Subgroups — #35411346

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	#24917179	C₂	1	1	yes	maximal, characteristic
2	#24916362	C₂	1	2	yes	maximal, complemented
3	C₂×#19127818	C₂	1	1	yes	maximal, characteristic, complemented
4	#24915885	C₂	1	1	yes	maximal, characteristic, complemented
5	#24908253	C₂	1	1	yes	maximal, characteristic, complemented
6	#24908135	C₂	1	2	yes	maximal, complemented
7	#24907961	C₂	1	2	yes	maximal, complemented
8	#24907514	C₂	1	1	yes	maximal, characteristic, complemented
9	#24907344	C₂	1	1	yes	maximal, characteristic, complemented
10	#24907265	C₂	1	2	yes	maximal, complemented
11	C₈₃×#1976	C₂	1	1	yes	maximal, characteristic, complemented
12	#19128499	C₂²	1	2	yes	—
13	C₂×#14581800	C₂²	1	1	yes	characteristic
14	C₂×#14581799	C₂²	1	2	yes	—
15	C₂×#14581798	C₂²	1	1	yes	characteristic
16	#19128169	C₂²	1	1	yes	characteristic
17	#19127973	C₄	1	2	yes	complemented
18	#19127968	C₄	1	2	yes	complemented
19	#19127961	C₄	1	4	yes	complemented
20	#19127820	—	2	4	no	—
21	#19127818	—	2	1	no	—
22	#19127818	—	2	1	no	—
23	#19127818	—	2	1	no	—
24	#19127818	—	2	1	no	—
25	#19127815	—	2	4	no	—
26	#19127749	C₂²	1	2	yes	—
27	C₂×#14581728	C₂²	1	1	yes	characteristic
28	C₂×#14581728	C₂²	1	1	yes	characteristic
29	#19127719	C₂²	1	2	yes	—
30	C₂×#14581719	C₂²	1	2	yes	—
31	#19127685	C₂²	1	2	yes	—
32	#19127658	—	2	1	no	—
33	#19127657	C₂²	1	1	yes	characteristic
34	#19127657	C₂²	1	2	yes	—
35	#19127655	—	2	1	no	—
36	#19127653	—	2	1	no	—
37	M₁₆×Dic₈₃	C₂²	1	1	yes	characteristic
38	C₂×C₈×Dic₈₃	C₂²	1	1	yes	characteristic
39	C₄×C₈×D₈₃	—	2	1	no	—
40	#19127471	C₂²	1	2	yes	—
41	#19127471	C₂²	1	2	yes	—
42	#19127460	C₂²	1	2	yes	—
43	C₂×#135×C₈₃	C₂²	1	1	yes	characteristic
44	#427×C₈₃	C₂²	1	1	yes	characteristic
45	#421×C₈₃	C₂²	1	2	yes	—
46	#410×C₈₃	C₂²	1	2	yes	—
47	#405×C₈₃	C₂²	1	1	yes	characteristic
48	C₂×#13050590	C₂³	1	1	yes	characteristic
49	#14581823	C₂×C₄	1	4	yes	—
50	#14581822	—	2	2	no	—
51	#14581818	C₂×C₄	1	4	yes	—
52	#14581817	—	2	2	no	—
53	#14581812	—	2	4	no	—
54	#14581800	—	2	1	no	—
55	#14581800	—	2	1	no	—
56	#14581800	D₄	1	2	yes	—
57	#14581800	D₄	1	2	yes	—
58	#14581799	—	2	2	no	—
59	#14581799	—	2	2	no	—
60	#14581799	—	2	2	no	—
61	#14581799	—	2	2	no	—
62	#14581798	—	2	1	no	—
63	#14581798	—	2	1	no	—
64	#14581798	C₂×C₄	1	2	yes	—
65	#14581798	C₂×C₄	1	2	yes	—
66	C₂×#13050574	—	2	2	no	—
67	C₂×#13050574	C₂³	1	2	yes	—
68	C₂×#13050574	C₂³	1	1	yes	characteristic
69	C₂×#13050574	C₂³	1	2	yes	—
70	C₂×#13050573	—	2	1	no	—
71	C₂×#13050573	—	2	1	no	—
72	C₂²×C₈₃⋊C₈	—	2	2	no	—
73	C₂²×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
74	C₂×C₈×D₈₃	—	2	1	no	—
75	C₂×C₈×D₈₃	—	2	1	no	—
76	#14581757	—	2	1	no	—
77	#14581754	—	2	1	no	—
78	(C₂²⋊D₈₃)⋊C₄	—	2	2	no	—
79	#14581749	—	2	1	no	—
80	C₂×C₄×Dic₈₃	C₂³	1	1	yes	characteristic
81	C₄²×D₈₃	—	2	1	no	—
82	#14581728	—	2	1	no	—
83	#14581728	—	2	1	no	—
84	#14581728	C₂×C₄	1	2	yes	complemented
85	#14581728	C₂×C₄	1	2	yes	complemented
86	#14581727	—	2	4	no	—
87	#14581720	—	2	4	no	—
88	#14581719	—	2	2	no	—
89	#14581719	—	2	2	no	—
90	#14581711	C₂×C₄	1	4	yes	complemented
91	#14581709	C₂×C₄	1	4	yes	complemented
92	#14581703	—	2	2	no	—
93	#14581703	—	2	1	no	—
94	#14581702	—	2	1	no	—
95	C₄×C₈₃⋊C₈	—	2	2	no	—
96	C₄×C₈₃⋊C₈	—	2	1	no	—
97	C₈×Dic₈₃	—	2	1	no	—
98	C₈×Dic₈₃	D₄	1	1	yes	characteristic
99	C₈×Dic₈₃	D₄	1	1	yes	characteristic
100	C₈×Dic₈₃	D₄	1	1	yes	characteristic
101	C₈×Dic₈₃	D₄	1	1	yes	characteristic
102	C₂×#41×C₈₃	C₂³	1	2	yes	—
103	#135×C₈₃	—	2	1	no	—
104	#135×C₈₃	—	2	1	no	—
105	#135×C₈₃	—	2	1	no	—
106	#135×C₈₃	—	2	1	no	—
107	C₂×Q₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic, complemented
108	C₂×SD₁₆×C₈₃	C₂×C₄	1	2	yes	complemented
109	C₂×D₈×C₈₃	C₂×C₄	1	1	yes	characteristic, complemented
110	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
112	#117×C₈₃	C₂³	1	2	yes	—
113	#117×C₈₃	C₂³	1	1	yes	characteristic
114	#107×C₈₃	—	2	1	no	—
115	#106×C₈₃	—	2	1	no	—
116	#104×C₈₃	—	2	4	no	—
117	#99×C₈₃	—	2	4	no	—
118	#97×C₈₃	—	2	1	no	—
119	C₄×C₈×C₈₃	—	2	1	no	—
120	#13050590	—	2	1	no	—
121	#13050590	—	2	1	no	—
122	#13050590	C₂²×C₄	1	2	yes	—
123	#13050590	C₂×D₄	1	2	yes	—
124	C₂×Dic₁₆₆	#41	1	1	yes	characteristic
125	C₂×D₃₃₂	#41	1	1	yes	characteristic
126	C₂×C₂²⋊D₈₃	—	2	1	no	—
127	C₂²×Dic₈₃	—	2	1	no	—
128	C₂×C₄×D₈₃	—	2	1	no	—
129	C₂×C₄×D₈₃	—	2	2	no	—
130	#13050580	—	2	4	no	—
131	#13050578	—	2	4	no	—
132	#13050577	—	2	4	no	—
133	#13050575	—	2	4	no	—
134	#13050574	—	2	1	no	—
135	#13050574	—	2	2	no	—
136	#13050574	—	2	2	no	—
137	#13050574	—	2	2	no	—
138	#13050574	—	4	2	no	—
139	#13050574	—	4	2	no	—
140	#13050574	C₂²×C₄	1	2	yes	—
141	#13050574	C₂²×C₄	1	4	yes	—
142	#13050573	—	2	2	no	—
143	#13050573	—	2	2	no	—
144	#13050573	—	2	2	no	—
145	#13050573	—	2	2	no	—
146	C₂×C₈₃⋊C₈	—	2	1	no	—
147	C₂×C₈₃⋊C₈	—	2	2	no	—
148	C₂×C₈₃⋊C₈	—	2	2	no	—
149	C₂×C₈₃⋊C₈	—	4	2	no	—
150	C₂×C₈₃⋊C₈	—	4	2	no	—
151	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈₃⋊C₈	#41	1	1	yes	characteristic
156	C₂×C₈₃⋊C₈	#41	1	1	yes	characteristic
157	C₈×D₈₃	—	2	2	no	—
158	C₈×D₈₃	—	2	2	no	—
159	C₈×D₈₃	—	2	2	no	—
160	C₈×D₈₃	—	2	2	no	—
161	Dic₈₃⋊C₄	—	2	2	no	—
162	(C₂×D₈₃)⋊C₄	—	2	2	no	—
163	C₄×Dic₈₃	—	2	2	no	—
164	C₄×Dic₈₃	—	2	1	no	—
165	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
166	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
167	#41×C₈₃	—	2	2	no	—
168	#41×C₈₃	—	2	2	no	—
169	#41×C₈₃	—	2	2	no	—
170	#41×C₈₃	—	2	2	no	—
171	C₂×Q₈×C₈₃	C₂²×C₄	1	2	yes	—
172	C₂×D₄×C₈₃	—	2	2	no	—
173	C₂×D₄×C₈₃	C₂²×C₄	1	2	yes	—
174	C₂²×C₄×C₈₃	—	2	2	no	—
175	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
176	Q₁₆×C₈₃	—	2	1	no	—
177	Q₁₆×C₈₃	—	2	1	no	—
178	SD₁₆×C₈₃	—	2	2	no	—
179	SD₁₆×C₈₃	—	2	2	no	—
180	D₈×C₈₃	—	2	1	no	—
181	D₈×C₈₃	—	2	1	no	—
182	M₁₆×C₈₃	—	2	1	no	—
183	M₁₆×C₈₃	C₂×D₄	1	2	yes	—
184	C₂×C₈×C₈₃	—	2	1	no	—
185	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₈₃	C₂×D₄	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	1	no	—
192	C₄⋊C₄×C₈₃	—	2	2	no	—
193	C₂²⋊C₄×C₈₃	—	2	2	no	—
194	C₂²⋊C₄×C₈₃	#41	1	2	yes	—
195	C₄²×C₈₃	—	2	1	no	—
196	C₄²×C₈₃	—	2	2	no	—
197	C₂³×C₈₃	—	2	2	no	—
198	C₂³×C₈₃	C₂×#41	1	1	yes	characteristic
199	C₂²×D₈₃	—	2	1	no	—
200	Q₈×C₈₃	—	2	2	no	—
201	Q₈×C₈₃	—	2	2	no	—
202	D₄×C₈₃	—	2	2	no	—
203	D₄×C₈₃	—	2	2	no	—
204	D₄×C₈₃	—	4	2	no	—
205	D₄×C₈₃	—	4	2	no	—
206	C₂×C₄×C₈₃	—	2	2	no	—
207	C₂×C₄×C₈₃	—	2	2	no	—
208	C₂×C₄×C₈₃	—	4	2	no	—
209	C₂×C₄×C₈₃	—	4	2	no	—
210	C₂×C₄×C₈₃	—	4	2	no	—
211	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
217	C₂²⋊D₈₃	—	2	2	no	—
218	C₂²⋊D₈₃	—	2	2	no	—
219	C₂×Dic₈₃	—	2	1	no	—
220	C₂×Dic₈₃	—	2	1	no	—
221	C₂×Dic₈₃	—	2	1	no	—
222	C₂×Dic₈₃	—	4	2	no	—
223	D₃₃₂	—	2	1	no	—
224	D₃₃₂	C₄×D₄	1	2	yes	—
225	C₄×D₈₃	—	2	2	no	—
226	C₄×D₈₃	—	2	2	no	—
227	C₄×D₈₃	—	4	4	no	—
228	Dic₁₆₆	—	2	1	no	—
229	Dic₁₆₆	C₄×D₄	1	2	yes	—
230	C₈×C₈₃	—	2	2	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	C₈₃⋊C₈	—	2	2	no	—
236	C₈₃⋊C₈	—	2	4	no	—
237	C₈₃⋊C₈	—	4	2	no	—
238	C₈₃⋊C₈	#121	1	1	yes	characteristic
239	C₈₃⋊C₈	#121	1	1	yes	characteristic
240	C₈₃⋊C₈	#121	1	1	yes	characteristic
241	C₈₃⋊C₈	#121	1	1	yes	characteristic
242	C₂²×C₈₃	—	4	1	no	—
243	C₂²×C₈₃	—	4	2	no	—
244	C₂²×C₈₃	—	8	2	no	—
245	C₂²×C₈₃	C₄×#41	1	1	yes	characteristic
246	C₂²×C₈₃	#525	1	1	yes	characteristic
247	C₂²×C₈₃	#532	1	1	yes	characteristic
248	C₂×D₈₃	—	2	2	no	—
249	C₂×D₈₃	—	4	2	no	—
250	C₄×C₈₃	—	4	2	no	—
251	C₄×C₈₃	—	4	2	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	—	2	2	no	—
259	Dic₈₃	—	4	1	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	—	8	2	no	—
265	C₂×C₈₃	C₄×#121	1	1	yes	characteristic
266	D₈₃	—	4	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	D₈₃	1	1	yes	characteristic, complemented
272	#1953	—	83	1	no	—
273	#1932	—	83	2	no	—
274	#1906	—	83	2	no	—
275	#1814	—	83	1	no	—
276	#1772	—	83	1	no	—
277	#1757	—	83	2	no	—
278	C₈₃	#21558	1	1	yes	characteristic, complemented, Sylow
279	#575	—	83	2	no	—
280	C₂×#135	C₂×D₈₃	1	1	yes	characteristic
281	C₂×#131	—	83	2	no	—
282	C₂×#131	—	83	1	no	—
283	C₂×#131	—	83	1	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	1	no	—
290	#443	—	166	1	no	—
291	#443	—	166	1	no	—
292	#443	—	166	1	no	—
293	#443	—	166	4	no	—
294	#430	—	83	2	no	—
295	C₂×#108	—	83	1	no	—
296	C₂×#108	—	83	1	no	—
297	#427	C₂×D₈₃	1	1	yes	characteristic
298	#421	—	83	2	no	—
299	#421	C₂×D₈₃	1	2	yes	—
300	C₂×#104	—	83	2	no	—
301	#413	—	83	2	no	—
302	#410	C₂×D₈₃	1	2	yes	—
303	#405	—	83	1	no	—
304	#405	—	83	2	no	—
305	#405	—	166	1	no	—
306	#405	—	166	1	no	—
307	#405	C₂×D₈₃	1	1	yes	characteristic
308	C₄×M₁₆	—	83	1	no	—
309	C₄×M₁₆	—	166	1	no	—
310	C₂×C₄×C₈	—	83	1	no	—
311	C₂×C₄×C₈	—	166	1	no	—
312	#344	—	83	2	no	—
313	#344	—	83	2	no	—
314	#339	—	83	2	no	—
315	C₂×#41	—	83	1	no	—
316	C₂×#41	C₂²×D₈₃	1	2	yes	—
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	—	2	1	no	—
322	#135	—	2	1	no	—
323	#135	—	2	1	no	—
324	#135	—	2	1	no	—
325	#135	—	166	4	no	—
326	C₂×Q₁₆	C₄×D₈₃	1	1	yes	characteristic, complemented
327	C₂×SD₁₆	C₄×D₈₃	1	2	yes	complemented
328	C₂×D₈	C₄×D₈₃	1	1	yes	characteristic, complemented
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	2	no	—
343	C₂×M₁₆	—	83	2	no	—
344	C₂×M₁₆	—	166	1	no	—
345	C₂×M₁₆	—	166	2	no	—
346	C₂×M₁₆	—	166	1	no	—
347	C₂×M₁₆	C₂²×D₈₃	1	1	yes	characteristic
348	C₂²×C₈	—	83	1	no	—
349	C₂²×C₈	—	166	1	no	—
350	C₂²×C₈	—	166	2	no	—
351	C₂²×C₈	—	166	1	no	—
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	—	166	1	no	—
357	#117	C₂²×D₈₃	1	2	yes	—
358	#117	C₂²×D₈₃	1	1	yes	characteristic
359	C₂×C₄²	—	83	1	no	—
360	C₂×C₄²	—	166	1	no	—
361	#108	—	83	2	no	—
362	#108	—	83	2	no	—
363	#108	—	166	4	no	—
364	#108	—	166	1	no	—
365	#108	—	166	1	no	—
366	#107	—	2	1	no	—
367	#106	—	2	1	no	—
368	#104	—	2	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	—	2	4	no	—
375	#97	—	2	1	no	—
376	#97	—	166	1	no	—
377	#97	—	166	2	no	—
378	#97	—	166	1	no	—
379	C₄×C₈	—	2	1	no	—
380	C₄×C₈	—	83	1	no	—
381	C₄×C₈	—	83	1	no	—
382	C₄×C₈	—	83	1	no	—
383	C₄×C₈	—	83	1	no	—
384	C₄×C₈	—	166	1	no	—
385	C₄×C₈	—	166	2	no	—
386	C₄×C₈	—	166	1	no	—
387	#41	—	2	2	no	—
388	#41	—	2	2	no	—
389	#41	—	2	2	no	—
390	#41	—	2	2	no	—
391	#41	—	83	2	no	—
392	#41	—	83	2	no	—
393	#41	—	166	1	no	—
394	#41	—	166	1	no	—
395	C₂×Q₈	—	83	1	no	—
396	C₂×Q₈	C₂×C₄×D₈₃	1	2	yes	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	83	1	no	—
399	C₂×D₄	—	166	1	no	—
400	C₂×D₄	C₂×C₄×D₈₃	1	2	yes	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	166	2	no	—
403	C₂²×C₄	—	166	1	no	—
404	C₂²×C₄	—	166	1	no	—
405	C₂²×C₄	C₂³×D₈₃	1	1	yes	characteristic
406	Q₁₆	—	2	1	no	—
407	Q₁₆	—	2	1	no	—
408	Q₁₆	—	166	4	no	—
409	SD₁₆	—	2	2	no	—
410	SD₁₆	—	2	2	no	—
411	SD₁₆	—	166	4	no	—
412	SD₁₆	—	166	4	no	—
413	D₈	—	2	1	no	—
414	D₈	—	2	1	no	—
415	D₈	—	166	4	no	—
416	M₁₆	—	2	1	no	—
417	M₁₆	—	332	2	no	—
418	M₁₆	—	332	2	no	—
419	M₁₆	—	83	2	no	—
420	M₁₆	—	83	4	no	—
421	M₁₆	—	166	2	no	—
422	M₁₆	—	166	2	no	—
423	M₁₆	—	166	2	no	—
424	M₁₆	—	166	2	no	—
425	M₁₆	—	166	2	no	—
426	M₁₆	—	166	1	no	—
427	M₁₆	—	166	2	no	—
428	M₁₆	—	166	2	no	—
429	M₁₆	D₄×D₈₃	1	2	yes	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	332	2	no	—
432	C₂×C₈	—	332	2	no	—
433	C₂×C₈	—	83	1	no	—
434	C₂×C₈	—	83	1	no	—
435	C₂×C₈	—	83	1	no	—
436	C₂×C₈	—	83	1	no	—
437	C₂×C₈	—	83	1	no	—
438	C₂×C₈	—	83	1	no	—
439	C₂×C₈	—	166	2	no	—
440	C₂×C₈	—	166	2	no	—
441	C₂×C₈	—	166	2	no	—
442	C₂×C₈	—	166	1	no	—
443	C₂×C₈	—	166	2	no	—
444	C₂×C₈	—	166	2	no	—
445	C₂×C₈	—	166	2	no	—
446	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
447	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
448	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
449	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
450	C₂×C₈	#13050589	1	1	yes	characteristic
451	C₂×C₈	#13050589	1	1	yes	characteristic
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	166	2	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	166	2	no	—
457	C₂²⋊C₄	#13050589	1	2	yes	—
458	C₄²	—	2	1	no	—
459	C₄²	—	2	2	no	—
460	C₄²	—	83	1	no	—
461	C₄²	—	83	1	no	—
462	C₄²	—	166	2	no	—
463	C₄²	—	166	1	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	166	1	no	—
466	C₂³	C₂×#13050589	1	1	yes	characteristic
467	Q₈	—	2	2	no	—
468	Q₈	—	2	2	no	—
469	Q₈	—	83	2	no	—
470	Q₈	—	166	1	no	—
471	D₄	—	2	2	no	—
472	D₄	—	2	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	83	2	no	—
476	D₄	—	166	2	no	—
477	D₄	—	166	2	no	—
478	D₄	—	166	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	332	4	no	—
485	C₂×C₄	—	332	2	no	—
486	C₂×C₄	—	166	1	no	—
487	C₂×C₄	—	166	1	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	C₂×D₄×D₈₃	1	1	yes	characteristic
494	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
495	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
496	C₂×C₄	C₂×#13050589	1	1	yes	characteristic
497	C₈	—	2	2	no	—
498	C₈	—	332	2	no	—
499	C₈	—	83	1	no	—
500	C₈	—	83	1	no	—
501	C₈	—	83	1	no	—
502	C₈	—	83	1	no	—
503	C₈	—	166	4	no	—
504	C₈	—	166	2	no	—
505	C₈	(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
506	C₈	(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
507	C₈	(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
508	C₈	(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
509	C₂²	—	4	1	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	332	2	no	—
513	C₂²	—	166	2	no	—
514	C₂²	C₄×#13050589	1	1	yes	characteristic
515	C₂²	#19128211	1	1	yes	characteristic
516	C₂²	#19128249	1	1	yes	characteristic
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	8	2	no	—
520	C₄	—	332	1	no	—
521	C₄	—	166	2	no	—
522	C₄	—	166	2	no	—
523	C₄	C₄×D₄×D₈₃	1	1	yes	characteristic
524	C₄	C₂×(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
525	C₄	#121×D₈₃	1	1	yes	characteristic
526	C₄	#19128230	1	1	yes	characteristic
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	8	2	no	—
531	C₂	—	332	2	no	—
532	C₂	#24909979	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#121×D₈₃
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₃
Fitting	C₈₃×#1976	C₂
socle	C₂×C₈₃	C₄×#121
prime radical	#24917179	C₂
cosocle	C₂²×C₄×C₈₃	C₂⁴
hypercenter	#1976	D₈₃
hypocenter	C₈₃	#21558
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1976

Complements

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

N	H ≅ G/N	type
2. #24916362	C₂	semidirect
3. C₂×#19127818	C₂	semidirect
4. #24915885	C₂	semidirect
5. #24908253	C₂	semidirect
6. #24908135	C₂	semidirect
7. #24907961	C₂	semidirect
8. #24907514	C₂	semidirect
9. #24907344	C₂	semidirect
10. #24907265	C₂	semidirect
11. C₈₃×#1976	C₂	semidirect
17. #19127973	C₄	semidirect
18. #19127968	C₄	semidirect
19. #19127961	C₄	semidirect
84. #14581728	C₂×C₄	semidirect
85. #14581728	C₂×C₄	semidirect
90. #14581711	C₂×C₄	semidirect
91. #14581709	C₂×C₄	semidirect
107. C₂×Q₁₆×C₈₃	C₂×C₄	semidirect
108. C₂×SD₁₆×C₈₃	C₂×C₄	semidirect
109. C₂×D₈×C₈₃	C₂×C₄	semidirect
271. #1976	D₈₃	semidirect
278. C₈₃	#21558	semidirect
326. C₂×Q₁₆	C₄×D₈₃	semidirect
327. C₂×SD₁₆	C₄×D₈₃	semidirect
328. C₂×D₈	C₄×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
#24917179	2
#24916362	2
C₂×#19127818	2
#24915885	2
#24908253	2
#24908135	2
#24907961	2
#24907514	2
#24907344	2
#24907265	2
C₈₃×#1976	2
#21558	83