Subgroups — #35374490

Order 21248.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24917517	C₂	1	1	yes	maximal, characteristic
2	#24916571	C₂	1	1	yes	maximal, characteristic, complemented
3	#24906339	C₂	1	1	yes	maximal, characteristic, complemented
4	#24906325	C₂	1	1	yes	maximal, characteristic, complemented
5	#24906304	C₂	1	1	yes	maximal, characteristic, complemented
6	#24906290	C₂	1	1	yes	maximal, characteristic, complemented
7	#24906285	C₂	1	1	yes	maximal, characteristic, complemented
8	#24906275	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#13050578	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#13050575	C₂	1	1	yes	maximal, characteristic, complemented
11	#24906249	C₂	1	1	yes	maximal, characteristic, complemented
12	#24905895	C₂	1	1	yes	maximal, characteristic, complemented
13	#24905862	C₂	1	1	yes	maximal, characteristic, complemented
14	#24905763	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#13050590	C₂²	1	1	yes	characteristic
17	#19128022	C₄	1	1	yes	characteristic
18	#19128022	C₄	1	1	yes	characteristic
19	#19127993	C₄	1	1	yes	characteristic
20	#19127988	C₄	1	1	yes	characteristic
21	#19127898	C₄	1	1	yes	characteristic
22	#19127893	C₄	1	1	yes	characteristic
23	#19127844	C₄	1	1	yes	characteristic
24	#19127844	C₄	1	1	yes	characteristic
25	C₈×Dic₁₆₆	C₂²	1	1	yes	characteristic
26	C₈×Dic₁₆₆	C₂²	1	1	yes	characteristic
27	C₄×#13050578	C₂²	1	1	yes	characteristic
28	C₄×#13050578	C₂²	1	1	yes	characteristic
29	C₄×#13050575	C₂²	1	1	yes	characteristic
30	C₄×#13050575	C₂²	1	1	yes	characteristic
31	C₈×D₃₃₂	C₂²	1	1	yes	characteristic
32	C₈×D₃₃₂	C₂²	1	1	yes	characteristic
33	(C₂²⋊D₈₃)⋊C₈	—	2	1	no	—
34	(C₂²⋊D₈₃)⋊C₈	—	2	1	no	—
35	#19127754	C₂²	1	1	yes	characteristic
36	#19127754	C₂²	1	1	yes	characteristic
37	#19127753	—	2	1	no	—
38	C₂×C₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
39	C₄⋊C₈×D₈₃	—	2	1	no	—
40	#19127453	C₂²	1	1	yes	characteristic
41	#19127453	C₂²	1	1	yes	characteristic
42	#19127451	C₂²	1	1	yes	characteristic
43	#19127451	C₂²	1	1	yes	characteristic
44	#19127431	C₂²	1	1	yes	characteristic
45	#19127431	C₂²	1	1	yes	characteristic
46	D₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
47	D₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
48	D₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
49	D₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
50	#19127428	C₂²	1	1	yes	characteristic
51	#19127428	C₂²	1	1	yes	characteristic
52	#19127423	C₂²	1	1	yes	characteristic
53	#19127423	C₂²	1	1	yes	characteristic
54	#19127422	C₂²	1	1	yes	characteristic
55	C₈×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
56	#532×C₈₃	C₂²	1	1	yes	characteristic
57	#436×C₈₃	C₂²	1	1	yes	characteristic
58	#436×C₈₃	C₂²	1	1	yes	characteristic
59	#435×C₈₃	—	2	1	no	—
60	#435×C₈₃	—	2	1	no	—
61	C₈×D₄×C₈₃	C₂²	1	1	yes	characteristic
62	C₈×D₄×C₈₃	C₂²	1	1	yes	characteristic
63	#432×C₈₃	C₂²	1	1	yes	characteristic
64	#431×C₈₃	C₂²	1	1	yes	characteristic
65	#408×C₈₃	—	2	1	no	—
66	#408×C₈₃	—	2	1	no	—
67	C₂×#13050590	C₂×C₄	1	1	yes	characteristic
68	C₂×#13050578	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	C₂×#13050575	C₂×C₄	1	1	yes	characteristic
72	C₂²×C₈₃⋊C₈	—	2	1	no	—
73	C₂×C₈×D₈₃	—	2	1	no	—
74	C₂×C₈×D₈₃	—	2	1	no	—
75	C₄×Dic₁₆₆	C₂×C₄	1	1	yes	characteristic
76	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
77	C₄×D₃₃₂	C₂×C₄	1	1	yes	characteristic
78	C₄×D₃₃₂	C₂³	1	1	yes	characteristic
79	C₄×C₂²⋊D₈₃	—	2	1	no	—
80	C₄×C₂²⋊D₈₃	—	2	1	no	—
81	#14581751	C₂×C₄	1	1	yes	characteristic
82	#14581749	—	2	1	no	—
83	C₄²×D₈₃	—	2	1	no	—
84	#14581725	C₂×C₄	1	1	yes	characteristic
85	#14581725	C₂×C₄	1	1	yes	characteristic
86	#14581723	C₂×C₄	1	1	yes	characteristic
87	#14581723	C₂×C₄	1	1	yes	characteristic
88	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
89	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
90	C₄⋊(C₈₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
91	C₄⋊(C₈₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
92	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
93	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
94	Dic₈₃⋊C₈	—	2	1	no	—
95	Dic₈₃⋊C₈	—	2	1	no	—
96	#14581715	C₂×C₄	1	1	yes	characteristic
97	#14581715	C₂×C₄	1	1	yes	characteristic
98	#14581713	C₂×C₄	1	1	yes	characteristic
99	#14581713	C₂×C₄	1	1	yes	characteristic
100	#14581713	C₂×C₄	1	1	yes	characteristic
101	#14581713	C₂×C₄	1	1	yes	characteristic
102	#14581712	C₂×C₄	1	1	yes	characteristic
103	#14581712	C₂×C₄	1	1	yes	characteristic
104	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
105	C₂²⋊(C₈₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
106	C₂²⋊(C₈₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
107	(C₂×D₈₃)⋊C₈	—	2	1	no	—
108	(C₂×D₈₃)⋊C₈	—	2	1	no	—
109	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
110	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
111	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
112	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
113	C₈×Dic₈₃	—	2	1	no	—
114	C₈×Dic₈₃	—	2	1	no	—
115	C₂×#41×C₈₃	—	2	1	no	—
116	C₂×M₁₆×C₈₃	—	2	1	no	—
117	C₂×M₁₆×C₈₃	—	2	1	no	—
118	C₂²×C₈×C₈₃	—	2	1	no	—
119	C₂²×C₈×C₈₃	—	2	1	no	—
120	C₄⋊Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
121	#127×C₈₃	C₂×C₄	1	1	yes	characteristic
122	#124×C₈₃	—	2	1	no	—
123	#121×C₈₃	—	2	1	no	—
124	#121×C₈₃	C₂×C₄	1	1	yes	characteristic
125	#121×C₈₃	C₂×C₄	1	1	yes	characteristic
126	C₄×D₄×C₈₃	—	2	1	no	—
127	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
128	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
130	C₄⋊C₈×C₈₃	D₄	1	1	yes	characteristic
131	C₄⋊C₈×C₈₃	D₄	1	1	yes	characteristic
132	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
133	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
134	C₂²⋊C₈×C₈₃	—	2	1	no	—
135	C₂²⋊C₈×C₈₃	—	2	1	no	—
136	C₂²⋊C₈×C₈₃	—	2	1	no	—
137	C₂²⋊C₈×C₈₃	—	2	1	no	—
138	C₂²⋊C₈×C₈₃	—	2	1	no	—
139	C₂²⋊C₈×C₈₃	D₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₈₃	D₄	1	1	yes	characteristic
141	#97×C₈₃	—	2	1	no	—
142	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
144	#13050590	—	2	2	no	—
145	#13050590	—	2	2	no	—
146	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
147	C₂×D₃₃₂	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₂²⋊D₈₃	—	2	1	no	—
149	C₂×C₄×D₈₃	—	2	1	no	—
150	C₂×C₄×D₈₃	—	2	1	no	—
151	C₂×C₄×D₈₃	—	2	1	no	—
152	#13050578	—	2	2	no	—
153	#13050578	—	2	2	no	—
154	#13050575	—	2	2	no	—
155	#13050575	—	2	2	no	—
156	C₂×C₈₃⋊C₈	—	2	1	no	—
157	C₂×C₈₃⋊C₈	—	2	1	no	—
158	C₂×C₈₃⋊C₈	—	2	1	no	—
159	C₂×C₈₃⋊C₈	—	2	1	no	—
160	C₂×C₈₃⋊C₈	—	8	1	no	—
161	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
165	C₈×D₈₃	—	8	1	no	—
166	C₈×D₈₃	—	8	1	no	—
167	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
168	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
169	Dic₈₃⋊C₄	—	2	1	no	—
170	Dic₈₃⋊C₄	—	2	1	no	—
171	C₂²⋊Dic₈₃	—	2	1	no	—
172	(C₂×D₈₃)⋊C₄	—	2	1	no	—
173	(C₂×D₈₃)⋊C₄	—	2	1	no	—
174	C₄×Dic₈₃	—	2	1	no	—
175	C₄×Dic₈₃	—	2	1	no	—
176	C₄×Dic₈₃	—	2	1	no	—
177	#41×C₈₃	—	8	1	no	—
178	#41×C₈₃	—	8	1	no	—
179	C₂×Q₈×C₈₃	—	2	1	no	—
180	C₂×D₄×C₈₃	—	2	1	no	—
181	C₂×D₄×C₈₃	—	2	1	no	—
182	C₂×D₄×C₈₃	—	2	1	no	—
183	C₂×D₄×C₈₃	—	2	1	no	—
184	C₂×D₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
185	C₂×D₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₈₃	—	2	1	no	—
187	C₂²×C₄×C₈₃	—	2	1	no	—
188	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
191	M₁₆×C₈₃	—	8	1	no	—
192	M₁₆×C₈₃	—	8	1	no	—
193	C₂×C₈×C₈₃	—	2	1	no	—
194	C₂×C₈×C₈₃	—	2	1	no	—
195	C₂×C₈×C₈₃	—	8	1	no	—
196	C₂×C₈×C₈₃	—	8	1	no	—
197	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
198	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
199	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
200	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
201	C₄⋊C₄×C₈₃	—	2	1	no	—
202	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
203	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
204	C₂²⋊C₄×C₈₃	—	2	1	no	—
205	C₂²⋊C₄×C₈₃	—	2	1	no	—
206	C₂²⋊C₄×C₈₃	—	2	1	no	—
207	C₂²⋊C₄×C₈₃	—	2	1	no	—
208	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
209	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₈₃	#41	1	1	yes	characteristic
211	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
212	C₂³×C₈₃	—	2	1	no	—
213	C₂³×C₈₃	—	2	1	no	—
214	C₂³×C₈₃	C₄×D₄	1	1	yes	characteristic
215	C₂²×D₈₃	—	2	1	no	—
216	Q₈×C₈₃	—	8	1	no	—
217	D₄×C₈₃	—	2	1	no	—
218	D₄×C₈₃	—	2	1	no	—
219	D₄×C₈₃	—	2	1	no	—
220	D₄×C₈₃	—	2	1	no	—
221	D₄×C₈₃	—	8	1	no	—
222	D₄×C₈₃	—	8	1	no	—
223	D₄×C₈₃	—	8	1	no	—
224	D₄×C₈₃	—	8	1	no	—
225	C₂×C₄×C₈₃	—	2	1	no	—
226	C₂×C₄×C₈₃	—	2	1	no	—
227	C₂×C₄×C₈₃	—	2	1	no	—
228	C₂×C₄×C₈₃	—	2	1	no	—
229	C₂×C₄×C₈₃	—	2	1	no	—
230	C₂×C₄×C₈₃	—	2	1	no	—
231	C₂×C₄×C₈₃	—	4	1	no	—
232	C₂×C₄×C₈₃	—	4	1	no	—
233	C₂×C₄×C₈₃	—	4	1	no	—
234	C₂×C₄×C₈₃	—	4	1	no	—
235	C₂×C₄×C₈₃	—	4	1	no	—
236	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
238	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
239	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
240	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
242	C₂²⋊D₈₃	—	2	4	no	—
243	C₂×Dic₈₃	—	2	1	no	—
244	C₂×Dic₈₃	—	2	1	no	—
245	C₂×Dic₈₃	—	2	1	no	—
246	D₃₃₂	—	2	1	no	—
247	D₃₃₂	#131	1	2	yes	—
248	C₄×D₈₃	—	2	4	no	—
249	C₄×D₈₃	—	4	1	no	—
250	C₄×D₈₃	—	4	1	no	—
251	C₄×D₈₃	—	8	1	no	—
252	Dic₁₆₆	—	2	1	no	—
253	Dic₁₆₆	#131	1	2	yes	—
254	C₈×C₈₃	—	2	1	no	—
255	C₈×C₈₃	—	2	1	no	—
256	C₈×C₈₃	—	2	1	no	—
257	C₈×C₈₃	—	2	1	no	—
258	C₈×C₈₃	—	4	1	no	—
259	C₈×C₈₃	—	4	1	no	—
260	C₈₃⋊C₈	—	2	1	no	—
261	C₈₃⋊C₈	—	2	1	no	—
262	C₈₃⋊C₈	—	2	1	no	—
263	C₈₃⋊C₈	—	2	1	no	—
264	C₈₃⋊C₈	—	4	1	no	—
265	C₈₃⋊C₈	—	4	1	no	—
266	C₈₃⋊C₈	—	4	1	no	—
267	C₈₃⋊C₈	—	4	1	no	—
268	C₂²×C₈₃	—	2	1	no	—
269	C₂²×C₈₃	—	2	1	no	—
270	C₂²×C₈₃	—	2	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	—	4	1	no	—
276	C₂²×C₈₃	—	4	1	no	—
277	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
278	C₂×D₈₃	—	2	2	no	—
279	C₂×D₈₃	—	4	1	no	—
280	C₂×D₈₃	—	4	1	no	—
281	C₄×C₈₃	—	2	1	no	—
282	C₄×C₈₃	—	2	1	no	—
283	C₄×C₈₃	—	2	1	no	—
284	C₄×C₈₃	—	2	1	no	—
285	C₄×C₈₃	—	4	1	no	—
286	C₄×C₈₃	—	4	1	no	—
287	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
288	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
289	C₄×C₈₃	#576	1	1	yes	characteristic
290	C₄×C₈₃	#577	1	1	yes	characteristic
291	Dic₈₃	—	2	2	no	—
292	Dic₈₃	—	4	1	no	—
293	Dic₈₃	—	4	1	no	—
294	#17920	—	83	1	no	maximal, Sylow
295	C₂×C₈₃	—	4	1	no	—
296	C₂×C₈₃	—	8	1	no	—
297	C₂×C₈₃	—	8	1	no	—
298	C₂×C₈₃	#2929	1	1	yes	characteristic
299	C₂×C₈₃	#2946	1	1	yes	characteristic
300	C₂×C₈₃	#2957	1	1	yes	characteristic
301	D₈₃	—	4	2	no	—
302	#3106	—	83	1	no	—
303	#2988	—	83	1	no	—
304	#2981	D₈₃	1	1	yes	characteristic, complemented
305	#1588	—	83	1	no	—
306	#1586	—	83	1	no	—
307	#1583	—	83	1	no	—
308	#1581	—	83	1	no	—
309	#1580	—	83	1	no	—
310	SD₁₆⋊C₈	—	83	1	no	—
311	C₈×SD₁₆	—	83	1	no	—
312	C₈×D₈	—	83	1	no	—
313	#1573	—	83	1	no	—
314	#1488	—	83	1	no	—
315	#1480	—	83	1	no	—
316	#1454	—	83	1	no	—
317	C₈₃	#17920	1	1	yes	characteristic, complemented, Sylow
318	#532	C₂×D₈₃	1	1	yes	characteristic
319	C₄×#41	—	83	1	no	—
320	#482	—	83	1	no	—
321	#482	—	83	1	no	—
322	#477	—	83	1	no	—
323	#476	—	83	1	no	—
324	#460	—	83	1	no	—
325	#459	—	83	1	no	—
326	#449	—	83	1	no	—
327	#449	—	83	1	no	—
328	C₈×Q₈	—	83	1	no	—
329	C₈×Q₈	—	83	1	no	—
330	C₄×SD₁₆	—	83	1	no	—
331	C₄×SD₁₆	—	83	1	no	—
332	C₄×D₈	—	83	1	no	—
333	C₄×D₈	—	83	1	no	—
334	#436	C₂×D₈₃	1	1	yes	characteristic
335	#436	C₂×D₈₃	1	1	yes	characteristic
336	#435	—	2	1	no	—
337	#435	—	2	1	no	—
338	C₈×D₄	—	83	1	no	—
339	C₈×D₄	—	83	1	no	—
340	C₈×D₄	—	166	1	no	—
341	C₈×D₄	—	166	1	no	—
342	C₈×D₄	C₂×D₈₃	1	1	yes	characteristic
343	C₈×D₄	C₂×D₈₃	1	1	yes	characteristic
344	#432	C₂×D₈₃	1	1	yes	characteristic
345	#431	—	83	1	no	—
346	#431	—	83	1	no	—
347	#431	—	166	1	no	—
348	#431	C₂×D₈₃	1	1	yes	characteristic
349	C₂×C₄⋊C₈	—	83	1	no	—
350	C₂×C₄⋊C₈	—	166	1	no	—
351	#408	—	2	1	no	—
352	#408	—	2	1	no	—
353	#335	—	83	1	no	—
354	#335	—	83	1	no	—
355	#334	—	83	1	no	—
356	#334	—	83	1	no	—
357	Q₈⋊C₈	—	83	1	no	—
358	Q₈⋊C₈	—	83	1	no	—
359	D₄⋊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	—	83	1	no	—
365	#322	—	83	1	no	—
366	#322	—	83	1	no	—
367	#322	—	83	1	no	—
368	C₈²	—	83	1	no	—
369	C₂×#41	—	2	1	no	—
370	C₂×#41	—	83	1	no	—
371	C₂×SD₁₆	—	83	1	no	—
372	C₂×SD₁₆	—	83	1	no	—
373	C₂×D₈	—	83	1	no	—
374	C₂×D₈	—	83	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	—	2	1	no	—
379	C₂²×C₈	—	166	1	no	—
380	C₂²×C₈	—	166	1	no	—
381	C₂²×C₈	—	166	1	no	—
382	C₄⋊Q₈	C₄×D₈₃	1	1	yes	characteristic
383	#127	C₄×D₈₃	1	1	yes	characteristic
384	#124	—	2	1	no	—
385	#121	—	2	1	no	—
386	#121	C₄×D₈₃	1	1	yes	characteristic
387	#121	C₄×D₈₃	1	1	yes	characteristic
388	C₄×Q₈	—	83	1	no	—
389	C₄×Q₈	—	83	1	no	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	83	1	no	—
392	C₄×D₄	—	83	1	no	—
393	C₄×D₄	—	166	1	no	—
394	C₄×D₄	—	166	1	no	—
395	C₄×D₄	C₂²×D₈₃	1	1	yes	characteristic
396	C₄×D₄	C₂²×D₈₃	1	1	yes	characteristic
397	#117	—	83	1	no	—
398	#117	—	166	1	no	—
399	C₂×C₄²	—	166	1	no	—
400	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
401	#107	—	83	1	no	—
402	#107	—	83	1	no	—
403	#106	—	83	1	no	—
404	#106	—	83	1	no	—
405	C₄⋊C₈	—	83	1	no	—
406	C₄⋊C₈	—	83	1	no	—
407	C₄⋊C₈	—	83	1	no	—
408	C₄⋊C₈	—	83	1	no	—
409	C₄⋊C₈	—	166	1	no	—
410	C₄⋊C₈	—	166	1	no	—
411	C₄⋊C₈	—	166	1	no	—
412	C₄⋊C₈	—	166	1	no	—
413	C₄⋊C₈	C₂²⋊D₈₃	1	1	yes	characteristic
414	C₄⋊C₈	C₂²⋊D₈₃	1	1	yes	characteristic
415	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
416	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
417	#103	—	83	1	no	—
418	#103	—	83	1	no	—
419	#102	—	83	1	no	—
420	#102	—	83	1	no	—
421	#102	—	83	1	no	—
422	#102	—	83	1	no	—
423	#102	—	83	1	no	—
424	#102	—	83	1	no	—
425	C₂²⋊C₈	—	2	1	no	—
426	C₂²⋊C₈	—	2	1	no	—
427	C₂²⋊C₈	—	2	1	no	—
428	C₂²⋊C₈	—	2	1	no	—
429	C₂²⋊C₈	—	2	1	no	—
430	C₂²⋊C₈	—	83	1	no	—
431	C₂²⋊C₈	—	83	1	no	—
432	C₂²⋊C₈	—	166	1	no	—
433	C₂²⋊C₈	—	166	1	no	—
434	C₂²⋊C₈	—	166	1	no	—
435	C₂²⋊C₈	C₂²⋊D₈₃	1	1	yes	characteristic
436	C₂²⋊C₈	C₂²⋊D₈₃	1	1	yes	characteristic
437	#97	—	2	1	no	—
438	C₄×C₈	—	83	1	no	—
439	C₄×C₈	—	83	1	no	—
440	C₄×C₈	—	83	1	no	—
441	C₄×C₈	—	83	1	no	—
442	C₄×C₈	—	166	1	no	—
443	C₄×C₈	—	166	1	no	—
444	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
445	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
446	#41	—	8	1	no	—
447	#41	—	8	1	no	—
448	#41	—	166	2	no	—
449	#41	—	166	2	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	83	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	83	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	—	166	1	no	—
463	C₂²×C₄	—	166	1	no	—
464	C₂²×C₄	—	166	1	no	—
465	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
466	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
467	C₂²×C₄	#13050590	1	1	yes	characteristic
468	SD₁₆	—	166	2	no	—
469	SD₁₆	—	166	2	no	—
470	D₈	—	166	2	no	—
471	D₈	—	166	2	no	—
472	M₁₆	—	8	1	no	—
473	M₁₆	—	8	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	8	1	no	—
477	C₂×C₈	—	8	1	no	—
478	C₂×C₈	—	83	1	no	—
479	C₂×C₈	—	83	1	no	—
480	C₂×C₈	—	83	1	no	—
481	C₂×C₈	—	83	1	no	—
482	C₂×C₈	—	664	1	no	—
483	C₂×C₈	—	664	1	no	—
484	C₂×C₈	—	664	1	no	—
485	C₂×C₈	—	166	1	no	—
486	C₂×C₈	—	166	1	no	—
487	C₂×C₈	—	166	1	no	—
488	C₂×C₈	—	166	1	no	—
489	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
490	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
491	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
492	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	83	1	no	—
495	C₄⋊C₄	—	83	1	no	—
496	C₄⋊C₄	—	166	1	no	—
497	C₄⋊C₄	—	166	1	no	—
498	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
499	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	166	1	no	—
505	C₂²⋊C₄	—	166	1	no	—
506	C₂²⋊C₄	—	166	1	no	—
507	C₄²	—	166	1	no	—
508	C₄²	—	166	1	no	—
509	C₄²	—	166	1	no	—
510	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
511	C₄²	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
512	C₄²	#13050590	1	1	yes	characteristic
513	C₄²	C₂³×D₈₃	1	1	yes	characteristic
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	166	1	no	—
517	C₂³	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
518	Q₈	—	8	1	no	—
519	Q₈	—	83	2	no	—
520	Q₈	—	166	1	no	—
521	D₄	—	2	1	no	—
522	D₄	—	2	1	no	—
523	D₄	—	2	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	8	1	no	—
526	D₄	—	8	1	no	—
527	D₄	—	8	1	no	—
528	D₄	—	8	1	no	—
529	D₄	—	83	2	no	—
530	D₄	—	166	4	no	—
531	D₄	—	166	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	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	—	4	1	no	—
543	C₂×C₄	—	332	1	no	—
544	C₂×C₄	—	332	1	no	—
545	C₂×C₄	—	664	1	no	—
546	C₂×C₄	—	166	4	no	—
547	C₂×C₄	—	166	1	no	—
548	C₂×C₄	—	166	1	no	—
549	C₂×C₄	—	166	1	no	—
550	C₂×C₄	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
551	C₂×C₄	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
552	C₂×C₄	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
553	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
554	C₂×C₄	C₂²×C₂²⋊D₈₃	1	1	yes	characteristic
555	C₂×C₄	C₂×#13050590	1	1	yes	characteristic
556	C₈	—	2	1	no	—
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	4	1	no	—
562	C₈	—	332	1	no	—
563	C₈	—	332	1	no	—
564	C₈	—	332	1	no	—
565	C₈	—	332	1	no	—
566	C₈	—	166	1	no	—
567	C₈	—	166	1	no	—
568	C₈	—	166	1	no	—
569	C₈	—	166	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	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	—	4	1	no	—
579	C₂²	—	332	1	no	—
580	C₂²	—	332	1	no	—
581	C₂²	—	166	2	no	—
582	C₂²	C₂×C₄×C₂²⋊D₈₃	1	1	yes	characteristic
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	332	1	no	—
590	C₄	—	332	1	no	—
591	C₄	—	166	2	no	—
592	C₄	#131×D₈₃	1	1	yes	characteristic
593	C₄	#131×D₈₃	1	1	yes	characteristic
594	C₄	#19128504	1	1	yes	characteristic
595	C₄	#19128512	1	1	yes	characteristic
596	C₂	—	4	1	no	—
597	C₂	—	8	1	no	—
598	C₂	—	8	1	no	—
599	C₂	—	332	2	no	—
600	C₂	#24916155	1	1	yes	characteristic
601	C₂	#24916295	1	1	yes	characteristic
602	C₂	#24916378	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₈₃
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₄²	C₂³×D₈₃
Fitting	C₈₃×#2981	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	#24917517	C₂
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	#2981	D₈₃
hypocenter	C₈₃	#17920
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2981

Complements

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

N	H ≅ G/N	type
2. #24916571	C₂	semidirect
3. #24906339	C₂	semidirect
4. #24906325	C₂	semidirect
5. #24906304	C₂	semidirect
6. #24906290	C₂	semidirect
7. #24906285	C₂	semidirect
8. #24906275	C₂	semidirect
9. C₈×#13050578	C₂	semidirect
10. C₈×#13050575	C₂	semidirect
11. #24906249	C₂	semidirect
12. #24905895	C₂	semidirect
13. #24905862	C₂	semidirect
14. #24905763	C₂	semidirect
15. C₈₃×#2981	C₂	semidirect
304. #2981	D₈₃	semidirect
317. C₈₃	#17920	semidirect

Maximal subgroups

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

subgroup	index
#24917517	2
#24916571	2
#24906339	2
#24906325	2
#24906304	2
#24906290	2
#24906285	2
#24906275	2
C₈×#13050578	2
C₈×#13050575	2
#24906249	2
#24905895	2
#24905862	2
#24905763	2
C₈₃×#2981	2
#17920	83