Subgroups — #35374355

Order 21248.

626 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	#24917481	C₂	1	1	yes	maximal, characteristic
2	#24916432	C₂	1	1	yes	maximal, characteristic, complemented
3	#41×C₈₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#24906338	C₂	1	1	yes	maximal, characteristic, complemented
5	#24906331	C₂	1	1	yes	maximal, characteristic, complemented
6	#24906324	C₂	1	1	yes	maximal, characteristic, complemented
7	#24906317	C₂	1	1	yes	maximal, characteristic, complemented
8	#24906284	C₂	1	1	yes	maximal, characteristic, complemented
9	#24906279	C₂	1	1	yes	maximal, characteristic, complemented
10	#24906278	C₂	1	1	yes	maximal, characteristic, complemented
11	#24906272	C₂	1	1	yes	maximal, characteristic, complemented
12	#24906244	C₂	1	1	yes	maximal, characteristic, complemented
13	#24905872	C₂	1	1	yes	maximal, characteristic, complemented
14	#24905756	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#1488	C₂	1	1	yes	maximal, characteristic, complemented
16	#19128235	C₂²	1	1	yes	characteristic
17	#19128042	C₄	1	1	yes	characteristic
18	#19128025	C₄	1	1	yes	characteristic
19	#19128008	C₄	1	1	yes	characteristic
20	#19128001	C₄	1	1	yes	characteristic
21	#19127923	C₄	1	1	yes	characteristic
22	#19127916	C₄	1	1	yes	characteristic
23	#19127863	C₄	1	1	yes	characteristic
24	#19127846	C₄	1	1	yes	characteristic
25	#19127828	C₂²	1	1	yes	characteristic
26	Q₈×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
27	Q₈×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
28	#19127825	C₂²	1	1	yes	characteristic
29	C₄×#13050580	C₂²	1	1	yes	characteristic
30	C₄×#13050577	C₂²	1	1	yes	characteristic
31	C₄×#13050578	C₂²	1	1	yes	characteristic
32	C₄×#13050575	C₂²	1	1	yes	characteristic
33	#19127778	C₂²	1	1	yes	characteristic
34	#19127769	—	2	1	no	—
35	D₄×C₈₃⋊C₈	—	2	1	no	—
36	D₄×C₈₃⋊C₈	—	2	1	no	—
37	D₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
38	D₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
39	#19127766	C₂²	1	1	yes	characteristic
40	(C₂²⋊D₈₃)⋊C₈	—	2	1	no	—
41	#19127763	—	2	1	no	—
42	#19127754	—	2	1	no	—
43	#19127754	C₂²	1	1	yes	characteristic
44	#19127754	C₂²	1	1	yes	characteristic
45	#19127658	—	2	1	no	—
46	C₂×C₄×C₈₃⋊C₈	—	2	1	no	—
47	C₂×C₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
48	#19127453	C₂²	1	1	yes	characteristic
49	#19127453	C₂²	1	1	yes	characteristic
50	#19127451	C₂²	1	1	yes	characteristic
51	#19127451	C₂²	1	1	yes	characteristic
52	#19127433	C₂²	1	1	yes	characteristic
53	#19127433	C₂²	1	1	yes	characteristic
54	#19127430	C₂²	1	1	yes	characteristic
55	#19127430	C₂²	1	1	yes	characteristic
56	#19127423	C₂²	1	1	yes	characteristic
57	#19127423	C₂²	1	1	yes	characteristic
58	#19127422	C₂²	1	1	yes	characteristic
59	#19127422	C₂²	1	1	yes	characteristic
60	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
61	#432×C₈₃	C₂²	1	1	yes	characteristic
62	#431×C₈₃	C₂²	1	1	yes	characteristic
63	Q₈⋊C₈×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	D₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
67	C₂×#13050580	C₂×C₄	1	1	yes	characteristic
68	C₂×#13050578	C₂×C₄	1	1	yes	characteristic
69	C₂×#13050577	C₂×C₄	1	1	yes	characteristic
70	C₂×#13050575	C₂×C₄	1	1	yes	characteristic
71	C₂×#13050573	—	2	1	no	—
72	C₂²×C₈₃⋊C₈	—	2	1	no	—
73	C₂²×C₈₃⋊C₈	—	2	1	no	—
74	C₂²×C₈₃⋊C₈	D₄	1	1	yes	characteristic
75	C₂²×C₈₃⋊C₈	D₄	1	1	yes	characteristic
76	C₂×C₈×D₈₃	—	2	1	no	—
77	#14581786	—	2	1	no	—
78	#14581784	C₂×C₄	1	1	yes	characteristic
79	#14581780	C₂×C₄	1	1	yes	characteristic
80	#14581775	—	2	1	no	—
81	#14581771	C₂×C₄	1	1	yes	characteristic
82	#14581766	C₂×C₄	1	1	yes	characteristic
83	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
84	C₄×D₃₃₂	C₂³	1	1	yes	characteristic
85	C₄×C₂²⋊D₈₃	—	2	1	no	—
86	#14581749	—	2	1	no	—
87	#14581725	C₂×C₄	1	1	yes	characteristic
88	#14581725	C₂×C₄	1	1	yes	characteristic
89	#14581723	C₂×C₄	1	1	yes	characteristic
90	#14581723	C₂×C₄	1	1	yes	characteristic
91	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
92	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
93	C₄⋊(C₈₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
94	C₄⋊(C₈₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
95	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
96	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
97	Dic₈₃⋊C₈	—	2	1	no	—
98	Dic₈₃⋊C₈	—	2	1	no	—
99	#14581716	C₂×C₄	1	1	yes	characteristic
100	#14581716	C₂×C₄	1	1	yes	characteristic
101	#14581715	C₂×C₄	1	1	yes	characteristic
102	#14581715	C₂×C₄	1	1	yes	characteristic
103	#14581713	C₂×C₄	1	1	yes	characteristic
104	#14581713	C₂×C₄	1	1	yes	characteristic
105	#14581712	C₂×C₄	1	1	yes	characteristic
106	#14581712	C₂×C₄	1	1	yes	characteristic
107	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
108	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
109	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
110	C₂²⋊(C₈₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
111	C₂²⋊(C₈₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
112	(C₂×D₈₃)⋊C₈	—	2	1	no	—
113	(C₂×D₈₃)⋊C₈	—	2	1	no	—
114	#14581702	—	2	1	no	—
115	C₄×C₈₃⋊C₈	—	2	1	no	—
116	C₄×C₈₃⋊C₈	—	2	1	no	—
117	C₄×C₈₃⋊C₈	—	2	1	no	—
118	C₄×C₈₃⋊C₈	D₄	1	1	yes	characteristic
119	C₄×C₈₃⋊C₈	D₄	1	1	yes	characteristic
120	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
121	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
122	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
123	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
124	C₈×Dic₈₃	—	2	1	no	—
125	C₂×#41×C₈₃	C₂×C₄	1	1	yes	characteristic
126	C₄×Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
127	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
128	C₄×D₄×C₈₃	—	2	1	no	—
129	C₄×D₄×C₈₃	—	2	1	no	—
130	C₄×D₄×C₈₃	C₂×C₄	1	1	yes	characteristic
131	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
132	#117×C₈₃	—	2	1	no	—
133	#117×C₈₃	C₂×C₄	1	1	yes	characteristic
134	C₂×C₄²×C₈₃	—	2	1	no	—
135	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₈₃	—	2	1	no	—
137	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
138	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
139	C₂²⋊C₈×C₈₃	—	2	1	no	—
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	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
145	C₂×D₃₃₂	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₂²⋊D₈₃	—	2	1	no	—
147	C₂×C₄×D₈₃	—	2	1	no	—
148	#13050580	—	2	2	no	—
149	#13050578	—	2	2	no	—
150	#13050577	—	2	2	no	—
151	#13050575	—	2	2	no	—
152	#13050573	—	4	2	no	—
153	C₂×C₈₃⋊C₈	—	2	1	no	—
154	C₂×C₈₃⋊C₈	—	2	1	no	—
155	C₂×C₈₃⋊C₈	—	4	1	no	—
156	C₂×C₈₃⋊C₈	—	4	1	no	—
157	C₂×C₈₃⋊C₈	—	4	2	no	—
158	C₂×C₈₃⋊C₈	—	4	2	no	—
159	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
164	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
165	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
167	C₈×D₈₃	—	4	2	no	—
168	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
169	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
170	Dic₈₃⋊C₄	—	2	1	no	—
171	Dic₈₃⋊C₄	—	2	1	no	—
172	Dic₈₃⋊C₄	—	2	1	no	—
173	Dic₈₃⋊C₄	—	2	1	no	—
174	C₂²⋊Dic₈₃	—	2	1	no	—
175	(C₂×D₈₃)⋊C₄	—	2	1	no	—
176	(C₂×D₈₃)⋊C₄	—	2	1	no	—
177	(C₂×D₈₃)⋊C₄	—	2	1	no	—
178	(C₂×D₈₃)⋊C₄	—	2	1	no	—
179	C₄×Dic₈₃	—	2	1	no	—
180	#41×C₈₃	—	2	2	no	—
181	#41×C₈₃	—	2	2	no	—
182	C₂×Q₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
183	C₂×D₄×C₈₃	—	2	1	no	—
184	C₂×D₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₈₃	—	2	1	no	—
186	C₂²×C₄×C₈₃	—	2	1	no	—
187	C₂²×C₄×C₈₃	—	2	1	no	—
188	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
191	C₂×C₈×C₈₃	—	2	1	no	—
192	C₂×C₈×C₈₃	—	2	1	no	—
193	C₂×C₈×C₈₃	—	2	1	no	—
194	C₂×C₈×C₈₃	—	2	1	no	—
195	C₄⋊C₄×C₈₃	—	2	1	no	—
196	C₄⋊C₄×C₈₃	—	2	1	no	—
197	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
198	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
199	C₂²⋊C₄×C₈₃	—	2	1	no	—
200	C₂²⋊C₄×C₈₃	—	2	1	no	—
201	C₂²⋊C₄×C₈₃	—	2	1	no	—
202	C₄²×C₈₃	—	2	1	no	—
203	C₄²×C₈₃	—	2	1	no	—
204	C₄²×C₈₃	—	2	1	no	—
205	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
206	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₈₃	#41	1	1	yes	characteristic
208	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
209	C₂³×C₈₃	—	2	1	no	—
210	C₂³×C₈₃	C₄×D₄	1	1	yes	characteristic
211	C₂²×D₈₃	—	2	1	no	—
212	Q₈×C₈₃	—	2	1	no	—
213	Q₈×C₈₃	#131	1	2	yes	—
214	D₄×C₈₃	—	2	4	no	—
215	D₄×C₈₃	—	2	1	no	—
216	D₄×C₈₃	#131	1	2	yes	—
217	C₂×C₄×C₈₃	—	2	4	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	—	2	1	no	—
222	C₂×C₄×C₈₃	—	2	1	no	—
223	C₂×C₄×C₈₃	—	2	1	no	—
224	C₂×C₄×C₈₃	—	2	1	no	—
225	C₂×C₄×C₈₃	—	4	1	no	—
226	C₂×C₄×C₈₃	—	4	2	no	—
227	C₂×C₄×C₈₃	—	4	1	no	—
228	C₂×C₄×C₈₃	—	4	1	no	—
229	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
235	C₂²⋊D₈₃	—	4	2	no	—
236	C₂×Dic₈₃	—	2	1	no	—
237	C₂×Dic₈₃	—	2	1	no	—
238	C₂×Dic₈₃	—	2	1	no	—
239	D₃₃₂	—	2	1	no	—
240	D₃₃₂	—	2	1	no	—
241	C₄×D₈₃	—	4	1	no	—
242	C₄×D₈₃	—	4	1	no	—
243	Dic₁₆₆	—	2	1	no	—
244	Dic₁₆₆	—	2	1	no	—
245	C₈×C₈₃	—	4	1	no	—
246	C₈×C₈₃	—	4	1	no	—
247	C₈×C₈₃	—	4	1	no	—
248	C₈×C₈₃	—	4	1	no	—
249	C₈₃⋊C₈	—	2	1	no	—
250	C₈₃⋊C₈	—	2	1	no	—
251	C₈₃⋊C₈	—	2	1	no	—
252	C₈₃⋊C₈	—	2	1	no	—
253	C₈₃⋊C₈	—	2	1	no	—
254	C₈₃⋊C₈	—	2	1	no	—
255	C₈₃⋊C₈	—	2	1	no	—
256	C₈₃⋊C₈	—	2	1	no	—
257	C₈₃⋊C₈	—	4	1	no	—
258	C₈₃⋊C₈	—	4	1	no	—
259	C₂²×C₈₃	—	2	1	no	—
260	C₂²×C₈₃	—	2	2	no	—
261	C₂²×C₈₃	—	2	1	no	—
262	C₂²×C₈₃	—	2	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	—	4	1	no	—
267	C₂×D₈₃	—	4	1	no	—
268	C₂×D₈₃	—	4	1	no	—
269	C₄×C₈₃	—	2	1	no	—
270	C₄×C₈₃	—	2	2	no	—
271	C₄×C₈₃	—	2	1	no	—
272	C₄×C₈₃	—	2	1	no	—
273	C₄×C₈₃	—	2	1	no	—
274	C₄×C₈₃	—	4	1	no	—
275	C₄×C₈₃	—	4	1	no	—
276	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
277	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
278	C₄×C₈₃	#575	1	1	yes	characteristic
279	C₄×C₈₃	#575	1	1	yes	characteristic
280	Dic₈₃	—	4	1	no	—
281	Dic₈₃	—	4	1	no	—
282	Dic₈₃	—	4	1	no	—
283	#17909	—	83	1	no	maximal, Sylow
284	C₂×C₈₃	—	4	1	no	—
285	C₂×C₈₃	—	4	2	no	—
286	C₂×C₈₃	#2929	1	1	yes	characteristic
287	C₂×C₈₃	#2943	1	1	yes	characteristic
288	C₂×C₈₃	#2955	1	1	yes	characteristic
289	D₈₃	—	8	1	no	—
290	#3102	—	83	1	no	—
291	#2966	—	83	1	no	—
292	C₈×#41	—	83	1	no	—
293	#1588	—	83	1	no	—
294	#1587	—	83	1	no	—
295	#1586	—	83	1	no	—
296	#1585	—	83	1	no	—
297	#1580	—	83	1	no	—
298	#1579	—	83	1	no	—
299	SD₁₆⋊C₈	—	83	1	no	—
300	SD₁₆⋊C₈	—	83	1	no	—
301	#1572	—	83	1	no	—
302	#1488	D₈₃	1	1	yes	characteristic, complemented
303	#1482	—	83	1	no	—
304	#1452	—	83	1	no	—
305	C₈₃	#17909	1	1	yes	characteristic, complemented, Sylow
306	#529	—	83	1	no	—
307	C₄×#41	C₂×D₈₃	1	1	yes	characteristic
308	#485	—	83	1	no	—
309	#482	—	83	1	no	—
310	#479	—	83	1	no	—
311	#478	—	83	1	no	—
312	#464	—	83	1	no	—
313	#463	—	83	1	no	—
314	#452	—	83	1	no	—
315	#449	—	83	1	no	—
316	#446	—	83	1	no	—
317	C₈×Q₈	—	83	1	no	—
318	C₈×Q₈	—	83	1	no	—
319	C₈×Q₈	—	83	1	no	—
320	C₄×Q₁₆	—	83	1	no	—
321	C₄×SD₁₆	—	83	1	no	—
322	C₄×SD₁₆	—	83	1	no	—
323	C₄×D₈	—	83	1	no	—
324	#436	—	83	1	no	—
325	#435	—	166	1	no	—
326	C₈×D₄	—	83	1	no	—
327	C₈×D₄	—	83	1	no	—
328	C₈×D₄	—	83	1	no	—
329	C₈×D₄	—	166	1	no	—
330	C₈×D₄	—	166	1	no	—
331	C₈×D₄	—	166	1	no	—
332	#433	—	166	1	no	—
333	#432	C₂×D₈₃	1	1	yes	characteristic
334	#431	—	83	1	no	—
335	#431	—	83	1	no	—
336	#431	—	166	1	no	—
337	#431	C₂×D₈₃	1	1	yes	characteristic
338	#405	—	166	1	no	—
339	C₂×C₄×C₈	—	83	1	no	—
340	C₂×C₄×C₈	—	166	1	no	—
341	#335	—	83	1	no	—
342	#335	—	83	1	no	—
343	#334	—	83	1	no	—
344	#334	—	83	1	no	—
345	Q₈⋊C₈	—	83	1	no	—
346	Q₈⋊C₈	—	83	1	no	—
347	Q₈⋊C₈	C₂×D₈₃	1	1	yes	characteristic
348	Q₈⋊C₈	C₂×D₈₃	1	1	yes	characteristic
349	D₄⋊C₈	—	83	1	no	—
350	D₄⋊C₈	—	83	1	no	—
351	D₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic
352	D₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic
353	#322	—	83	1	no	—
354	#322	—	83	1	no	—
355	#322	—	83	1	no	—
356	#322	—	83	1	no	—
357	C₂×#41	C₄×D₈₃	1	1	yes	characteristic
358	C₂×Q₁₆	—	83	1	no	—
359	C₂×SD₁₆	—	83	1	no	—
360	C₂×SD₁₆	—	83	1	no	—
361	C₂×D₈	—	83	1	no	—
362	C₂×M₁₆	—	166	1	no	—
363	C₂²×C₈	—	83	1	no	—
364	C₂²×C₈	—	83	1	no	—
365	C₂²×C₈	—	166	1	no	—
366	C₂²×C₈	—	166	1	no	—
367	C₂²×C₈	—	166	1	no	—
368	#126	—	166	1	no	—
369	#125	—	83	1	no	—
370	#124	—	83	1	no	—
371	#123	—	166	1	no	—
372	C₂²⋊Q₈	—	83	1	no	—
373	#121	—	83	1	no	—
374	C₄×Q₈	—	83	1	no	—
375	C₄×Q₈	C₄×D₈₃	1	1	yes	characteristic
376	C₄×Q₈	C₂²×D₈₃	1	1	yes	characteristic
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	83	1	no	—
380	C₄×D₄	—	166	1	no	—
381	C₄×D₄	C₄×D₈₃	1	1	yes	characteristic
382	C₄×D₄	C₂²×D₈₃	1	1	yes	characteristic
383	#117	—	2	1	no	—
384	#117	—	166	1	no	—
385	#117	C₄×D₈₃	1	1	yes	characteristic
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
388	#107	—	83	1	no	—
389	#107	—	83	1	no	—
390	#106	—	83	1	no	—
391	#106	—	83	1	no	—
392	C₄⋊C₈	—	2	1	no	—
393	C₄⋊C₈	—	83	1	no	—
394	C₄⋊C₈	—	83	1	no	—
395	C₄⋊C₈	—	83	1	no	—
396	C₄⋊C₈	—	83	1	no	—
397	C₄⋊C₈	—	166	1	no	—
398	C₄⋊C₈	—	166	1	no	—
399	C₄⋊C₈	—	166	1	no	—
400	C₄⋊C₈	—	166	1	no	—
401	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
402	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
403	#103	—	83	1	no	—
404	#103	—	83	1	no	—
405	#103	—	83	1	no	—
406	#103	—	83	1	no	—
407	#102	—	83	1	no	—
408	#102	—	83	1	no	—
409	#102	—	83	1	no	—
410	#102	—	83	1	no	—
411	C₂²⋊C₈	—	2	1	no	—
412	C₂²⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	—	83	1	no	—
414	C₂²⋊C₈	—	83	1	no	—
415	C₂²⋊C₈	—	166	1	no	—
416	C₂²⋊C₈	—	166	1	no	—
417	C₂²⋊C₈	—	166	1	no	—
418	C₂²⋊C₈	—	166	1	no	—
419	C₂²⋊C₈	—	166	1	no	—
420	#97	—	2	1	no	—
421	#97	—	166	1	no	—
422	C₄×C₈	—	83	1	no	—
423	C₄×C₈	—	83	1	no	—
424	C₄×C₈	—	83	1	no	—
425	C₄×C₈	—	83	1	no	—
426	C₄×C₈	—	83	1	no	—
427	C₄×C₈	—	83	1	no	—
428	C₄×C₈	—	166	1	no	—
429	C₄×C₈	—	166	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	#41	—	2	2	no	—
435	#41	—	2	2	no	—
436	C₂×Q₈	—	83	1	no	—
437	C₂×Q₈	C₂×C₄×D₈₃	1	1	yes	characteristic
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	83	1	no	—
440	C₂×D₄	—	166	1	no	—
441	C₂×D₄	C₂×C₄×D₈₃	1	1	yes	characteristic
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	166	1	no	—
446	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
447	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
448	C₂²×C₄	#13050589	1	1	yes	characteristic
449	Q₁₆	—	166	2	no	—
450	SD₁₆	—	166	2	no	—
451	SD₁₆	—	166	2	no	—
452	D₈	—	166	2	no	—
453	M₁₆	—	332	2	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	332	2	no	—
459	C₂×C₈	—	332	2	no	—
460	C₂×C₈	—	332	2	no	—
461	C₂×C₈	—	332	1	no	—
462	C₂×C₈	—	332	1	no	—
463	C₂×C₈	—	83	1	no	—
464	C₂×C₈	—	83	1	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	—	83	1	no	—
470	C₂×C₈	—	83	1	no	—
471	C₂×C₈	—	166	1	no	—
472	C₂×C₈	—	166	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	83	1	no	—
476	C₄⋊C₄	—	83	1	no	—
477	C₄⋊C₄	—	166	1	no	—
478	C₄⋊C₄	—	166	1	no	—
479	C₄⋊C₄	—	166	1	no	—
480	C₄⋊C₄	—	166	1	no	—
481	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
482	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	166	1	no	—
487	C₂²⋊C₄	—	166	1	no	—
488	C₂²⋊C₄	—	166	1	no	—
489	C₂²⋊C₄	—	166	1	no	—
490	C₂²⋊C₄	—	166	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	166	1	no	—
495	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
496	C₄²	D₄×D₈₃	1	1	yes	characteristic
497	C₄²	#13050589	1	1	yes	characteristic
498	C₄²	C₂³×D₈₃	1	1	yes	characteristic
499	C₂³	—	2	1	no	—
500	C₂³	—	166	1	no	—
501	C₂³	(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
502	Q₈	—	2	1	no	—
503	Q₈	—	166	1	no	—
504	Q₈	—	166	1	no	—
505	Q₈	#14581800	1	2	yes	—
506	D₄	—	2	4	no	—
507	D₄	—	2	1	no	—
508	D₄	—	332	2	no	—
509	D₄	—	166	1	no	—
510	D₄	—	166	1	no	—
511	D₄	#14581800	1	2	yes	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	332	1	no	—
525	C₂×C₄	—	332	1	no	—
526	C₂×C₄	—	166	1	no	—
527	C₂×C₄	—	166	1	no	—
528	C₂×C₄	—	166	1	no	—
529	C₂×C₄	(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
530	C₂×C₄	(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
531	C₂×C₄	(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
532	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
533	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
534	C₂×C₄	C₂×#13050589	1	1	yes	characteristic
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	1	no	—
538	C₈	—	4	1	no	—
539	C₈	—	332	1	no	—
540	C₈	—	332	1	no	—
541	C₈	—	166	1	no	—
542	C₈	—	166	1	no	—
543	C₈	—	166	1	no	—
544	C₈	—	166	1	no	—
545	C₈	—	166	1	no	—
546	C₈	—	166	1	no	—
547	C₈	—	166	1	no	—
548	C₈	—	166	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	332	1	no	—
556	C₂²	—	332	1	no	—
557	C₂²	—	332	1	no	—
558	C₂²	C₂×(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	2	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	332	1	no	—
567	C₄	—	332	1	no	—
568	C₄	—	332	1	no	—
569	C₄	C₂×#14581800	1	1	yes	characteristic
570	C₄	C₂×#14581800	1	1	yes	characteristic
571	C₄	#19128498	1	1	yes	characteristic
572	C₄	#19128498	1	1	yes	characteristic
573	C₂	—	4	1	no	—
574	C₂	—	4	2	no	—
575	C₂	—	664	1	no	—
576	C₂	#24916153	1	1	yes	characteristic
577	C₂	#24916259	1	1	yes	characteristic
578	C₂	#24916362	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×#1488	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	#19127846	C₄
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	#1488	D₈₃
hypocenter	C₈₃	#17909
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1488

Complements

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

N	H ≅ G/N	type
2. #24916432	C₂	semidirect
3. #41×C₈₃⋊C₈	C₂	semidirect
4. #24906338	C₂	semidirect
5. #24906331	C₂	semidirect
6. #24906324	C₂	semidirect
7. #24906317	C₂	semidirect
8. #24906284	C₂	semidirect
9. #24906279	C₂	semidirect
10. #24906278	C₂	semidirect
11. #24906272	C₂	semidirect
12. #24906244	C₂	semidirect
13. #24905872	C₂	semidirect
14. #24905756	C₂	semidirect
15. C₈₃×#1488	C₂	semidirect
302. #1488	D₈₃	semidirect
305. C₈₃	#17909	semidirect

Maximal subgroups

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

subgroup	index
#24917481	2
#24916432	2
#41×C₈₃⋊C₈	2
#24906338	2
#24906331	2
#24906324	2
#24906317	2
#24906284	2
#24906279	2
#24906278	2
#24906272	2
#24906244	2
#24905872	2
#24905756	2
C₈₃×#1488	2
#17909	83