋊C₈	—	2	1	no	—
429	C₂²⋊C₈	—	166	1	no	—
430	C₂²⋊C₈	—	166	1	no	—
431	C₂²⋊C₈	—	166	1	no	—
432	C₂²⋊C₈	—	166	1	no	—
433	C₂²⋊C₈	—	166	1	no	—
434	C₂²⋊C₈	—	166	1	no	—
435	#97	—	83	1	no	—
436	#97	—	83	1	no	—
437	#97	—	166	1	no	—
438	#97	—	166	1	no	—
439	C₄×C₈	—	83	1	no	—
440	C₄×C₈	—	83	1	no	—
441	C₄×C₈	—	83	1	no	—
442	C₄×C₈	—	83	1	no	—
443	C₄×C₈	—	83	1	no	—
444	C₄×C₈	—	166	1	no	—
445	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
446	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
447	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
448	#41	—	332	2	no	—
449	#41	—	332	2	no	—
450	C₂×Q₈	—	83	1	no	—
451	C₂×Q₈	—	166	1	no	—
452	C₂×D₄	—	83	1	no	—
453	C₂×D₄	—	166	1	no	—
454	C₂×D₄	—	166	1	no	—
455	C₂×D₄	—	166	1	no	—
456	C₂×D₄	—	166	1	no	—
457	C₂×D₄	—	166	1	no	—
458	C₂×D₄	C₂×C₄×D₈₃	1	1	yes	characteristic
459	C₂×D₄	C₂×C₄×D₈₃	1	1	yes	characteristic
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	83	1	no	—
463	C₂²×C₄	—	83	1	no	—
464	C₂²×C₄	—	83	1	no	—
465	C₂²×C₄	—	166	1	no	—
466	SD₁₆	—	166	2	no	—
467	SD₁₆	—	166	2	no	—
468	D₈	—	2	2	no	—
469	D₈	—	166	2	no	—
470	M₁₆	—	4	2	no	—
471	M₁₆	—	4	2	no	—
472	M₁₆	—	332	2	no	—
473	M₁₆	—	332	2	no	—
474	M₁₆	—	166	2	no	—
475	M₁₆	—	166	2	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	332	1	no	—
480	C₂×C₈	—	332	2	no	—
481	C₂×C₈	—	332	2	no	—
482	C₂×C₈	—	332	2	no	—
483	C₂×C₈	—	83	1	no	—
484	C₂×C₈	—	83	1	no	—
485	C₂×C₈	—	83	1	no	—
486	C₂×C₈	—	83	1	no	—
487	C₂×C₈	—	166	1	no	—
488	C₂×C₈	—	166	1	no	—
489	C₂×C₈	—	166	1	no	—
490	C₂×C₈	—	166	2	no	—
491	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
492	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
493	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
494	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
495	C₄⋊C₄	—	83	1	no	—
496	C₄⋊C₄	—	83	1	no	—
497	C₄⋊C₄	—	166	1	no	—
498	C₄⋊C₄	—	166	1	no	—
499	C₄⋊C₄	—	166	1	no	—
500	C₄⋊C₄	—	166	1	no	—
501	C₄⋊C₄	—	166	1	no	—
502	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
503	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
504	C₂²⋊C₄	—	2	1	no	—
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	166	1	no	—
507	C₂²⋊C₄	—	166	1	no	—
508	C₂²⋊C₄	—	166	1	no	—
509	C₂²⋊C₄	—	166	1	no	—
510	C₂²⋊C₄	—	166	1	no	—
511	C₂²⋊C₄	—	166	1	no	—
512	C₂²⋊C₄	—	166	1	no	—
513	C₄²	—	83	1	no	—
514	C₄²	—	83	1	no	—
515	C₄²	—	83	1	no	—
516	C₄²	—	166	1	no	—
517	C₄²	C₂³×D₈₃	1	1	yes	characteristic
518	C₂³	—	2	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	—	83	1	no	—
521	C₂³	—	166	1	no	—
522	Q₈	—	332	2	no	—
523	Q₈	—	166	1	no	—
524	Q₈	—	166	1	no	—
525	D₄	—	2	1	no	—
526	D₄	—	2	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	2	1	no	—
529	D₄	—	332	2	no	—
530	D₄	—	332	2	no	—
531	D₄	—	332	2	no	—
532	D₄	—	332	2	no	—
533	D₄	—	332	2	no	—
534	D₄	—	166	1	no	—
535	D₄	—	166	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	332	1	no	—
543	C₂×C₄	—	332	1	no	—
544	C₂×C₄	—	332	1	no	—
545	C₂×C₄	—	83	1	no	—
546	C₂×C₄	—	83	1	no	—
547	C₂×C₄	—	83	1	no	—
548	C₂×C₄	—	166	1	no	—
549	C₂×C₄	—	166	1	no	—
550	C₂×C₄	—	166	1	no	—
551	C₂×C₄	—	166	1	no	—
552	C₂×C₄	—	166	1	no	—
553	C₂×C₄	—	166	1	no	—
554	C₂×C₄	—	166	1	no	—
555	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
556	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
557	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	4	1	no	—
562	C₈	—	4	1	no	—
563	C₈	—	332	1	no	—
564	C₈	—	332	1	no	—
565	C₈	—	332	1	no	—
566	C₈	—	83	2	no	—
567	C₈	—	166	1	no	—
568	C₈	—	166	1	no	—
569	C₈	—	166	1	no	—
570	C₈	#14581800	1	2	yes	complemented
571	C₈	#14581816	1	2	yes	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	332	1	no	—
579	C₂²	—	332	1	no	—
580	C₂²	—	332	1	no	—
581	C₂²	—	166	1	no	—
582	C₂²	—	166	1	no	—
583	C₂²	—	166	1	no	—
584	C₂²	C₄×D₄×D₈₃	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	332	1	no	—
589	C₄	—	332	1	no	—
590	C₄	—	332	1	no	—
591	C₄	—	166	1	no	—
592	C₄	—	166	1	no	—
593	C₄	—	166	1	no	—
594	C₄	#131×D₈₃	1	1	yes	characteristic
595	C₄	C₂×#14581800	1	1	yes	characteristic
596	C₄	C₂×#14581816	1	1	yes	characteristic
597	C₄	#19128498	1	1	yes	characteristic
598	C₂	—	8	1	no	—
599	C₂	—	8	1	no	—
600	C₂	—	332	1	no	—
601	C₂	—	664	1	no	—
602	C₂	#24916172	1	1	yes	characteristic
603	C₂	C₄×#14581816	1	1	yes	characteristic
604	C₂	#24916361	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₃
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₄²	C₂³×D₈₃
Fitting	C₈₃×#1589	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	#24918056	C₂
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	#1589	D₈₃
hypocenter	C₈₃	#17966
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1589

Complements

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

N	H ≅ G/N	type
2. #24916441	C₂	semidirect
3. #24916172	C₂	semidirect
4. #24906355	C₂	semidirect
5. #24906351	C₂	semidirect
6. #24906346	C₂	semidirect
7. #24906287	C₂	semidirect
8. #24906284	C₂	semidirect
9. #24906274	C₂	semidirect
10. #24906272	C₂	semidirect
11. #24906229	C₂	semidirect
12. #24905930	C₂	semidirect
13. #24905925	C₂	semidirect
14. C₈×#13050573	C₂	semidirect
15. C₈₃×#1589	C₂	semidirect
260. C₈×C₈₃	#131	semidirect
268. C₈₃⋊C₈	#131	semidirect
309. #1589	D₈₃	semidirect
318. C₈₃	#17966	semidirect
570. C₈	#14581800	semidirect

Maximal subgroups

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

subgroup	index
#24918056	2
#24916441	2
#24916172	2
#24906355	2
#24906351	2
#24906346	2
#24906287	2
#24906284	2
#24906274	2
#24906272	2
#24906229	2
#24905930	2
#24905925	2
C₈×#13050573	2
C₈₃×#1589	2
#17966	83