Subgroups — #35375027

Order 21248.

622 conjugacy classes of subgroups.

The subgroup lattice has 602 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	#24916613	C₂	1	1	yes	maximal, characteristic, complemented
3	#24916537	C₂	1	1	yes	maximal, characteristic, complemented
4	#24906377	C₂	1	1	yes	maximal, characteristic, complemented
5	#24906364	C₂	1	1	yes	maximal, characteristic, complemented
6	#24906356	C₂	1	1	yes	maximal, characteristic, complemented
7	#24906345	C₂	1	1	yes	maximal, characteristic, complemented
8	#24906285	C₂	1	1	yes	maximal, characteristic, complemented
9	#24906275	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#13050579	C₂	1	1	yes	maximal, characteristic, complemented
11	#24906229	C₂	1	1	yes	maximal, characteristic, complemented
12	#24905920	C₂	1	1	yes	maximal, characteristic, complemented
13	#24905912	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#13050573	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×D₈×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
16	#19128248	C₂²	1	1	yes	characteristic
17	#19128233	C₂²	1	1	yes	characteristic
18	#19128109	C₄	1	1	yes	characteristic
19	#19128089	C₄	1	1	yes	characteristic
20	#19128064	C₄	1	1	yes	characteristic
21	#19128059	C₄	1	1	yes	characteristic
22	#19127953	C₄	1	1	yes	characteristic
23	#19127951	C₄	1	1	yes	characteristic
24	#19127948	C₄	1	1	yes	characteristic
25	#19127946	C₄	1	1	yes	characteristic
26	#19127828	C₂²	1	1	yes	characteristic
27	C₈×Dic₁₆₆	C₂²	1	1	yes	characteristic
28	C₄×#13050579	C₂²	1	1	yes	characteristic
29	C₄×#13050578	C₂²	1	1	yes	characteristic
30	C₄×#13050575	C₂²	1	1	yes	characteristic
31	#19127779	C₂²	1	1	yes	characteristic
32	#19127779	C₂²	1	1	yes	characteristic
33	#19127778	C₂²	1	1	yes	characteristic
34	#19127776	—	2	1	no	—
35	#19127775	—	2	1	no	—
36	#19127772	—	2	1	no	—
37	#19127772	—	2	1	no	—
38	C₈×D₃₃₂	C₂²	1	1	yes	characteristic
39	#19127759	—	2	1	no	—
40	#19127757	C₂²	1	1	yes	characteristic
41	#19127752	C₂²	1	1	yes	characteristic
42	#19127727	—	2	1	no	—
43	#19127723	C₂²	1	1	yes	characteristic
44	#19127667	—	2	1	no	—
45	#19127666	—	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	C₈×D₄×C₈₃	C₂²	1	1	yes	characteristic
62	C₈×D₄×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	C₂×#13050574	—	2	1	no	—
72	C₂×#13050574	—	2	1	no	—
73	C₂×#13050573	—	2	1	no	—
74	C₂×#13050573	—	2	1	no	—
75	C₂×#13050573	C₂×C₄	1	1	yes	characteristic
76	C₂×#13050573	C₂×C₄	1	1	yes	characteristic
77	C₂×C₈×D₈₃	—	2	1	no	—
78	C₂×C₈×D₈₃	—	2	1	no	—
79	#14581791	C₂×C₄	1	1	yes	characteristic
80	#14581788	C₂×C₄	1	1	yes	characteristic
81	#14581785	—	2	1	no	—
82	#14581783	C₂×C₄	1	1	yes	characteristic
83	#14581779	C₂×C₄	1	1	yes	characteristic
84	#14581778	—	2	1	no	—
85	#14581774	—	2	1	no	—
86	#14581772	C₂×C₄	1	1	yes	characteristic
87	#14581767	C₂×C₄	1	1	yes	characteristic
88	#14581765	—	2	1	no	—
89	#14581763	C₂×C₄	1	1	yes	characteristic
90	#14581763	C₂×C₄	1	1	yes	characteristic
91	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
92	C₄×D₃₃₂	C₂³	1	1	yes	characteristic
93	C₄×C₂²⋊D₈₃	—	2	1	no	—
94	C₄×C₂²⋊D₈₃	—	2	1	no	—
95	#14581751	—	2	1	no	—
96	C₄²×D₈₃	C₂³	1	1	yes	characteristic
97	#14581725	C₂×C₄	1	1	yes	characteristic
98	#14581724	C₂×C₄	1	1	yes	characteristic
99	#14581723	C₂×C₄	1	1	yes	characteristic
100	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
101	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
102	Dic₈₃⋊C₈	—	2	1	no	—
103	Dic₈₃⋊C₈	—	2	1	no	—
104	Dic₈₃⋊C₈	—	2	1	no	—
105	Dic₈₃⋊C₈	D₄	1	1	yes	characteristic
106	Dic₈₃⋊C₈	D₄	1	1	yes	characteristic
107	#14581717	C₂×C₄	1	1	yes	characteristic
108	#14581715	C₂×C₄	1	1	yes	characteristic
109	#14581714	C₂×C₄	1	1	yes	characteristic
110	#14581713	C₂×C₄	1	1	yes	characteristic
111	#14581713	C₂×C₄	1	1	yes	characteristic
112	#14581712	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
114	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
115	(C₂×D₈₃)⋊C₈	—	2	1	no	—
116	(C₂×D₈₃)⋊C₈	—	2	1	no	—
117	(C₂×D₈₃)⋊C₈	—	2	1	no	—
118	(C₂×D₈₃)⋊C₈	D₄	1	1	yes	characteristic
119	(C₂×D₈₃)⋊C₈	D₄	1	1	yes	characteristic
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	—	2	1	no	—
129	C₂×D₈×C₈₃	C₂×C₄	1	1	yes	characteristic
130	C₂²×C₈×C₈₃	—	2	1	no	—
131	C₂²×C₈×C₈₃	—	2	1	no	—
132	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
133	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
134	#107×C₈₃	C₂×C₄	1	1	yes	characteristic
135	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
137	#102×C₈₃	C₂×C₄	1	1	yes	characteristic
138	#102×C₈₃	C₂×C₄	1	1	yes	characteristic
139	C₂²⋊C₈×C₈₃	—	2	1	no	—
140	C₂²⋊C₈×C₈₃	—	2	1	no	—
141	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
144	#13050590	—	8	1	no	—
145	#13050590	—	8	1	no	—
146	C₂×Dic₁₆₆	—	2	1	no	—
147	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₃₃₂	—	2	1	no	—
149	C₂×D₃₃₂	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₂²⋊D₈₃	—	2	1	no	—
151	C₂×C₂²⋊D₈₃	—	2	1	no	—
152	C₂×C₂²⋊D₈₃	—	2	1	no	—
153	C₂×C₂²⋊D₈₃	—	2	1	no	—
154	C₂×C₄×D₈₃	—	2	1	no	—
155	C₂×C₄×D₈₃	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₄×D₈₃	C₂×D₄	1	1	yes	characteristic
157	C₂×C₄×D₈₃	#41	1	1	yes	characteristic
158	#13050579	—	2	2	no	—
159	#13050578	—	2	2	no	—
160	#13050575	—	2	2	no	—
161	#13050574	—	8	1	no	—
162	#13050574	—	8	1	no	—
163	#13050573	—	2	2	no	—
164	#13050573	—	2	2	no	—
165	#13050573	—	8	1	no	—
166	#13050573	—	8	1	no	—
167	C₂×C₈₃⋊C₈	—	2	1	no	—
168	C₂×C₈₃⋊C₈	—	2	1	no	—
169	C₂×C₈₃⋊C₈	—	2	1	no	—
170	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
173	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
174	C₈×D₈₃	—	4	2	no	—
175	C₈×D₈₃	—	8	1	no	—
176	C₄⋊Dic₈₃	—	2	1	no	—
177	C₄⋊Dic₈₃	—	2	1	no	—
178	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
179	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
180	Dic₈₃⋊C₄	—	2	1	no	—
181	Dic₈₃⋊C₄	—	2	1	no	—
182	Dic₈₃⋊C₄	—	2	1	no	—
183	C₂²⋊Dic₈₃	—	2	1	no	—
184	C₂²⋊Dic₈₃	—	2	1	no	—
185	C₂²⋊Dic₈₃	—	2	1	no	—
186	C₂²⋊Dic₈₃	—	2	1	no	—
187	(C₂×D₈₃)⋊C₄	—	2	1	no	—
188	(C₂×D₈₃)⋊C₄	—	2	1	no	—
189	(C₂×D₈₃)⋊C₄	—	2	1	no	—
190	C₄×Dic₈₃	—	2	1	no	—
191	C₄×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
192	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
193	C₄×Dic₈₃	#41	1	1	yes	characteristic
194	C₂×D₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
195	C₂×D₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₈₃	—	2	1	no	—
197	C₂²×C₄×C₈₃	—	2	1	no	—
198	D₈×C₈₃	—	2	2	no	—
199	C₂×C₈×C₈₃	—	2	1	no	—
200	C₂×C₈×C₈₃	—	2	1	no	—
201	C₂×C₈×C₈₃	—	2	1	no	—
202	C₂×C₈×C₈₃	—	8	1	no	—
203	C₂×C₈×C₈₃	—	8	1	no	—
204	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
207	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
208	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
209	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
210	C₂²⋊C₄×C₈₃	—	2	1	no	—
211	C₂²⋊C₄×C₈₃	—	2	1	no	—
212	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
213	C₂³×C₈₃	—	2	1	no	—
214	C₂³×C₈₃	—	2	1	no	—
215	C₂²×D₈₃	—	2	1	no	—
216	C₂²×D₈₃	C₄×D₄	1	1	yes	characteristic
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	C₂×C₄×C₈₃	—	2	1	no	—
222	C₂×C₄×C₈₃	—	2	1	no	—
223	C₂×C₄×C₈₃	—	4	1	no	—
224	C₂×C₄×C₈₃	—	4	1	no	—
225	C₂×C₄×C₈₃	—	4	1	no	—
226	C₂×C₄×C₈₃	—	4	1	no	—
227	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
230	C₂²⋊D₈₃	—	8	1	no	—
231	C₂²⋊D₈₃	—	8	1	no	—
232	C₂²⋊D₈₃	—	8	1	no	—
233	C₂²⋊D₈₃	—	8	1	no	—
234	C₂×Dic₈₃	—	2	1	no	—
235	C₂×Dic₈₃	—	2	1	no	—
236	C₂×Dic₈₃	—	2	1	no	—
237	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
238	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
239	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
240	D₃₃₂	—	2	1	no	—
241	D₃₃₂	—	2	1	no	—
242	D₃₃₂	—	8	1	no	—
243	C₄×D₈₃	—	2	1	no	—
244	C₄×D₈₃	—	2	1	no	—
245	C₄×D₈₃	—	2	1	no	—
246	C₄×D₈₃	—	2	1	no	—
247	C₄×D₈₃	—	4	1	no	—
248	C₄×D₈₃	—	4	1	no	—
249	C₄×D₈₃	—	4	1	no	—
250	Dic₁₆₆	—	2	1	no	—
251	Dic₁₆₆	—	2	1	no	—
252	Dic₁₆₆	—	8	1	no	—
253	C₈×C₈₃	—	2	2	no	—
254	C₈×C₈₃	—	2	1	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	#131	1	2	yes	—
260	C₈₃⋊C₈	—	2	1	no	—
261	C₈₃⋊C₈	—	2	1	no	—
262	C₈₃⋊C₈	—	2	1	no	—
263	C₈₃⋊C₈	—	4	1	no	—
264	C₈₃⋊C₈	—	4	1	no	—
265	C₈₃⋊C₈	—	4	1	no	—
266	C₈₃⋊C₈	#131	1	2	yes	—
267	C₂²×C₈₃	—	4	1	no	—
268	C₂²×C₈₃	—	4	1	no	—
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	C₂×C₄×D₄	1	1	yes	characteristic
274	C₂×D₈₃	—	2	1	no	—
275	C₂×D₈₃	—	2	1	no	—
276	C₂×D₈₃	—	2	1	no	—
277	C₂×D₈₃	—	4	1	no	—
278	C₂×D₈₃	—	4	1	no	—
279	C₂×D₈₃	—	4	1	no	—
280	C₄×C₈₃	—	2	1	no	—
281	C₄×C₈₃	—	4	1	no	—
282	C₄×C₈₃	—	4	1	no	—
283	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
284	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
285	C₄×C₈₃	#576	1	1	yes	characteristic
286	C₄×C₈₃	#577	1	1	yes	characteristic
287	Dic₈₃	—	2	1	no	—
288	Dic₈₃	—	2	1	no	—
289	Dic₈₃	—	2	1	no	—
290	Dic₈₃	—	4	1	no	—
291	Dic₈₃	—	4	1	no	—
292	Dic₈₃	—	4	1	no	—
293	#17968	—	83	1	no	maximal, Sylow
294	C₂×C₈₃	—	8	1	no	—
295	C₂×C₈₃	—	8	1	no	—
296	C₂×C₈₃	#2931	1	1	yes	characteristic
297	C₂×C₈₃	#2946	1	1	yes	characteristic
298	C₂×C₈₃	#2956	1	1	yes	characteristic
299	D₈₃	—	4	1	no	—
300	D₈₃	—	8	1	no	—
301	#3171	—	83	1	no	—
302	#2993	—	83	1	no	—
303	#2981	—	83	1	no	—
304	#1594	—	83	1	no	—
305	#1592	—	83	1	no	—
306	#1590	—	83	1	no	—
307	#1589	—	83	1	no	—
308	#1580	—	83	1	no	—
309	SD₁₆⋊C₈	—	83	1	no	—
310	C₈×SD₁₆	—	83	1	no	—
311	C₈×D₈	D₈₃	1	1	yes	characteristic, complemented
312	#1569	—	83	1	no	—
313	#1494	—	83	1	no	—
314	#1492	—	83	1	no	—
315	C₈×M₁₆	—	83	1	no	—
316	C₈₃	#17968	1	1	yes	characteristic, complemented, Sylow
317	#532	—	83	1	no	—
318	#529	—	83	1	no	—
319	#501	—	83	1	no	—
320	#496	—	83	1	no	—
321	#490	—	83	1	no	—
322	#489	—	83	1	no	—
323	#469	—	83	1	no	—
324	#469	—	83	1	no	—
325	#468	—	83	1	no	—
326	#468	—	83	1	no	—
327	#446	—	83	1	no	—
328	C₈×Q₈	—	83	1	no	—
329	C₄×SD₁₆	—	83	1	no	—
330	C₄×SD₁₆	—	83	1	no	—
331	C₄×D₈	—	83	1	no	—
332	C₄×D₈	C₂×D₈₃	1	1	yes	characteristic
333	#436	—	83	1	no	—
334	#436	—	83	1	no	—
335	#436	—	83	1	no	—
336	#436	—	166	1	no	—
337	#435	—	166	1	no	—
338	#435	—	166	1	no	—
339	#435	—	166	1	no	—
340	C₈×D₄	—	83	1	no	—
341	C₈×D₄	C₂×D₈₃	1	1	yes	characteristic
342	C₈×D₄	C₂×D₈₃	1	1	yes	characteristic
343	#433	—	166	1	no	—
344	#432	—	83	1	no	—
345	#431	—	83	1	no	—
346	#424	—	166	1	no	—
347	#423	—	83	1	no	—
348	#408	—	166	1	no	—
349	#408	—	166	1	no	—
350	C₄×M₁₆	—	83	1	no	—
351	C₂×C₄×C₈	—	83	1	no	—
352	#335	—	83	1	no	—
353	#335	C₂×D₈₃	1	1	yes	characteristic
354	#334	—	83	1	no	—
355	#334	—	83	1	no	—
356	Q₈⋊C₈	—	83	1	no	—
357	Q₈⋊C₈	—	83	1	no	—
358	D₄⋊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	C₂×D₈₃	1	1	yes	characteristic
363	D₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic
364	#322	—	83	1	no	—
365	#322	—	83	1	no	—
366	C₈²	—	83	1	no	—
367	C₈²	C₂×D₈₃	1	1	yes	characteristic
368	C₂×#41	—	166	1	no	—
369	C₂×SD₁₆	—	83	1	no	—
370	C₂×SD₁₆	—	83	1	no	—
371	C₂×D₈	—	83	1	no	—
372	C₂×D₈	C₄×D₈₃	1	1	yes	characteristic
373	C₂×M₁₆	—	83	1	no	—
374	C₂×M₁₆	—	83	1	no	—
375	C₂×M₁₆	—	166	1	no	—
376	C₂×M₁₆	—	166	1	no	—
377	C₂×M₁₆	—	166	1	no	—
378	C₂×M₁₆	—	166	1	no	—
379	C₂²×C₈	—	2	1	no	—
380	C₂²×C₈	—	2	1	no	—
381	C₂²×C₈	—	166	1	no	—
382	C₂²×C₈	—	166	1	no	—
383	C₄⋊Q₈	—	83	1	no	—
384	#127	—	83	1	no	—
385	#126	—	166	1	no	—
386	#125	—	83	1	no	—
387	#124	—	83	1	no	—
388	#124	—	166	1	no	—
389	#123	—	166	1	no	—
390	C₂²⋊Q₈	—	83	1	no	—
391	#121	—	83	1	no	—
392	#121	—	83	1	no	—
393	#121	—	83	1	no	—
394	#121	—	166	1	no	—
395	C₄×Q₈	—	83	1	no	—
396	C₄×D₄	—	83	1	no	—
397	C₄×D₄	—	166	1	no	—
398	C₄×D₄	—	166	1	no	—
399	C₄×D₄	C₂²×D₈₃	1	1	yes	characteristic
400	C₄×D₄	C₂²×D₈₃	1	1	yes	characteristic
401	#117	—	166	1	no	—
402	C₂×C₄²	—	83	1	no	—
403	#107	—	83	1	no	—
404	#107	C₄×D₈₃	1	1	yes	characteristic
405	#106	—	83	1	no	—
406	#106	—	83	1	no	—
407	C₄⋊C₈	—	83	1	no	—
408	C₄⋊C₈	—	83	1	no	—
409	C₄⋊C₈	—	83	1	no	—
410	C₄⋊C₈	—	83	1	no	—
411	C₄⋊C₈	—	166	1	no	—
412	C₄⋊C₈	—	166	1	no	—
413	C₄⋊C₈	—	166	1	no	—
414	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
415	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
416	#103	—	83	1	no	—
417	#103	—	83	1	no	—
418	#102	—	83	1	no	—
419	#102	—	83	1	no	—
420	#102	—	83	1	no	—
421	#102	—	83	1	no	—
422	#102	C₄×D₈₃	1	1	yes	characteristic
423	#102	C₄×D₈₃	1	1	yes	characteristic
424	C₂²⋊C₈	—	2	1	no	—
425	C₂²⋊C₈	—	2	1	no	—
426	C₂²⋊C₈	—	83	1	no	—
427	C₂²⋊C₈	—	83	1	no	—
428	C₂²⋊C₈	—	166	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	#97	—	83	1	no	—
434	#97	—	83	1	no	—
435	#97	—	166	1	no	—
436	#97	—	166	1	no	—
437	C₄×C₈	—	83	1	no	—
438	C₄×C₈	—	83	1	no	—
439	C₄×C₈	—	83	1	no	—
440	C₄×C₈	—	166	1	no	—
441	C₄×C₈	—	166	1	no	—
442	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
443	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
444	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
445	#41	—	664	1	no	—
446	#41	—	664	1	no	—
447	C₂×Q₈	—	83	1	no	—
448	C₂×Q₈	—	166	1	no	—
449	C₂×D₄	—	83	1	no	—
450	C₂×D₄	—	166	1	no	—
451	C₂×D₄	—	166	1	no	—
452	C₂×D₄	—	166	1	no	—
453	C₂×D₄	—	166	1	no	—
454	C₂×D₄	—	166	1	no	—
455	C₂×D₄	C₂×C₄×D₈₃	1	1	yes	characteristic
456	C₂×D₄	C₂×C₄×D₈₃	1	1	yes	characteristic
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	83	1	no	—
460	C₂²×C₄	—	83	1	no	—
461	C₂²×C₄	—	83	1	no	—
462	C₂²×C₄	—	166	1	no	—
463	SD₁₆	—	166	2	no	—
464	SD₁₆	—	166	2	no	—
465	D₈	—	2	2	no	—
466	D₈	—	166	2	no	—
467	M₁₆	—	664	1	no	—
468	M₁₆	—	664	1	no	—
469	M₁₆	—	664	1	no	—
470	M₁₆	—	664	1	no	—
471	M₁₆	—	166	2	no	—
472	M₁₆	—	166	2	no	—
473	C₂×C₈	—	2	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	—	332	2	no	—
479	C₂×C₈	—	83	1	no	—
480	C₂×C₈	—	83	1	no	—
481	C₂×C₈	—	83	1	no	—
482	C₂×C₈	—	83	1	no	—
483	C₂×C₈	—	664	1	no	—
484	C₂×C₈	—	166	1	no	—
485	C₂×C₈	—	166	1	no	—
486	C₂×C₈	—	166	1	no	—
487	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
488	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
489	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
490	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
491	C₄⋊C₄	—	83	1	no	—
492	C₄⋊C₄	—	83	1	no	—
493	C₄⋊C₄	—	166	1	no	—
494	C₄⋊C₄	—	166	1	no	—
495	C₄⋊C₄	—	166	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	—	166	1	no	—
503	C₂²⋊C₄	—	166	1	no	—
504	C₂²⋊C₄	—	166	1	no	—
505	C₂²⋊C₄	—	166	1	no	—
506	C₂²⋊C₄	—	166	1	no	—
507	C₂²⋊C₄	—	166	1	no	—
508	C₂²⋊C₄	—	166	1	no	—
509	C₄²	—	83	1	no	—
510	C₄²	—	83	1	no	—
511	C₄²	—	83	1	no	—
512	C₄²	—	166	1	no	—
513	C₄²	C₂³×D₈₃	1	1	yes	characteristic
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	83	1	no	—
517	C₂³	—	166	1	no	—
518	Q₈	—	664	1	no	—
519	Q₈	—	166	1	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	—	664	1	no	—
526	D₄	—	664	1	no	—
527	D₄	—	664	1	no	—
528	D₄	—	664	1	no	—
529	D₄	—	664	1	no	—
530	D₄	—	166	1	no	—
531	D₄	—	166	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	332	1	no	—
539	C₂×C₄	—	332	1	no	—
540	C₂×C₄	—	332	1	no	—
541	C₂×C₄	—	83	1	no	—
542	C₂×C₄	—	83	1	no	—
543	C₂×C₄	—	83	1	no	—
544	C₂×C₄	—	166	1	no	—
545	C₂×C₄	—	166	1	no	—
546	C₂×C₄	—	166	1	no	—
547	C₂×C₄	—	166	1	no	—
548	C₂×C₄	—	166	1	no	—
549	C₂×C₄	—	166	1	no	—
550	C₂×C₄	—	166	1	no	—
551	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
552	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
553	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
554	C₈	—	2	2	no	—
555	C₈	—	2	1	no	—
556	C₈	—	2	1	no	—
557	C₈	—	2	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	332	1	no	—
561	C₈	—	332	1	no	—
562	C₈	—	332	1	no	—
563	C₈	—	83	2	no	—
564	C₈	—	166	1	no	—
565	C₈	—	166	1	no	—
566	C₈	—	166	1	no	—
567	C₈	#14581798	1	2	yes	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	332	1	no	—
575	C₂²	—	332	1	no	—
576	C₂²	—	332	1	no	—
577	C₂²	—	166	1	no	—
578	C₂²	—	166	1	no	—
579	C₂²	—	166	1	no	—
580	C₂²	C₄×D₄×D₈₃	1	1	yes	characteristic
581	C₄	—	2	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	332	1	no	—
585	C₄	—	332	1	no	—
586	C₄	—	332	1	no	—
587	C₄	—	166	1	no	—
588	C₄	—	166	1	no	—
589	C₄	—	166	1	no	—
590	C₄	#131×D₈₃	1	1	yes	characteristic
591	C₄	C₂×#14581798	1	1	yes	characteristic
592	C₄	#19128502	1	1	yes	characteristic
593	C₄	#19128508	1	1	yes	characteristic
594	C₂	—	8	1	no	—
595	C₂	—	8	1	no	—
596	C₂	—	332	1	no	—
597	C₂	—	664	1	no	—
598	C₂	#24916170	1	1	yes	characteristic
599	C₂	#24916288	1	1	yes	characteristic
600	C₂	#24916368	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₃
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₄²	C₂³×D₈₃
Fitting	C₈×D₈×C₈₃	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	#24918056	C₂
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	C₈×D₈	D₈₃
hypocenter	C₈₃	#17968
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈×D₈

Complements

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

N	H ≅ G/N	type
2. #24916613	C₂	semidirect
3. #24916537	C₂	semidirect
4. #24906377	C₂	semidirect
5. #24906364	C₂	semidirect
6. #24906356	C₂	semidirect
7. #24906345	C₂	semidirect
8. #24906285	C₂	semidirect
9. #24906275	C₂	semidirect
10. C₈×#13050579	C₂	semidirect
11. #24906229	C₂	semidirect
12. #24905920	C₂	semidirect
13. #24905912	C₂	semidirect
14. C₈×#13050573	C₂	semidirect
15. C₈×D₈×C₈₃	C₂	semidirect
311. C₈×D₈	D₈₃	semidirect
316. C₈₃	#17968	semidirect

Maximal subgroups

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

subgroup	index
#24918056	2
#24916613	2
#24916537	2
#24906377	2
#24906364	2
#24906356	2
#24906345	2
#24906285	2
#24906275	2
C₈×#13050579	2
#24906229	2
#24905920	2
#24905912	2
C₈×#13050573	2
C₈×D₈×C₈₃	2
#17968	83