Subgroups — #35409832

Order 21248.

708 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24909959	C₂	1	1	yes	maximal, characteristic
2	#24908072	C₂	1	1	yes	maximal, characteristic
3	#24908071	C₂	1	1	yes	maximal, characteristic
4	#24908066	C₂	1	1	yes	maximal, characteristic
5	#24908023	C₂	1	1	yes	maximal, characteristic, complemented
6	#24908020	C₂	1	1	yes	maximal, characteristic, complemented
7	#24908018	C₂	1	1	yes	maximal, characteristic, complemented
8	#24908017	C₂	1	1	yes	maximal, characteristic, complemented
9	#24907322	C₂	1	1	yes	maximal, characteristic, complemented
10	#24907319	C₂	1	1	yes	maximal, characteristic, complemented
11	#24907231	C₂	1	1	yes	maximal, characteristic
12	#24907231	C₂	1	1	yes	maximal, characteristic
13	#24907210	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₈×Dic₈₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#1923	C₂	1	1	yes	maximal, characteristic
16	C₂×#14581751	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×Dic₈₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×Dic₈₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×#14581702	C₂²	1	1	yes	characteristic
23	C₂×#14581702	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₈×Dic₈₃	C₂²	1	1	yes	characteristic
26	C₂×C₈×Dic₈₃	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₈₃	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₈₃	C₂²	1	1	yes	characteristic
29	#19127595	C₄	1	1	yes	characteristic
30	#19127595	C₄	1	1	yes	characteristic
31	#19127589	C₄	1	1	yes	characteristic
32	#19127589	C₄	1	1	yes	characteristic
33	#19127586	C₄	1	1	yes	characteristic
34	#19127586	C₄	1	1	yes	characteristic
35	#19127584	C₄	1	1	yes	characteristic
36	#19127584	C₄	1	1	yes	characteristic
37	C₄×Dic₈₃⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×Dic₈₃⋊C₄	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊Dic₈₃	C₂²	1	1	yes	characteristic
40	#19127547	C₂²	1	1	yes	characteristic
41	C₄²×Dic₈₃	C₂²	1	1	yes	characteristic
42	#19127456	C₂²	1	1	yes	characteristic
43	#19127456	C₂²	1	1	yes	characteristic
44	#19127455	C₂²	1	1	yes	characteristic
45	#19127455	C₂²	1	1	yes	characteristic
46	#19127455	C₂²	1	1	yes	characteristic
47	#19127455	C₂²	1	1	yes	characteristic
48	#19127455	C₂²	1	1	yes	characteristic
49	#19127455	C₂²	1	1	yes	characteristic
50	#19127455	C₂²	1	1	yes	characteristic
51	#19127455	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
55	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
57	#336×C₈₃	C₂²	1	1	yes	characteristic
58	#336×C₈₃	C₂²	1	1	yes	characteristic
59	C₂²×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
60	C₂²×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
63	#14581751	—	2	2	no	—
64	#14581751	—	2	2	no	—
65	C₂×C₄⋊Dic₈₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄⋊Dic₈₃	C₂×C₄	1	1	yes	characteristic
67	C₂×Dic₈₃⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×Dic₈₃⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×Dic₈₃⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×Dic₈₃⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₂²⋊Dic₈₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₂²⋊Dic₈₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₂²⋊Dic₈₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₂²⋊Dic₈₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×Dic₈₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×Dic₈₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×Dic₈₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×Dic₈₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×Dic₈₃	C₂³	1	1	yes	characteristic
80	C₂×C₄×Dic₈₃	C₂³	1	1	yes	characteristic
81	C₂×C₄×Dic₈₃	C₂³	1	1	yes	characteristic
82	C₂×C₄×Dic₈₃	C₂³	1	1	yes	characteristic
83	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
84	Dic₈₃⋊C₈	—	2	2	no	—
85	Dic₈₃⋊C₈	—	2	2	no	—
86	C₂²⋊(C₈₃⋊C₈)	—	2	2	no	—
87	C₂²⋊(C₈₃⋊C₈)	—	2	2	no	—
88	#14581702	—	2	2	no	—
89	#14581702	—	2	2	no	—
90	C₄×C₈₃⋊C₈	—	2	2	no	—
91	C₈×Dic₈₃	—	2	2	no	—
92	C₈×Dic₈₃	—	2	2	no	—
93	C₈×Dic₈₃	—	2	2	no	—
94	C₈×Dic₈₃	—	2	2	no	—
95	C₈₃⋊#95	C₂×C₄	1	1	yes	characteristic
96	C₈₃⋊#95	C₂×C₄	1	1	yes	characteristic
97	C₈₃⋊#95	C₂×C₄	1	1	yes	characteristic
98	C₈₃⋊#95	C₂×C₄	1	1	yes	characteristic
99	C₈₃⋊#95	C₂×C₄	1	1	yes	characteristic
100	C₈₃⋊#95	C₂×C₄	1	1	yes	characteristic
101	C₈₃⋊#95	C₂×C₄	1	1	yes	characteristic
102	C₈₃⋊#95	C₂×C₄	1	1	yes	characteristic
103	C₈₃⋊#95	C₂×C₄	1	1	yes	characteristic
104	C₈₃⋊#95	C₂×C₄	1	1	yes	characteristic
105	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
114	C₄⋊C₈×C₈₃	—	2	2	no	—
115	C₂²⋊C₈×C₈₃	—	2	2	no	—
116	C₂²⋊C₈×C₈₃	—	2	2	no	—
117	C₄×C₈×C₈₃	—	2	2	no	—
118	#95×C₈₃	C₂×C₄	1	1	yes	characteristic
119	#95×C₈₃	C₂×C₄	1	1	yes	characteristic
120	C₂²×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
123	C₂²×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
126	C₂²×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈₃⋊C₈	—	2	1	no	—
129	C₂×C₈₃⋊C₈	—	2	1	no	—
130	C₂×C₈₃⋊C₈	—	2	1	no	—
131	C₂×C₈₃⋊C₈	—	2	1	no	—
132	C₂×C₈₃⋊C₈	—	2	1	no	—
133	C₂×C₈₃⋊C₈	—	2	1	no	—
134	C₂×C₈₃⋊C₈	—	2	1	no	—
135	C₂×C₈₃⋊C₈	—	2	1	no	—
136	C₂×C₈₃⋊C₈	—	2	1	no	—
137	C₂×C₈₃⋊C₈	—	2	1	no	—
138	C₂×C₈₃⋊C₈	#41	1	2	yes	—
139	C₂×C₈₃⋊C₈	#41	1	2	yes	—
140	C₄⋊Dic₈₃	—	2	2	no	—
141	C₄⋊Dic₈₃	—	2	2	no	—
142	Dic₈₃⋊C₄	—	2	2	no	—
143	Dic₈₃⋊C₄	—	2	2	no	—
144	Dic₈₃⋊C₄	—	2	2	no	—
145	Dic₈₃⋊C₄	—	2	2	no	—
146	C₂²⋊Dic₈₃	—	2	2	no	—
147	C₂²⋊Dic₈₃	—	2	2	no	—
148	C₂²⋊Dic₈₃	—	2	2	no	—
149	C₂²⋊Dic₈₃	—	2	2	no	—
150	C₄×Dic₈₃	—	2	2	no	—
151	C₄×Dic₈₃	—	2	2	no	—
152	C₄×Dic₈₃	—	2	1	no	—
153	C₄×Dic₈₃	—	2	1	no	—
154	C₄×Dic₈₃	—	2	1	no	—
155	C₄×Dic₈₃	—	2	1	no	—
156	C₄×Dic₈₃	—	2	1	no	—
157	C₄×Dic₈₃	—	2	1	no	—
158	C₄×Dic₈₃	—	2	2	no	—
159	C₄×Dic₈₃	—	2	2	no	—
160	C₄×Dic₈₃	#41	1	2	yes	—
161	C₄×Dic₈₃	#41	1	2	yes	—
162	C₂⁴×C₈₃	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₈₃	—	2	1	no	—
164	C₂²×C₄×C₈₃	—	2	1	no	—
165	C₂²×C₄×C₈₃	—	2	1	no	—
166	C₂²×C₄×C₈₃	—	2	1	no	—
167	C₂²×C₄×C₈₃	—	2	1	no	—
168	C₂²×C₄×C₈₃	—	2	1	no	—
169	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
175	C₂×C₈×C₈₃	—	2	1	no	—
176	C₂×C₈×C₈₃	—	2	1	no	—
177	C₂×C₈×C₈₃	—	2	1	no	—
178	C₂×C₈×C₈₃	—	2	1	no	—
179	C₂×C₈×C₈₃	—	2	1	no	—
180	C₂×C₈×C₈₃	—	2	1	no	—
181	C₂×C₈×C₈₃	—	2	1	no	—
182	C₂×C₈×C₈₃	—	2	1	no	—
183	C₂×C₈×C₈₃	—	2	1	no	—
184	C₂×C₈×C₈₃	—	2	1	no	—
185	C₂×C₈×C₈₃	#41	1	2	yes	—
186	C₂×C₈×C₈₃	#41	1	2	yes	—
187	C₂²⋊C₄×C₈₃	—	2	2	no	—
188	C₂²⋊C₄×C₈₃	—	2	2	no	—
189	C₄²×C₈₃	—	2	1	no	—
190	C₄²×C₈₃	—	2	1	no	—
191	C₄²×C₈₃	—	2	1	no	—
192	C₄²×C₈₃	—	2	1	no	—
193	C₂³×C₈₃	—	2	1	no	—
194	C₂³×C₈₃	—	2	1	no	—
195	C₂³×C₈₃	—	2	1	no	—
196	C₂³×C₈₃	—	2	1	no	—
197	C₂³×C₈₃	—	2	1	no	—
198	C₂³×C₈₃	—	2	1	no	—
199	C₂³×C₈₃	—	2	1	no	—
200	C₂³×C₈₃	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₈₃	—	2	1	no	—
202	C₂×C₄×C₈₃	—	2	1	no	—
203	C₂×C₄×C₈₃	—	2	1	no	—
204	C₂×C₄×C₈₃	—	2	1	no	—
205	C₂×C₄×C₈₃	—	2	1	no	—
206	C₂×C₄×C₈₃	—	2	1	no	—
207	C₂×C₄×C₈₃	—	2	1	no	—
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	—	2	1	no	—
213	C₂×C₄×C₈₃	—	2	1	no	—
214	C₂×C₄×C₈₃	—	4	1	no	—
215	C₂×C₄×C₈₃	—	4	1	no	—
216	C₂×C₄×C₈₃	—	4	1	no	—
217	C₂×C₄×C₈₃	—	4	1	no	—
218	C₂×C₄×C₈₃	#131	1	2	yes	—
219	C₂×C₄×C₈₃	#131	1	2	yes	—
220	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
226	C₂×Dic₈₃	—	2	1	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	—	2	1	no	—
232	C₂×Dic₈₃	—	2	1	no	—
233	C₂×Dic₈₃	—	2	1	no	—
234	C₂×Dic₈₃	—	2	1	no	—
235	C₂×Dic₈₃	—	2	1	no	—
236	C₂×Dic₈₃	—	2	1	no	—
237	C₂×Dic₈₃	—	2	1	no	—
238	C₂×Dic₈₃	—	2	1	no	—
239	C₂×Dic₈₃	—	2	1	no	—
240	C₂×Dic₈₃	—	2	1	no	—
241	C₂×Dic₈₃	—	2	1	no	—
242	C₂×Dic₈₃	—	2	1	no	—
243	C₂×Dic₈₃	—	2	1	no	—
244	C₂×Dic₈₃	—	2	1	no	—
245	C₂×Dic₈₃	—	2	1	no	—
246	C₂×Dic₈₃	#117	1	2	yes	—
247	C₂×Dic₈₃	#117	1	2	yes	—
248	C₂×Dic₈₃	#131	1	2	yes	—
249	C₂×Dic₈₃	#131	1	2	yes	—
250	C₈×C₈₃	—	2	2	no	—
251	C₈×C₈₃	—	2	2	no	—
252	C₈×C₈₃	—	4	1	no	—
253	C₈×C₈₃	—	4	1	no	—
254	C₈₃⋊C₈	—	2	2	no	—
255	C₈₃⋊C₈	—	2	2	no	—
256	C₈₃⋊C₈	—	4	1	no	—
257	C₈₃⋊C₈	—	4	1	no	—
258	C₂²×C₈₃	—	4	1	no	—
259	C₂²×C₈₃	—	4	1	no	—
260	C₂²×C₈₃	—	4	1	no	—
261	C₂²×C₈₃	—	4	1	no	—
262	C₂²×C₈₃	—	4	1	no	—
263	C₂²×C₈₃	—	4	1	no	—
264	C₂²×C₈₃	—	4	1	no	—
265	C₂²×C₈₃	C₂×#117	1	1	yes	characteristic
266	C₂²×C₈₃	C₄×#41	1	1	yes	characteristic
267	C₂²×C₈₃	C₄×#41	1	1	yes	characteristic
268	C₂²×C₈₃	C₂×#131	1	1	yes	characteristic
269	C₂²×C₈₃	C₂×#131	1	1	yes	characteristic
270	C₂²×C₈₃	C₂×#131	1	1	yes	characteristic
271	C₂²×C₈₃	C₂×#131	1	1	yes	characteristic
272	C₄×C₈₃	—	2	2	no	—
273	C₄×C₈₃	—	2	2	no	—
274	C₄×C₈₃	—	4	1	no	—
275	C₄×C₈₃	—	4	1	no	—
276	C₄×C₈₃	—	4	1	no	—
277	C₄×C₈₃	#529	1	1	yes	characteristic
278	C₄×C₈₃	#529	1	1	yes	characteristic
279	C₄×C₈₃	#529	1	1	yes	characteristic
280	C₄×C₈₃	#529	1	1	yes	characteristic
281	Dic₈₃	—	2	2	no	—
282	Dic₈₃	—	2	2	no	—
283	Dic₈₃	—	2	2	no	—
284	Dic₈₃	—	2	2	no	—
285	Dic₈₃	—	4	1	no	—
286	Dic₈₃	—	4	1	no	—
287	Dic₈₃	—	4	1	no	—
288	Dic₈₃	—	4	1	no	—
289	#21432	—	83	1	no	maximal, Sylow
290	C₂×C₈₃	—	8	1	no	—
291	C₂×C₈₃	#2298	1	1	yes	characteristic
292	C₂×C₈₃	#2922	1	1	yes	characteristic
293	C₂×C₈₃	#2922	1	1	yes	characteristic
294	C₂×C₈₃	#2966	1	1	yes	characteristic
295	C₂×C₈₃	#2966	1	1	yes	characteristic
296	C₂×C₈₃	#2966	1	1	yes	characteristic
297	C₂×C₈₃	#2966	1	1	yes	characteristic
298	#2298	—	83	1	no	—
299	#1923	—	83	1	no	—
300	#1923	—	83	1	no	—
301	#1923	—	83	1	no	—
302	#1923	D₈₃	1	1	yes	characteristic
303	#1916	—	83	1	no	—
304	#1916	—	83	1	no	—
305	#1916	—	83	1	no	—
306	#1916	—	83	1	no	—
307	#1768	—	83	1	no	—
308	#1768	—	83	1	no	—
309	#1750	—	83	1	no	—
310	#1750	—	83	1	no	—
311	#1745	—	83	1	no	—
312	C₄²×C₈	—	83	1	no	—
313	C₈₃	#21432	1	1	yes	characteristic, complemented, Sylow
314	C₂×#117	—	83	1	no	—
315	C₂×C₄⋊C₈	—	83	1	no	—
316	C₂×C₄⋊C₈	—	83	1	no	—
317	C₂×C₄⋊C₈	—	83	1	no	—
318	C₂×C₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic
319	C₂×C₂²⋊C₈	—	83	1	no	—
320	C₂×C₂²⋊C₈	—	83	1	no	—
321	C₂×C₂²⋊C₈	C₂×D₈₃	1	1	yes	characteristic
322	C₂×C₂²⋊C₈	C₂×D₈₃	1	1	yes	characteristic
323	C₂×#97	—	83	1	no	—
324	C₂×#97	—	83	1	no	—
325	C₂×C₄×C₈	—	83	1	no	—
326	C₂×C₄×C₈	—	83	1	no	—
327	C₂×C₄×C₈	—	83	1	no	—
328	C₂×C₄×C₈	—	83	1	no	—
329	C₂×C₄×C₈	—	83	1	no	—
330	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
331	#388	—	83	1	no	—
332	#388	—	83	1	no	—
333	#388	—	83	1	no	—
334	#388	—	83	1	no	—
335	#387	—	83	1	no	—
336	#387	—	83	1	no	—
337	#387	—	83	1	no	—
338	#387	—	83	1	no	—
339	C₄×C₄⋊C₄	—	83	1	no	—
340	C₄×C₄⋊C₄	—	83	1	no	—
341	C₄×C₂²⋊C₄	—	83	1	no	—
342	C₄×C₂²⋊C₄	C₂×D₈₃	1	1	yes	characteristic
343	#376	—	83	1	no	—
344	C₄³	—	83	1	no	—
345	#336	—	83	1	no	—
346	#336	—	83	1	no	—
347	#336	—	83	1	no	—
348	#336	—	83	1	no	—
349	#336	—	83	1	no	—
350	#336	—	83	1	no	—
351	#336	—	83	1	no	—
352	#336	—	83	1	no	—
353	#336	—	83	1	no	—
354	#336	—	83	1	no	—
355	#336	C₂×D₈₃	1	1	yes	characteristic
356	#336	C₂×D₈₃	1	1	yes	characteristic
357	C₂³×C₄	C₂²×D₈₃	1	1	yes	characteristic
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	C₂²×D₈₃	1	1	yes	characteristic
363	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
364	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
365	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
366	#117	—	166	2	no	—
367	#117	—	166	2	no	—
368	C₂×C₄⋊C₄	—	83	1	no	—
369	C₂×C₄⋊C₄	—	83	1	no	—
370	C₂×C₄⋊C₄	—	83	1	no	—
371	C₂×C₄⋊C₄	—	83	1	no	—
372	C₂×C₄⋊C₄	—	83	1	no	—
373	C₂×C₄⋊C₄	—	83	1	no	—
374	C₂×C₂²⋊C₄	—	83	1	no	—
375	C₂×C₂²⋊C₄	—	83	1	no	—
376	C₂×C₂²⋊C₄	—	83	1	no	—
377	C₂×C₂²⋊C₄	—	83	1	no	—
378	C₂×C₂²⋊C₄	C₄×D₈₃	1	1	yes	characteristic
379	C₂×C₂²⋊C₄	C₄×D₈₃	1	1	yes	characteristic
380	C₂×C₄²	—	83	1	no	—
381	C₂×C₄²	—	83	1	no	—
382	C₂×C₄²	—	83	1	no	—
383	C₂×C₄²	—	83	1	no	—
384	C₂×C₄²	—	83	1	no	—
385	C₂×C₄²	—	83	1	no	—
386	C₂×C₄²	—	83	1	no	—
387	C₂×C₄²	—	83	1	no	—
388	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
389	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
390	C₄⋊C₈	—	2	2	no	—
391	C₄⋊C₈	—	166	2	no	—
392	C₄⋊C₈	—	166	2	no	—
393	C₄⋊C₈	—	166	2	no	—
394	C₂²⋊C₈	—	2	2	no	—
395	C₂²⋊C₈	—	2	2	no	—
396	C₂²⋊C₈	—	166	2	no	—
397	C₂²⋊C₈	—	166	2	no	—
398	#97	—	166	2	no	—
399	#97	—	166	2	no	—
400	C₄×C₈	—	2	2	no	—
401	C₄×C₈	—	166	2	no	—
402	C₄×C₈	—	166	2	no	—
403	C₄×C₈	—	166	2	no	—
404	C₄×C₈	—	166	2	no	—
405	C₄×C₈	—	166	2	no	—
406	#95	—	83	1	no	—
407	#95	—	83	1	no	—
408	#95	—	83	1	no	—
409	#95	—	83	1	no	—
410	#95	—	83	1	no	—
411	#95	—	83	1	no	—
412	#95	—	83	1	no	—
413	#95	—	83	1	no	—
414	#95	—	83	1	no	—
415	#95	—	83	1	no	—
416	#95	C₄×D₈₃	1	1	yes	characteristic
417	#95	C₄×D₈₃	1	1	yes	characteristic
418	C₂⁴	C₂×C₄×D₈₃	1	1	yes	characteristic
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	83	1	no	—
426	C₂²×C₄	—	83	1	no	—
427	C₂²×C₄	—	83	1	no	—
428	C₂²×C₄	—	83	1	no	—
429	C₂²×C₄	—	83	1	no	—
430	C₂²×C₄	—	83	1	no	—
431	C₂²×C₄	—	83	1	no	—
432	C₂²×C₄	—	83	1	no	—
433	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
434	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
435	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
436	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
437	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
438	C₂²×C₄	C₂³×D₈₃	1	1	yes	characteristic
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	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	—	83	2	no	—
450	C₂×C₈	—	83	2	no	—
451	C₂×C₈	—	166	1	no	—
452	C₂×C₈	—	166	1	no	—
453	C₂×C₈	—	166	1	no	—
454	C₂×C₈	—	166	1	no	—
455	C₂×C₈	—	166	1	no	—
456	C₂×C₈	—	166	1	no	—
457	C₂×C₈	—	166	1	no	—
458	C₂×C₈	—	166	1	no	—
459	C₂×C₈	—	166	1	no	—
460	C₂×C₈	—	166	1	no	—
461	C₂×C₈	#13050589	1	2	yes	—
462	C₂×C₈	#13050589	1	2	yes	—
463	C₄⋊C₄	—	166	2	no	—
464	C₄⋊C₄	—	166	2	no	—
465	C₄⋊C₄	—	166	2	no	—
466	C₄⋊C₄	—	166	2	no	—
467	C₄⋊C₄	—	166	2	no	—
468	C₄⋊C₄	—	166	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	166	2	no	—
472	C₂²⋊C₄	—	166	2	no	—
473	C₂²⋊C₄	—	166	2	no	—
474	C₂²⋊C₄	—	166	2	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	83	2	no	—
480	C₄²	—	83	2	no	—
481	C₄²	—	166	2	no	—
482	C₄²	—	166	2	no	—
483	C₄²	—	166	2	no	—
484	C₄²	—	166	2	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	—	166	1	no	—
491	C₂³	—	2	1	no	—
492	C₂³	—	2	1	no	—
493	C₂³	—	2	1	no	—
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	1	no	—
498	C₂³	C₂²×C₄×D₈₃	1	1	yes	characteristic
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
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	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	83	2	no	—
517	C₂×C₄	—	83	2	no	—
518	C₂×C₄	—	83	2	no	—
519	C₂×C₄	—	83	2	no	—
520	C₂×C₄	—	166	1	no	—
521	C₂×C₄	—	166	1	no	—
522	C₂×C₄	—	166	1	no	—
523	C₂×C₄	—	166	1	no	—
524	C₂×C₄	—	166	1	no	—
525	C₂×C₄	—	166	1	no	—
526	C₂×C₄	—	166	1	no	—
527	C₂×C₄	—	166	1	no	—
528	C₂×C₄	—	166	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	—	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	#14581798	1	2	yes	—
541	C₂×C₄	#14581800	1	2	yes	—
542	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
543	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
544	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
545	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
546	C₂×C₄	C₂×#13050589	1	1	yes	characteristic
547	C₂×C₄	C₂×#13050589	1	1	yes	characteristic
548	C₈	—	2	2	no	—
549	C₈	—	2	2	no	—
550	C₈	—	4	1	no	—
551	C₈	—	4	1	no	—
552	C₈	—	332	1	no	—
553	C₈	—	332	1	no	—
554	C₈	—	166	2	no	—
555	C₈	—	166	2	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	#117×D₈₃	1	1	yes	characteristic
564	C₂²	C₄×#13050589	1	1	yes	characteristic
565	C₂²	C₄×#13050589	1	1	yes	characteristic
566	C₂²	#131×D₈₃	1	1	yes	characteristic
567	C₂²	#131×D₈₃	1	1	yes	characteristic
568	C₂²	C₂×#14581798	1	1	yes	characteristic
569	C₂²	C₂×#14581800	1	1	yes	characteristic
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	1	no	—
575	C₄	—	332	1	no	—
576	C₄	—	332	1	no	—
577	C₄	—	332	1	no	—
578	C₄	—	332	1	no	—
579	C₄	—	166	2	no	—
580	C₄	—	166	2	no	—
581	C₄	—	166	2	no	—
582	C₄	—	166	2	no	—
583	C₄	#19128228	1	1	yes	characteristic
584	C₄	#19128230	1	1	yes	characteristic
585	C₄	#19128232	1	1	yes	characteristic
586	C₄	#19128234	1	1	yes	characteristic
587	C₂	—	8	1	no	—
588	C₂	#24909957	1	1	yes	characteristic
589	C₂	#24916102	1	1	yes	characteristic
590	C₂	#24916104	1	1	yes	characteristic
591	C₂	#24916431	1	1	yes	characteristic
592	C₂	#24916433	1	1	yes	characteristic
593	C₂	#24916435	1	1	yes	characteristic
594	C₂	#24916441	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₃
commutator, socle	C₂³×C₈₃	C₂³×C₄
Fitting	C₈₃×#1923	C₂
prime radical	C₂⁴×C₈₃	C₂²×C₄
cosocle	C₂²×C₄×C₈₃	C₂⁴
hypercenter	#1923	D₈₃
hypocenter	C₈₃	#21432
LCS	G ▷ C₂³×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1923

Complements

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

N	H ≅ G/N	type
5. #24908023	C₂	semidirect
6. #24908020	C₂	semidirect
7. #24908018	C₂	semidirect
8. #24908017	C₂	semidirect
9. #24907322	C₂	semidirect
10. #24907319	C₂	semidirect
13. #24907210	C₂	semidirect
14. C₄×C₈×Dic₈₃	C₂	semidirect
313. C₈₃	#21432	semidirect

Maximal subgroups

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

subgroup	index
#24909959	2
#24908072	2
#24908071	2
#24908066	2
#24908023	2
#24908020	2
#24908018	2
#24908017	2
#24907322	2
#24907319	2
#24907231	2
#24907210	2
C₄×C₈×Dic₈₃	2
C₈₃×#1923	2
#21432	83