Subgroups — #35374151

Order 21248.

682 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24916429	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#14581812	C₂	1	1	yes	maximal, characteristic
3	#24906358	C₂	1	2	yes	maximal, complemented
4	#24906353	C₂	1	2	yes	maximal, complemented
5	#24906351	C₂	1	2	yes	maximal, complemented
6	#24906346	C₂	1	2	yes	maximal, complemented
7	#24906209	C₂	1	1	yes	maximal, characteristic, complemented
8	#24905845	C₂	1	1	yes	maximal, characteristic, complemented
9	#24905843	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₈×C₈₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14581812	C₄	1	1	yes	characteristic
13	C₄×#13050590	C₂²	1	1	yes	characteristic
14	#19127831	C₂²	1	2	yes	—
15	C₄×#13050580	C₄	1	1	yes	characteristic
16	C₄×#13050580	C₂²	1	1	yes	characteristic
17	C₄×#13050577	C₄	1	1	yes	characteristic
18	C₄×#13050577	C₂²	1	1	yes	characteristic
19	C₄×#13050578	C₄	1	1	yes	characteristic
20	C₄×#13050578	C₂²	1	1	yes	characteristic
21	C₄×#13050575	C₄	1	1	yes	characteristic
22	C₄×#13050575	C₂²	1	1	yes	characteristic
23	#19127780	C₂²	1	2	yes	—
24	#19127772	—	2	2	no	—
25	#19127754	C₂²	1	1	yes	characteristic
26	#19127752	—	2	1	no	—
27	#19127737	C₄	1	1	yes	characteristic
28	#19127697	C₄	1	1	yes	characteristic
29	#19127695	C₄	1	1	yes	characteristic
30	C₄×#13050573	—	2	1	no	—
31	C₂×C₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
33	#19127453	C₂²	1	2	yes	—
34	#19127451	C₂²	1	2	yes	—
35	Q₈⋊(C₈₃⋊C₈)	C₂²	1	2	yes	—
36	#19127431	C₂²	1	2	yes	—
37	D₄⋊(C₈₃⋊C₈)	C₂²	1	2	yes	—
38	#19127428	C₂²	1	2	yes	—
39	C₈×C₈₃⋊C₈	C₂²	1	2	yes	—
40	C₈×C₈₃⋊C₈	C₂²	1	2	yes	—
41	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
42	#446×C₈₃	C₂²	1	2	yes	—
43	#436×C₈₃	C₂²	1	2	yes	—
44	#435×C₈₃	—	2	2	no	—
45	#431×C₈₃	—	2	1	no	—
46	#431×C₈₃	C₂²	1	1	yes	characteristic
47	C₄×M₁₆×C₈₃	—	2	1	no	—
48	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
49	C₂×#13050590	C₂×C₄	1	1	yes	characteristic
50	#14581812	—	2	4	no	—
51	C₂×#13050580	C₂×C₄	1	1	yes	characteristic
52	C₂×#13050578	C₂×C₄	1	1	yes	characteristic
53	C₂×#13050577	C₂×C₄	1	1	yes	characteristic
54	C₂×#13050575	C₂×C₄	1	1	yes	characteristic
55	C₂×#13050573	—	2	2	no	—
56	C₂²×C₈₃⋊C₈	—	2	1	no	—
57	C₂²×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
59	C₄×Dic₁₆₆	C₂×C₄	1	1	yes	characteristic
60	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
61	C₄×D₃₃₂	C₂×C₄	1	1	yes	characteristic
62	C₄×D₃₃₂	C₂³	1	1	yes	characteristic
63	C₄×C₂²⋊D₈₃	—	2	1	no	—
64	C₄×C₂²⋊D₈₃	—	2	1	no	—
65	#14581751	C₂×C₄	1	1	yes	characteristic
66	#14581749	—	2	1	no	—
67	C₄²×D₈₃	—	2	1	no	—
68	#14581725	C₂×C₄	1	1	yes	characteristic
69	#14581725	C₂×C₄	1	1	yes	characteristic
70	#14581723	C₂×C₄	1	1	yes	characteristic
71	#14581723	C₂×C₄	1	1	yes	characteristic
72	C₄⋊(C₈₃⋊C₈)	C₂³	1	2	yes	—
73	Dic₈₃⋊C₈	—	2	2	no	—
74	#14581716	C₂×C₄	1	1	yes	characteristic
75	#14581716	C₂×C₄	1	1	yes	characteristic
76	#14581715	C₂×C₄	1	1	yes	characteristic
77	#14581715	C₂×C₄	1	1	yes	characteristic
78	#14581713	C₂×C₄	1	1	yes	characteristic
79	#14581713	C₂×C₄	1	1	yes	characteristic
80	#14581712	C₂×C₄	1	1	yes	characteristic
81	#14581712	C₂×C₄	1	1	yes	characteristic
82	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
83	(C₂×D₈₃)⋊C₈	—	2	2	no	—
84	#14581702	—	2	2	no	—
85	C₄×C₈₃⋊C₈	—	2	1	no	—
86	C₄×C₈₃⋊C₈	—	2	1	no	—
87	C₄×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
88	C₄×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
89	C₄×C₈₃⋊C₈	C₂³	1	2	yes	—
90	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
91	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
92	C₂×#41×C₈₃	C₂×C₄	1	1	yes	characteristic
93	C₂×M₁₆×C₈₃	—	2	2	no	—
94	C₂²×C₈×C₈₃	D₄	1	2	yes	—
95	C₄×Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
96	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₈₃	—	2	1	no	—
98	C₄×D₄×C₈₃	—	2	1	no	—
99	C₄×D₄×C₈₃	C₂×C₄	1	1	yes	characteristic
100	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
101	#117×C₈₃	—	2	1	no	—
102	#117×C₈₃	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₈₃	—	2	1	no	—
104	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
105	C₄⋊C₈×C₈₃	—	2	2	no	—
106	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
107	C₂²⋊C₈×C₈₃	—	2	1	no	—
108	C₂²⋊C₈×C₈₃	—	2	2	no	—
109	#97×C₈₃	—	2	2	no	—
110	C₄×C₈×C₈₃	—	2	1	no	—
111	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
112	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
113	C₄×C₈×C₈₃	C₂³	1	2	yes	—
114	#13050590	—	2	2	no	—
115	#13050590	—	2	2	no	—
116	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
117	C₂×D₃₃₂	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₂²⋊D₈₃	—	2	1	no	—
119	C₂×C₄×D₈₃	—	2	1	no	—
120	C₂×C₄×D₈₃	—	2	1	no	—
121	C₂×C₄×D₈₃	—	2	1	no	—
122	#13050580	—	2	2	no	—
123	#13050578	—	2	2	no	—
124	#13050577	—	2	2	no	—
125	#13050575	—	2	2	no	—
126	#13050573	—	4	4	no	—
127	C₂×C₈₃⋊C₈	—	2	4	no	—
128	C₂×C₈₃⋊C₈	—	2	2	no	—
129	C₂×C₈₃⋊C₈	—	2	2	no	—
130	C₂×C₈₃⋊C₈	—	2	2	no	—
131	C₂×C₈₃⋊C₈	M₁₆	1	4	yes	complemented
132	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
136	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
137	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
138	Dic₈₃⋊C₄	—	2	1	no	—
139	Dic₈₃⋊C₄	—	2	1	no	—
140	C₂²⋊Dic₈₃	—	2	1	no	—
141	(C₂×D₈₃)⋊C₄	—	2	1	no	—
142	(C₂×D₈₃)⋊C₄	—	2	1	no	—
143	C₄×Dic₈₃	—	2	1	no	—
144	C₄×Dic₈₃	—	2	1	no	—
145	C₄×Dic₈₃	—	2	1	no	—
146	#41×C₈₃	—	2	2	no	—
147	#41×C₈₃	—	2	2	no	—
148	C₂×Q₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×D₄×C₈₃	—	2	1	no	—
150	C₂×D₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₈₃	—	2	1	no	—
152	C₂²×C₄×C₈₃	—	2	1	no	—
153	C₂²×C₄×C₈₃	—	2	1	no	—
154	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
157	M₁₆×C₈₃	—	4	4	no	—
158	C₂×C₈×C₈₃	—	2	4	no	—
159	C₂×C₈×C₈₃	—	2	2	no	—
160	C₂×C₈×C₈₃	C₂×D₄	1	2	yes	—
161	C₂×C₈×C₈₃	C₂×D₄	1	2	yes	—
162	C₄⋊C₄×C₈₃	—	2	1	no	—
163	C₄⋊C₄×C₈₃	—	2	1	no	—
164	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
165	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
166	C₂²⋊C₄×C₈₃	—	2	1	no	—
167	C₂²⋊C₄×C₈₃	—	2	1	no	—
168	C₂²⋊C₄×C₈₃	—	2	1	no	—
169	C₄²×C₈₃	—	2	1	no	—
170	C₄²×C₈₃	—	2	1	no	—
171	C₄²×C₈₃	—	2	1	no	—
172	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₈₃	#41	1	1	yes	characteristic
175	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
176	C₂³×C₈₃	—	2	1	no	—
177	C₂³×C₈₃	C₄×D₄	1	1	yes	characteristic
178	C₂²×D₈₃	—	2	1	no	—
179	Q₈×C₈₃	—	2	1	no	—
180	Q₈×C₈₃	—	2	1	no	—
181	D₄×C₈₃	—	2	1	no	—
182	D₄×C₈₃	—	2	1	no	—
183	D₄×C₈₃	—	4	2	no	—
184	C₂×C₄×C₈₃	—	2	2	no	—
185	C₂×C₄×C₈₃	—	2	2	no	—
186	C₂×C₄×C₈₃	—	2	1	no	—
187	C₂×C₄×C₈₃	—	2	1	no	—
188	C₂×C₄×C₈₃	—	2	1	no	—
189	C₂×C₄×C₈₃	—	4	2	no	—
190	C₂×C₄×C₈₃	—	4	2	no	—
191	C₂×C₄×C₈₃	—	4	2	no	—
192	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₈₃	C₂×M₁₆	1	2	yes	—
196	C₂×C₄×C₈₃	#131	1	2	yes	—
197	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
200	C₂²⋊D₈₃	—	4	2	no	—
201	C₂×Dic₈₃	—	2	1	no	—
202	C₂×Dic₈₃	—	2	1	no	—
203	C₂×Dic₈₃	—	2	1	no	—
204	D₃₃₂	—	2	1	no	—
205	D₃₃₂	—	2	1	no	—
206	C₄×D₈₃	—	4	2	no	—
207	C₄×D₈₃	—	4	2	no	—
208	C₄×D₈₃	—	4	2	no	—
209	Dic₁₆₆	—	2	1	no	—
210	Dic₁₆₆	—	2	1	no	—
211	C₈×C₈₃	—	2	2	no	—
212	C₈×C₈₃	—	4	2	no	—
213	C₈×C₈₃	#135	1	4	yes	complemented
214	C₈₃⋊C₈	—	2	4	no	—
215	C₈₃⋊C₈	—	2	1	no	—
216	C₈₃⋊C₈	—	2	1	no	—
217	C₈₃⋊C₈	—	4	2	no	—
218	C₈₃⋊C₈	C₂×M₁₆	1	2	yes	—
219	C₈₃⋊C₈	C₂×M₁₆	1	2	yes	—
220	C₂²×C₈₃	—	2	1	no	—
221	C₂²×C₈₃	—	2	1	no	—
222	C₂²×C₈₃	—	4	1	no	—
223	C₂²×C₈₃	—	4	1	no	—
224	C₂²×C₈₃	—	4	1	no	—
225	C₂²×C₈₃	#436	1	2	yes	—
226	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
227	C₂×D₈₃	—	4	1	no	—
228	C₂×D₈₃	—	4	1	no	—
229	C₂×D₈₃	—	4	1	no	—
230	C₄×C₈₃	—	2	1	no	—
231	C₄×C₈₃	—	2	1	no	—
232	C₄×C₈₃	—	4	1	no	—
233	C₄×C₈₃	—	4	1	no	—
234	C₄×C₈₃	—	4	1	no	—
235	C₄×C₈₃	#436	1	2	yes	—
236	C₄×C₈₃	#443	1	2	yes	—
237	C₄×C₈₃	C₂²×M₁₆	1	1	yes	characteristic
238	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
239	C₄×C₈₃	C₂×#135	1	2	yes	—
240	Dic₈₃	—	4	1	no	—
241	Dic₈₃	—	4	1	no	—
242	Dic₈₃	—	4	1	no	—
243	#17886	—	83	1	no	maximal, Sylow
244	C₂×C₈₃	—	2	2	no	—
245	C₂×C₈₃	—	8	1	no	—
246	C₂×C₈₃	C₂×#436	1	1	yes	characteristic
247	C₂×C₈₃	C₄×#135	1	1	yes	characteristic
248	C₂×C₈₃	C₂×#443	1	1	yes	characteristic
249	D₈₃	—	8	1	no	—
250	#2965	—	83	1	no	—
251	#2965	D₈₃	1	1	yes	characteristic, complemented
252	C₄×#135	—	83	1	no	—
253	#1591	—	83	2	no	—
254	#1590	—	83	2	no	—
255	#1590	—	83	2	no	—
256	#1589	—	83	2	no	—
257	#1564	—	83	1	no	—
258	#1476	—	83	1	no	—
259	#1476	—	83	1	no	—
260	C₂×C₈²	—	83	1	no	—
261	C₈₃	#17886	1	1	yes	characteristic, complemented, Sylow
262	C₂×#135	—	83	1	no	—
263	C₄×#41	—	83	1	no	—
264	C₄×#41	C₂×D₈₃	1	1	yes	characteristic
265	#446	—	83	2	no	—
266	#446	C₂×D₈₃	1	2	yes	—
267	C₄×Q₁₆	—	83	1	no	—
268	C₄×Q₁₆	—	83	1	no	—
269	C₄×SD₁₆	—	83	1	no	—
270	C₄×SD₁₆	—	83	1	no	—
271	C₄×SD₁₆	—	83	1	no	—
272	C₄×SD₁₆	—	83	1	no	—
273	C₄×D₈	—	83	1	no	—
274	C₄×D₈	—	83	1	no	—
275	#436	—	83	2	no	—
276	#436	C₂×D₈₃	1	2	yes	—
277	#435	—	2	2	no	—
278	#435	—	166	2	no	—
279	#431	—	2	1	no	—
280	#431	—	83	1	no	—
281	#431	—	166	1	no	—
282	#431	C₂×D₈₃	1	1	yes	characteristic
283	#427	—	83	1	no	—
284	#416	—	83	1	no	—
285	#416	—	83	1	no	—
286	C₄×M₁₆	—	2	1	no	—
287	C₄×M₁₆	—	166	1	no	—
288	C₂×C₄×C₈	—	83	1	no	—
289	C₂×C₄×C₈	—	83	1	no	—
290	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
291	#335	—	83	2	no	—
292	#334	—	83	2	no	—
293	Q₈⋊C₈	—	83	2	no	—
294	Q₈⋊C₈	—	83	2	no	—
295	D₄⋊C₈	—	83	2	no	—
296	D₄⋊C₈	—	83	2	no	—
297	C₈²	—	83	2	no	—
298	C₈²	—	83	2	no	—
299	C₂×#41	—	83	1	no	—
300	C₂×#41	C₄×D₈₃	1	1	yes	characteristic
301	#135	—	166	4	no	—
302	C₂×Q₁₆	—	83	1	no	—
303	C₂×SD₁₆	—	83	1	no	—
304	C₂×SD₁₆	—	83	1	no	—
305	C₂×D₈	—	83	1	no	—
306	C₂×M₁₆	—	2	2	no	—
307	C₂×M₁₆	—	166	2	no	—
308	C₂²×C₈	—	83	1	no	—
309	C₂²×C₈	—	83	1	no	—
310	C₂²×C₈	—	166	1	no	—
311	C₂²×C₈	C₂²⋊D₈₃	1	2	yes	—
312	C₄×Q₈	—	83	1	no	—
313	C₄×Q₈	—	83	1	no	—
314	C₄×Q₈	C₄×D₈₃	1	1	yes	characteristic
315	C₄×Q₈	C₂²×D₈₃	1	1	yes	characteristic
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	—	83	1	no	—
319	C₄×D₄	—	83	1	no	—
320	C₄×D₄	—	166	1	no	—
321	C₄×D₄	—	166	1	no	—
322	C₄×D₄	C₄×D₈₃	1	1	yes	characteristic
323	C₄×D₄	C₂²×D₈₃	1	1	yes	characteristic
324	#117	—	2	1	no	—
325	#117	—	83	1	no	—
326	#117	—	166	1	no	—
327	#117	C₄×D₈₃	1	1	yes	characteristic
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	—	166	1	no	—
330	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
331	#107	—	83	1	no	—
332	#107	—	83	1	no	—
333	#106	—	83	1	no	—
334	#106	—	83	1	no	—
335	C₄⋊C₈	—	2	2	no	—
336	C₄⋊C₈	—	83	2	no	—
337	C₄⋊C₈	—	166	2	no	—
338	C₄⋊C₈	C₂²×D₈₃	1	2	yes	—
339	#103	—	83	1	no	—
340	#103	—	83	1	no	—
341	#103	—	83	1	no	—
342	#103	—	83	1	no	—
343	#102	—	83	1	no	—
344	#102	—	83	1	no	—
345	#102	—	83	1	no	—
346	#102	—	83	1	no	—
347	C₂²⋊C₈	—	2	1	no	—
348	C₂²⋊C₈	—	2	2	no	—
349	C₂²⋊C₈	—	166	1	no	—
350	C₂²⋊C₈	—	166	2	no	—
351	#97	—	2	2	no	—
352	#97	—	166	2	no	—
353	C₄×C₈	—	2	1	no	—
354	C₄×C₈	—	83	1	no	—
355	C₄×C₈	—	83	1	no	—
356	C₄×C₈	—	83	1	no	—
357	C₄×C₈	—	83	1	no	—
358	C₄×C₈	—	83	2	no	—
359	C₄×C₈	—	166	1	no	—
360	C₄×C₈	—	166	1	no	—
361	C₄×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
362	C₄×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
363	C₄×C₈	C₂²×D₈₃	1	2	yes	—
364	#41	—	2	2	no	—
365	#41	—	2	2	no	—
366	#41	—	166	2	no	—
367	#41	—	166	2	no	—
368	C₂×Q₈	—	83	1	no	—
369	C₂×Q₈	C₂×C₄×D₈₃	1	1	yes	characteristic
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	83	1	no	—
372	C₂×D₄	—	166	1	no	—
373	C₂×D₄	C₂×C₄×D₈₃	1	1	yes	characteristic
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	166	1	no	—
378	C₂²×C₄	—	166	1	no	—
379	C₂²×C₄	—	166	1	no	—
380	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
381	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
382	C₂²×C₄	#13050590	1	1	yes	characteristic
383	Q₁₆	—	166	2	no	—
384	SD₁₆	—	166	2	no	—
385	SD₁₆	—	166	2	no	—
386	D₈	—	166	2	no	—
387	M₁₆	—	4	4	no	—
388	M₁₆	—	332	4	no	—
389	C₂×C₈	—	2	4	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	83	4	no	—
392	C₂×C₈	—	83	1	no	—
393	C₂×C₈	—	83	1	no	—
394	C₂×C₈	—	83	1	no	—
395	C₂×C₈	—	83	1	no	—
396	C₂×C₈	—	166	2	no	—
397	C₂×C₈	—	166	4	no	—
398	C₂×C₈	—	166	2	no	—
399	C₂×C₈	—	166	2	no	—
400	C₂×C₈	C₂×C₂²⋊D₈₃	1	2	yes	—
401	C₂×C₈	C₂×C₂²⋊D₈₃	1	2	yes	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	83	1	no	—
405	C₄⋊C₄	—	83	1	no	—
406	C₄⋊C₄	—	166	1	no	—
407	C₄⋊C₄	—	166	1	no	—
408	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
409	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	166	1	no	—
414	C₂²⋊C₄	—	166	1	no	—
415	C₂²⋊C₄	—	166	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	166	1	no	—
420	C₄²	—	166	1	no	—
421	C₄²	—	166	1	no	—
422	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
423	C₄²	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
424	C₄²	#13050590	1	1	yes	characteristic
425	C₄²	C₂³×D₈₃	1	1	yes	characteristic
426	C₂³	—	2	1	no	—
427	C₂³	—	166	1	no	—
428	C₂³	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
429	Q₈	—	2	1	no	—
430	Q₈	—	2	1	no	—
431	Q₈	—	166	1	no	—
432	Q₈	—	166	1	no	—
433	D₄	—	2	1	no	—
434	D₄	—	2	1	no	—
435	D₄	—	4	2	no	—
436	D₄	—	332	2	no	—
437	D₄	—	166	1	no	—
438	D₄	—	166	1	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	332	2	no	—
448	C₂×C₄	—	332	2	no	—
449	C₂×C₄	—	332	2	no	—
450	C₂×C₄	—	166	1	no	—
451	C₂×C₄	—	166	1	no	—
452	C₂×C₄	—	166	1	no	—
453	C₂×C₄	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
454	C₂×C₄	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
455	C₂×C₄	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
456	C₂×C₄	M₁₆×D₈₃	1	2	yes	—
457	C₂×C₄	#14581800	1	2	yes	—
458	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
459	C₂×C₄	C₂²×C₂²⋊D₈₃	1	1	yes	characteristic
460	C₂×C₄	C₂×#13050590	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	4	2	no	—
463	C₈	—	332	2	no	—
464	C₈	—	83	2	no	—
465	C₈	—	83	2	no	—
466	C₈	—	166	4	no	—
467	C₈	—	166	1	no	—
468	C₈	—	166	1	no	—
469	C₈	#14581812	1	4	yes	complemented
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	332	1	no	—
476	C₂²	—	332	1	no	—
477	C₂²	—	332	1	no	—
478	C₂²	#19127777	1	2	yes	—
479	C₂²	C₂×C₄×C₂²⋊D₈₃	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	4	1	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	332	1	no	—
486	C₄	—	332	1	no	—
487	C₄	—	332	1	no	—
488	C₄	#19127777	1	2	yes	—
489	C₄	#19127816	1	2	yes	—
490	C₄	C₂×M₁₆×D₈₃	1	1	yes	characteristic
491	C₄	C₂×#14581800	1	1	yes	characteristic
492	C₄	C₂×#14581812	1	2	yes	—
493	C₂	—	2	2	no	—
494	C₂	—	8	1	no	—
495	C₂	—	664	1	no	—
496	C₂	C₂×#19127777	1	1	yes	characteristic
497	C₂	C₄×#14581812	1	1	yes	characteristic
498	C₂	C₂×#19127816	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×C₂²⋊D₈₃
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₄²	C₂³×D₈₃
Fitting	C₈₃×#2965	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	C₂×#14581812	C₄
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	#2965	D₈₃
hypocenter	C₈₃	#17886
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ #2965

Complements

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

N	H ≅ G/N	type
1. #24916429	C₂	semidirect
3. #24906358	C₂	semidirect
4. #24906353	C₂	semidirect
5. #24906351	C₂	semidirect
6. #24906346	C₂	semidirect
7. #24906209	C₂	semidirect
8. #24905845	C₂	semidirect
9. #24905843	C₂	semidirect
10. C₂×C₈×C₈₃⋊C₈	C₂	semidirect
11. C₈₃×#2965	C₂	semidirect
131. C₂×C₈₃⋊C₈	M₁₆	semidirect
213. C₈×C₈₃	#135	semidirect
251. #2965	D₈₃	semidirect
261. C₈₃	#17886	semidirect
469. C₈	#14581812	semidirect

Maximal subgroups

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

subgroup	index
#24916429	2
C₄×#14581812	2
#24906358	2
#24906353	2
#24906351	2
#24906346	2
#24906209	2
#24905845	2
#24905843	2
C₂×C₈×C₈₃⋊C₈	2
C₈₃×#2965	2
#17886	83