Subgroups — #35374217

Order 21248.

636 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24916578	C₂	1	1	yes	maximal, characteristic
2	#24916545	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#14581821	C₂	1	1	yes	maximal, characteristic
4	#24906371	C₂	1	1	yes	maximal, characteristic, complemented
5	#24906370	C₂	1	1	yes	maximal, characteristic, complemented
6	#24906366	C₂	1	1	yes	maximal, characteristic, complemented
7	#24906365	C₂	1	1	yes	maximal, characteristic, complemented
8	#24906361	C₂	1	1	yes	maximal, characteristic, complemented
9	#24906357	C₂	1	1	yes	maximal, characteristic, complemented
10	#24906356	C₂	1	1	yes	maximal, characteristic, complemented
11	#24906212	C₂	1	1	yes	maximal, characteristic, complemented
12	#24905842	C₂	1	1	yes	maximal, characteristic
13	Q₈⋊C₈×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#13050573	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#1590	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14581821	C₄	1	1	yes	characteristic
17	C₄×#13050589	C₂²	1	1	yes	characteristic
18	C₄×Q₈×D₈₃	C₂²	1	1	yes	characteristic
19	#19127832	C₂²	1	1	yes	characteristic
20	#19127831	C₂²	1	1	yes	characteristic
21	#19127831	C₂²	1	1	yes	characteristic
22	#19127830	—	2	1	no	—
23	#19127829	—	2	1	no	—
24	#19127828	C₂²	1	1	yes	characteristic
25	#19127828	C₂²	1	1	yes	characteristic
26	#19127807	C₄	1	1	yes	characteristic
27	#19127805	C₄	1	1	yes	characteristic
28	#19127802	C₄	1	1	yes	characteristic
29	#19127798	C₄	1	1	yes	characteristic
30	C₄×Dic₃₃₂	C₂²	1	1	yes	characteristic
31	C₄×#13050580	C₂²	1	1	yes	characteristic
32	C₄×#13050578	C₂²	1	1	yes	characteristic
33	#19127779	C₂²	1	1	yes	characteristic
34	#19127775	—	2	1	no	—
35	#19127770	—	2	1	no	—
36	#19127757	—	2	1	no	—
37	#19127756	—	2	1	no	—
38	#19127755	—	2	1	no	—
39	#19127753	C₂²	1	1	yes	characteristic
40	#19127752	C₂²	1	1	yes	characteristic
41	#19127740	C₄	1	1	yes	characteristic
42	#19127724	—	2	1	no	—
43	C₄⋊C₈×D₈₃	C₂²	1	1	yes	characteristic
44	#19127708	C₄	1	1	yes	characteristic
45	#19127699	C₄	1	1	yes	characteristic
46	C₄×#13050573	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₈₃	C₂²	1	1	yes	characteristic
48	#19127454	C₂²	1	1	yes	characteristic
49	#19127453	C₂²	1	1	yes	characteristic
50	#19127451	C₂²	1	1	yes	characteristic
51	#19127433	C₂²	1	1	yes	characteristic
52	#19127433	C₂²	1	1	yes	characteristic
53	Q₈⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
54	#19127431	C₂²	1	1	yes	characteristic
55	#19127431	C₂²	1	1	yes	characteristic
56	D₄⋊(C₈₃⋊C₈)	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	#446×C₈₃	C₂²	1	1	yes	characteristic
61	C₄×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic
62	#436×C₈₃	C₂²	1	1	yes	characteristic
63	#334×C₈₃	C₂²	1	1	yes	characteristic
64	Q₈⋊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×#13050589	C₂×C₄	1	1	yes	characteristic
68	C₂×Q₈×D₈₃	C₂×C₄	1	1	yes	characteristic
69	#14581821	—	2	4	no	—
70	C₂×Dic₃₃₂	C₂×C₄	1	1	yes	characteristic
71	C₂×#13050580	C₂×C₄	1	1	yes	characteristic
72	C₂×#13050578	C₂×C₄	1	1	yes	characteristic
73	C₂×#13050574	—	2	1	no	—
74	C₂×#13050573	C₂×C₄	1	1	yes	characteristic
75	C₂×#13050573	C₂×C₄	1	1	yes	characteristic
76	C₂×C₈×D₈₃	—	2	1	no	—
77	C₂×C₈×D₈₃	—	2	1	no	—
78	Q₈×Dic₈₃	C₂×C₄	1	1	yes	characteristic
79	C₄×Dic₁₆₆	—	2	1	no	—
80	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
81	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
82	#14581757	—	2	1	no	—
83	#14581757	C₂×C₄	1	1	yes	characteristic
84	#14581757	C₂×C₄	1	1	yes	characteristic
85	D₄×Dic₈₃	C₂×C₄	1	1	yes	characteristic
86	C₄×C₂²⋊D₈₃	—	2	1	no	—
87	(C₂²⋊D₈₃)⋊C₄	—	2	1	no	—
88	#14581750	C₂×C₄	1	1	yes	characteristic
89	#14581748	—	2	1	no	—
90	C₄⋊C₄×D₈₃	—	2	1	no	—
91	C₄⋊C₄×D₈₃	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄×Dic₈₃	—	2	1	no	—
93	C₄²×D₈₃	—	2	1	no	—
94	C₄²×D₈₃	C₂³	1	1	yes	characteristic
95	#14581726	C₂×C₄	1	1	yes	characteristic
96	#14581725	C₂×C₄	1	1	yes	characteristic
97	#14581723	C₂×C₄	1	1	yes	characteristic
98	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
99	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
100	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
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	Dic₈₃⋊C₈	D₄	1	1	yes	characteristic
107	Dic₈₃⋊C₈	D₄	1	1	yes	characteristic
108	#14581717	C₂×C₄	1	1	yes	characteristic
109	#14581717	C₂×C₄	1	1	yes	characteristic
110	#14581716	C₂×C₄	1	1	yes	characteristic
111	#14581715	C₂×C₄	1	1	yes	characteristic
112	#14581715	C₂×C₄	1	1	yes	characteristic
113	#14581713	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
115	(C₂×D₈₃)⋊C₈	—	2	1	no	—
116	(C₂×D₈₃)⋊C₈	D₄	1	1	yes	characteristic
117	(C₂×D₈₃)⋊C₈	D₄	1	1	yes	characteristic
118	#14581703	—	2	1	no	—
119	#14581702	—	2	1	no	—
120	#14581702	—	2	1	no	—
121	#14581702	—	2	1	no	—
122	#14581702	—	2	1	no	—
123	#14581702	C₂×C₄	1	1	yes	characteristic
124	#14581702	C₂×C₄	1	1	yes	characteristic
125	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
126	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
127	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
128	C₈×Dic₈₃	—	2	1	no	—
129	C₈×Dic₈₃	—	2	1	no	—
130	C₂×SD₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic
131	C₂×M₁₆×C₈₃	—	2	1	no	—
132	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
133	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
134	#106×C₈₃	C₂×C₄	1	1	yes	characteristic
135	C₄⋊C₈×C₈₃	—	2	1	no	—
136	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
138	#103×C₈₃	C₂×C₄	1	1	yes	characteristic
139	#102×C₈₃	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₈₃	—	2	1	no	—
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	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
145	#13050589	—	2	2	no	—
146	#13050589	—	2	2	no	—
147	C₂×Dic₁₆₆	—	2	1	no	—
148	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
149	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
150	Q₈×D₈₃	—	2	2	no	—
151	Q₈×D₈₃	—	2	2	no	—
152	C₂×C₂²⋊D₈₃	—	2	1	no	—
153	C₂²×Dic₈₃	—	2	1	no	—
154	C₂²×Dic₈₃	—	2	1	no	—
155	C₂×C₄×D₈₃	—	2	1	no	—
156	C₂×C₄×D₈₃	—	2	1	no	—
157	C₂×C₄×D₈₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₄×D₈₃	C₂×D₄	1	1	yes	characteristic
159	C₂×C₄×D₈₃	#41	1	1	yes	characteristic
160	Dic₃₃₂	—	2	2	no	—
161	#13050580	—	2	2	no	—
162	#13050578	—	2	2	no	—
163	#13050574	—	8	1	no	—
164	#13050573	—	2	2	no	—
165	#13050573	M₁₆	1	4	yes	complemented
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	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
172	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
173	C₈×D₈₃	—	4	2	no	—
174	C₈×D₈₃	—	8	1	no	—
175	C₄⋊Dic₈₃	—	2	1	no	—
176	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
177	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
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	Dic₈₃⋊C₄	—	2	1	no	—
183	C₂²⋊Dic₈₃	—	2	1	no	—
184	(C₂×D₈₃)⋊C₄	—	2	1	no	—
185	C₄×Dic₈₃	—	2	1	no	—
186	C₄×Dic₈₃	—	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	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×Q₈×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	SD₁₆×C₈₃	—	2	2	no	—
198	M₁₆×C₈₃	—	8	1	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	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
205	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
206	C₄⋊C₄×C₈₃	—	2	1	no	—
207	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
208	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
209	C₂²⋊C₄×C₈₃	—	2	1	no	—
210	C₄²×C₈₃	—	2	1	no	—
211	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
212	C₂³×C₈₃	—	2	1	no	—
213	C₂²×D₈₃	C₄×D₄	1	1	yes	characteristic
214	Q₈×C₈₃	—	2	1	no	—
215	Q₈×C₈₃	—	2	1	no	—
216	D₄×C₈₃	—	2	1	no	—
217	D₄×C₈₃	—	2	1	no	—
218	C₂×C₄×C₈₃	—	2	1	no	—
219	C₂×C₄×C₈₃	—	2	1	no	—
220	C₂×C₄×C₈₃	—	2	1	no	—
221	C₂×C₄×C₈₃	—	4	1	no	—
222	C₂×C₄×C₈₃	—	4	1	no	—
223	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
224	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
226	C₂²⋊D₈₃	—	4	2	no	—
227	C₂×Dic₈₃	—	2	1	no	—
228	C₂×Dic₈₃	—	2	1	no	—
229	C₂×Dic₈₃	—	2	1	no	—
230	C₂×Dic₈₃	—	2	1	no	—
231	C₂×Dic₈₃	—	4	2	no	—
232	C₂×Dic₈₃	—	8	1	no	—
233	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
234	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
235	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
236	C₄×D₈₃	—	2	1	no	—
237	C₄×D₈₃	—	2	1	no	—
238	C₄×D₈₃	—	4	1	no	—
239	C₄×D₈₃	—	4	2	no	—
240	C₄×D₈₃	—	8	1	no	—
241	C₄×D₈₃	C₂×M₁₆	1	2	yes	—
242	C₄×D₈₃	#131	1	2	yes	—
243	Dic₁₆₆	—	2	1	no	—
244	Dic₁₆₆	—	2	1	no	—
245	Dic₁₆₆	—	2	1	no	—
246	Dic₁₆₆	—	2	1	no	—
247	Dic₁₆₆	—	4	2	no	—
248	C₈×C₈₃	—	2	2	no	—
249	C₈×C₈₃	—	2	1	no	—
250	C₈×C₈₃	—	2	1	no	—
251	C₈×C₈₃	—	2	1	no	—
252	C₈×C₈₃	—	4	1	no	—
253	C₈×C₈₃	—	4	1	no	—
254	C₈×C₈₃	C₂×M₁₆	1	2	yes	—
255	C₈₃⋊C₈	—	2	1	no	—
256	C₈₃⋊C₈	—	2	1	no	—
257	C₈₃⋊C₈	—	2	1	no	—
258	C₈₃⋊C₈	—	4	1	no	—
259	C₈₃⋊C₈	—	4	1	no	—
260	C₈₃⋊C₈	—	4	1	no	—
261	C₈₃⋊C₈	C₂×M₁₆	1	2	yes	—
262	C₂²×C₈₃	—	4	1	no	—
263	C₂²×C₈₃	—	4	1	no	—
264	C₂²×C₈₃	—	4	1	no	—
265	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
266	C₂×D₈₃	—	2	1	no	—
267	C₂×D₈₃	—	2	1	no	—
268	C₂×D₈₃	#436	1	2	yes	—
269	C₄×C₈₃	—	2	1	no	—
270	C₄×C₈₃	—	4	1	no	—
271	C₄×C₈₃	—	4	1	no	—
272	C₄×C₈₃	—	4	1	no	—
273	C₄×C₈₃	C₂²×M₁₆	1	1	yes	characteristic
274	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
275	C₄×C₈₃	#577	1	1	yes	characteristic
276	C₄×C₈₃	#578	1	1	yes	characteristic
277	Dic₈₃	—	2	1	no	—
278	Dic₈₃	—	2	1	no	—
279	Dic₈₃	—	4	1	no	—
280	Dic₈₃	—	4	1	no	—
281	Dic₈₃	—	4	1	no	—
282	Dic₈₃	—	4	1	no	—
283	Dic₈₃	#436	1	2	yes	—
284	#17894	—	83	1	no	maximal, Sylow
285	C₂×C₈₃	—	8	1	no	—
286	C₂×C₈₃	C₂×#436	1	1	yes	characteristic
287	C₂×C₈₃	#2947	1	1	yes	characteristic
288	C₂×C₈₃	#2956	1	1	yes	characteristic
289	D₈₃	—	2	2	no	—
290	#2989	—	83	1	no	—
291	#2983	—	83	1	no	—
292	C₄×#137	—	83	1	no	—
293	#1593	—	83	1	no	—
294	#1593	—	83	1	no	—
295	#1592	—	83	1	no	—
296	#1592	—	83	1	no	—
297	#1591	—	83	1	no	—
298	#1591	—	83	1	no	—
299	#1590	—	83	1	no	—
300	#1590	D₈₃	1	1	yes	characteristic, complemented
301	#1565	—	83	1	no	—
302	#1476	—	83	1	no	—
303	C₂×Q₈⋊C₈	—	83	1	no	—
304	C₈×M₁₆	—	83	1	no	—
305	C₈₃	#17894	1	1	yes	characteristic, complemented, Sylow
306	C₂×#137	—	83	1	no	—
307	C₄×#41	—	83	1	no	—
308	C₂×C₄×Q₈	—	83	1	no	—
309	#446	—	83	1	no	—
310	#446	—	83	1	no	—
311	#446	—	83	1	no	—
312	#446	—	83	1	no	—
313	#446	—	83	1	no	—
314	#446	—	166	1	no	—
315	#446	—	166	1	no	—
316	#446	C₂×D₈₃	1	1	yes	characteristic
317	#441	—	83	1	no	—
318	#441	—	83	1	no	—
319	#440	—	83	1	no	—
320	#440	—	83	1	no	—
321	C₄×Q₁₆	—	83	1	no	—
322	C₄×Q₁₆	—	83	1	no	—
323	C₄×SD₁₆	—	83	1	no	—
324	C₄×SD₁₆	C₂×D₈₃	1	1	yes	characteristic
325	#436	—	83	1	no	—
326	#436	C₂×D₈₃	1	1	yes	characteristic
327	#435	—	166	1	no	—
328	#435	—	166	1	no	—
329	#432	—	166	1	no	—
330	#432	—	166	1	no	—
331	#432	—	166	1	no	—
332	#431	—	83	1	no	—
333	#431	—	83	1	no	—
334	#428	—	83	1	no	—
335	#423	—	166	1	no	—
336	C₂×C₄⋊C₈	—	83	1	no	—
337	#419	—	83	1	no	—
338	#417	—	83	1	no	—
339	C₄×M₁₆	—	83	1	no	—
340	C₂×C₄×C₈	—	83	1	no	—
341	#335	—	83	1	no	—
342	#335	—	83	1	no	—
343	#334	—	83	1	no	—
344	#334	C₂×D₈₃	1	1	yes	characteristic
345	Q₈⋊C₈	—	83	1	no	—
346	Q₈⋊C₈	—	83	1	no	—
347	Q₈⋊C₈	—	83	1	no	—
348	Q₈⋊C₈	—	83	1	no	—
349	Q₈⋊C₈	—	83	1	no	—
350	Q₈⋊C₈	C₂×D₈₃	1	1	yes	characteristic
351	D₄⋊C₈	—	83	1	no	—
352	D₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic
353	#322	—	83	1	no	—
354	#322	—	83	1	no	—
355	C₈²	—	83	1	no	—
356	C₈²	C₂×D₈₃	1	1	yes	characteristic
357	C₂×#41	—	83	1	no	—
358	C₂²×Q₈	—	83	1	no	—
359	#137	—	166	4	no	—
360	C₂×Q₁₆	—	83	1	no	—
361	C₂×Q₁₆	—	83	1	no	—
362	C₂×SD₁₆	—	83	1	no	—
363	C₂×SD₁₆	C₄×D₈₃	1	1	yes	characteristic
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	83	1	no	—
366	C₂×M₁₆	—	83	1	no	—
367	C₂×M₁₆	—	166	1	no	—
368	C₂²×C₈	—	166	1	no	—
369	C₂²×C₈	—	166	1	no	—
370	C₄×Q₈	—	83	1	no	—
371	C₄×Q₈	—	83	1	no	—
372	C₄×Q₈	—	83	1	no	—
373	C₄×Q₈	—	83	1	no	—
374	C₄×Q₈	—	83	1	no	—
375	C₄×Q₈	—	166	1	no	—
376	C₄×Q₈	—	166	1	no	—
377	C₄×Q₈	C₂²×D₈₃	1	1	yes	characteristic
378	C₄×D₄	—	83	1	no	—
379	C₄×D₄	—	166	1	no	—
380	C₄×D₄	—	166	1	no	—
381	C₄×D₄	C₂²×D₈₃	1	1	yes	characteristic
382	#117	—	83	1	no	—
383	#117	—	166	1	no	—
384	C₂×C₄⋊C₄	—	83	1	no	—
385	C₂×C₄⋊C₄	—	166	1	no	—
386	C₂×C₄²	—	83	1	no	—
387	C₂×C₄²	—	166	1	no	—
388	C₂×C₄²	—	166	1	no	—
389	#107	—	83	1	no	—
390	#107	—	83	1	no	—
391	#106	—	83	1	no	—
392	#106	C₄×D₈₃	1	1	yes	characteristic
393	C₄⋊C₈	—	2	1	no	—
394	C₄⋊C₈	—	83	1	no	—
395	C₄⋊C₈	—	83	1	no	—
396	C₄⋊C₈	—	83	1	no	—
397	C₄⋊C₈	—	83	1	no	—
398	C₄⋊C₈	—	166	1	no	—
399	C₄⋊C₈	—	166	1	no	—
400	C₄⋊C₈	—	166	1	no	—
401	C₄⋊C₈	—	166	1	no	—
402	C₄⋊C₈	—	166	1	no	—
403	C₄⋊C₈	—	166	1	no	—
404	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
405	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
406	#103	—	83	1	no	—
407	#103	—	83	1	no	—
408	#103	—	83	1	no	—
409	#103	—	83	1	no	—
410	#103	—	83	1	no	—
411	#103	C₄×D₈₃	1	1	yes	characteristic
412	#102	—	83	1	no	—
413	#102	C₄×D₈₃	1	1	yes	characteristic
414	C₂²⋊C₈	—	2	1	no	—
415	C₂²⋊C₈	—	83	1	no	—
416	C₂²⋊C₈	—	83	1	no	—
417	C₂²⋊C₈	—	166	1	no	—
418	C₂²⋊C₈	—	166	1	no	—
419	#97	—	2	1	no	—
420	#97	—	83	1	no	—
421	#97	—	83	1	no	—
422	#97	—	166	1	no	—
423	#97	—	166	1	no	—
424	#97	—	166	1	no	—
425	#97	—	166	1	no	—
426	#97	—	166	1	no	—
427	C₄×C₈	—	83	1	no	—
428	C₄×C₈	—	83	1	no	—
429	C₄×C₈	—	83	1	no	—
430	C₄×C₈	—	166	1	no	—
431	C₄×C₈	—	166	1	no	—
432	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
433	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
434	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
435	#41	—	166	2	no	—
436	#41	—	166	2	no	—
437	C₂×Q₈	—	83	1	no	—
438	C₂×Q₈	—	83	1	no	—
439	C₂×Q₈	—	166	1	no	—
440	C₂×Q₈	—	166	2	no	—
441	C₂×Q₈	—	166	2	no	—
442	C₂×Q₈	C₂×C₄×D₈₃	1	1	yes	characteristic
443	C₂×D₄	—	166	1	no	—
444	C₂×D₄	C₂×C₄×D₈₃	1	1	yes	characteristic
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	83	1	no	—
447	C₂²×C₄	—	83	1	no	—
448	C₂²×C₄	—	83	1	no	—
449	C₂²×C₄	—	166	1	no	—
450	C₂²×C₄	—	166	1	no	—
451	C₂²×C₄	—	166	1	no	—
452	C₂²×C₄	—	166	1	no	—
453	Q₁₆	—	166	2	no	—
454	Q₁₆	—	166	2	no	—
455	SD₁₆	—	2	2	no	—
456	SD₁₆	—	166	2	no	—
457	M₁₆	—	8	1	no	—
458	M₁₆	—	83	4	no	—
459	M₁₆	—	664	1	no	—
460	M₁₆	—	166	2	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	332	2	no	—
465	C₂×C₈	—	83	1	no	—
466	C₂×C₈	—	83	1	no	—
467	C₂×C₈	—	83	1	no	—
468	C₂×C₈	—	83	1	no	—
469	C₂×C₈	—	664	1	no	—
470	C₂×C₈	—	166	1	no	—
471	C₂×C₈	—	166	1	no	—
472	C₂×C₈	—	166	1	no	—
473	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
474	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
475	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
476	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	83	1	no	—
479	C₄⋊C₄	—	83	1	no	—
480	C₄⋊C₄	—	166	1	no	—
481	C₄⋊C₄	—	166	1	no	—
482	C₄⋊C₄	—	166	1	no	—
483	C₄⋊C₄	—	166	1	no	—
484	C₄⋊C₄	—	166	1	no	—
485	C₄⋊C₄	—	166	1	no	—
486	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
487	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	166	1	no	—
490	C₂²⋊C₄	—	166	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	83	1	no	—
493	C₄²	—	83	1	no	—
494	C₄²	—	83	1	no	—
495	C₄²	—	166	1	no	—
496	C₄²	—	166	1	no	—
497	C₄²	—	166	1	no	—
498	C₄²	—	166	1	no	—
499	C₄²	—	166	1	no	—
500	C₄²	—	166	1	no	—
501	C₄²	C₂³×D₈₃	1	1	yes	characteristic
502	C₂³	—	2	1	no	—
503	C₂³	—	83	1	no	—
504	Q₈	—	2	1	no	—
505	Q₈	—	2	1	no	—
506	Q₈	—	332	2	no	—
507	Q₈	—	166	1	no	—
508	Q₈	—	166	1	no	—
509	Q₈	—	166	1	no	—
510	Q₈	—	166	1	no	—
511	D₄	—	2	1	no	—
512	D₄	—	2	1	no	—
513	D₄	—	332	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	332	1	no	—
520	C₂×C₄	—	332	2	no	—
521	C₂×C₄	—	332	2	no	—
522	C₂×C₄	—	83	1	no	—
523	C₂×C₄	—	83	2	no	—
524	C₂×C₄	—	83	2	no	—
525	C₂×C₄	—	83	1	no	—
526	C₂×C₄	—	83	1	no	—
527	C₂×C₄	—	664	1	no	—
528	C₂×C₄	—	664	1	no	—
529	C₂×C₄	—	166	1	no	—
530	C₂×C₄	—	166	1	no	—
531	C₂×C₄	—	166	1	no	—
532	C₂×C₄	—	166	1	no	—
533	C₂×C₄	—	166	1	no	—
534	C₂×C₄	—	166	1	no	—
535	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
536	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
537	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
538	C₈	—	2	2	no	—
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	332	1	no	—
545	C₈	—	332	1	no	—
546	C₈	—	332	1	no	—
547	C₈	—	83	2	no	—
548	C₈	—	166	1	no	—
549	C₈	—	166	1	no	—
550	C₈	—	166	1	no	—
551	C₈	M₁₆×D₈₃	1	2	yes	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	83	2	no	—
556	C₂²	—	166	1	no	—
557	C₂²	—	166	1	no	—
558	C₂²	C₄×D₄×D₈₃	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	332	1	no	—
564	C₄	—	332	1	no	—
565	C₄	—	332	1	no	—
566	C₄	—	332	1	no	—
567	C₄	—	83	2	no	—
568	C₄	—	166	1	no	—
569	C₄	—	166	1	no	—
570	C₄	C₂×M₁₆×D₈₃	1	1	yes	characteristic
571	C₄	#131×D₈₃	1	1	yes	characteristic
572	C₄	#19128507	1	1	yes	characteristic
573	C₄	#19128515	1	1	yes	characteristic
574	C₂	—	8	1	no	—
575	C₂	—	166	2	no	—
576	C₂	#436×D₈₃	1	1	yes	characteristic
577	C₂	#24916299	1	1	yes	characteristic
578	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	C₈₃×#1590	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	C₂×#13050589	C₂×C₄
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	#1590	D₈₃
hypocenter	C₈₃	#17894
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1590

Complements

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

N	H ≅ G/N	type
2. #24916545	C₂	semidirect
4. #24906371	C₂	semidirect
5. #24906370	C₂	semidirect
6. #24906366	C₂	semidirect
7. #24906365	C₂	semidirect
8. #24906361	C₂	semidirect
9. #24906357	C₂	semidirect
10. #24906356	C₂	semidirect
11. #24906212	C₂	semidirect
13. Q₈⋊C₈×D₈₃	C₂	semidirect
14. C₈×#13050573	C₂	semidirect
15. C₈₃×#1590	C₂	semidirect
165. #13050573	M₁₆	semidirect
300. #1590	D₈₃	semidirect
305. C₈₃	#17894	semidirect

Maximal subgroups

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

subgroup	index
#24916578	2
#24916545	2
C₄×#14581821	2
#24906371	2
#24906370	2
#24906366	2
#24906365	2
#24906361	2
#24906357	2
#24906356	2
#24906212	2
#24905842	2
Q₈⋊C₈×D₈₃	2
C₈×#13050573	2
C₈₃×#1590	2
#17894	83