Subgroups — #35376127

Order 21248.

618 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24916551	C₂	1	1	yes	maximal, characteristic
2	#24916549	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₁₆×D₈₃	C₂	1	1	yes	maximal, characteristic
4	#24906370	C₂	1	1	yes	maximal, characteristic, complemented
5	#24906369	C₂	1	1	yes	maximal, characteristic, complemented
6	#24906315	C₂	1	1	yes	maximal, characteristic, complemented
7	#24906314	C₂	1	1	yes	maximal, characteristic, complemented
8	#24906312	C₂	1	1	yes	maximal, characteristic, complemented
9	#24906280	C₂	1	1	yes	maximal, characteristic, complemented
10	#24906279	C₂	1	1	yes	maximal, characteristic, complemented
11	#24906225	C₂	1	1	yes	maximal, characteristic
12	#24905908	C₂	1	1	yes	maximal, characteristic
13	#24905908	C₂	1	1	yes	maximal, characteristic
14	#24905751	C₂	1	1	yes	maximal, characteristic
15	C₈₃×#1584	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₁₆×D₈₃	C₄	1	1	yes	characteristic
17	C₄×Q₈×D₈₃	C₂²	1	1	yes	characteristic
18	C₄×Q₈×D₈₃	C₂²	1	1	yes	characteristic
19	#19127832	C₂²	1	1	yes	characteristic
20	#19127831	—	2	1	no	—
21	#19127831	C₂²	1	1	yes	characteristic
22	#19127830	—	2	1	no	—
23	#19127829	—	2	1	no	—
24	#19127828	—	2	1	no	—
25	#19127828	C₂²	1	1	yes	characteristic
26	Q₈×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
27	C₈×Dic₁₆₆	C₂²	1	1	yes	characteristic
28	#19127825	C₂²	1	1	yes	characteristic
29	C₄×Dic₃₃₂	C₂²	1	1	yes	characteristic
30	Q₁₆×Dic₈₃	C₄	1	1	yes	characteristic
31	#19127795	C₄	1	1	yes	characteristic
32	C₄×#13050580	C₂²	1	1	yes	characteristic
33	C₄×#13050580	C₂²	1	1	yes	characteristic
34	#19127793	C₄	1	1	yes	characteristic
35	#19127793	C₄	1	1	yes	characteristic
36	#19127757	—	2	1	no	—
37	#19127757	C₂²	1	1	yes	characteristic
38	#19127757	C₂²	1	1	yes	characteristic
39	#19127756	—	2	1	no	—
40	#19127753	—	2	1	no	—
41	#19127752	—	2	1	no	—
42	#19127752	C₂²	1	1	yes	characteristic
43	#107×D₈₃	C₄	1	1	yes	characteristic
44	#103×D₈₃	C₄	1	1	yes	characteristic
45	#103×D₈₃	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	#19127451	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	Q₈⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
55	#19127431	C₂²	1	1	yes	characteristic
56	#19127431	C₂²	1	1	yes	characteristic
57	#19127423	C₂²	1	1	yes	characteristic
58	#19127423	C₂²	1	1	yes	characteristic
59	#19127423	C₂²	1	1	yes	characteristic
60	#446×C₈₃	C₂²	1	1	yes	characteristic
61	C₈×Q₈×C₈₃	C₂²	1	1	yes	characteristic
62	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
63	#335×C₈₃	C₂²	1	1	yes	characteristic
64	Q₈⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
65	Q₈⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
66	#322×C₈₃	C₂²	1	1	yes	characteristic
67	C₂×Q₈×D₈₃	C₂×C₄	1	1	yes	characteristic
68	C₂×Q₈×D₈₃	C₂×C₄	1	1	yes	characteristic
69	C₂×Dic₃₃₂	C₂×C₄	1	1	yes	characteristic
70	C₂×#13050580	C₂×C₄	1	1	yes	characteristic
71	C₂×#13050580	C₂×C₄	1	1	yes	characteristic
72	Q₁₆×D₈₃	—	2	4	no	—
73	C₂×#13050573	—	2	1	no	—
74	C₂×C₈×D₈₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₈₃	C₂×C₄	1	1	yes	characteristic
76	Q₈×Dic₈₃	C₂×C₄	1	1	yes	characteristic
77	Q₈×Dic₈₃	C₂×C₄	1	1	yes	characteristic
78	C₄×Dic₁₆₆	—	2	1	no	—
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	—	2	1	no	—
84	#14581757	C₂×C₄	1	1	yes	characteristic
85	#14581757	C₂×C₄	1	1	yes	characteristic
86	C₄⋊C₄×D₈₃	—	2	1	no	—
87	C₄⋊C₄×D₈₃	—	2	1	no	—
88	C₄⋊C₄×D₈₃	C₂×C₄	1	1	yes	characteristic
89	C₄⋊C₄×D₈₃	C₂×C₄	1	1	yes	characteristic
90	C₄²×D₈₃	—	2	1	no	—
91	C₄²×D₈₃	—	2	1	no	—
92	C₄²×D₈₃	C₂³	1	1	yes	characteristic
93	#14581726	C₂×C₄	1	1	yes	characteristic
94	#14581725	C₂×C₄	1	1	yes	characteristic
95	#14581725	C₂×C₄	1	1	yes	characteristic
96	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
97	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
98	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
99	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
105	Dic₈₃⋊C₈	D₄	1	1	yes	characteristic
106	#14581717	C₂×C₄	1	1	yes	characteristic
107	#14581717	C₂×C₄	1	1	yes	characteristic
108	#14581716	C₂×C₄	1	1	yes	characteristic
109	#14581716	C₂×C₄	1	1	yes	characteristic
110	#14581715	C₂×C₄	1	1	yes	characteristic
111	#14581715	C₂×C₄	1	1	yes	characteristic
112	(C₂×D₈₃)⋊C₈	—	2	1	no	—
113	(C₂×D₈₃)⋊C₈	—	2	1	no	—
114	(C₂×D₈₃)⋊C₈	D₄	1	1	yes	characteristic
115	(C₂×D₈₃)⋊C₈	D₄	1	1	yes	characteristic
116	#14581703	—	2	1	no	—
117	#14581702	—	2	1	no	—
118	#14581702	—	2	1	no	—
119	#14581702	—	2	1	no	—
120	#14581702	—	2	1	no	—
121	#14581702	—	2	1	no	—
122	C₄×C₈₃⋊C₈	—	2	1	no	—
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	C₂×C₄	1	1	yes	characteristic
129	C₈×Dic₈₃	C₂×C₄	1	1	yes	characteristic
130	C₂×Q₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic
131	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
132	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
133	#107×C₈₃	C₂×C₄	1	1	yes	characteristic
134	C₄⋊C₈×C₈₃	—	2	1	no	—
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	#103×C₈₃	C₂×C₄	1	1	yes	characteristic
140	#97×C₈₃	—	2	1	no	—
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	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
145	C₂×Dic₁₆₆	—	2	1	no	—
146	C₂×Dic₁₆₆	—	2	1	no	—
147	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
148	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
149	Q₈×D₈₃	—	2	2	no	—
150	Q₈×D₈₃	—	2	2	no	—
151	Q₈×D₈₃	—	4	1	no	—
152	Q₈×D₈₃	—	4	1	no	—
153	C₂×C₄×D₈₃	—	2	1	no	—
154	C₂×C₄×D₈₃	—	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	#13050580	M₁₆	1	4	yes	complemented
163	#13050573	—	4	2	no	—
164	C₂×C₈₃⋊C₈	—	2	1	no	—
165	C₂×C₈₃⋊C₈	—	2	1	no	—
166	C₂×C₈₃⋊C₈	—	2	1	no	—
167	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
170	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
171	C₈×D₈₃	—	2	2	no	—
172	C₈×D₈₃	—	4	1	no	—
173	C₄⋊Dic₈₃	—	2	1	no	—
174	C₄⋊Dic₈₃	—	2	1	no	—
175	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
176	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
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	Dic₈₃⋊C₄	—	2	1	no	—
183	C₄×Dic₈₃	—	2	1	no	—
184	C₄×Dic₈₃	—	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	C₂²×C₄	1	1	yes	characteristic
190	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
191	C₄×Dic₈₃	#41	1	1	yes	characteristic
192	C₂×Q₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
193	C₂×Q₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
194	Q₁₆×C₈₃	—	2	2	no	—
195	C₂×C₈×C₈₃	—	2	1	no	—
196	C₂×C₈×C₈₃	—	2	1	no	—
197	C₂×C₈×C₈₃	—	2	1	no	—
198	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
201	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
202	C₄⋊C₄×C₈₃	—	2	1	no	—
203	C₄⋊C₄×C₈₃	—	2	1	no	—
204	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
205	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
206	C₄²×C₈₃	—	2	1	no	—
207	C₄²×C₈₃	—	2	1	no	—
208	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
209	C₂²×D₈₃	C₄×D₄	1	1	yes	characteristic
210	Q₈×C₈₃	—	2	1	no	—
211	Q₈×C₈₃	—	2	1	no	—
212	Q₈×C₈₃	—	2	1	no	—
213	Q₈×C₈₃	C₂×M₁₆	1	2	yes	—
214	C₂×C₄×C₈₃	—	2	1	no	—
215	C₂×C₄×C₈₃	—	2	1	no	—
216	C₂×C₄×C₈₃	—	2	1	no	—
217	C₂×C₄×C₈₃	—	2	1	no	—
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	C₂×Dic₈₃	—	2	1	no	—
222	C₂×Dic₈₃	—	2	1	no	—
223	C₂×Dic₈₃	—	2	1	no	—
224	C₂×Dic₈₃	—	2	1	no	—
225	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
226	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
227	C₂×Dic₈₃	C₄×D₄	1	1	yes	characteristic
228	C₄×D₈₃	—	2	2	no	—
229	C₄×D₈₃	—	2	1	no	—
230	C₄×D₈₃	—	2	1	no	—
231	C₄×D₈₃	—	2	1	no	—
232	C₄×D₈₃	—	2	1	no	—
233	C₄×D₈₃	—	4	2	no	—
234	C₄×D₈₃	—	4	2	no	—
235	C₄×D₈₃	—	4	2	no	—
236	C₄×D₈₃	—	4	2	no	—
237	Dic₁₆₆	—	2	1	no	—
238	Dic₁₆₆	—	2	1	no	—
239	Dic₁₆₆	—	2	1	no	—
240	Dic₁₆₆	—	4	2	no	—
241	Dic₁₆₆	—	4	2	no	—
242	Dic₁₆₆	C₂×M₁₆	1	2	yes	—
243	C₈×C₈₃	—	2	1	no	—
244	C₈×C₈₃	—	2	1	no	—
245	C₈×C₈₃	—	2	1	no	—
246	C₈×C₈₃	—	2	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	—	4	1	no	—
256	C₈₃⋊C₈	C₂×M₁₆	1	2	yes	—
257	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
258	C₂×D₈₃	—	2	1	no	—
259	C₂×D₈₃	—	2	1	no	—
260	C₂×D₈₃	#444	1	2	yes	—
261	C₄×C₈₃	—	2	2	no	—
262	C₄×C₈₃	—	2	1	no	—
263	C₄×C₈₃	—	4	1	no	—
264	C₄×C₈₃	—	4	1	no	—
265	C₄×C₈₃	—	4	1	no	—
266	C₄×C₈₃	C₂²×M₁₆	1	1	yes	characteristic
267	C₄×C₈₃	#568	1	1	yes	characteristic
268	C₄×C₈₃	#578	1	1	yes	characteristic
269	C₄×C₈₃	#578	1	1	yes	characteristic
270	Dic₈₃	—	2	2	no	—
271	Dic₈₃	—	2	1	no	—
272	Dic₈₃	—	2	1	no	—
273	Dic₈₃	—	2	1	no	—
274	Dic₈₃	—	4	1	no	—
275	Dic₈₃	—	4	1	no	—
276	Dic₈₃	—	4	1	no	—
277	#18062	—	83	1	no	maximal, Sylow
278	C₂×C₈₃	D₄×M₁₆	1	1	yes	characteristic
279	C₂×C₈₃	#2950	1	1	yes	characteristic
280	C₂×C₈₃	C₂×#444	1	1	yes	characteristic
281	D₈₃	—	2	2	no	—
282	#2984	—	83	1	no	—
283	#2984	—	83	1	no	—
284	C₂×C₄×Q₁₆	—	83	1	no	—
285	#1593	—	83	1	no	—
286	#1593	—	83	1	no	—
287	#1584	—	83	1	no	—
288	#1584	—	83	1	no	—
289	#1584	—	83	1	no	—
290	#1584	D₈₃	1	1	yes	characteristic, complemented
291	#1579	—	83	1	no	—
292	#1579	—	83	1	no	—
293	#1568	—	83	1	no	—
294	#1491	—	83	1	no	—
295	#1491	—	83	1	no	—
296	#1451	—	83	1	no	—
297	C₈₃	#18062	1	1	yes	characteristic, complemented, Sylow
298	C₂²×Q₁₆	—	83	1	no	—
299	C₂×C₄×Q₈	—	83	1	no	—
300	C₂×C₄×Q₈	—	83	1	no	—
301	#446	—	83	1	no	—
302	#446	—	83	1	no	—
303	#446	—	83	1	no	—
304	#446	—	166	1	no	—
305	#446	—	166	1	no	—
306	#446	—	166	1	no	—
307	#446	—	166	1	no	—
308	#446	C₂×D₈₃	1	1	yes	characteristic
309	C₈×Q₈	—	83	1	no	—
310	C₈×Q₈	—	83	1	no	—
311	C₈×Q₈	—	83	1	no	—
312	C₈×Q₈	C₂×D₈₃	1	1	yes	characteristic
313	C₄×Q₁₆	—	83	1	no	—
314	C₄×Q₁₆	—	83	1	no	—
315	C₄×Q₁₆	—	83	1	no	—
316	C₄×Q₁₆	—	83	1	no	—
317	C₄×Q₁₆	—	83	1	no	—
318	C₄×Q₁₆	—	83	1	no	—
319	C₄×Q₁₆	—	83	1	no	—
320	C₄×Q₁₆	C₂×D₈₃	1	1	yes	characteristic
321	#432	—	83	1	no	—
322	#432	—	83	1	no	—
323	#432	—	166	1	no	—
324	#432	—	166	1	no	—
325	#431	—	83	1	no	—
326	#431	—	166	1	no	—
327	#431	—	166	1	no	—
328	C₂×#107	—	83	1	no	—
329	C₂×#103	—	83	1	no	—
330	C₂×#103	—	83	1	no	—
331	C₄×M₁₆	—	83	1	no	—
332	C₂×C₄×C₈	—	83	1	no	—
333	#335	—	83	1	no	—
334	#335	C₂×D₈₃	1	1	yes	characteristic
335	#334	—	83	1	no	—
336	#334	—	83	1	no	—
337	Q₈⋊C₈	—	83	1	no	—
338	Q₈⋊C₈	—	83	1	no	—
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	C₂×D₈₃	1	1	yes	characteristic
344	Q₈⋊C₈	C₂×D₈₃	1	1	yes	characteristic
345	#322	—	83	1	no	—
346	#322	—	83	1	no	—
347	#322	—	83	1	no	—
348	#322	C₂×D₈₃	1	1	yes	characteristic
349	C₂²×Q₈	—	83	1	no	—
350	C₂²×Q₈	—	83	1	no	—
351	C₂×Q₁₆	—	83	1	no	—
352	C₂×Q₁₆	—	83	1	no	—
353	C₂×Q₁₆	—	83	1	no	—
354	C₂×Q₁₆	—	166	4	no	—
355	C₂×Q₁₆	C₄×D₈₃	1	1	yes	characteristic
356	C₂×M₁₆	—	166	1	no	—
357	C₂²×C₈	—	83	1	no	—
358	C₂²×C₈	—	83	1	no	—
359	C₄×Q₈	—	83	1	no	—
360	C₄×Q₈	—	83	1	no	—
361	C₄×Q₈	—	83	1	no	—
362	C₄×Q₈	—	83	1	no	—
363	C₄×Q₈	—	83	1	no	—
364	C₄×Q₈	—	83	1	no	—
365	C₄×Q₈	—	166	1	no	—
366	C₄×Q₈	—	166	1	no	—
367	C₄×Q₈	—	166	1	no	—
368	C₄×Q₈	—	166	1	no	—
369	C₄×Q₈	C₂²×D₈₃	1	1	yes	characteristic
370	C₄×Q₈	C₂²×D₈₃	1	1	yes	characteristic
371	C₂×C₄⋊C₄	—	83	1	no	—
372	C₂×C₄⋊C₄	—	83	1	no	—
373	C₂×C₄⋊C₄	—	166	1	no	—
374	C₂×C₄⋊C₄	—	166	1	no	—
375	C₂×C₄²	—	83	1	no	—
376	C₂×C₄²	—	166	1	no	—
377	C₂×C₄²	—	166	1	no	—
378	#107	—	83	1	no	—
379	#107	—	83	1	no	—
380	#107	—	83	1	no	—
381	#107	C₄×D₈₃	1	1	yes	characteristic
382	C₄⋊C₈	—	2	1	no	—
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	—	83	1	no	—
385	C₄⋊C₈	—	83	1	no	—
386	C₄⋊C₈	—	83	1	no	—
387	C₄⋊C₈	—	83	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	—	166	1	no	—
394	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
395	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
396	#103	—	83	1	no	—
397	#103	—	83	1	no	—
398	#103	—	83	1	no	—
399	#103	—	83	1	no	—
400	#103	—	83	1	no	—
401	#103	—	83	1	no	—
402	#103	C₄×D₈₃	1	1	yes	characteristic
403	#103	C₄×D₈₃	1	1	yes	characteristic
404	C₂²⋊C₈	—	83	1	no	—
405	C₂²⋊C₈	—	83	1	no	—
406	C₂²⋊C₈	—	166	1	no	—
407	C₂²⋊C₈	—	166	1	no	—
408	#97	—	2	1	no	—
409	#97	—	166	1	no	—
410	#97	—	166	1	no	—
411	#97	—	166	1	no	—
412	#97	—	166	1	no	—
413	#97	—	166	1	no	—
414	#97	—	166	1	no	—
415	C₄×C₈	—	2	1	no	—
416	C₄×C₈	—	83	1	no	—
417	C₄×C₈	—	83	1	no	—
418	C₄×C₈	—	83	1	no	—
419	C₄×C₈	—	83	1	no	—
420	C₄×C₈	—	83	1	no	—
421	C₄×C₈	—	166	1	no	—
422	C₄×C₈	—	166	1	no	—
423	C₄×C₈	—	166	1	no	—
424	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
425	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
426	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
427	C₂×Q₈	—	332	1	no	—
428	C₂×Q₈	—	332	1	no	—
429	C₂×Q₈	—	83	1	no	—
430	C₂×Q₈	—	83	1	no	—
431	C₂×Q₈	—	166	1	no	—
432	C₂×Q₈	—	166	1	no	—
433	C₂×Q₈	—	166	2	no	—
434	C₂×Q₈	—	166	2	no	—
435	C₂×Q₈	C₂×C₄×D₈₃	1	1	yes	characteristic
436	C₂×Q₈	C₂×C₄×D₈₃	1	1	yes	characteristic
437	C₂²×C₄	—	83	1	no	—
438	C₂²×C₄	—	83	1	no	—
439	C₂²×C₄	—	83	1	no	—
440	C₂²×C₄	—	166	1	no	—
441	C₂²×C₄	—	166	1	no	—
442	C₂²×C₄	—	166	1	no	—
443	C₂²×C₄	—	166	1	no	—
444	Q₁₆	—	2	2	no	—
445	Q₁₆	—	83	4	no	—
446	Q₁₆	—	166	2	no	—
447	Q₁₆	—	166	2	no	—
448	M₁₆	—	332	2	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	332	1	no	—
453	C₂×C₈	—	83	1	no	—
454	C₂×C₈	—	83	1	no	—
455	C₂×C₈	—	83	1	no	—
456	C₂×C₈	—	83	1	no	—
457	C₂×C₈	—	166	2	no	—
458	C₂×C₈	—	166	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	D₄×D₈₃	1	1	yes	characteristic
464	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	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	C₂×C₄×D₈₃	1	1	yes	characteristic
478	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	83	1	no	—
482	C₄²	—	83	1	no	—
483	C₄²	—	83	1	no	—
484	C₄²	—	166	1	no	—
485	C₄²	—	166	1	no	—
486	C₄²	—	166	1	no	—
487	C₄²	—	166	1	no	—
488	C₄²	—	166	1	no	—
489	C₄²	—	166	1	no	—
490	C₄²	C₂³×D₈₃	1	1	yes	characteristic
491	C₂³	—	83	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	2	1	no	—
494	Q₈	—	2	1	no	—
495	Q₈	—	332	2	no	—
496	Q₈	—	332	2	no	—
497	Q₈	—	83	2	no	—
498	Q₈	—	166	1	no	—
499	Q₈	—	166	1	no	—
500	Q₈	—	166	1	no	—
501	Q₈	M₁₆×D₈₃	1	2	yes	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	332	2	no	—
507	C₂×C₄	—	332	2	no	—
508	C₂×C₄	—	332	2	no	—
509	C₂×C₄	—	332	2	no	—
510	C₂×C₄	—	83	1	no	—
511	C₂×C₄	—	83	1	no	—
512	C₂×C₄	—	83	1	no	—
513	C₂×C₄	—	166	2	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	—	166	1	no	—
521	C₂×C₄	—	166	1	no	—
522	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
523	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
524	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	2	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	4	1	no	—
532	C₈	—	332	1	no	—
533	C₈	—	332	1	no	—
534	C₈	—	332	1	no	—
535	C₈	—	83	2	no	—
536	C₈	—	166	1	no	—
537	C₈	—	166	1	no	—
538	C₈	—	166	1	no	—
539	C₂²	—	83	2	no	—
540	C₂²	—	166	1	no	—
541	C₂²	—	166	1	no	—
542	C₂²	C₄×D₄×D₈₃	1	1	yes	characteristic
543	C₄	—	2	1	no	—
544	C₄	—	2	2	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	332	1	no	—
549	C₄	—	332	1	no	—
550	C₄	—	332	1	no	—
551	C₄	—	166	1	no	—
552	C₄	—	166	1	no	—
553	C₄	—	166	2	no	—
554	C₄	—	166	1	no	—
555	C₄	C₂×M₁₆×D₈₃	1	1	yes	characteristic
556	C₄	#19128466	1	1	yes	characteristic
557	C₄	#19128514	1	1	yes	characteristic
558	C₄	#19128515	1	1	yes	characteristic
559	C₂	—	166	2	no	—
560	C₂	#24916196	1	1	yes	characteristic
561	C₂	#24916326	1	1	yes	characteristic
562	C₂	#444×D₈₃	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×#1584	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	C₂²×D₈₃	C₄×D₄
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	#1584	D₈₃
hypocenter	C₈₃	#18062
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1584

Complements

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

N	H ≅ G/N	type
4. #24906370	C₂	semidirect
5. #24906369	C₂	semidirect
6. #24906315	C₂	semidirect
7. #24906314	C₂	semidirect
8. #24906312	C₂	semidirect
9. #24906280	C₂	semidirect
10. #24906279	C₂	semidirect
15. C₈₃×#1584	C₂	semidirect
162. #13050580	M₁₆	semidirect
290. #1584	D₈₃	semidirect
297. C₈₃	#18062	semidirect

Maximal subgroups

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

subgroup	index
#24916551	2
#24916549	2
C₄×Q₁₆×D₈₃	2
#24906370	2
#24906369	2
#24906315	2
#24906314	2
#24906312	2
#24906280	2
#24906279	2
#24906225	2
#24905908	2
#24905751	2
C₈₃×#1584	2
#18062	83