Subgroups — #35411345

Order 21248.

876 conjugacy classes of subgroups.

The subgroup lattice has 534 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	#24916367	C₂	1	2	yes	maximal, complemented
3	C₂×#19127819	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#14581798	C₂	1	1	yes	maximal, characteristic, complemented
5	#24908359	C₂	1	1	yes	maximal, characteristic, complemented
6	#24908254	C₂	1	1	yes	maximal, characteristic, complemented
7	#24908133	C₂	1	2	yes	maximal, complemented
8	#24907963	C₂	1	2	yes	maximal, complemented
9	#24907514	C₂	1	1	yes	maximal, characteristic, complemented
10	#24907264	C₂	1	2	yes	maximal, complemented
11	C₈₃×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	#19128501	C₂²	1	2	yes	—
13	C₂×#14581814	C₂²	1	1	yes	characteristic
14	C₂×#14581798	C₂²	1	2	yes	—
15	C₂×#14581798	C₂²	1	1	yes	characteristic
16	C₂×#14581798	C₂²	1	1	yes	characteristic
17	C₄×#13050590	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	#19127824	—	2	4	no	—
22	#19127819	—	2	1	no	—
23	#19127819	—	2	1	no	—
24	#19127819	—	2	1	no	—
25	#19127819	—	2	1	no	—
26	#19127819	—	2	4	no	—
27	#19127750	C₂²	1	2	yes	—
28	C₂×#14581728	C₂²	1	1	yes	characteristic
29	#19127719	C₂²	1	2	yes	—
30	#19127719	C₂²	1	2	yes	—
31	C₂×#14581720	C₂²	1	2	yes	—
32	#19127683	C₂²	1	2	yes	—
33	#19127674	C₂²	1	2	yes	—
34	#19127656	C₂²	1	1	yes	characteristic
35	#19127656	C₂²	1	1	yes	characteristic
36	#19127655	—	2	1	no	—
37	#19127655	—	2	1	no	—
38	C₄×#13050574	C₂²	1	1	yes	characteristic
39	C₄×#13050573	—	2	1	no	—
40	C₄×C₈×D₈₃	—	2	1	no	—
41	#19127473	C₂²	1	2	yes	—
42	#19127471	C₂²	1	2	yes	—
43	C₂×#108×C₈₃	C₂²	1	1	yes	characteristic
44	#427×C₈₃	C₂²	1	1	yes	characteristic
45	#405×C₈₃	C₂²	1	2	yes	—
46	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
47	#339×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	#14581798	—	2	2	no	—
63	#14581798	—	2	2	no	—
64	#14581798	—	2	2	no	—
65	#14581798	—	2	2	no	—
66	#14581798	—	2	1	no	—
67	#14581798	—	2	1	no	—
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	#14581798	D₄	1	2	yes	—
73	#14581798	D₄	1	2	yes	—
74	C₂×#13050574	C₂³	1	2	yes	—
75	C₂×#13050574	C₂³	1	1	yes	characteristic
76	C₂×#13050574	C₂³	1	1	yes	characteristic
77	C₂×#13050573	—	2	1	no	—
78	C₂×#13050573	—	2	1	no	—
79	C₂×#13050573	—	2	2	no	—
80	C₂×C₈×D₈₃	—	2	1	no	—
81	C₂×C₈×D₈₃	—	2	1	no	—
82	C₂×C₈×D₈₃	—	2	2	no	—
83	C₄×Dic₁₆₆	—	2	1	no	—
84	C₄×D₃₃₂	—	2	1	no	—
85	C₄×C₂²⋊D₈₃	—	2	2	no	—
86	#14581751	C₂³	1	1	yes	characteristic
87	#14581749	—	2	1	no	—
88	C₄²×D₈₃	—	2	1	no	—
89	#14581728	—	2	4	no	—
90	#14581728	—	2	1	no	—
91	#14581728	—	2	1	no	—
92	#14581720	—	2	4	no	—
93	#14581720	—	2	4	no	—
94	#14581720	—	2	2	no	—
95	#14581720	—	2	2	no	—
96	#14581710	C₂×C₄	1	4	yes	complemented
97	#14581708	C₂×C₄	1	4	yes	complemented
98	#14581706	—	2	4	no	—
99	#14581703	—	2	1	no	—
100	#14581702	—	2	1	no	—
101	#14581702	—	2	1	no	—
102	C₄×C₈₃⋊C₈	—	2	1	no	—
103	C₈×Dic₈₃	—	2	1	no	—
104	C₈×Dic₈₃	—	2	1	no	—
105	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
106	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
108	#117×C₈₃	C₂³	1	2	yes	—
109	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
110	#108×C₈₃	C₂×C₄	1	2	yes	complemented
111	#108×C₈₃	C₂×C₄	1	2	yes	complemented
112	#107×C₈₃	—	2	1	no	—
113	#106×C₈₃	—	2	1	no	—
114	#97×C₈₃	—	2	2	no	—
115	C₄×C₈×C₈₃	—	2	2	no	—
116	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
117	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
118	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
119	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
120	#13050590	—	2	1	no	—
121	#13050590	—	2	1	no	—
122	#13050590	—	2	2	no	—
123	#13050590	—	2	2	no	—
124	#13050590	—	2	2	no	—
125	#13050590	—	2	2	no	—
126	#13050590	C₂²×C₄	1	2	yes	—
127	#13050590	C₂×D₄	1	2	yes	—
128	C₂×Dic₁₆₆	C₂²×C₄	1	2	yes	—
129	C₂×Dic₁₆₆	#41	1	1	yes	characteristic
130	C₂×D₃₃₂	C₂²×C₄	1	2	yes	—
131	C₂×D₃₃₂	#41	1	1	yes	characteristic
132	C₂×C₂²⋊D₈₃	—	2	1	no	—
133	C₂×C₂²⋊D₈₃	—	2	2	no	—
134	C₂×C₄×D₈₃	—	2	1	no	—
135	C₂×C₄×D₈₃	—	2	2	no	—
136	C₂×C₄×D₈₃	—	2	2	no	—
137	Dic₃₃₂	—	2	4	no	—
138	Dic₃₃₂	—	2	1	no	—
139	Dic₃₃₂	—	2	1	no	—
140	#13050579	—	2	4	no	—
141	#13050579	—	2	4	no	—
142	#13050579	—	2	2	no	—
143	#13050579	—	2	2	no	—
144	D₆₆₄	—	2	4	no	—
145	D₆₆₄	—	2	1	no	—
146	D₆₆₄	—	2	1	no	—
147	#13050574	—	2	1	no	—
148	#13050574	—	2	1	no	—
149	#13050574	—	2	2	no	—
150	#13050574	—	2	2	no	—
151	#13050574	C₂²×C₄	1	2	yes	—
152	#13050574	C₂×D₄	1	2	yes	—
153	#13050573	—	2	2	no	—
154	#13050573	—	2	2	no	—
155	#13050573	—	2	2	no	—
156	#13050573	—	2	2	no	—
157	#13050573	—	4	2	no	—
158	#13050573	—	4	2	no	—
159	C₂×C₈₃⋊C₈	—	2	1	no	—
160	C₂×C₈₃⋊C₈	—	2	1	no	—
161	C₂×C₈₃⋊C₈	—	2	2	no	—
162	C₈×D₈₃	—	2	2	no	—
163	C₈×D₈₃	—	2	2	no	—
164	C₈×D₈₃	—	2	2	no	—
165	C₈×D₈₃	—	2	2	no	—
166	C₈×D₈₃	—	4	2	no	—
167	C₈×D₈₃	—	4	2	no	—
168	C₄⋊Dic₈₃	—	2	1	no	—
169	Dic₈₃⋊C₄	—	2	2	no	—
170	C₂²⋊Dic₈₃	#41	1	2	yes	—
171	(C₂×D₈₃)⋊C₄	—	2	2	no	—
172	C₄×Dic₈₃	—	2	2	no	—
173	C₄×Dic₈₃	—	2	1	no	—
174	C₂²×C₄×C₈₃	—	2	1	no	—
175	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
176	M₁₆×C₈₃	—	2	2	no	—
177	M₁₆×C₈₃	C₂²×C₄	1	4	yes	—
178	C₂×C₈×C₈₃	—	2	2	no	—
179	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₈₃	C₂×D₄	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	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
188	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
189	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
190	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
191	C₄⋊C₄×C₈₃	—	2	2	no	—
192	C₂²⋊C₄×C₈₃	—	2	2	no	—
193	C₄²×C₈₃	—	2	1	no	—
194	C₄²×C₈₃	—	2	2	no	—
195	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
197	C₂³×C₈₃	C₂×#41	1	1	yes	characteristic
198	C₂²×D₈₃	—	2	1	no	—
199	C₂²×D₈₃	—	2	2	no	—
200	C₂×C₄×C₈₃	—	2	1	no	—
201	C₂×C₄×C₈₃	—	2	1	no	—
202	C₂×C₄×C₈₃	—	4	2	no	—
203	C₂×C₄×C₈₃	—	4	2	no	—
204	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
210	C₂²⋊D₈₃	—	2	2	no	—
211	C₂²⋊D₈₃	—	2	2	no	—
212	C₂²⋊D₈₃	—	4	2	no	—
213	C₂²⋊D₈₃	—	4	2	no	—
214	C₂×Dic₈₃	—	2	1	no	—
215	C₂×Dic₈₃	—	2	2	no	—
216	C₂×Dic₈₃	—	2	2	no	—
217	D₃₃₂	—	2	2	no	—
218	D₃₃₂	—	2	2	no	—
219	D₃₃₂	—	2	1	no	—
220	D₃₃₂	C₄×D₄	1	2	yes	—
221	C₄×D₈₃	—	2	2	no	—
222	C₄×D₈₃	—	2	2	no	—
223	C₄×D₈₃	—	4	4	no	—
224	C₄×D₈₃	—	4	2	no	—
225	C₄×D₈₃	—	4	2	no	—
226	Dic₁₆₆	—	2	1	no	—
227	Dic₁₆₆	—	2	2	no	—
228	Dic₁₆₆	—	2	2	no	—
229	Dic₁₆₆	C₄×D₄	1	2	yes	—
230	C₈×C₈₃	—	2	4	no	—
231	C₈×C₈₃	C₄×D₄	1	1	yes	characteristic
232	C₈×C₈₃	C₄×D₄	1	1	yes	characteristic
233	C₈×C₈₃	C₄×D₄	1	1	yes	characteristic
234	C₈×C₈₃	C₄×D₄	1	1	yes	characteristic
235	C₈×C₈₃	#121	1	1	yes	characteristic
236	C₈×C₈₃	#121	1	1	yes	characteristic
237	C₈×C₈₃	#121	1	1	yes	characteristic
238	C₈×C₈₃	#121	1	1	yes	characteristic
239	C₈₃⋊C₈	—	2	2	no	—
240	C₈₃⋊C₈	—	2	2	no	—
241	C₈₃⋊C₈	—	4	2	no	—
242	C₂²×C₈₃	—	4	1	no	—
243	C₂²×C₈₃	C₄×#41	1	1	yes	characteristic
244	C₂²×C₈₃	#525	1	1	yes	characteristic
245	C₂²×C₈₃	#532	1	1	yes	characteristic
246	C₂×D₈₃	—	2	2	no	—
247	C₂×D₈₃	—	4	2	no	—
248	C₂×D₈₃	—	4	2	no	—
249	C₂×D₈₃	—	8	2	no	—
250	C₄×C₈₃	—	2	2	no	—
251	C₄×C₈₃	—	4	1	no	—
252	C₄×C₈₃	—	8	2	no	—
253	C₄×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
254	C₄×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
255	C₄×C₈₃	C₂×#121	1	1	yes	characteristic
256	C₄×C₈₃	#529	1	1	yes	characteristic
257	Dic₈₃	—	2	2	no	—
258	Dic₈₃	—	4	2	no	—
259	Dic₈₃	—	4	2	no	—
260	#21558	—	83	1	no	maximal, Sylow
261	C₂×C₈₃	—	2	1	no	—
262	C₂×C₈₃	—	2	1	no	—
263	C₂×C₈₃	—	2	1	no	—
264	C₂×C₈₃	C₄×#121	1	1	yes	characteristic
265	D₈₃	—	4	2	no	—
266	D₈₃	—	8	2	no	—
267	#3067	—	83	1	no	—
268	#2955	—	83	2	no	—
269	C₂×#443	—	83	1	no	—
270	C₄×#131	—	83	1	no	—
271	#1976	—	83	1	no	—
272	#1953	—	83	1	no	—
273	#1932	—	83	2	no	—
274	#1906	—	83	2	no	—
275	#1814	—	83	1	no	—
276	#1772	D₈₃	1	1	yes	characteristic, complemented
277	#1757	—	83	2	no	—
278	C₈₃	#21558	1	1	yes	characteristic, complemented, Sylow
279	#575	—	83	2	no	—
280	C₂×#135	—	83	1	no	—
281	C₂×#131	—	83	1	no	—
282	C₂×#131	—	83	1	no	—
283	C₂×#131	—	83	2	no	—
284	C₄×#41	—	83	1	no	—
285	#473	—	83	2	no	—
286	#472	—	83	2	no	—
287	#471	—	83	4	no	—
288	#444	—	166	4	no	—
289	#443	—	166	4	no	—
290	#443	—	166	1	no	—
291	#443	—	166	1	no	—
292	#443	—	166	1	no	—
293	#443	—	166	1	no	—
294	#430	—	83	2	no	—
295	C₂×#108	—	83	1	no	—
296	C₂×#108	C₂×D₈₃	1	1	yes	characteristic
297	#427	C₂×D₈₃	1	1	yes	characteristic
298	#421	—	83	2	no	—
299	#421	—	83	2	no	—
300	C₂×#104	—	83	2	no	—
301	#413	—	83	2	no	—
302	#410	—	83	2	no	—
303	#405	—	83	1	no	—
304	#405	—	83	1	no	—
305	#405	—	166	1	no	—
306	#405	—	166	1	no	—
307	#405	C₂×D₈₃	1	2	yes	—
308	C₄×M₁₆	—	83	1	no	—
309	C₄×M₁₆	—	166	1	no	—
310	C₂×C₄×C₈	—	166	1	no	—
311	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
312	#344	—	83	2	no	—
313	#344	—	83	2	no	—
314	#339	C₂×D₈₃	1	2	yes	—
315	C₂×#41	—	83	1	no	—
316	C₂×#41	—	83	2	no	—
317	#137	—	83	4	no	—
318	#137	—	166	2	no	—
319	AGL(1,ℤ/8)	—	83	4	no	—
320	AGL(1,ℤ/8)	—	166	2	no	—
321	#135	—	166	4	no	—
322	#135	—	166	1	no	—
323	#135	—	166	1	no	—
324	#135	—	166	1	no	—
325	#135	—	166	1	no	—
326	C₂×Q₁₆	—	83	1	no	—
327	C₂×SD₁₆	—	83	2	no	—
328	C₂×D₈	—	83	1	no	—
329	#131	—	83	2	no	—
330	#131	—	83	2	no	—
331	#131	—	83	2	no	—
332	#131	—	83	2	no	—
333	#131	—	166	2	no	—
334	#131	—	166	2	no	—
335	#131	—	166	2	no	—
336	#131	—	166	2	no	—
337	#131	—	166	1	no	—
338	#131	—	166	1	no	—
339	#131	—	166	1	no	—
340	#131	—	166	1	no	—
341	C₂×M₁₆	—	83	1	no	—
342	C₂×M₁₆	—	83	1	no	—
343	C₂×M₁₆	—	83	2	no	—
344	C₂×M₁₆	—	166	1	no	—
345	C₂×M₁₆	—	166	1	no	—
346	C₂×M₁₆	—	166	2	no	—
347	C₂×M₁₆	C₂²×D₈₃	1	2	yes	—
348	C₂²×C₈	—	166	2	no	—
349	C₂²×C₈	—	166	1	no	—
350	C₂²×C₈	—	166	1	no	—
351	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
352	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
353	C₄×Q₈	—	166	1	no	—
354	C₄×D₄	—	166	1	no	—
355	C₄×D₄	—	166	2	no	—
356	#117	—	83	1	no	—
357	#117	—	166	1	no	—
358	#117	C₂²×D₈₃	1	2	yes	—
359	C₂×C₄²	—	166	1	no	—
360	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
361	#108	—	166	4	no	—
362	#108	—	166	1	no	—
363	#108	—	166	1	no	—
364	#108	C₄×D₈₃	1	2	yes	complemented
365	#108	C₄×D₈₃	1	2	yes	complemented
366	#107	—	2	1	no	—
367	#106	—	2	1	no	—
368	#104	—	166	4	no	—
369	#104	—	166	4	no	—
370	#104	—	166	2	no	—
371	#104	—	166	2	no	—
372	#101	—	83	4	no	—
373	#100	—	83	4	no	—
374	#99	—	166	4	no	—
375	#97	—	2	2	no	—
376	#97	—	166	1	no	—
377	#97	—	166	1	no	—
378	#97	—	166	1	no	—
379	C₄×C₈	—	2	2	no	—
380	C₄×C₈	—	166	1	no	—
381	C₄×C₈	—	166	1	no	—
382	C₄×C₈	—	166	1	no	—
383	C₄×C₈	D₃₃₂	1	1	yes	characteristic
384	C₄×C₈	D₃₃₂	1	1	yes	characteristic
385	C₄×C₈	D₃₃₂	1	1	yes	characteristic
386	C₄×C₈	D₃₃₂	1	1	yes	characteristic
387	#41	—	83	2	no	—
388	#41	—	83	2	no	—
389	#41	—	166	2	no	—
390	#41	—	166	2	no	—
391	#41	—	166	2	no	—
392	#41	—	166	2	no	—
393	#41	—	166	1	no	—
394	#41	—	166	1	no	—
395	C₂×Q₈	—	83	2	no	—
396	C₂×Q₈	—	83	1	no	—
397	C₂×D₄	—	83	2	no	—
398	C₂×D₄	—	83	1	no	—
399	C₂×D₄	—	166	2	no	—
400	C₂×D₄	—	166	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	166	2	no	—
403	C₂²×C₄	—	166	2	no	—
404	C₂²×C₄	—	166	1	no	—
405	C₂²×C₄	C₂³×D₈₃	1	1	yes	characteristic
406	Q₁₆	—	166	4	no	—
407	Q₁₆	—	166	1	no	—
408	Q₁₆	—	166	1	no	—
409	SD₁₆	—	166	4	no	—
410	SD₁₆	—	166	4	no	—
411	SD₁₆	—	166	2	no	—
412	SD₁₆	—	166	2	no	—
413	D₈	—	166	4	no	—
414	D₈	—	166	1	no	—
415	D₈	—	166	1	no	—
416	M₁₆	—	2	2	no	—
417	M₁₆	—	332	2	no	—
418	M₁₆	—	332	2	no	—
419	M₁₆	—	83	2	no	—
420	M₁₆	—	83	2	no	—
421	M₁₆	—	166	2	no	—
422	M₁₆	—	166	2	no	—
423	M₁₆	—	166	1	no	—
424	M₁₆	—	166	1	no	—
425	M₁₆	—	166	2	no	—
426	M₁₆	—	166	2	no	—
427	M₁₆	—	166	2	no	—
428	M₁₆	—	166	2	no	—
429	M₁₆	C₂×C₄×D₈₃	1	4	yes	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	332	2	no	—
432	C₂×C₈	—	332	2	no	—
433	C₂×C₈	—	166	2	no	—
434	C₂×C₈	—	166	1	no	—
435	C₂×C₈	—	166	1	no	—
436	C₂×C₈	—	166	2	no	—
437	C₂×C₈	—	166	2	no	—
438	C₂×C₈	—	166	2	no	—
439	C₂×C₈	—	166	2	no	—
440	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
441	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
442	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
443	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
444	C₂×C₈	C₂×D₃₃₂	1	1	yes	characteristic
445	C₂×C₈	C₂×D₃₃₂	1	1	yes	characteristic
446	C₂×C₈	C₂×D₃₃₂	1	1	yes	characteristic
447	C₂×C₈	C₂×D₃₃₂	1	1	yes	characteristic
448	C₂×C₈	#13050590	1	1	yes	characteristic
449	C₂×C₈	#13050590	1	1	yes	characteristic
450	C₂×C₈	#13050591	1	1	yes	characteristic
451	C₂×C₈	#13050591	1	1	yes	characteristic
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	166	2	no	—
454	C₄⋊C₄	—	166	1	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	83	2	no	—
457	C₂²⋊C₄	—	166	2	no	—
458	C₄²	—	2	1	no	—
459	C₄²	—	2	2	no	—
460	C₄²	—	166	2	no	—
461	C₄²	—	166	1	no	—
462	C₄²	C₂×D₃₃₂	1	1	yes	characteristic
463	C₄²	C₂×D₃₃₂	1	1	yes	characteristic
464	C₂³	—	166	1	no	—
465	C₂³	—	166	2	no	—
466	C₂³	#41×D₈₃	1	1	yes	characteristic
467	Q₈	—	83	2	no	—
468	Q₈	—	166	2	no	—
469	Q₈	—	166	2	no	—
470	Q₈	—	166	1	no	—
471	D₄	—	332	2	no	—
472	D₄	—	332	2	no	—
473	D₄	—	83	2	no	—
474	D₄	—	166	2	no	—
475	D₄	—	166	2	no	—
476	D₄	—	166	2	no	—
477	D₄	—	166	2	no	—
478	D₄	—	166	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	332	4	no	—
484	C₂×C₄	—	332	2	no	—
485	C₂×C₄	—	332	2	no	—
486	C₂×C₄	—	166	2	no	—
487	C₂×C₄	—	166	2	no	—
488	C₂×C₄	—	166	1	no	—
489	C₂×C₄	—	166	2	no	—
490	C₂×C₄	—	166	2	no	—
491	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
492	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
493	C₂×C₄	C₂²×D₃₃₂	1	1	yes	characteristic
494	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
495	C₂×C₄	C₂×#13050590	1	1	yes	characteristic
496	C₂×C₄	C₂×#13050591	1	1	yes	characteristic
497	C₈	—	2	4	no	—
498	C₈	—	332	2	no	—
499	C₈	—	166	2	no	—
500	C₈	—	166	2	no	—
501	C₈	C₄×D₃₃₂	1	1	yes	characteristic
502	C₈	C₄×D₃₃₂	1	1	yes	characteristic
503	C₈	C₄×D₃₃₂	1	1	yes	characteristic
504	C₈	C₄×D₃₃₂	1	1	yes	characteristic
505	C₈	#14581767	1	1	yes	characteristic
506	C₈	#14581767	1	1	yes	characteristic
507	C₈	#14581767	1	1	yes	characteristic
508	C₈	#14581767	1	1	yes	characteristic
509	C₂²	—	4	1	no	—
510	C₂²	—	332	2	no	—
511	C₂²	—	332	2	no	—
512	C₂²	—	664	2	no	—
513	C₂²	—	166	2	no	—
514	C₂²	C₄×#13050591	1	1	yes	characteristic
515	C₂²	#19128213	1	1	yes	characteristic
516	C₂²	#19128248	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	4	1	no	—
519	C₄	—	8	2	no	—
520	C₄	—	332	2	no	—
521	C₄	—	332	2	no	—
522	C₄	—	166	2	no	—
523	C₄	C₄×D₄×D₈₃	1	1	yes	characteristic
524	C₄	C₂×C₄×D₃₃₂	1	1	yes	characteristic
525	C₄	C₂×#14581767	1	1	yes	characteristic
526	C₄	#19128238	1	1	yes	characteristic
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	332	2	no	—
531	C₂	—	664	2	no	—
532	C₂	C₄×#14581767	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#14581767
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₃
Fitting	C₈₃×#1772	C₂
socle	C₂×C₈₃	C₄×#121
prime radical	#24917184	C₂
cosocle	C₂²×C₄×C₈₃	C₂⁴
hypercenter	#1772	D₈₃
hypocenter	C₈₃	#21558
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
2. #24916367	C₂	semidirect
3. C₂×#19127819	C₂	semidirect
4. C₄×#14581798	C₂	semidirect
5. #24908359	C₂	semidirect
6. #24908254	C₂	semidirect
7. #24908133	C₂	semidirect
8. #24907963	C₂	semidirect
9. #24907514	C₂	semidirect
10. #24907264	C₂	semidirect
11. C₈₃×#1772	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
96. #14581710	C₂×C₄	semidirect
97. #14581708	C₂×C₄	semidirect
110. #108×C₈₃	C₂×C₄	semidirect
111. #108×C₈₃	C₂×C₄	semidirect
276. #1772	D₈₃	semidirect
278. C₈₃	#21558	semidirect
364. #108	C₄×D₈₃	semidirect
365. #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
#24916367	2
C₂×#19127819	2
C₄×#14581798	2
#24908359	2
#24908254	2
#24908133	2
#24907963	2
#24907514	2
#24907264	2
C₈₃×#1772	2
#21558	83