Subgroups — #35411349

Order 21248.

868 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24917184	C₂	1	1	yes	maximal, characteristic
2	#24916365	C₂	1	2	yes	maximal, complemented
3	C₂×#19127822	C₂	1	1	yes	maximal, characteristic, complemented
4	#24915890	C₂	1	1	yes	maximal, characteristic, complemented
5	#24908361	C₂	1	1	yes	maximal, characteristic, complemented
6	#24908131	C₂	1	2	yes	maximal, complemented
7	#24907965	C₂	1	2	yes	maximal, complemented
8	#24907518	C₂	1	1	yes	maximal, characteristic, complemented
9	#24907350	C₂	1	1	yes	maximal, characteristic, complemented
10	#24907262	C₂	1	2	yes	maximal, complemented
11	C₈₃×#1953	C₂	1	1	yes	maximal, characteristic, complemented
12	#19128501	C₂²	1	2	yes	—
13	C₂×#14581814	C₂²	1	1	yes	characteristic
14	C₂×#14581800	C₂²	1	2	yes	—
15	C₂×#14581800	C₂²	1	1	yes	characteristic
16	C₂×#14581798	C₂²	1	1	yes	characteristic
17	#19128169	C₂²	1	1	yes	characteristic
18	#19127977	C₄	1	2	yes	complemented
19	#19127972	C₄	1	2	yes	complemented
20	#19127965	C₄	1	4	yes	complemented
21	#19127822	—	2	1	no	—
22	#19127822	—	2	1	no	—
23	#19127822	—	2	1	no	—
24	#19127822	—	2	1	no	—
25	#19127822	—	2	4	no	—
26	#19127817	—	2	4	no	—
27	#19127739	C₂²	1	1	yes	characteristic
28	#19127717	C₂²	1	2	yes	—
29	#19127717	C₂²	1	2	yes	—
30	C₂×#14581718	C₂²	1	2	yes	—
31	#19127683	C₂²	1	2	yes	—
32	#19127674	C₂²	1	2	yes	—
33	#19127659	C₂²	1	2	yes	—
34	#19127658	—	2	1	no	—
35	#19127657	C₂²	1	1	yes	characteristic
36	#19127655	—	2	1	no	—
37	M₁₆×Dic₈₃	C₂²	1	1	yes	characteristic
38	C₄×#13050573	—	2	1	no	—
39	C₂×#14581702	C₂²	1	1	yes	characteristic
40	#97×D₈₃	—	2	1	no	—
41	#19127472	C₂²	1	2	yes	—
42	#19127462	C₂²	1	2	yes	—
43	#430×C₈₃	C₂²	1	2	yes	—
44	C₂×#108×C₈₃	C₂²	1	1	yes	characteristic
45	C₂×#108×C₈₃	C₂²	1	1	yes	characteristic
46	#405×C₈₃	C₂²	1	1	yes	characteristic
47	#344×C₈₃	C₂²	1	2	yes	—
48	C₂×#13050590	C₂³	1	2	yes	—
49	C₂×#13050590	C₂³	1	1	yes	characteristic
50	#14581825	—	2	2	no	—
51	#14581825	C₂×C₄	1	4	yes	—
52	#14581820	—	2	2	no	—
53	#14581820	C₂×C₄	1	4	yes	—
54	#14581814	—	2	4	no	—
55	#14581814	—	2	1	no	—
56	#14581814	—	2	1	no	—
57	#14581814	—	2	1	no	—
58	#14581814	—	2	1	no	—
59	C₂×Dic₃₃₂	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂×#13050579	C₂×C₄	1	2	yes	complemented
61	C₂×D₆₆₄	C₂×C₄	1	1	yes	characteristic, complemented
62	#14581800	—	2	2	no	—
63	#14581800	—	2	2	no	—
64	#14581800	—	2	2	no	—
65	#14581800	—	2	2	no	—
66	#14581800	—	2	2	no	—
67	#14581800	D₄	1	4	yes	—
68	#14581798	—	2	1	no	—
69	#14581798	—	2	1	no	—
70	#14581798	C₂×C₄	1	2	yes	—
71	#14581798	C₂×C₄	1	2	yes	—
72	C₂×#13050574	C₂³	1	1	yes	characteristic
73	C₂×#13050573	—	2	1	no	—
74	C₂×#13050573	—	2	2	no	—
75	C₂×#13050573	—	2	1	no	—
76	C₂²×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
77	C₂×C₈×D₈₃	—	2	1	no	—
78	C₂×C₈×D₈₃	—	2	2	no	—
79	C₂×C₈×D₈₃	—	2	1	no	—
80	#14581757	—	2	1	no	—
81	#14581754	—	2	1	no	—
82	(C₂²⋊D₈₃)⋊C₄	—	2	2	no	—
83	#14581751	C₂³	1	2	yes	—
84	#14581749	—	2	1	no	—
85	C₂×C₄×Dic₈₃	C₂³	1	1	yes	characteristic
86	C₄²×D₈₃	—	2	1	no	—
87	#14581726	—	2	1	no	—
88	#14581724	—	2	1	no	—
89	#14581718	—	2	4	no	—
90	#14581718	—	2	2	no	—
91	#14581718	—	2	2	no	—
92	#14581718	—	2	4	no	—
93	#14581710	C₂×C₄	1	4	yes	complemented
94	#14581708	C₂×C₄	1	4	yes	complemented
95	#14581706	—	2	4	no	—
96	#14581703	—	2	1	no	—
97	#14581702	—	2	2	no	—
98	#14581702	—	2	1	no	—
99	#14581702	D₄	1	1	yes	characteristic
100	#14581702	D₄	1	1	yes	characteristic
101	#14581702	D₄	1	1	yes	characteristic
102	#14581702	D₄	1	1	yes	characteristic
103	C₄×C₈₃⋊C₈	—	2	1	no	—
104	C₈×Dic₈₃	—	2	2	no	—
105	C₈×Dic₈₃	—	2	1	no	—
106	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
107	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
108	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
110	#117×C₈₃	C₂³	1	1	yes	characteristic
111	#108×C₈₃	—	2	4	no	—
112	#108×C₈₃	—	2	1	no	—
113	#108×C₈₃	—	2	1	no	—
114	#108×C₈₃	C₂×C₄	1	2	yes	complemented
115	#108×C₈₃	C₂×C₄	1	2	yes	complemented
116	#97×C₈₃	—	2	1	no	—
117	C₄×C₈×C₈₃	—	2	1	no	—
118	#13050590	—	2	1	no	—
119	#13050590	—	2	1	no	—
120	#13050590	—	2	2	no	—
121	#13050590	—	2	2	no	—
122	#13050590	—	2	2	no	—
123	#13050590	—	2	2	no	—
124	#13050590	C₂²×C₄	1	2	yes	—
125	#13050590	C₂×D₄	1	2	yes	—
126	C₂×Dic₁₆₆	C₂²×C₄	1	2	yes	—
127	C₂×Dic₁₆₆	#41	1	1	yes	characteristic
128	C₂×D₃₃₂	C₂²×C₄	1	2	yes	—
129	C₂×D₃₃₂	#41	1	1	yes	characteristic
130	C₂×C₂²⋊D₈₃	—	2	1	no	—
131	C₂×C₂²⋊D₈₃	—	2	2	no	—
132	C₂²×Dic₈₃	—	2	1	no	—
133	C₂×C₄×D₈₃	—	2	1	no	—
134	C₂×C₄×D₈₃	—	2	2	no	—
135	C₂×C₄×D₈₃	—	2	2	no	—
136	Dic₃₃₂	—	2	4	no	—
137	Dic₃₃₂	—	2	1	no	—
138	Dic₃₃₂	—	2	1	no	—
139	#13050579	—	2	4	no	—
140	#13050579	—	2	4	no	—
141	#13050579	—	2	2	no	—
142	#13050579	—	2	2	no	—
143	D₆₆₄	—	2	4	no	—
144	D₆₆₄	—	2	1	no	—
145	D₆₆₄	—	2	1	no	—
146	#13050574	—	2	1	no	—
147	#13050574	C₂²×C₄	1	2	yes	—
148	#13050573	—	2	2	no	—
149	#13050573	—	2	2	no	—
150	#13050573	—	2	4	no	—
151	#13050573	—	4	2	no	—
152	#13050573	—	4	2	no	—
153	C₂×C₈₃⋊C₈	—	2	1	no	—
154	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈₃⋊C₈	C₂×D₄	1	2	yes	—
157	C₂×C₈₃⋊C₈	#41	1	2	yes	—
158	C₈×D₈₃	—	2	2	no	—
159	C₈×D₈₃	—	2	2	no	—
160	C₈×D₈₃	—	2	4	no	—
161	C₈×D₈₃	—	4	2	no	—
162	C₈×D₈₃	—	4	2	no	—
163	C₄⋊Dic₈₃	—	2	2	no	—
164	Dic₈₃⋊C₄	—	2	2	no	—
165	C₂²⋊Dic₈₃	—	2	2	no	—
166	(C₂×D₈₃)⋊C₄	—	2	2	no	—
167	C₄×Dic₈₃	—	2	2	no	—
168	C₄×Dic₈₃	—	2	1	no	—
169	C₄×Dic₈₃	—	2	2	no	—
170	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
171	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
173	M₁₆×C₈₃	—	2	1	no	—
174	M₁₆×C₈₃	—	2	2	no	—
175	M₁₆×C₈₃	—	2	2	no	—
176	M₁₆×C₈₃	—	2	2	no	—
177	M₁₆×C₈₃	C₂²×C₄	1	4	yes	—
178	M₁₆×C₈₃	C₂×D₄	1	2	yes	—
179	C₂×C₈×C₈₃	—	2	1	no	—
180	C₂×C₈×C₈₃	—	2	2	no	—
181	C₂×C₈×C₈₃	—	2	2	no	—
182	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
187	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
188	C₄⋊C₄×C₈₃	—	2	1	no	—
189	C₂²⋊C₄×C₈₃	#41	1	2	yes	—
190	C₄²×C₈₃	—	2	1	no	—
191	C₂³×C₈₃	C₂×#41	1	1	yes	characteristic
192	C₂²×D₈₃	—	2	1	no	—
193	C₂²×D₈₃	—	2	2	no	—
194	C₂×C₄×C₈₃	—	2	2	no	—
195	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
196	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
201	C₂²⋊D₈₃	—	2	2	no	—
202	C₂²⋊D₈₃	—	2	2	no	—
203	C₂²⋊D₈₃	—	4	2	no	—
204	C₂²⋊D₈₃	—	4	2	no	—
205	C₂×Dic₈₃	—	2	1	no	—
206	C₂×Dic₈₃	—	2	2	no	—
207	C₂×Dic₈₃	—	2	1	no	—
208	C₂×Dic₈₃	—	2	1	no	—
209	C₂×Dic₈₃	—	4	2	no	—
210	C₂×Dic₈₃	—	8	1	no	—
211	D₃₃₂	—	2	2	no	—
212	D₃₃₂	—	2	2	no	—
213	D₃₃₂	—	2	1	no	—
214	D₃₃₂	C₄×D₄	1	2	yes	—
215	C₄×D₈₃	—	2	2	no	—
216	C₄×D₈₃	—	2	2	no	—
217	C₄×D₈₃	—	4	2	no	—
218	C₄×D₈₃	—	4	2	no	—
219	C₄×D₈₃	—	8	2	no	—
220	Dic₁₆₆	—	2	1	no	—
221	Dic₁₆₆	—	2	2	no	—
222	Dic₁₆₆	—	2	2	no	—
223	Dic₁₆₆	C₄×D₄	1	2	yes	—
224	C₈×C₈₃	—	2	4	no	—
225	C₈×C₈₃	—	2	2	no	—
226	C₈×C₈₃	—	4	2	no	—
227	C₈×C₈₃	C₄×D₄	1	1	yes	characteristic
228	C₈×C₈₃	C₄×D₄	1	1	yes	characteristic
229	C₈×C₈₃	C₄×D₄	1	1	yes	characteristic
230	C₈×C₈₃	C₄×D₄	1	1	yes	characteristic
231	C₈₃⋊C₈	—	2	2	no	—
232	C₈₃⋊C₈	#121	1	2	yes	—
233	C₈₃⋊C₈	#121	1	2	yes	—
234	C₂²×C₈₃	—	4	1	no	—
235	C₂²×C₈₃	C₄×#41	1	1	yes	characteristic
236	C₂²×C₈₃	#525	1	1	yes	characteristic
237	C₂²×C₈₃	#532	1	1	yes	characteristic
238	C₂×D₈₃	—	2	2	no	—
239	C₂×D₈₃	—	4	2	no	—
240	C₂×D₈₃	—	4	2	no	—
241	C₂×D₈₃	—	8	2	no	—
242	C₄×C₈₃	—	4	2	no	—
243	C₄×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
244	C₄×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
245	C₄×C₈₃	C₂×#121	1	1	yes	characteristic
246	C₄×C₈₃	#529	1	1	yes	characteristic
247	Dic₈₃	—	2	2	no	—
248	Dic₈₃	—	4	1	no	—
249	Dic₈₃	—	4	1	no	—
250	Dic₈₃	—	4	2	no	—
251	Dic₈₃	—	8	2	no	—
252	#21559	—	83	1	no	maximal, Sylow
253	C₂×C₈₃	—	2	1	no	—
254	C₂×C₈₃	—	2	1	no	—
255	C₂×C₈₃	—	2	1	no	—
256	C₂×C₈₃	C₄×#121	1	1	yes	characteristic
257	D₈₃	—	4	2	no	—
258	D₈₃	—	8	2	no	—
259	#3067	—	83	1	no	—
260	#2955	—	83	2	no	—
261	C₂×#444	—	83	1	no	—
262	#2875	—	83	1	no	—
263	#1976	—	83	1	no	—
264	#1953	D₈₃	1	1	yes	characteristic, complemented
265	#1932	—	83	2	no	—
266	#1906	—	83	2	no	—
267	#1814	—	83	1	no	—
268	#1773	—	83	1	no	—
269	#1757	—	83	2	no	—
270	C₈₃	#21559	1	1	yes	characteristic, complemented, Sylow
271	#575	—	83	2	no	—
272	C₂×#135	—	83	1	no	—
273	C₂×#131	—	83	1	no	—
274	C₂×#131	—	83	2	no	—
275	C₂×#131	—	83	1	no	—
276	C₄×#41	—	83	1	no	—
277	#473	—	83	2	no	—
278	#472	—	83	2	no	—
279	#471	—	83	4	no	—
280	#444	—	166	1	no	—
281	#444	—	166	1	no	—
282	#444	—	166	1	no	—
283	#444	—	166	1	no	—
284	#444	—	166	4	no	—
285	#443	—	166	4	no	—
286	#430	C₂×D₈₃	1	2	yes	—
287	C₂×#108	C₂×D₈₃	1	1	yes	characteristic
288	C₂×#108	C₂×D₈₃	1	1	yes	characteristic
289	#427	—	83	1	no	—
290	#421	—	83	2	no	—
291	#421	—	83	2	no	—
292	C₂×#104	—	83	2	no	—
293	#413	—	83	2	no	—
294	#410	—	83	2	no	—
295	#405	—	83	2	no	—
296	#405	—	83	1	no	—
297	#405	—	166	1	no	—
298	#405	—	166	1	no	—
299	#405	C₂×D₈₃	1	1	yes	characteristic
300	C₄×M₁₆	—	83	1	no	—
301	C₄×M₁₆	—	166	1	no	—
302	C₂×#97	—	83	1	no	—
303	C₂×#97	—	166	1	no	—
304	#344	—	83	2	no	—
305	#344	C₂×D₈₃	1	2	yes	—
306	#339	—	83	2	no	—
307	C₂×#41	—	83	1	no	—
308	C₂×#41	—	83	2	no	—
309	#137	—	83	4	no	—
310	#137	—	166	2	no	—
311	AGL(1,ℤ/8)	—	83	4	no	—
312	AGL(1,ℤ/8)	—	166	2	no	—
313	#135	—	166	4	no	—
314	#135	—	166	1	no	—
315	#135	—	166	1	no	—
316	#135	—	166	1	no	—
317	#135	—	166	1	no	—
318	C₂×Q₁₆	—	83	1	no	—
319	C₂×SD₁₆	—	83	2	no	—
320	C₂×D₈	—	83	1	no	—
321	#131	—	83	4	no	—
322	#131	—	83	2	no	—
323	#131	—	83	2	no	—
324	#131	—	166	2	no	—
325	#131	—	166	2	no	—
326	#131	—	166	2	no	—
327	#131	—	166	2	no	—
328	#131	—	166	2	no	—
329	#131	—	166	1	no	—
330	#131	—	166	1	no	—
331	C₂×M₁₆	—	83	1	no	—
332	C₂×M₁₆	—	166	2	no	—
333	C₂×M₁₆	—	166	1	no	—
334	C₂×M₁₆	—	166	1	no	—
335	C₂×M₁₆	C₂²×D₈₃	1	2	yes	—
336	C₂×M₁₆	C₂²×D₈₃	1	2	yes	—
337	C₂×M₁₆	C₂²×D₈₃	1	1	yes	characteristic
338	C₂²×C₈	—	83	1	no	—
339	C₂²×C₈	—	166	2	no	—
340	C₂²×C₈	—	166	1	no	—
341	C₂²×C₈	—	166	1	no	—
342	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
343	C₄×Q₈	—	166	1	no	—
344	C₄×D₄	—	166	1	no	—
345	C₄×D₄	—	166	2	no	—
346	#117	—	83	2	no	—
347	#117	—	166	1	no	—
348	#117	C₂²×D₈₃	1	1	yes	characteristic
349	C₂×C₄²	—	83	1	no	—
350	C₂×C₄²	—	166	1	no	—
351	#108	—	2	4	no	—
352	#108	—	2	1	no	—
353	#108	—	2	1	no	—
354	#108	C₄×D₈₃	1	2	yes	complemented
355	#108	C₄×D₈₃	1	2	yes	complemented
356	#107	—	166	1	no	—
357	#106	—	166	1	no	—
358	#104	—	166	2	no	—
359	#104	—	166	2	no	—
360	#104	—	166	4	no	—
361	#104	—	166	4	no	—
362	#101	—	83	4	no	—
363	#100	—	83	4	no	—
364	#99	—	166	4	no	—
365	#97	—	2	1	no	—
366	#97	—	83	1	no	—
367	#97	—	83	1	no	—
368	#97	—	83	1	no	—
369	#97	—	83	1	no	—
370	#97	—	166	1	no	—
371	#97	—	166	1	no	—
372	#97	—	166	2	no	—
373	C₄×C₈	—	2	1	no	—
374	C₄×C₈	—	166	1	no	—
375	C₄×C₈	—	166	1	no	—
376	C₄×C₈	—	166	2	no	—
377	#41	—	83	2	no	—
378	#41	—	83	2	no	—
379	#41	—	166	2	no	—
380	#41	—	166	2	no	—
381	#41	—	166	2	no	—
382	#41	—	166	2	no	—
383	#41	—	166	1	no	—
384	#41	—	166	1	no	—
385	C₂×Q₈	—	83	2	no	—
386	C₂×Q₈	—	83	1	no	—
387	C₂×D₄	—	83	2	no	—
388	C₂×D₄	—	83	1	no	—
389	C₂×D₄	—	166	2	no	—
390	C₂×D₄	—	166	1	no	—
391	C₂²×C₄	—	166	2	no	—
392	C₂²×C₄	—	166	2	no	—
393	C₂²×C₄	—	166	1	no	—
394	C₂²×C₄	—	166	1	no	—
395	C₂²×C₄	C₂³×D₈₃	1	1	yes	characteristic
396	Q₁₆	—	166	4	no	—
397	Q₁₆	—	166	1	no	—
398	Q₁₆	—	166	1	no	—
399	SD₁₆	—	166	4	no	—
400	SD₁₆	—	166	4	no	—
401	SD₁₆	—	166	2	no	—
402	SD₁₆	—	166	2	no	—
403	D₈	—	166	4	no	—
404	D₈	—	166	1	no	—
405	D₈	—	166	1	no	—
406	M₁₆	—	2	1	no	—
407	M₁₆	—	2	2	no	—
408	M₁₆	—	2	2	no	—
409	M₁₆	—	2	2	no	—
410	M₁₆	—	332	2	no	—
411	M₁₆	—	332	2	no	—
412	M₁₆	—	83	2	no	—
413	M₁₆	—	166	4	no	—
414	M₁₆	—	166	1	no	—
415	M₁₆	—	166	2	no	—
416	M₁₆	—	166	2	no	—
417	M₁₆	C₂×C₄×D₈₃	1	4	yes	—
418	M₁₆	D₄×D₈₃	1	2	yes	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	332	2	no	—
423	C₂×C₈	—	332	2	no	—
424	C₂×C₈	—	83	1	no	—
425	C₂×C₈	—	83	2	no	—
426	C₂×C₈	—	83	1	no	—
427	C₂×C₈	—	83	2	no	—
428	C₂×C₈	—	166	4	no	—
429	C₂×C₈	—	166	1	no	—
430	C₂×C₈	—	166	2	no	—
431	C₂×C₈	—	166	2	no	—
432	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
433	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
434	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
435	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
436	C₂×C₈	#13050591	1	1	yes	characteristic
437	C₂×C₈	#13050591	1	1	yes	characteristic
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	166	2	no	—
440	C₄⋊C₄	—	166	2	no	—
441	C₂²⋊C₄	—	166	2	no	—
442	C₂²⋊C₄	—	166	2	no	—
443	C₂²⋊C₄	#13050591	1	2	yes	—
444	C₄²	—	2	1	no	—
445	C₄²	—	83	1	no	—
446	C₄²	—	83	1	no	—
447	C₄²	—	166	2	no	—
448	C₄²	—	166	2	no	—
449	C₄²	—	166	1	no	—
450	C₂³	—	166	1	no	—
451	C₂³	—	166	2	no	—
452	C₂³	C₂×#13050591	1	1	yes	characteristic
453	Q₈	—	83	2	no	—
454	Q₈	—	166	2	no	—
455	Q₈	—	166	2	no	—
456	Q₈	—	166	1	no	—
457	D₄	—	332	2	no	—
458	D₄	—	332	2	no	—
459	D₄	—	83	2	no	—
460	D₄	—	166	2	no	—
461	D₄	—	166	2	no	—
462	D₄	—	166	2	no	—
463	D₄	—	166	2	no	—
464	D₄	—	166	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	332	2	no	—
467	C₂×C₄	—	332	2	no	—
468	C₂×C₄	—	332	2	no	—
469	C₂×C₄	—	664	2	no	—
470	C₂×C₄	—	664	1	no	—
471	C₂×C₄	—	166	2	no	—
472	C₂×C₄	—	166	1	no	—
473	C₂×C₄	—	166	1	no	—
474	C₂×C₄	—	166	1	no	—
475	C₂×C₄	—	166	2	no	—
476	C₂×C₄	—	166	2	no	—
477	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
478	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
479	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
480	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
481	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
482	C₂×C₄	C₂×#13050591	1	1	yes	characteristic
483	C₈	—	2	4	no	—
484	C₈	—	2	2	no	—
485	C₈	—	4	2	no	—
486	C₈	—	83	2	no	—
487	C₈	—	83	2	no	—
488	C₈	—	166	2	no	—
489	C₈	#14581754	1	1	yes	characteristic
490	C₈	#14581754	1	1	yes	characteristic
491	C₈	#14581754	1	1	yes	characteristic
492	C₈	#14581754	1	1	yes	characteristic
493	C₂²	—	4	1	no	—
494	C₂²	—	332	2	no	—
495	C₂²	—	332	2	no	—
496	C₂²	—	664	2	no	—
497	C₂²	—	166	2	no	—
498	C₂²	C₄×#13050591	1	1	yes	characteristic
499	C₂²	#19128214	1	1	yes	characteristic
500	C₂²	#19128252	1	1	yes	characteristic
501	C₄	—	4	2	no	—
502	C₄	—	332	1	no	—
503	C₄	—	332	1	no	—
504	C₄	—	332	2	no	—
505	C₄	—	664	2	no	—
506	C₄	—	166	2	no	—
507	C₄	C₄×D₄×D₈₃	1	1	yes	characteristic
508	C₄	C₂×#14581754	1	1	yes	characteristic
509	C₄	#121×D₈₃	1	1	yes	characteristic
510	C₄	#19128236	1	1	yes	characteristic
511	C₂	—	2	1	no	—
512	C₂	—	2	1	no	—
513	C₂	—	2	1	no	—
514	C₂	—	332	2	no	—
515	C₂	—	664	2	no	—
516	C₂	#24909971	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#121×D₈₃
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₃
Fitting	C₈₃×#1953	C₂
socle	C₂×C₈₃	C₄×#121
prime radical	#24917184	C₂
cosocle	C₂²×C₄×C₈₃	C₂⁴
hypercenter	#1953	D₈₃
hypocenter	C₈₃	#21559
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1953

Complements

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

N	H ≅ G/N	type
2. #24916365	C₂	semidirect
3. C₂×#19127822	C₂	semidirect
4. #24915890	C₂	semidirect
5. #24908361	C₂	semidirect
6. #24908131	C₂	semidirect
7. #24907965	C₂	semidirect
8. #24907518	C₂	semidirect
9. #24907350	C₂	semidirect
10. #24907262	C₂	semidirect
11. C₈₃×#1953	C₂	semidirect
18. #19127977	C₄	semidirect
19. #19127972	C₄	semidirect
20. #19127965	C₄	semidirect
59. C₂×Dic₃₃₂	C₂×C₄	semidirect
60. C₂×#13050579	C₂×C₄	semidirect
61. C₂×D₆₆₄	C₂×C₄	semidirect
93. #14581710	C₂×C₄	semidirect
94. #14581708	C₂×C₄	semidirect
114. #108×C₈₃	C₂×C₄	semidirect
115. #108×C₈₃	C₂×C₄	semidirect
264. #1953	D₈₃	semidirect
270. C₈₃	#21559	semidirect
354. #108	C₄×D₈₃	semidirect
355. #108	C₄×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
#24917184	2
#24916365	2
C₂×#19127822	2
#24915890	2
#24908361	2
#24908131	2
#24907965	2
#24907518	2
#24907350	2
#24907262	2
C₈₃×#1953	2
#21559	83