Subgroups — #35414839

Order 21248.

662 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	#24916100	C₂	1	1	yes	maximal, characteristic
2	#24916099	C₂	1	1	yes	maximal, characteristic
3	C₂×#19127726	C₂	1	1	yes	maximal, characteristic
4	#24908239	C₂	1	1	yes	maximal, characteristic, complemented
5	#24908238	C₂	1	1	yes	maximal, characteristic, complemented
6	#24908237	C₂	1	1	yes	maximal, characteristic, complemented
7	#24908237	C₂	1	1	yes	maximal, characteristic, complemented
8	#24908236	C₂	1	1	yes	maximal, characteristic, complemented
9	#24908235	C₂	1	1	yes	maximal, characteristic, complemented
10	#24908235	C₂	1	1	yes	maximal, characteristic, complemented
11	#24907504	C₂	1	1	yes	maximal, characteristic
12	#24907502	C₂	1	1	yes	maximal, characteristic
13	#24907500	C₂	1	1	yes	maximal, characteristic
14	#24907498	C₂	1	1	yes	maximal, characteristic
15	C₈₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#13050573	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₈₃	C₂²	1	1	yes	characteristic
18	C₂×#14581749	C₂²	1	1	yes	characteristic
19	#19127763	—	2	1	no	—
20	#19127763	—	2	1	no	—
21	#19127761	—	2	1	no	—
22	#19127761	—	2	1	no	—
23	#19127761	—	2	1	no	—
24	#19127761	—	2	1	no	—
25	#19127760	—	2	1	no	—
26	#19127760	—	2	1	no	—
27	C₂×#14581728	C₂²	1	1	yes	characteristic
28	C₂×#14581728	C₂²	1	1	yes	characteristic
29	C₂×#14581727	C₂²	1	1	yes	characteristic
30	C₂×#14581727	C₂²	1	1	yes	characteristic
31	C₂×#14581727	C₂²	1	1	yes	characteristic
32	C₂×#14581727	C₂²	1	1	yes	characteristic
33	#19127726	C₄	1	2	yes	—
34	#19127726	C₄	1	2	yes	—
35	#19127726	C₄	1	2	yes	—
36	#19127726	C₄	1	2	yes	—
37	#19127725	C₂²	1	1	yes	characteristic
38	#19127724	C₂²	1	1	yes	characteristic
39	#19127724	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
41	C₂×Dic₈₃⋊C₈	C₂²	1	1	yes	characteristic
42	C₂×Dic₈₃⋊C₈	C₂²	1	1	yes	characteristic
43	#19127664	C₂²	1	1	yes	characteristic
44	#19127664	C₂²	1	1	yes	characteristic
45	#19127664	C₂²	1	1	yes	characteristic
46	#19127664	C₂²	1	1	yes	characteristic
47	C₄×#13050574	C₂²	1	1	yes	characteristic
48	M₁₆×Dic₈₃	C₂²	1	1	yes	characteristic
49	M₁₆×Dic₈₃	C₂²	1	1	yes	characteristic
50	#19127466	C₂²	1	1	yes	characteristic
51	#19127466	C₂²	1	1	yes	characteristic
52	#19127465	C₂²	1	1	yes	characteristic
53	#19127465	C₂²	1	1	yes	characteristic
54	#19127465	C₂²	1	1	yes	characteristic
55	#19127465	C₂²	1	1	yes	characteristic
56	C₂×#108×C₈₃	C₂²	1	1	yes	characteristic
57	C₂×#108×C₈₃	C₂²	1	1	yes	characteristic
58	#423×C₈₃	C₂²	1	1	yes	characteristic
59	C₂×C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
60	C₄×M₁₆×C₈₃	C₂²	1	1	yes	characteristic
61	#341×C₈₃	C₂²	1	1	yes	characteristic
62	#341×C₈₃	C₂²	1	1	yes	characteristic
63	C₂²×C₄×D₈₃	C₂³	1	1	yes	characteristic
64	C₂×#13050574	C₂³	1	1	yes	characteristic
65	C₂×#13050574	C₂³	1	1	yes	characteristic
66	C₂×#13050574	C₂³	1	1	yes	characteristic
67	C₂×#13050574	C₂³	1	1	yes	characteristic
68	C₂×#13050573	—	4	1	no	—
69	C₂×#13050573	—	4	1	no	—
70	C₂×#13050573	C₂×C₄	1	2	yes	—
71	C₂×#13050573	C₂×C₄	1	2	yes	—
72	C₂²×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
74	C₂×C₈×D₈₃	—	4	1	no	—
75	C₂×C₈×D₈₃	—	4	1	no	—
76	C₂×C₈×D₈₃	C₂×C₄	1	2	yes	—
77	C₂×C₈×D₈₃	C₂×C₄	1	2	yes	—
78	#14581749	C₂×C₄	1	1	yes	characteristic
79	#14581749	C₂×C₄	1	1	yes	characteristic
80	#14581749	C₂×C₄	1	1	yes	characteristic
81	#14581749	C₂×C₄	1	1	yes	characteristic
82	#14581749	D₄	1	1	yes	characteristic
83	#14581749	D₄	1	1	yes	characteristic
84	#14581749	D₄	1	1	yes	characteristic
85	#14581749	D₄	1	1	yes	characteristic
86	C₂×Dic₈₃⋊C₄	Q₈	1	1	yes	characteristic
87	C₂×Dic₈₃⋊C₄	Q₈	1	1	yes	characteristic
88	C₂×(C₂×D₈₃)⋊C₄	Q₈	1	1	yes	characteristic
89	C₂×(C₂×D₈₃)⋊C₄	Q₈	1	1	yes	characteristic
90	C₂×C₄×Dic₈₃	C₂³	1	1	yes	characteristic
91	#14581728	—	4	1	no	—
92	#14581728	—	4	1	no	—
93	#14581727	—	4	1	no	—
94	#14581727	—	4	1	no	—
95	#14581727	—	4	1	no	—
96	#14581727	—	4	1	no	—
97	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
98	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
99	C₄⋊(C₈₃⋊C₈)	C₂×C₄	1	2	yes	—
100	C₄⋊(C₈₃⋊C₈)	C₂×C₄	1	2	yes	—
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	C₂×C₄	1	2	yes	—
106	Dic₈₃⋊C₈	C₂×C₄	1	2	yes	—
107	Dic₈₃⋊C₈	C₂×C₄	1	2	yes	—
108	Dic₈₃⋊C₈	C₂×C₄	1	2	yes	—
109	(C₂×D₈₃)⋊C₈	—	2	1	no	—
110	(C₂×D₈₃)⋊C₈	—	2	1	no	—
111	(C₂×D₈₃)⋊C₈	—	2	1	no	—
112	(C₂×D₈₃)⋊C₈	—	2	1	no	—
113	(C₂×D₈₃)⋊C₈	—	2	1	no	—
114	(C₂×D₈₃)⋊C₈	—	2	1	no	—
115	(C₂×D₈₃)⋊C₈	—	2	1	no	—
116	(C₂×D₈₃)⋊C₈	—	2	1	no	—
117	#14581703	—	2	1	no	—
118	#14581702	—	2	1	no	—
119	#14581702	—	2	1	no	—
120	C₄×C₈₃⋊C₈	—	2	1	no	—
121	C₈×Dic₈₃	—	2	1	no	—
122	C₈×Dic₈₃	—	2	1	no	—
123	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
124	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
125	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
126	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
127	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
130	#108×C₈₃	—	4	1	no	—
131	#108×C₈₃	—	4	1	no	—
132	C₄⋊C₈×C₈₃	—	2	1	no	—
133	C₄⋊C₈×C₈₃	—	2	1	no	—
134	C₄⋊C₈×C₈₃	C₂×C₄	1	2	yes	—
135	C₄⋊C₈×C₈₃	C₂×C₄	1	2	yes	—
136	#97×C₈₃	—	2	1	no	—
137	C₄×C₈×C₈₃	—	2	1	no	—
138	C₂³×D₈₃	C₂×Q₈	1	1	yes	characteristic
139	C₂²×Dic₈₃	C₂×Q₈	1	1	yes	characteristic
140	C₂²×Dic₈₃	C₂×Q₈	1	1	yes	characteristic
141	C₂²×Dic₈₃	C₂×Q₈	1	1	yes	characteristic
142	C₂×C₄×D₈₃	—	2	1	no	—
143	C₂×C₄×D₈₃	—	2	1	no	—
144	C₂×C₄×D₈₃	—	2	1	no	—
145	C₂×C₄×D₈₃	—	2	1	no	—
146	C₂×C₄×D₈₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₄×D₈₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₄×D₈₃	C₂×D₄	1	1	yes	characteristic
149	C₂×C₄×D₈₃	C₂×D₄	1	1	yes	characteristic
150	#13050574	—	2	1	no	—
151	#13050574	—	2	1	no	—
152	#13050574	—	2	1	no	—
153	#13050574	—	2	1	no	—
154	#13050574	—	2	1	no	—
155	#13050574	—	2	1	no	—
156	#13050574	—	2	1	no	—
157	#13050574	—	2	1	no	—
158	#13050573	—	4	2	no	—
159	#13050573	—	4	2	no	—
160	C₂×C₈₃⋊C₈	—	2	1	no	—
161	C₂×C₈₃⋊C₈	—	2	1	no	—
162	C₂×C₈₃⋊C₈	—	2	1	no	—
163	C₂×C₈₃⋊C₈	—	2	1	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	—	2	1	no	—
168	C₂×C₈₃⋊C₈	C₂²×C₄	1	2	yes	—
169	C₂×C₈₃⋊C₈	C₂²×C₄	1	2	yes	—
170	C₈×D₈₃	—	4	2	no	—
171	C₈×D₈₃	—	4	2	no	—
172	Dic₈₃⋊C₄	C₄⋊C₄	1	1	yes	characteristic
173	Dic₈₃⋊C₄	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	Dic₈₃⋊C₄	C₄⋊C₄	1	1	yes	characteristic
179	Dic₈₃⋊C₄	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	(C₂×D₈₃)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
185	(C₂×D₈₃)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
186	(C₂×D₈₃)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
187	(C₂×D₈₃)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
188	C₄×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
189	C₄×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
190	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
191	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₈₃	C₂×Q₈	1	1	yes	characteristic
193	C₂²×C₄×C₈₃	C₂×Q₈	1	1	yes	characteristic
194	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
195	M₁₆×C₈₃	—	2	1	no	—
196	M₁₆×C₈₃	—	2	1	no	—
197	M₁₆×C₈₃	—	2	1	no	—
198	M₁₆×C₈₃	—	2	1	no	—
199	M₁₆×C₈₃	—	2	1	no	—
200	M₁₆×C₈₃	—	2	1	no	—
201	M₁₆×C₈₃	—	2	1	no	—
202	M₁₆×C₈₃	—	2	1	no	—
203	C₂×C₈×C₈₃	—	2	1	no	—
204	C₂×C₈×C₈₃	—	2	1	no	—
205	C₂×C₈×C₈₃	—	2	1	no	—
206	C₂×C₈×C₈₃	—	2	1	no	—
207	C₂×C₈×C₈₃	—	2	1	no	—
208	C₂×C₈×C₈₃	—	2	1	no	—
209	C₂×C₈×C₈₃	—	2	1	no	—
210	C₂×C₈×C₈₃	—	2	1	no	—
211	C₂×C₈×C₈₃	C₂²×C₄	1	2	yes	—
212	C₂×C₈×C₈₃	C₂²×C₄	1	2	yes	—
213	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
214	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
215	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
217	C₂³×C₈₃	C₂²×Q₈	1	1	yes	characteristic
218	C₂²×D₈₃	—	2	1	no	—
219	C₂²×D₈₃	—	2	1	no	—
220	C₂²×D₈₃	—	4	1	no	—
221	C₂²×D₈₃	—	4	1	no	—
222	C₂²×D₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
223	C₂²×D₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₈₃	—	4	1	no	—
225	C₂×C₄×C₈₃	—	4	1	no	—
226	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂×C₄×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×C₄×C₈₃	2₋¹⁺⁴	1	1	yes	characteristic
235	C₂×C₄×C₈₃	2₋¹⁺⁴	1	1	yes	characteristic
236	C₂×Dic₈₃	—	2	1	no	—
237	C₂×Dic₈₃	—	2	1	no	—
238	C₂×Dic₈₃	—	4	1	no	—
239	C₂×Dic₈₃	—	4	1	no	—
240	C₂×Dic₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
241	C₂×Dic₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
242	C₂×Dic₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
243	C₂×Dic₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
244	C₂×Dic₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
245	C₂×Dic₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
246	C₄×D₈₃	—	2	1	no	—
247	C₄×D₈₃	—	2	1	no	—
248	C₄×D₈₃	—	2	1	no	—
249	C₄×D₈₃	—	2	1	no	—
250	C₄×D₈₃	—	2	1	no	—
251	C₄×D₈₃	—	2	1	no	—
252	C₄×D₈₃	—	2	1	no	—
253	C₄×D₈₃	—	2	1	no	—
254	C₈×C₈₃	—	2	2	no	—
255	C₈×C₈₃	—	2	2	no	—
256	C₈×C₈₃	—	4	1	no	—
257	C₈×C₈₃	—	4	1	no	—
258	C₈×C₈₃	—	4	1	no	—
259	C₈×C₈₃	—	4	1	no	—
260	C₈₃⋊C₈	—	2	2	no	—
261	C₈₃⋊C₈	—	2	2	no	—
262	C₈₃⋊C₈	—	4	1	no	—
263	C₈₃⋊C₈	—	4	1	no	—
264	C₈₃⋊C₈	—	4	1	no	—
265	C₈₃⋊C₈	—	4	1	no	—
266	C₂²×C₈₃	—	2	1	no	—
267	C₂²×C₈₃	—	2	1	no	—
268	C₂²×C₈₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
269	C₂²×C₈₃	#544	1	1	yes	characteristic
270	C₂²×C₈₃	#544	1	1	yes	characteristic
271	C₂×D₈₃	—	2	1	no	—
272	C₂×D₈₃	—	2	1	no	—
273	C₂×D₈₃	—	2	1	no	—
274	C₂×D₈₃	—	2	1	no	—
275	C₂×D₈₃	—	2	1	no	—
276	C₂×D₈₃	—	2	1	no	—
277	C₂×D₈₃	—	4	2	no	—
278	C₂×D₈₃	—	4	2	no	—
279	C₄×C₈₃	—	2	1	no	—
280	C₄×C₈₃	—	2	1	no	—
281	C₄×C₈₃	—	2	1	no	—
282	C₄×C₈₃	—	2	1	no	—
283	C₄×C₈₃	#518	1	1	yes	characteristic
284	C₄×C₈₃	#519	1	1	yes	characteristic
285	C₄×C₈₃	#537	1	1	yes	characteristic
286	C₄×C₈₃	#537	1	1	yes	characteristic
287	Dic₈₃	—	2	1	no	—
288	Dic₈₃	—	2	1	no	—
289	Dic₈₃	—	2	1	no	—
290	Dic₈₃	—	2	1	no	—
291	Dic₈₃	—	2	1	no	—
292	Dic₈₃	—	2	1	no	—
293	#21971	—	83	1	no	maximal, Sylow
294	C₂×C₈₃	—	2	1	no	—
295	C₂×C₈₃	—	2	1	no	—
296	C₂×C₈₃	#2316	1	1	yes	characteristic
297	C₂×C₈₃	#2916	1	1	yes	characteristic
298	C₂×C₈₃	#2916	1	1	yes	characteristic
299	D₈₃	—	4	1	no	—
300	D₈₃	—	4	1	no	—
301	#2921	—	83	1	no	—
302	#2921	—	83	1	no	—
303	C₂×#424	—	83	1	no	—
304	#1950	—	83	1	no	—
305	#1950	—	83	1	no	—
306	#1950	—	83	1	no	—
307	#1950	—	83	1	no	—
308	#1950	—	83	1	no	—
309	#1950	—	83	1	no	—
310	#1950	—	83	1	no	—
311	#1950	D₈₃	1	1	yes	characteristic, complemented
312	#1811	—	83	1	no	—
313	#1811	—	83	1	no	—
314	#1810	—	83	1	no	—
315	#1810	—	83	1	no	—
316	C₈₃	#21971	1	1	yes	characteristic, complemented, Sylow
317	C₂²×M₁₆	—	83	1	no	—
318	C₂³×C₈	—	83	1	no	—
319	C₂×#117	—	83	1	no	—
320	#433	—	166	1	no	—
321	#433	—	166	1	no	—
322	#433	—	166	1	no	—
323	#433	—	166	1	no	—
324	#433	—	166	1	no	—
325	#433	—	166	1	no	—
326	#433	—	166	1	no	—
327	#433	—	166	1	no	—
328	C₂×#108	—	83	1	no	—
329	C₂×#108	—	83	1	no	—
330	C₂×#108	—	83	1	no	—
331	C₂×#108	—	83	1	no	—
332	C₂×#108	—	83	1	no	—
333	C₂×#108	—	83	1	no	—
334	C₂×#108	C₂×D₈₃	1	1	yes	characteristic
335	C₂×#108	C₂×D₈₃	1	1	yes	characteristic
336	#424	—	83	2	no	—
337	#424	—	83	2	no	—
338	#424	—	83	2	no	—
339	#424	—	83	2	no	—
340	#423	—	83	1	no	—
341	#423	—	83	1	no	—
342	#423	—	83	1	no	—
343	#423	C₂×D₈₃	1	1	yes	characteristic
344	C₂×C₄⋊C₈	—	83	1	no	—
345	C₂×C₄⋊C₈	—	83	1	no	—
346	C₂×C₄⋊C₈	—	83	1	no	—
347	C₂×C₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic
348	#407	—	83	1	no	—
349	#407	—	83	1	no	—
350	#407	—	83	1	no	—
351	#407	—	83	1	no	—
352	C₄×M₁₆	—	83	1	no	—
353	C₄×M₁₆	—	83	1	no	—
354	C₄×M₁₆	—	83	1	no	—
355	C₄×M₁₆	C₂×D₈₃	1	1	yes	characteristic
356	#341	—	83	1	no	—
357	#341	—	83	1	no	—
358	#341	—	83	1	no	—
359	#341	—	83	1	no	—
360	#341	—	83	1	no	—
361	#341	—	83	1	no	—
362	#341	C₂×D₈₃	1	1	yes	characteristic
363	#341	C₂×D₈₃	1	1	yes	characteristic
364	C₂³×C₄	—	83	1	no	—
365	C₂×M₁₆	—	332	1	no	—
366	C₂×M₁₆	—	332	1	no	—
367	C₂×M₁₆	—	83	2	no	—
368	C₂×M₁₆	—	83	2	no	—
369	C₂×M₁₆	—	83	1	no	—
370	C₂×M₁₆	—	83	1	no	—
371	C₂×M₁₆	—	83	1	no	—
372	C₂×M₁₆	—	83	1	no	—
373	C₂×M₁₆	C₂²×D₈₃	1	1	yes	characteristic
374	C₂×M₁₆	C₂²×D₈₃	1	1	yes	characteristic
375	C₂×M₁₆	C₂²×D₈₃	1	1	yes	characteristic
376	C₂×M₁₆	C₂²×D₈₃	1	1	yes	characteristic
377	C₂²×C₈	—	332	1	no	—
378	C₂²×C₈	—	332	1	no	—
379	C₂²×C₈	—	83	2	no	—
380	C₂²×C₈	—	83	2	no	—
381	C₂²×C₈	—	83	1	no	—
382	C₂²×C₈	—	83	1	no	—
383	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
384	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
385	#117	—	83	1	no	—
386	#117	—	83	1	no	—
387	#117	—	83	1	no	—
388	#117	—	83	1	no	—
389	#117	—	83	1	no	—
390	#117	—	83	1	no	—
391	#117	—	83	1	no	—
392	#117	—	83	1	no	—
393	C₂×C₄⋊C₄	—	83	1	no	—
394	C₂×C₄⋊C₄	—	83	1	no	—
395	C₂×C₂²⋊C₄	—	83	1	no	—
396	C₂×C₂²⋊C₄	—	83	1	no	—
397	C₂×C₄²	—	83	1	no	—
398	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
399	#108	—	4	1	no	—
400	#108	—	4	1	no	—
401	#108	—	332	1	no	—
402	#108	—	332	1	no	—
403	#108	—	332	1	no	—
404	#108	—	332	1	no	—
405	#108	—	332	1	no	—
406	#108	—	332	1	no	—
407	C₄⋊C₈	—	2	1	no	—
408	C₄⋊C₈	—	2	1	no	—
409	C₄⋊C₈	—	83	2	no	—
410	C₄⋊C₈	—	83	2	no	—
411	C₄⋊C₈	—	83	2	no	—
412	C₄⋊C₈	—	83	2	no	—
413	C₄⋊C₈	—	83	2	no	—
414	C₄⋊C₈	—	83	2	no	—
415	C₄⋊C₈	—	166	1	no	—
416	C₄⋊C₈	—	166	1	no	—
417	C₄⋊C₈	—	166	1	no	—
418	C₄⋊C₈	—	166	1	no	—
419	C₄⋊C₈	—	166	1	no	—
420	C₄⋊C₈	—	166	1	no	—
421	C₄⋊C₈	C₄×D₈₃	1	2	yes	—
422	C₄⋊C₈	C₄×D₈₃	1	2	yes	—
423	C₂²⋊C₈	—	166	1	no	—
424	C₂²⋊C₈	—	166	1	no	—
425	C₂²⋊C₈	—	166	1	no	—
426	C₂²⋊C₈	—	166	1	no	—
427	C₂²⋊C₈	—	166	1	no	—
428	C₂²⋊C₈	—	166	1	no	—
429	C₂²⋊C₈	—	166	1	no	—
430	C₂²⋊C₈	—	166	1	no	—
431	#97	—	2	1	no	—
432	#97	—	166	1	no	—
433	#97	—	166	1	no	—
434	#97	—	166	1	no	—
435	C₄×C₈	—	2	1	no	—
436	C₄×C₈	—	166	1	no	—
437	C₄×C₈	—	166	1	no	—
438	C₄×C₈	—	166	1	no	—
439	C₂⁴	—	83	1	no	—
440	C₂²×C₄	—	83	1	no	—
441	C₂²×C₄	—	83	1	no	—
442	C₂²×C₄	—	83	1	no	—
443	C₂²×C₄	—	83	1	no	—
444	C₂²×C₄	—	83	1	no	—
445	C₂²×C₄	—	83	1	no	—
446	C₂²×C₄	—	83	1	no	—
447	C₂²×C₄	—	166	1	no	—
448	C₂²×C₄	—	166	1	no	—
449	C₂²×C₄	—	166	1	no	—
450	C₂²×C₄	—	166	1	no	—
451	C₂²×C₄	Q₈×D₈₃	1	1	yes	characteristic
452	C₂²×C₄	Q₈×D₈₃	1	1	yes	characteristic
453	C₂²×C₄	C₂³×D₈₃	1	1	yes	characteristic
454	M₁₆	—	2	1	no	—
455	M₁₆	—	2	1	no	—
456	M₁₆	—	2	1	no	—
457	M₁₆	—	2	1	no	—
458	M₁₆	—	2	1	no	—
459	M₁₆	—	2	1	no	—
460	M₁₆	—	2	1	no	—
461	M₁₆	—	2	1	no	—
462	M₁₆	—	332	2	no	—
463	M₁₆	—	332	2	no	—
464	M₁₆	—	166	1	no	—
465	M₁₆	—	166	1	no	—
466	M₁₆	—	166	1	no	—
467	M₁₆	—	166	1	no	—
468	M₁₆	—	166	1	no	—
469	M₁₆	—	166	1	no	—
470	M₁₆	—	166	1	no	—
471	M₁₆	—	166	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	332	2	no	—
481	C₂×C₈	—	332	2	no	—
482	C₂×C₈	—	83	2	no	—
483	C₂×C₈	—	83	2	no	—
484	C₂×C₈	—	166	1	no	—
485	C₂×C₈	—	166	1	no	—
486	C₂×C₈	—	166	1	no	—
487	C₂×C₈	—	166	1	no	—
488	C₂×C₈	—	166	1	no	—
489	C₂×C₈	—	166	1	no	—
490	C₂×C₈	—	166	1	no	—
491	C₂×C₈	—	166	1	no	—
492	C₂×C₈	C₂×C₄×D₈₃	1	2	yes	—
493	C₂×C₈	C₂×C₄×D₈₃	1	2	yes	—
494	C₄⋊C₄	—	83	1	no	—
495	C₄⋊C₄	—	83	1	no	—
496	C₄⋊C₄	—	83	1	no	—
497	C₄⋊C₄	—	83	1	no	—
498	C₄⋊C₄	—	83	1	no	—
499	C₄⋊C₄	—	83	1	no	—
500	C₄⋊C₄	—	83	1	no	—
501	C₄⋊C₄	—	83	1	no	—
502	C₂²⋊C₄	—	83	1	no	—
503	C₂²⋊C₄	—	83	1	no	—
504	C₂²⋊C₄	—	83	1	no	—
505	C₂²⋊C₄	—	83	1	no	—
506	C₂²⋊C₄	—	83	1	no	—
507	C₂²⋊C₄	—	83	1	no	—
508	C₂²⋊C₄	—	83	1	no	—
509	C₂²⋊C₄	—	83	1	no	—
510	C₄²	—	83	1	no	—
511	C₄²	—	83	1	no	—
512	C₄²	—	83	1	no	—
513	C₄²	—	83	1	no	—
514	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
515	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
516	C₄²	D₄×D₈₃	1	1	yes	characteristic
517	C₄²	D₄×D₈₃	1	1	yes	characteristic
518	C₂³	—	332	1	no	—
519	C₂³	—	332	1	no	—
520	C₂³	—	83	1	no	—
521	C₂³	—	83	1	no	—
522	C₂³	—	166	1	no	—
523	C₂³	—	166	1	no	—
524	C₂³	C₂×Q₈×D₈₃	1	1	yes	characteristic
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	332	1	no	—
528	C₂×C₄	—	332	1	no	—
529	C₂×C₄	—	83	1	no	—
530	C₂×C₄	—	83	1	no	—
531	C₂×C₄	—	83	1	no	—
532	C₂×C₄	—	83	1	no	—
533	C₂×C₄	—	83	1	no	—
534	C₂×C₄	—	83	1	no	—
535	C₂×C₄	—	166	1	no	—
536	C₂×C₄	—	166	1	no	—
537	C₂×C₄	—	166	1	no	—
538	C₂×C₄	—	166	1	no	—
539	C₂×C₄	—	166	1	no	—
540	C₂×C₄	—	166	1	no	—
541	C₂×C₄	—	166	1	no	—
542	C₂×C₄	—	166	1	no	—
543	C₂×C₄	—	166	1	no	—
544	C₂×C₄	—	166	1	no	—
545	C₂×C₄	C₄⋊C₄×D₈₃	1	1	yes	characteristic
546	C₂×C₄	C₄⋊C₄×D₈₃	1	1	yes	characteristic
547	C₂×C₄	C₄⋊C₄×D₈₃	1	1	yes	characteristic
548	C₂×C₄	C₄⋊C₄×D₈₃	1	1	yes	characteristic
549	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
550	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
551	C₂×C₄	#14581837	1	1	yes	characteristic
552	C₂×C₄	#14581838	1	1	yes	characteristic
553	C₂×C₄	#14581839	1	1	yes	characteristic
554	C₂×C₄	#14581840	1	1	yes	characteristic
555	C₈	—	2	2	no	—
556	C₈	—	2	2	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	332	1	no	—
562	C₈	—	332	1	no	—
563	C₈	—	332	1	no	—
564	C₈	—	332	1	no	—
565	C₈	—	166	2	no	—
566	C₈	—	166	2	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	332	2	no	—
570	C₂²	—	332	2	no	—
571	C₂²	—	166	1	no	—
572	C₂²	—	166	1	no	—
573	C₂²	—	166	1	no	—
574	C₂²	—	166	1	no	—
575	C₂²	—	166	1	no	—
576	C₂²	—	166	1	no	—
577	C₂²	C₂×C₄⋊C₄×D₈₃	1	1	yes	characteristic
578	C₂²	#19128328	1	1	yes	characteristic
579	C₂²	#19128331	1	1	yes	characteristic
580	C₄	—	2	1	no	—
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	—	2	1	no	—
584	C₄	—	166	1	no	—
585	C₄	—	166	1	no	—
586	C₄	—	166	1	no	—
587	C₄	—	166	1	no	—
588	C₄	—	166	1	no	—
589	C₄	—	166	1	no	—
590	C₄	#19128173	1	1	yes	characteristic
591	C₄	#19128177	1	1	yes	characteristic
592	C₄	#19128280	1	1	yes	characteristic
593	C₄	#19128281	1	1	yes	characteristic
594	C₂	—	2	1	no	—
595	C₂	—	2	1	no	—
596	C₂	—	332	1	no	—
597	C₂	—	332	1	no	—
598	C₂	#24910078	1	1	yes	characteristic
599	C₂	#24916071	1	1	yes	characteristic
600	C₂	#24916073	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₃
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₃
Fitting	C₈₃×#1950	C₂
socle	C₂²×C₈₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₈₃	C₂×Q₈
cosocle	C₂²×C₄×C₈₃	C₂⁴
hypercenter	#1950	D₈₃
hypocenter	C₈₃	#21971
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1950

Complements

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

N	H ≅ G/N	type
4. #24908239	C₂	semidirect
5. #24908238	C₂	semidirect
6. #24908237	C₂	semidirect
7. #24908237	C₂	semidirect
8. #24908236	C₂	semidirect
9. #24908235	C₂	semidirect
10. #24908235	C₂	semidirect
15. C₈₃×#1950	C₂	semidirect
311. #1950	D₈₃	semidirect
316. C₈₃	#21971	semidirect

Maximal subgroups

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

subgroup	index
#24916100	2
#24916099	2
C₂×#19127726	2
#24908239	2
#24908238	2
#24908237	2
#24908236	2
#24908235	2
#24907504	2
#24907502	2
#24907500	2
#24907498	2
C₈₃×#1950	2
#21971	83