Subgroups — #35373633

Order 21248.

610 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24916419	C₂	1	1	yes	maximal, characteristic
2	#24916130	C₂	1	1	yes	maximal, characteristic
3	#24916124	C₂	1	1	yes	maximal, characteristic
4	#24906243	C₂	1	1	yes	maximal, characteristic, complemented
5	#24906240	C₂	1	1	yes	maximal, characteristic, complemented
6	#24906240	C₂	1	1	yes	maximal, characteristic, complemented
7	#24906236	C₂	1	1	yes	maximal, characteristic, complemented
8	#24906236	C₂	1	1	yes	maximal, characteristic, complemented
9	#24906225	C₂	1	1	yes	maximal, characteristic, complemented
10	#24906224	C₂	1	1	yes	maximal, characteristic, complemented
11	#24906217	C₂	1	1	yes	maximal, characteristic, complemented
12	#24906210	C₂	1	1	yes	maximal, characteristic, complemented
13	#24906209	C₂	1	1	yes	maximal, characteristic, complemented
14	#334×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#1572	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#13050590	C₂²	1	1	yes	characteristic
17	#19127825	C₄	1	1	yes	characteristic
18	#19127825	C₄	1	1	yes	characteristic
19	#19127766	C₄	1	1	yes	characteristic
20	#19127766	C₄	1	1	yes	characteristic
21	(C₂²⋊D₈₃)⋊C₈	C₄	1	1	yes	characteristic
22	(C₂²⋊D₈₃)⋊C₈	C₄	1	1	yes	characteristic
23	(C₂²⋊D₈₃)⋊C₈	C₄	1	1	yes	characteristic
24	(C₂²⋊D₈₃)⋊C₈	C₄	1	1	yes	characteristic
25	#19127763	—	2	1	no	—
26	#19127760	—	2	1	no	—
27	#19127759	—	2	1	no	—
28	#19127759	—	2	1	no	—
29	#19127758	C₂²	1	1	yes	characteristic
30	#19127757	C₂²	1	1	yes	characteristic
31	#19127757	C₂²	1	1	yes	characteristic
32	#19127754	C₂²	1	1	yes	characteristic
33	#19127753	C₂²	1	1	yes	characteristic
34	#19127753	C₂²	1	1	yes	characteristic
35	#19127752	C₂²	1	1	yes	characteristic
36	#19127752	C₂²	1	1	yes	characteristic
37	#19127723	C₂²	1	1	yes	characteristic
38	#19127723	C₂²	1	1	yes	characteristic
39	C₄⋊C₈×D₈₃	C₂²	1	1	yes	characteristic
40	C₄⋊C₈×D₈₃	C₂²	1	1	yes	characteristic
41	#19127666	—	2	1	no	—
42	#19127666	—	2	1	no	—
43	#19127658	—	2	1	no	—
44	#19127655	—	2	1	no	—
45	C₂×C₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₈₃	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₈₃	C₂²	1	1	yes	characteristic
48	#19127454	C₂²	1	1	yes	characteristic
49	#19127454	C₂²	1	1	yes	characteristic
50	#19127453	C₂²	1	1	yes	characteristic
51	#19127453	C₂²	1	1	yes	characteristic
52	#19127453	C₂²	1	1	yes	characteristic
53	#19127453	C₂²	1	1	yes	characteristic
54	#19127452	C₂²	1	1	yes	characteristic
55	#19127452	C₂²	1	1	yes	characteristic
56	#19127451	C₂²	1	1	yes	characteristic
57	#19127451	C₂²	1	1	yes	characteristic
58	#19127451	C₂²	1	1	yes	characteristic
59	#19127451	C₂²	1	1	yes	characteristic
60	#432×C₈₃	C₂²	1	1	yes	characteristic
61	#431×C₈₃	C₂²	1	1	yes	characteristic
62	#431×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	C₂×#13050590	D₄	1	1	yes	characteristic
68	C₂×#13050573	—	2	1	no	—
69	C₂×#13050573	—	2	1	no	—
70	C₂²×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₈₃	—	2	1	no	—
73	C₂×C₈×D₈₃	—	2	1	no	—
74	C₂×C₈×D₈₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₈₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₈×D₈₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₈×D₈₃	C₂×C₄	1	1	yes	characteristic
78	C₄×Dic₁₆₆	C₂×C₄	1	1	yes	characteristic
79	C₄×Dic₁₆₆	Q₈	1	1	yes	characteristic
80	C₄×D₃₃₂	C₂×C₄	1	1	yes	characteristic
81	C₄×D₃₃₂	Q₈	1	1	yes	characteristic
82	C₄×C₂²⋊D₈₃	C₂×C₄	1	1	yes	characteristic
83	C₄×C₂²⋊D₈₃	C₂×C₄	1	1	yes	characteristic
84	C₄×C₂²⋊D₈₃	Q₈	1	1	yes	characteristic
85	C₄×C₂²⋊D₈₃	Q₈	1	1	yes	characteristic
86	#14581751	D₄	1	1	yes	characteristic
87	#14581749	D₄	1	1	yes	characteristic
88	#14581749	D₄	1	1	yes	characteristic
89	C₄²×D₈₃	C₂³	1	1	yes	characteristic
90	C₄²×D₈₃	C₂³	1	1	yes	characteristic
91	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
92	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
93	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
94	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
95	Dic₈₃⋊C₈	—	2	1	no	—
96	Dic₈₃⋊C₈	—	2	1	no	—
97	Dic₈₃⋊C₈	—	2	1	no	—
98	Dic₈₃⋊C₈	—	2	1	no	—
99	Dic₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
100	Dic₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
101	Dic₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
102	Dic₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
103	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
104	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
105	(C₂×D₈₃)⋊C₈	—	2	1	no	—
106	(C₂×D₈₃)⋊C₈	—	2	1	no	—
107	(C₂×D₈₃)⋊C₈	—	2	1	no	—
108	(C₂×D₈₃)⋊C₈	—	2	1	no	—
109	(C₂×D₈₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
110	(C₂×D₈₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
111	(C₂×D₈₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
112	(C₂×D₈₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
113	#14581703	—	2	1	no	—
114	#14581702	—	2	1	no	—
115	#14581702	—	2	1	no	—
116	C₄×C₈₃⋊C₈	—	2	1	no	—
117	C₄×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
118	C₄×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
119	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
120	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
121	C₈×Dic₈₃	—	2	1	no	—
122	C₈×Dic₈₃	—	2	1	no	—
123	C₈×Dic₈₃	C₂×C₄	1	1	yes	characteristic
124	C₈×Dic₈₃	C₂×C₄	1	1	yes	characteristic
125	C₈×Dic₈₃	C₂×C₄	1	1	yes	characteristic
126	C₈×Dic₈₃	C₂×C₄	1	1	yes	characteristic
127	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
128	C₄⋊C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
129	C₄⋊C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
130	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
131	C₄⋊C₈×C₈₃	C₂³	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	C₂×C₄	1	1	yes	characteristic
137	C₂²⋊C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
138	#97×C₈₃	—	2	1	no	—
139	C₄×C₈×C₈₃	—	2	1	no	—
140	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
141	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
142	#13050590	—	2	2	no	—
143	#13050590	—	2	2	no	—
144	C₂×Dic₁₆₆	C₄⋊C₄	1	1	yes	characteristic
145	C₂×D₃₃₂	C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₂²⋊D₈₃	C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₂²⋊D₈₃	C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×D₈₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₄×D₈₃	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₄×D₈₃	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×D₈₃	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×D₈₃	C₂×Q₈	1	1	yes	characteristic
153	C₂×C₄×D₈₃	C₂×Q₈	1	1	yes	characteristic
154	#13050573	—	4	2	no	—
155	#13050573	—	4	2	no	—
156	C₂×C₈₃⋊C₈	—	2	2	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	—	2	1	no	—
161	C₂×C₈₃⋊C₈	—	4	1	no	—
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	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
166	C₈×D₈₃	—	2	2	no	—
167	C₈×D₈₃	—	2	2	no	—
168	C₈×D₈₃	—	4	1	no	—
169	C₈×D₈₃	—	4	1	no	—
170	C₈×D₈₃	—	4	2	no	—
171	C₈×D₈₃	—	4	2	no	—
172	C₄⋊Dic₈₃	C₄⋊C₄	1	1	yes	characteristic
173	C₄⋊Dic₈₃	C₄⋊C₄	1	1	yes	characteristic
174	Dic₈₃⋊C₄	C₄⋊C₄	1	1	yes	characteristic
175	Dic₈₃⋊C₄	C₄⋊C₄	1	1	yes	characteristic
176	Dic₈₃⋊C₄	C₄⋊C₄	1	1	yes	characteristic
177	Dic₈₃⋊C₄	C₄⋊C₄	1	1	yes	characteristic
178	C₂²⋊Dic₈₃	C₄⋊C₄	1	1	yes	characteristic
179	C₂²⋊Dic₈₃	C₄⋊C₄	1	1	yes	characteristic
180	(C₂×D₈₃)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
181	(C₂×D₈₃)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
182	(C₂×D₈₃)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
183	(C₂×D₈₃)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
184	C₄×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
185	C₄×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
186	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
187	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
188	C₄×Dic₈₃	C₂×Q₈	1	1	yes	characteristic
189	C₄×Dic₈₃	C₂×Q₈	1	1	yes	characteristic
190	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₈₃	C₂×Q₈	1	1	yes	characteristic
193	C₂×C₈×C₈₃	—	2	1	no	—
194	C₂×C₈×C₈₃	—	2	1	no	—
195	C₂×C₈×C₈₃	—	2	1	no	—
196	C₂×C₈×C₈₃	—	2	1	no	—
197	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
201	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
202	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₈₃	C₂×Q₈	1	1	yes	characteristic
204	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
205	C₂³×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂²×D₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂²×D₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₈₃	—	2	1	no	—
209	C₂×C₄×C₈₃	—	2	1	no	—
210	C₂×C₄×C₈₃	—	2	1	no	—
211	C₂×C₄×C₈₃	—	2	1	no	—
212	C₂×C₄×C₈₃	—	4	1	no	—
213	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₈₃	C₂²×Q₈	1	1	yes	characteristic
219	C₂²⋊D₈₃	—	2	2	no	—
220	C₂²⋊D₈₃	—	2	2	no	—
221	C₂×Dic₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
222	C₂×Dic₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
223	C₂×Dic₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
224	C₂×Dic₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
225	C₂×Dic₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
226	C₂×Dic₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
227	D₃₃₂	—	2	2	no	—
228	C₄×D₈₃	—	2	1	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	—	2	1	no	—
234	C₄×D₈₃	—	4	1	no	—
235	C₄×D₈₃	—	4	1	no	—
236	C₄×D₈₃	#135	1	2	yes	—
237	C₄×D₈₃	#135	1	2	yes	—
238	Dic₁₆₆	—	2	2	no	—
239	C₈×C₈₃	—	2	1	no	—
240	C₈×C₈₃	—	2	1	no	—
241	C₈×C₈₃	—	2	1	no	—
242	C₈×C₈₃	—	2	1	no	—
243	C₈×C₈₃	—	4	1	no	—
244	C₈×C₈₃	—	4	1	no	—
245	C₈×C₈₃	—	4	1	no	—
246	C₈×C₈₃	—	4	1	no	—
247	C₈₃⋊C₈	—	2	1	no	—
248	C₈₃⋊C₈	—	2	1	no	—
249	C₈₃⋊C₈	—	2	1	no	—
250	C₈₃⋊C₈	—	4	1	no	—
251	C₈₃⋊C₈	—	4	1	no	—
252	C₈₃⋊C₈	—	4	1	no	—
253	C₈₃⋊C₈	—	4	1	no	—
254	C₈₃⋊C₈	#131	1	2	yes	—
255	C₂²×C₈₃	—	2	1	no	—
256	C₂²×C₈₃	—	2	1	no	—
257	C₂²×C₈₃	—	2	1	no	—
258	C₂²×C₈₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
259	C₂×D₈₃	—	2	1	no	—
260	C₂×D₈₃	—	2	1	no	—
261	C₂×D₈₃	—	2	1	no	—
262	C₂×D₈₃	—	2	1	no	—
263	C₂×D₈₃	—	2	1	no	—
264	C₂×D₈₃	#427	1	2	yes	—
265	C₄×C₈₃	—	2	1	no	—
266	C₄×C₈₃	—	2	1	no	—
267	C₄×C₈₃	—	2	1	no	—
268	C₄×C₈₃	—	2	1	no	—
269	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
270	C₄×C₈₃	#568	1	1	yes	characteristic
271	C₄×C₈₃	C₂×#135	1	1	yes	characteristic
272	C₄×C₈₃	C₂×#135	1	1	yes	characteristic
273	Dic₈₃	—	2	1	no	—
274	Dic₈₃	—	2	1	no	—
275	Dic₈₃	—	2	1	no	—
276	Dic₈₃	—	2	1	no	—
277	Dic₈₃	—	2	1	no	—
278	Dic₈₃	#427	1	2	yes	—
279	#17827	—	83	1	no	maximal, Sylow
280	C₂×C₈₃	—	4	1	no	—
281	C₂×C₈₃	#2906	1	1	yes	characteristic
282	C₂×C₈₃	C₂×#427	1	1	yes	characteristic
283	C₂×C₈₃	#2916	1	1	yes	characteristic
284	D₈₃	—	2	2	no	—
285	D₈₃	—	4	1	no	—
286	C₈×#41	—	83	1	no	—
287	#2925	—	83	1	no	—
288	#2925	—	83	1	no	—
289	#1572	—	83	1	no	—
290	#1572	—	83	1	no	—
291	#1572	—	83	1	no	—
292	#1572	D₈₃	1	1	yes	characteristic, complemented
293	#1571	—	83	1	no	—
294	#1571	—	83	1	no	—
295	#1568	—	83	1	no	—
296	#1568	—	83	1	no	—
297	#1566	—	83	1	no	—
298	#1564	—	83	1	no	—
299	#1564	—	83	1	no	—
300	C₂×#334	—	83	1	no	—
301	C₈₃	#17827	1	1	yes	characteristic, complemented, Sylow
302	C₄×#41	—	83	1	no	—
303	C₈×Q₈	—	83	1	no	—
304	C₈×Q₈	—	83	1	no	—
305	C₈×D₄	—	83	1	no	—
306	C₈×D₄	—	83	1	no	—
307	C₈×D₄	—	83	1	no	—
308	C₈×D₄	—	83	1	no	—
309	C₈×D₄	—	83	1	no	—
310	C₈×D₄	—	83	1	no	—
311	#433	—	166	1	no	—
312	#433	—	166	1	no	—
313	#433	—	166	1	no	—
314	#433	—	166	1	no	—
315	#432	—	83	1	no	—
316	#432	—	83	1	no	—
317	#432	—	83	1	no	—
318	#432	C₂×D₈₃	1	1	yes	characteristic
319	#431	—	83	1	no	—
320	#431	—	83	1	no	—
321	#431	—	83	1	no	—
322	#431	—	83	1	no	—
323	#431	—	83	1	no	—
324	#431	C₂×D₈₃	1	1	yes	characteristic
325	#431	C₂×D₈₃	1	1	yes	characteristic
326	#423	—	83	1	no	—
327	#423	—	83	1	no	—
328	C₂×C₄⋊C₈	—	83	1	no	—
329	C₂×C₄⋊C₈	—	83	1	no	—
330	#408	—	166	1	no	—
331	#408	—	166	1	no	—
332	#405	—	166	1	no	—
333	#405	—	166	1	no	—
334	C₂×C₄×C₈	—	83	1	no	—
335	C₂×C₄×C₈	—	83	1	no	—
336	C₂×C₄×C₈	—	83	1	no	—
337	#335	—	83	1	no	—
338	#335	—	83	1	no	—
339	#335	—	83	1	no	—
340	#335	—	83	1	no	—
341	#335	—	83	1	no	—
342	#335	—	83	1	no	—
343	#335	C₂×D₈₃	1	1	yes	characteristic
344	#335	C₂×D₈₃	1	1	yes	characteristic
345	#334	—	83	1	no	—
346	#334	—	83	1	no	—
347	#334	—	83	1	no	—
348	#334	—	83	1	no	—
349	#334	—	83	1	no	—
350	#334	—	83	1	no	—
351	#334	C₂×D₈₃	1	1	yes	characteristic
352	#334	C₂×D₈₃	1	1	yes	characteristic
353	C₂×#41	—	83	1	no	—
354	C₂×M₁₆	—	166	1	no	—
355	C₂×M₁₆	—	166	1	no	—
356	C₂²×C₈	—	83	1	no	—
357	C₂²×C₈	—	83	1	no	—
358	C₂²×C₈	—	83	1	no	—
359	C₂²×C₈	—	83	1	no	—
360	C₂²×C₈	—	83	1	no	—
361	C₂²×C₈	—	83	1	no	—
362	C₂²×C₈	—	166	1	no	—
363	C₂²×C₈	—	166	1	no	—
364	C₄×Q₈	—	83	1	no	—
365	C₄×Q₈	—	83	1	no	—
366	C₄×D₄	—	83	1	no	—
367	C₄×D₄	—	83	1	no	—
368	C₄×D₄	—	83	1	no	—
369	C₄×D₄	—	83	1	no	—
370	C₄×D₄	—	83	1	no	—
371	C₄×D₄	—	83	1	no	—
372	#117	—	83	1	no	—
373	#117	—	83	1	no	—
374	#117	—	83	1	no	—
375	C₂×C₄²	—	83	1	no	—
376	C₂×C₄²	—	83	1	no	—
377	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
378	C₄⋊C₈	—	83	1	no	—
379	C₄⋊C₈	—	83	1	no	—
380	C₄⋊C₈	—	83	1	no	—
381	C₄⋊C₈	—	83	1	no	—
382	C₄⋊C₈	—	83	1	no	—
383	C₄⋊C₈	—	83	1	no	—
384	C₄⋊C₈	—	83	1	no	—
385	C₄⋊C₈	—	83	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	C₄×D₈₃	1	1	yes	characteristic
391	C₄⋊C₈	C₄×D₈₃	1	1	yes	characteristic
392	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
393	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
394	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
395	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
396	C₂²⋊C₈	—	2	1	no	—
397	C₂²⋊C₈	—	2	1	no	—
398	C₂²⋊C₈	—	83	1	no	—
399	C₂²⋊C₈	—	83	1	no	—
400	C₂²⋊C₈	—	83	1	no	—
401	C₂²⋊C₈	—	83	1	no	—
402	C₂²⋊C₈	—	166	1	no	—
403	C₂²⋊C₈	—	166	1	no	—
404	C₂²⋊C₈	—	166	1	no	—
405	C₂²⋊C₈	—	166	1	no	—
406	C₂²⋊C₈	—	166	1	no	—
407	C₂²⋊C₈	—	166	1	no	—
408	C₂²⋊C₈	C₄×D₈₃	1	1	yes	characteristic
409	C₂²⋊C₈	C₄×D₈₃	1	1	yes	characteristic
410	#97	—	2	1	no	—
411	#97	—	166	1	no	—
412	#97	—	166	1	no	—
413	#97	—	166	1	no	—
414	C₄×C₈	—	2	1	no	—
415	C₄×C₈	—	83	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	—	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	#41	—	166	2	no	—
429	#41	—	166	2	no	—
430	C₂×Q₈	—	83	1	no	—
431	C₂×D₄	—	83	1	no	—
432	C₂×D₄	—	83	1	no	—
433	C₂×D₄	—	83	1	no	—
434	C₂²×C₄	—	83	1	no	—
435	C₂²×C₄	—	83	1	no	—
436	C₂²×C₄	—	83	1	no	—
437	C₂²×C₄	—	83	1	no	—
438	C₂²×C₄	—	83	1	no	—
439	C₂²×C₄	—	83	1	no	—
440	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
441	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
442	C₂²×C₄	Q₈×D₈₃	1	1	yes	characteristic
443	M₁₆	—	332	2	no	—
444	M₁₆	—	332	2	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	332	1	no	—
450	C₂×C₈	—	332	1	no	—
451	C₂×C₈	—	332	2	no	—
452	C₂×C₈	—	332	2	no	—
453	C₂×C₈	—	332	1	no	—
454	C₂×C₈	—	83	1	no	—
455	C₂×C₈	—	83	1	no	—
456	C₂×C₈	—	83	1	no	—
457	C₂×C₈	—	83	1	no	—
458	C₂×C₈	—	166	2	no	—
459	C₂×C₈	—	166	2	no	—
460	C₂×C₈	—	166	1	no	—
461	C₂×C₈	—	166	1	no	—
462	C₂×C₈	—	166	1	no	—
463	C₂×C₈	—	166	1	no	—
464	C₂×C₈	—	166	2	no	—
465	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
466	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
467	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
468	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
469	C₄⋊C₄	—	83	1	no	—
470	C₄⋊C₄	—	83	1	no	—
471	C₄⋊C₄	—	83	1	no	—
472	C₄⋊C₄	—	83	1	no	—
473	C₄⋊C₄	—	83	1	no	—
474	C₄⋊C₄	—	83	1	no	—
475	C₂²⋊C₄	—	83	1	no	—
476	C₂²⋊C₄	—	83	1	no	—
477	C₂²⋊C₄	—	83	1	no	—
478	C₂²⋊C₄	—	83	1	no	—
479	C₂²⋊C₄	—	83	1	no	—
480	C₂²⋊C₄	—	83	1	no	—
481	C₄²	—	83	1	no	—
482	C₄²	—	83	1	no	—
483	C₄²	—	83	1	no	—
484	C₄²	—	83	1	no	—
485	C₄²	—	83	1	no	—
486	C₄²	—	83	1	no	—
487	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
488	C₄²	D₄×D₈₃	1	1	yes	characteristic
489	C₄²	Q₈×D₈₃	1	1	yes	characteristic
490	C₄²	C₂³×D₈₃	1	1	yes	characteristic
491	C₂³	—	83	1	no	—
492	C₂³	—	83	1	no	—
493	C₂³	C₄⋊C₄×D₈₃	1	1	yes	characteristic
494	Q₈	—	166	2	no	—
495	D₄	—	166	2	no	—
496	D₄	—	166	2	no	—
497	D₄	—	166	2	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	332	1	no	—
504	C₂×C₄	—	332	1	no	—
505	C₂×C₄	—	83	1	no	—
506	C₂×C₄	—	83	2	no	—
507	C₂×C₄	—	83	2	no	—
508	C₂×C₄	—	83	1	no	—
509	C₂×C₄	—	83	1	no	—
510	C₂×C₄	—	83	1	no	—
511	C₂×C₄	—	83	1	no	—
512	C₂×C₄	—	83	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	C₄⋊C₄×D₈₃	1	1	yes	characteristic
520	C₂×C₄	C₄⋊C₄×D₈₃	1	1	yes	characteristic
521	C₂×C₄	C₄⋊C₄×D₈₃	1	1	yes	characteristic
522	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
523	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
524	C₂×C₄	C₂×Q₈×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	—	4	1	no	—
533	C₈	—	332	1	no	—
534	C₈	—	332	1	no	—
535	C₈	—	332	1	no	—
536	C₈	—	332	1	no	—
537	C₈	—	83	2	no	—
538	C₈	—	166	1	no	—
539	C₈	—	166	1	no	—
540	C₈	—	166	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	83	2	no	—
545	C₂²	—	166	1	no	—
546	C₂²	—	166	1	no	—
547	C₂²	—	166	1	no	—
548	C₂²	—	166	1	no	—
549	C₂²	—	166	1	no	—
550	C₂²	C₂×C₄⋊C₄×D₈₃	1	1	yes	characteristic
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	2	1	no	—
555	C₄	—	83	2	no	—
556	C₄	—	166	1	no	—
557	C₄	—	166	1	no	—
558	C₄	—	166	1	no	—
559	C₄	—	166	1	no	—
560	C₄	—	166	1	no	—
561	C₄	#131×D₈₃	1	1	yes	characteristic
562	C₄	#19128466	1	1	yes	characteristic
563	C₄	#135×D₈₃	1	1	yes	characteristic
564	C₄	#135×D₈₃	1	1	yes	characteristic
565	C₂	—	4	1	no	—
566	C₂	—	332	1	no	—
567	C₂	—	166	2	no	—
568	C₂	#24916030	1	1	yes	characteristic
569	C₂	#427×D₈₃	1	1	yes	characteristic
570	C₂	#24916073	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×#1572	C₂
socle	C₂²×C₈₃	C₂²×C₄⋊C₄
prime radical	C₂×#13050590	D₄
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	#1572	D₈₃
hypocenter	C₈₃	#17827
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1572

Complements

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

N	H ≅ G/N	type
4. #24906243	C₂	semidirect
5. #24906240	C₂	semidirect
6. #24906240	C₂	semidirect
7. #24906236	C₂	semidirect
8. #24906236	C₂	semidirect
9. #24906225	C₂	semidirect
10. #24906224	C₂	semidirect
11. #24906217	C₂	semidirect
12. #24906210	C₂	semidirect
13. #24906209	C₂	semidirect
14. #334×D₈₃	C₂	semidirect
15. C₈₃×#1572	C₂	semidirect
292. #1572	D₈₃	semidirect
301. C₈₃	#17827	semidirect

Maximal subgroups

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

subgroup	index
#24916419	2
#24916130	2
#24916124	2
#24906243	2
#24906240	2
#24906236	2
#24906225	2
#24906224	2
#24906217	2
#24906210	2
#24906209	2
#334×D₈₃	2
C₈₃×#1572	2
#17827	83