Subgroups — #35375528

Order 21248.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24917545	C₂	1	1	yes	maximal, characteristic
2	#24916461	C₂	1	1	yes	maximal, characteristic
3	#24916414	C₂	1	1	yes	maximal, characteristic, complemented
4	#24906371	C₂	1	1	yes	maximal, characteristic, complemented
5	#24906352	C₂	1	1	yes	maximal, characteristic, complemented
6	#24906333	C₂	1	1	yes	maximal, characteristic, complemented
7	#24906319	C₂	1	1	yes	maximal, characteristic, complemented
8	#24906312	C₂	1	1	yes	maximal, characteristic, complemented
9	#24906305	C₂	1	1	yes	maximal, characteristic, complemented
10	#24906274	C₂	1	1	yes	maximal, characteristic, complemented
11	#24906269	C₂	1	1	yes	maximal, characteristic, complemented
12	#24905926	C₂	1	1	yes	maximal, characteristic
13	#24905857	C₂	1	1	yes	maximal, characteristic, complemented
14	#24905758	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#1574	C₂	1	1	yes	maximal, characteristic, complemented
16	#19128235	C₂²	1	1	yes	characteristic
17	C₂×C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
18	#19128032	C₄	1	1	yes	characteristic
19	#19128015	C₄	1	1	yes	characteristic
20	#19128009	C₄	1	1	yes	characteristic
21	#19128009	C₄	1	1	yes	characteristic
22	#19127924	C₄	1	1	yes	characteristic
23	#19127924	C₄	1	1	yes	characteristic
24	#19127859	C₄	1	1	yes	characteristic
25	#19127842	C₄	1	1	yes	characteristic
26	#19127830	—	2	1	no	—
27	#19127830	—	2	1	no	—
28	#19127828	C₂²	1	1	yes	characteristic
29	#19127828	C₂²	1	1	yes	characteristic
30	#19127828	C₂²	1	1	yes	characteristic
31	#19127825	C₂²	1	1	yes	characteristic
32	#19127825	C₂²	1	1	yes	characteristic
33	#19127825	C₂²	1	1	yes	characteristic
34	C₄×Dic₃₃₂	C₂²	1	1	yes	characteristic
35	C₄×Dic₃₃₂	C₂²	1	1	yes	characteristic
36	C₄×#13050579	C₂²	1	1	yes	characteristic
37	C₄×#13050579	C₂²	1	1	yes	characteristic
38	#19127778	C₂²	1	1	yes	characteristic
39	#19127776	—	2	1	no	—
40	#19127775	—	2	1	no	—
41	#19127766	C₂²	1	1	yes	characteristic
42	#19127760	—	2	1	no	—
43	#19127754	C₂²	1	1	yes	characteristic
44	#19127724	—	2	1	no	—
45	#19127655	—	2	1	no	—
46	C₄×#13050574	C₂²	1	1	yes	characteristic
47	M₁₆×Dic₈₃	—	2	1	no	—
48	#19127431	C₂²	1	1	yes	characteristic
49	#19127431	C₂²	1	1	yes	characteristic
50	#19127431	C₂²	1	1	yes	characteristic
51	#19127431	C₂²	1	1	yes	characteristic
52	#19127431	C₂²	1	1	yes	characteristic
53	#19127431	C₂²	1	1	yes	characteristic
54	#19127428	C₂²	1	1	yes	characteristic
55	#19127428	C₂²	1	1	yes	characteristic
56	#19127423	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	#431×C₈₃	C₂²	1	1	yes	characteristic
61	#431×C₈₃	C₂²	1	1	yes	characteristic
62	#423×C₈₃	C₂²	1	1	yes	characteristic
63	#335×C₈₃	C₂²	1	1	yes	characteristic
64	#335×C₈₃	C₂²	1	1	yes	characteristic
65	#334×C₈₃	C₂²	1	1	yes	characteristic
66	#334×C₈₃	C₂²	1	1	yes	characteristic
67	C₂²×Dic₁₆₆	C₂×C₄	1	1	yes	characteristic
68	C₂×Dic₃₃₂	C₂×C₄	1	1	yes	characteristic
69	C₂×Dic₃₃₂	C₂×C₄	1	1	yes	characteristic
70	C₂×#13050579	C₂×C₄	1	1	yes	characteristic
71	C₂×#13050579	C₂×C₄	1	1	yes	characteristic
72	C₂×#13050574	D₄	1	1	yes	characteristic
73	C₂×#13050574	D₄	1	1	yes	characteristic
74	C₂×#13050573	—	2	1	no	—
75	C₂×C₈×D₈₃	—	2	1	no	—
76	#14581786	—	2	1	no	—
77	#14581784	C₂×C₄	1	1	yes	characteristic
78	#14581780	C₂×C₄	1	1	yes	characteristic
79	#14581775	—	2	1	no	—
80	#14581771	C₂×C₄	1	1	yes	characteristic
81	#14581766	C₂×C₄	1	1	yes	characteristic
82	C₄×Dic₁₆₆	—	2	1	no	—
83	C₄×Dic₁₆₆	—	2	1	no	—
84	C₄×Dic₁₆₆	C₂×C₄	1	1	yes	characteristic
85	C₄×Dic₁₆₆	C₂×C₄	1	1	yes	characteristic
86	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
87	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
88	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
89	C₄×D₃₃₂	C₂³	1	1	yes	characteristic
90	C₄×C₂²⋊D₈₃	—	2	1	no	—
91	#14581749	—	2	1	no	—
92	C₂×C₄⋊Dic₈₃	C₂×C₄	1	1	yes	characteristic
93	C₂×Dic₈₃⋊C₄	—	2	1	no	—
94	C₂×C₄×Dic₈₃	—	2	1	no	—
95	#14581726	C₂×C₄	1	1	yes	characteristic
96	#14581726	C₂×C₄	1	1	yes	characteristic
97	#14581724	C₂×C₄	1	1	yes	characteristic
98	#14581724	C₂×C₄	1	1	yes	characteristic
99	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
100	Dic₈₃⋊C₈	—	2	1	no	—
101	Dic₈₃⋊C₈	—	2	1	no	—
102	Dic₈₃⋊C₈	—	2	1	no	—
103	Dic₈₃⋊C₈	—	2	1	no	—
104	Dic₈₃⋊C₈	—	2	1	no	—
105	Dic₈₃⋊C₈	—	2	1	no	—
106	#14581717	C₂×C₄	1	1	yes	characteristic
107	#14581717	C₂×C₄	1	1	yes	characteristic
108	#14581717	C₂×C₄	1	1	yes	characteristic
109	#14581717	C₂×C₄	1	1	yes	characteristic
110	#14581717	C₂×C₄	1	1	yes	characteristic
111	#14581717	C₂×C₄	1	1	yes	characteristic
112	#14581714	C₂×C₄	1	1	yes	characteristic
113	#14581714	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
115	(C₂×D₈₃)⋊C₈	—	2	1	no	—
116	(C₂×D₈₃)⋊C₈	—	2	1	no	—
117	#14581703	D₄	1	1	yes	characteristic
118	#14581703	D₄	1	1	yes	characteristic
119	#14581702	—	2	1	no	—
120	#14581702	—	2	1	no	—
121	#14581702	—	2	1	no	—
122	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
123	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
124	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
125	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
126	C₈×Dic₈₃	—	2	1	no	—
127	C₈×Dic₈₃	—	2	1	no	—
128	C₈×Dic₈₃	—	2	1	no	—
129	C₂×M₁₆×C₈₃	—	2	1	no	—
130	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
131	C₄⋊C₈×C₈₃	—	2	1	no	—
132	C₄⋊C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
133	C₄⋊C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
134	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
135	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
138	C₂²⋊C₈×C₈₃	—	2	1	no	—
139	C₂²⋊C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
141	C₄×C₈×C₈₃	—	2	1	no	—
142	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
144	C₂×Dic₁₆₆	—	2	2	no	—
145	C₂×Dic₁₆₆	—	2	1	no	—
146	C₂×Dic₁₆₆	—	4	1	no	—
147	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
148	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
149	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
150	C₂×D₃₃₂	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₂²⋊D₈₃	—	2	1	no	—
152	C₂²×Dic₈₃	—	2	1	no	—
153	C₂²×Dic₈₃	—	2	1	no	—
154	C₂×C₄×D₈₃	—	2	1	no	—
155	Dic₃₃₂	—	2	2	no	—
156	Dic₃₃₂	—	4	1	no	—
157	#13050579	—	2	2	no	—
158	#13050579	—	4	1	no	—
159	#13050574	—	2	2	no	—
160	#13050574	—	4	1	no	—
161	#13050573	—	4	2	no	—
162	C₂×C₈₃⋊C₈	—	2	1	no	—
163	C₂×C₈₃⋊C₈	—	2	1	no	—
164	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
165	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
167	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
168	C₈×D₈₃	—	4	2	no	—
169	C₄⋊Dic₈₃	—	2	1	no	—
170	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
171	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
172	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
173	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
174	Dic₈₃⋊C₄	—	2	1	no	—
175	Dic₈₃⋊C₄	—	2	1	no	—
176	Dic₈₃⋊C₄	—	2	1	no	—
177	Dic₈₃⋊C₄	—	2	1	no	—
178	Dic₈₃⋊C₄	—	2	1	no	—
179	Dic₈₃⋊C₄	—	2	1	no	—
180	Dic₈₃⋊C₄	—	2	1	no	—
181	Dic₈₃⋊C₄	—	2	1	no	—
182	C₂²⋊Dic₈₃	—	2	1	no	—
183	(C₂×D₈₃)⋊C₄	—	2	1	no	—
184	(C₂×D₈₃)⋊C₄	—	2	1	no	—
185	(C₂×D₈₃)⋊C₄	—	2	1	no	—
186	(C₂×D₈₃)⋊C₄	—	2	1	no	—
187	C₄×Dic₈₃	—	2	1	no	—
188	C₄×Dic₈₃	—	2	1	no	—
189	C₄×Dic₈₃	—	2	1	no	—
190	C₄×Dic₈₃	—	2	1	no	—
191	C₄×Dic₈₃	—	2	1	no	—
192	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
195	M₁₆×C₈₃	—	4	2	no	—
196	C₂×C₈×C₈₃	—	2	1	no	—
197	C₂×C₈×C₈₃	—	2	1	no	—
198	C₂×C₈×C₈₃	—	2	1	no	—
199	C₂×C₈×C₈₃	—	2	1	no	—
200	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
204	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
205	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₈₃	#41	1	1	yes	characteristic
207	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
208	C₂³×C₈₃	C₄×D₄	1	1	yes	characteristic
209	C₂²×D₈₃	—	2	1	no	—
210	C₂×C₄×C₈₃	—	2	1	no	—
211	C₂×C₄×C₈₃	—	2	1	no	—
212	C₂×C₄×C₈₃	—	2	1	no	—
213	C₂×C₄×C₈₃	—	2	1	no	—
214	C₂×C₄×C₈₃	—	4	1	no	—
215	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
221	C₂²⋊D₈₃	—	8	1	no	—
222	C₂×Dic₈₃	—	2	1	no	—
223	C₂×Dic₈₃	—	2	1	no	—
224	C₂×Dic₈₃	—	2	1	no	—
225	C₂×Dic₈₃	—	2	1	no	—
226	C₂×Dic₈₃	—	2	1	no	—
227	C₂×Dic₈₃	—	2	1	no	—
228	C₂×Dic₈₃	—	2	1	no	—
229	C₂×Dic₈₃	—	4	2	no	—
230	C₂×Dic₈₃	—	8	1	no	—
231	D₃₃₂	—	2	1	no	—
232	D₃₃₂	—	2	1	no	—
233	C₄×D₈₃	—	4	1	no	—
234	C₄×D₈₃	—	4	1	no	—
235	Dic₁₆₆	—	2	1	no	—
236	Dic₁₆₆	—	2	1	no	—
237	Dic₁₆₆	—	2	1	no	—
238	Dic₁₆₆	—	2	1	no	—
239	Dic₁₆₆	—	2	1	no	—
240	Dic₁₆₆	—	4	2	no	—
241	Dic₁₆₆	#131	1	2	yes	—
242	C₈×C₈₃	—	2	1	no	—
243	C₈×C₈₃	—	2	1	no	—
244	C₈×C₈₃	—	2	1	no	—
245	C₈×C₈₃	—	2	1	no	—
246	C₈×C₈₃	—	4	1	no	—
247	C₈×C₈₃	—	4	1	no	—
248	C₈×C₈₃	—	4	1	no	—
249	C₈×C₈₃	—	4	1	no	—
250	C₈₃⋊C₈	—	2	1	no	—
251	C₈₃⋊C₈	—	2	1	no	—
252	C₈₃⋊C₈	—	2	1	no	—
253	C₈₃⋊C₈	—	4	1	no	—
254	C₈₃⋊C₈	—	4	1	no	—
255	C₈₃⋊C₈	#137	1	2	yes	—
256	C₂²×C₈₃	—	2	1	no	—
257	C₂²×C₈₃	—	2	1	no	—
258	C₂²×C₈₃	—	2	1	no	—
259	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
260	C₂×D₈₃	—	4	1	no	—
261	C₂×D₈₃	—	4	1	no	—
262	C₂×D₈₃	—	4	1	no	—
263	C₄×C₈₃	—	2	1	no	—
264	C₄×C₈₃	—	2	1	no	—
265	C₄×C₈₃	—	2	1	no	—
266	C₄×C₈₃	—	2	1	no	—
267	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
268	C₄×C₈₃	#568	1	1	yes	characteristic
269	C₄×C₈₃	C₂×#137	1	1	yes	characteristic
270	C₄×C₈₃	#575	1	1	yes	characteristic
271	Dic₈₃	—	2	2	no	—
272	Dic₈₃	—	4	1	no	—
273	Dic₈₃	—	4	1	no	—
274	Dic₈₃	—	4	1	no	—
275	Dic₈₃	—	4	1	no	—
276	Dic₈₃	—	4	1	no	—
277	Dic₈₃	—	4	1	no	—
278	#18012	—	83	1	no	maximal, Sylow
279	C₂×C₈₃	—	4	1	no	—
280	C₂×C₈₃	#2933	1	1	yes	characteristic
281	C₂×C₈₃	C₄×#137	1	1	yes	characteristic
282	C₂×C₈₃	#2957	1	1	yes	characteristic
283	D₈₃	—	8	1	no	—
284	#3108	—	83	1	no	—
285	#2969	—	83	1	no	—
286	Q₈×M₁₆	—	83	1	no	—
287	#1593	—	83	1	no	—
288	#1590	—	83	1	no	—
289	#1587	—	83	1	no	—
290	#1585	—	83	1	no	—
291	#1584	—	83	1	no	—
292	#1583	—	83	1	no	—
293	SD₁₆⋊C₈	—	83	1	no	—
294	C₈×Q₁₆	—	83	1	no	—
295	#1574	D₈₃	1	1	yes	characteristic, complemented
296	#1495	—	83	1	no	—
297	#1479	—	83	1	no	—
298	#1453	—	83	1	no	—
299	C₈₃	#18012	1	1	yes	characteristic, complemented, Sylow
300	#529	—	83	1	no	—
301	C₂×C₄×Q₈	—	83	1	no	—
302	#483	—	83	1	no	—
303	#480	—	83	1	no	—
304	#479	—	83	1	no	—
305	#479	—	83	1	no	—
306	#464	—	83	1	no	—
307	#464	—	83	1	no	—
308	#451	—	83	1	no	—
309	#448	—	83	1	no	—
310	#446	—	83	1	no	—
311	#446	—	83	1	no	—
312	#446	—	83	1	no	—
313	#446	—	166	1	no	—
314	#446	—	166	1	no	—
315	C₈×Q₈	—	83	1	no	—
316	C₈×Q₈	—	83	1	no	—
317	C₈×Q₈	—	83	1	no	—
318	C₄×Q₁₆	—	83	1	no	—
319	C₄×Q₁₆	—	83	1	no	—
320	C₄×SD₁₆	—	83	1	no	—
321	C₄×SD₁₆	—	83	1	no	—
322	#436	—	83	1	no	—
323	#436	—	166	1	no	—
324	#435	—	166	1	no	—
325	C₈×D₄	—	83	1	no	—
326	#433	—	166	1	no	—
327	#431	—	83	1	no	—
328	#431	C₂×D₈₃	1	1	yes	characteristic
329	#431	C₂×D₈₃	1	1	yes	characteristic
330	#423	—	166	1	no	—
331	#423	C₂×D₈₃	1	1	yes	characteristic
332	#405	—	166	1	no	—
333	C₄×M₁₆	—	83	1	no	—
334	C₄×M₁₆	—	166	1	no	—
335	#335	C₂×D₈₃	1	1	yes	characteristic
336	#335	C₂×D₈₃	1	1	yes	characteristic
337	#334	C₂×D₈₃	1	1	yes	characteristic
338	#334	C₂×D₈₃	1	1	yes	characteristic
339	Q₈⋊C₈	—	83	1	no	—
340	Q₈⋊C₈	—	83	1	no	—
341	Q₈⋊C₈	—	83	1	no	—
342	Q₈⋊C₈	—	83	1	no	—
343	Q₈⋊C₈	—	83	1	no	—
344	Q₈⋊C₈	—	83	1	no	—
345	D₄⋊C₈	—	83	1	no	—
346	D₄⋊C₈	—	83	1	no	—
347	#322	—	83	1	no	—
348	#322	—	83	1	no	—
349	#322	—	83	1	no	—
350	C₈²	—	83	1	no	—
351	C₂²×Q₈	—	83	1	no	—
352	C₂×Q₁₆	—	83	1	no	—
353	C₂×Q₁₆	—	83	1	no	—
354	C₂×SD₁₆	—	83	1	no	—
355	C₂×SD₁₆	—	83	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	83	1	no	—
358	C₂×M₁₆	—	83	1	no	—
359	C₂×M₁₆	—	166	1	no	—
360	C₂²×C₈	—	166	1	no	—
361	#126	—	166	1	no	—
362	#125	—	83	1	no	—
363	#124	—	83	1	no	—
364	#123	—	166	1	no	—
365	C₂²⋊Q₈	—	83	1	no	—
366	#121	—	83	1	no	—
367	C₄×Q₈	—	83	1	no	—
368	C₄×Q₈	—	83	1	no	—
369	C₄×Q₈	—	83	1	no	—
370	C₄×Q₈	—	83	1	no	—
371	C₄×Q₈	—	83	1	no	—
372	C₄×Q₈	—	166	1	no	—
373	C₄×Q₈	—	166	1	no	—
374	C₄×D₄	—	83	1	no	—
375	C₄×D₄	—	166	1	no	—
376	#117	—	166	1	no	—
377	C₂×C₄⋊C₄	—	83	1	no	—
378	C₂×C₄⋊C₄	—	166	1	no	—
379	C₂×C₄²	—	166	1	no	—
380	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
381	#107	—	83	1	no	—
382	#107	—	83	1	no	—
383	#106	—	83	1	no	—
384	#106	—	83	1	no	—
385	C₄⋊C₈	—	2	1	no	—
386	C₄⋊C₈	—	166	1	no	—
387	C₄⋊C₈	—	166	1	no	—
388	C₄⋊C₈	—	166	1	no	—
389	C₄⋊C₈	—	166	1	no	—
390	C₄⋊C₈	—	166	1	no	—
391	C₄⋊C₈	—	166	1	no	—
392	C₄⋊C₈	—	166	1	no	—
393	C₄⋊C₈	C₄×D₈₃	1	1	yes	characteristic
394	C₄⋊C₈	C₄×D₈₃	1	1	yes	characteristic
395	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
396	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
397	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
398	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
399	#103	—	83	1	no	—
400	#103	—	83	1	no	—
401	#103	—	83	1	no	—
402	#103	—	83	1	no	—
403	#103	—	83	1	no	—
404	#103	—	83	1	no	—
405	#102	—	83	1	no	—
406	#102	—	83	1	no	—
407	C₂²⋊C₈	—	2	1	no	—
408	C₂²⋊C₈	—	166	1	no	—
409	C₂²⋊C₈	—	166	1	no	—
410	C₂²⋊C₈	—	166	1	no	—
411	C₂²⋊C₈	C₄×D₈₃	1	1	yes	characteristic
412	C₂²⋊C₈	C₄×D₈₃	1	1	yes	characteristic
413	#97	—	83	1	no	—
414	#97	—	83	1	no	—
415	#97	—	166	1	no	—
416	#97	—	166	1	no	—
417	#97	—	166	1	no	—
418	C₄×C₈	—	2	1	no	—
419	C₄×C₈	—	83	1	no	—
420	C₄×C₈	—	83	1	no	—
421	C₄×C₈	—	83	1	no	—
422	C₄×C₈	—	83	1	no	—
423	C₄×C₈	—	166	1	no	—
424	C₄×C₈	—	166	1	no	—
425	C₄×C₈	—	166	1	no	—
426	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
427	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
428	C₂×Q₈	—	332	1	no	—
429	C₂×Q₈	—	83	1	no	—
430	C₂×Q₈	—	83	1	no	—
431	C₂×Q₈	—	83	1	no	—
432	C₂×Q₈	—	166	2	no	—
433	C₂×Q₈	—	166	1	no	—
434	C₂×D₄	—	83	1	no	—
435	C₂×D₄	—	166	1	no	—
436	C₂²×C₄	—	166	1	no	—
437	C₂²×C₄	—	166	1	no	—
438	C₂²×C₄	—	166	1	no	—
439	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
440	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
441	C₂²×C₄	#13050591	1	1	yes	characteristic
442	Q₁₆	—	332	1	no	—
443	Q₁₆	—	166	2	no	—
444	SD₁₆	—	332	1	no	—
445	SD₁₆	—	166	2	no	—
446	M₁₆	—	4	2	no	—
447	M₁₆	—	332	2	no	—
448	M₁₆	—	332	1	no	—
449	M₁₆	—	166	2	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	332	2	no	—
455	C₂×C₈	—	83	1	no	—
456	C₂×C₈	—	83	1	no	—
457	C₂×C₈	—	83	1	no	—
458	C₂×C₈	—	83	1	no	—
459	C₂×C₈	—	166	1	no	—
460	C₂×C₈	—	166	1	no	—
461	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
462	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
463	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
464	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
465	C₄⋊C₄	—	83	1	no	—
466	C₄⋊C₄	—	83	1	no	—
467	C₄⋊C₄	—	83	1	no	—
468	C₄⋊C₄	—	83	1	no	—
469	C₄⋊C₄	—	166	1	no	—
470	C₄⋊C₄	—	166	1	no	—
471	C₄⋊C₄	—	166	1	no	—
472	C₄⋊C₄	—	166	1	no	—
473	C₄⋊C₄	—	166	1	no	—
474	C₄⋊C₄	—	166	1	no	—
475	C₄⋊C₄	—	166	1	no	—
476	C₄⋊C₄	—	166	1	no	—
477	C₄⋊C₄	—	166	1	no	—
478	C₂²⋊C₄	—	166	1	no	—
479	C₂²⋊C₄	—	166	1	no	—
480	C₂²⋊C₄	—	166	1	no	—
481	C₂²⋊C₄	—	166	1	no	—
482	C₂²⋊C₄	—	166	1	no	—
483	C₄²	—	166	1	no	—
484	C₄²	—	166	1	no	—
485	C₄²	—	166	1	no	—
486	C₄²	—	166	1	no	—
487	C₄²	—	166	1	no	—
488	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
489	C₄²	D₄×D₈₃	1	1	yes	characteristic
490	C₄²	#13050591	1	1	yes	characteristic
491	C₄²	C₂³×D₈₃	1	1	yes	characteristic
492	C₂³	—	166	1	no	—
493	C₂³	#14581754	1	1	yes	characteristic
494	Q₈	—	332	2	no	—
495	Q₈	—	83	2	no	—
496	Q₈	—	166	1	no	—
497	Q₈	—	166	1	no	—
498	Q₈	—	166	1	no	—
499	Q₈	—	166	1	no	—
500	Q₈	—	166	1	no	—
501	D₄	—	664	1	no	—
502	D₄	—	166	1	no	—
503	D₄	—	166	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	332	2	no	—
510	C₂×C₄	—	332	1	no	—
511	C₂×C₄	—	332	1	no	—
512	C₂×C₄	—	664	1	no	—
513	C₂×C₄	—	166	1	no	—
514	C₂×C₄	—	166	1	no	—
515	C₂×C₄	—	166	1	no	—
516	C₂×C₄	—	166	1	no	—
517	C₂×C₄	—	166	1	no	—
518	C₂×C₄	—	166	1	no	—
519	C₂×C₄	—	166	1	no	—
520	C₂×C₄	#14581754	1	1	yes	characteristic
521	C₂×C₄	#14581754	1	1	yes	characteristic
522	C₂×C₄	#14581754	1	1	yes	characteristic
523	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
524	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
525	C₂×C₄	C₂×#13050591	1	1	yes	characteristic
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	2	1	no	—
529	C₈	—	2	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	4	1	no	—
532	C₈	—	4	1	no	—
533	C₈	—	4	1	no	—
534	C₈	—	332	1	no	—
535	C₈	—	332	1	no	—
536	C₈	—	83	2	no	—
537	C₈	—	166	1	no	—
538	C₈	—	166	1	no	—
539	C₈	—	166	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	332	1	no	—
544	C₂²	—	332	1	no	—
545	C₂²	—	332	1	no	—
546	C₂²	C₂×#14581754	1	1	yes	characteristic
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	332	1	no	—
552	C₄	—	332	1	no	—
553	C₄	—	332	1	no	—
554	C₄	—	332	1	no	—
555	C₄	—	332	1	no	—
556	C₄	—	332	1	no	—
557	C₄	—	166	2	no	—
558	C₄	#131×D₈₃	1	1	yes	characteristic
559	C₄	#19128466	1	1	yes	characteristic
560	C₄	#137×D₈₃	1	1	yes	characteristic
561	C₄	#19128497	1	1	yes	characteristic
562	C₂	—	4	1	no	—
563	C₂	—	664	1	no	—
564	C₂	#24916187	1	1	yes	characteristic
565	C₂	#24916281	1	1	yes	characteristic
566	C₂	#24916379	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×#1574	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	#14581766	C₂×C₄
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	#1574	D₈₃
hypocenter	C₈₃	#18012
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1574

Complements

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

N	H ≅ G/N	type
3. #24916414	C₂	semidirect
4. #24906371	C₂	semidirect
5. #24906352	C₂	semidirect
6. #24906333	C₂	semidirect
7. #24906319	C₂	semidirect
8. #24906312	C₂	semidirect
9. #24906305	C₂	semidirect
10. #24906274	C₂	semidirect
11. #24906269	C₂	semidirect
13. #24905857	C₂	semidirect
14. #24905758	C₂	semidirect
15. C₈₃×#1574	C₂	semidirect
295. #1574	D₈₃	semidirect
299. C₈₃	#18012	semidirect

Maximal subgroups

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

subgroup	index
#24917545	2
#24916461	2
#24916414	2
#24906371	2
#24906352	2
#24906333	2
#24906319	2
#24906312	2
#24906305	2
#24906274	2
#24906269	2
#24905926	2
#24905857	2
#24905758	2
C₈₃×#1574	2
#18012	83