Subgroups — #35374113

Order 21248.

660 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24916576	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#14581812	C₂	1	1	yes	maximal, characteristic
3	#24906341	C₂	1	2	yes	maximal, complemented
4	#24906320	C₂	1	2	yes	maximal, complemented
5	#24906313	C₂	1	2	yes	maximal, complemented
6	#24906292	C₂	1	2	yes	maximal, complemented
7	C₂×#19127453	C₂	1	1	yes	maximal, characteristic, complemented
8	#24905850	C₂	1	1	yes	maximal, characteristic, complemented
9	#24905848	C₂	1	1	yes	maximal, characteristic, complemented
10	#24905756	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#2988	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	#19127769	—	2	2	no	—
25	#19127757	—	2	1	no	—
26	#19127754	C₂²	1	1	yes	characteristic
27	#19127737	C₄	1	1	yes	characteristic
28	#19127723	—	2	1	no	—
29	C₂×C₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
30	#19127697	C₄	1	1	yes	characteristic
31	#19127695	C₄	1	1	yes	characteristic
32	C₂×C₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
33	#19127453	C₂²	1	2	yes	—
34	#19127453	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	#19127423	C₂²	1	2	yes	—
40	#19127422	C₂²	1	2	yes	—
41	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
42	C₈×Q₈×C₈₃	C₂²	1	2	yes	—
43	C₈×D₄×C₈₃	—	2	2	no	—
44	C₈×D₄×C₈₃	C₂²	1	2	yes	—
45	#431×C₈₃	—	2	1	no	—
46	#431×C₈₃	C₂²	1	1	yes	characteristic
47	C₂×C₄⋊C₈×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)	—	2	1	no	—
73	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
74	C₄⋊(C₈₃⋊C₈)	C₂³	1	2	yes	—
75	Dic₈₃⋊C₈	—	2	2	no	—
76	#14581716	C₂×C₄	1	1	yes	characteristic
77	#14581716	C₂×C₄	1	1	yes	characteristic
78	#14581715	C₂×C₄	1	1	yes	characteristic
79	#14581715	C₂×C₄	1	1	yes	characteristic
80	#14581713	C₂×C₄	1	1	yes	characteristic
81	#14581713	C₂×C₄	1	1	yes	characteristic
82	#14581712	C₂×C₄	1	1	yes	characteristic
83	#14581712	C₂×C₄	1	1	yes	characteristic
84	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
85	(C₂×D₈₃)⋊C₈	—	2	2	no	—
86	#14581702	—	2	2	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	C₂²×C₈×C₈₃	—	2	1	no	—
94	C₂²×C₈×C₈₃	—	2	2	no	—
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	—	2	1	no	—
107	C₄⋊C₈×C₈₃	D₄	1	1	yes	characteristic
108	C₄⋊C₈×C₈₃	D₄	1	1	yes	characteristic
109	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
110	C₂²⋊C₈×C₈₃	—	2	2	no	—
111	C₂²⋊C₈×C₈₃	D₄	1	2	yes	—
112	C₄×C₈×C₈₃	—	2	2	no	—
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	—	8	2	no	—
127	C₂×C₈₃⋊C₈	—	2	2	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	—	8	1	no	—
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	M₁₆	1	4	yes	complemented
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	C₂×C₈×C₈₃	—	2	2	no	—
158	C₂×C₈×C₈₃	—	8	2	no	—
159	C₂×C₈×C₈₃	—	8	1	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	C₂×M₁₆	1	2	yes	—
181	D₄×C₈₃	—	2	4	no	—
182	D₄×C₈₃	—	2	1	no	—
183	D₄×C₈₃	C₂×M₁₆	1	2	yes	—
184	C₂×C₄×C₈₃	—	2	1	no	—
185	C₂×C₄×C₈₃	—	2	1	no	—
186	C₂×C₄×C₈₃	—	2	1	no	—
187	C₂×C₄×C₈₃	—	2	4	no	—
188	C₂×C₄×C₈₃	—	2	1	no	—
189	C₂×C₄×C₈₃	—	2	1	no	—
190	C₂×C₄×C₈₃	—	4	1	no	—
191	C₂×C₄×C₈₃	—	4	1	no	—
192	C₂×C₄×C₈₃	—	4	1	no	—
193	C₂×C₄×C₈₃	—	8	1	no	—
194	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₈₃	C₂×M₁₆	1	2	yes	—
198	C₂×C₄×C₈₃	#131	1	2	yes	—
199	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
202	C₂²⋊D₈₃	—	4	2	no	—
203	C₂×Dic₈₃	—	2	1	no	—
204	C₂×Dic₈₃	—	2	1	no	—
205	C₂×Dic₈₃	—	2	1	no	—
206	D₃₃₂	—	2	1	no	—
207	D₃₃₂	—	2	1	no	—
208	C₄×D₈₃	—	4	1	no	—
209	C₄×D₈₃	—	4	1	no	—
210	C₄×D₈₃	—	4	2	no	—
211	C₄×D₈₃	—	8	1	no	—
212	Dic₁₆₆	—	2	1	no	—
213	Dic₁₆₆	—	2	1	no	—
214	C₈×C₈₃	—	2	2	no	—
215	C₈×C₈₃	—	2	2	no	—
216	C₈×C₈₃	—	4	2	no	—
217	C₈₃⋊C₈	—	2	1	no	—
218	C₈₃⋊C₈	—	2	1	no	—
219	C₈₃⋊C₈	—	2	1	no	—
220	C₈₃⋊C₈	—	2	1	no	—
221	C₈₃⋊C₈	—	4	2	no	—
222	C₈₃⋊C₈	—	4	2	no	—
223	C₂²×C₈₃	—	2	1	no	—
224	C₂²×C₈₃	—	2	1	no	—
225	C₂²×C₈₃	—	2	2	no	—
226	C₂²×C₈₃	—	4	1	no	—
227	C₂²×C₈₃	—	4	1	no	—
228	C₂²×C₈₃	#435	1	2	yes	—
229	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
230	C₂×D₈₃	—	4	1	no	—
231	C₂×D₈₃	—	4	1	no	—
232	C₂×D₈₃	—	4	1	no	—
233	C₄×C₈₃	—	2	2	no	—
234	C₄×C₈₃	—	2	1	no	—
235	C₄×C₈₃	—	2	1	no	—
236	C₄×C₈₃	—	2	1	no	—
237	C₄×C₈₃	—	4	1	no	—
238	C₄×C₈₃	—	4	1	no	—
239	C₄×C₈₃	#435	1	2	yes	—
240	C₄×C₈₃	C₂²×M₁₆	1	1	yes	characteristic
241	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
242	C₄×C₈₃	#576	1	1	yes	characteristic
243	C₄×C₈₃	#578	1	1	yes	characteristic
244	Dic₈₃	—	4	1	no	—
245	Dic₈₃	—	4	1	no	—
246	Dic₈₃	—	4	1	no	—
247	#17881	—	83	1	no	maximal, Sylow
248	C₂×C₈₃	—	2	2	no	—
249	C₂×C₈₃	—	4	2	no	—
250	C₂×C₈₃	C₂×#435	1	1	yes	characteristic
251	C₂×C₈₃	#2951	1	1	yes	characteristic
252	C₂×C₈₃	#2957	1	1	yes	characteristic
253	D₈₃	—	8	1	no	—
254	#2989	—	83	1	no	—
255	#2988	D₈₃	1	1	yes	characteristic, complemented
256	C₄×#135	—	83	1	no	—
257	#1588	—	83	2	no	—
258	#1585	—	83	2	no	—
259	#1584	—	83	2	no	—
260	#1581	—	83	2	no	—
261	C₂×#335	—	83	1	no	—
262	#1477	—	83	1	no	—
263	#1477	—	83	1	no	—
264	#1452	—	83	1	no	—
265	C₈₃	#17881	1	1	yes	characteristic, complemented, Sylow
266	C₂×#135	—	83	1	no	—
267	C₄×#41	—	83	1	no	—
268	C₄×#41	C₂×D₈₃	1	1	yes	characteristic
269	#446	—	83	2	no	—
270	C₈×Q₈	C₂×D₈₃	1	2	yes	—
271	C₄×Q₁₆	—	83	1	no	—
272	C₄×Q₁₆	—	83	1	no	—
273	C₄×SD₁₆	—	83	1	no	—
274	C₄×SD₁₆	—	83	1	no	—
275	C₄×SD₁₆	—	83	1	no	—
276	C₄×SD₁₆	—	83	1	no	—
277	C₄×D₈	—	83	1	no	—
278	C₄×D₈	—	83	1	no	—
279	#436	—	83	2	no	—
280	#435	—	166	2	no	—
281	C₈×D₄	—	2	2	no	—
282	C₈×D₄	C₂×D₈₃	1	2	yes	—
283	#432	—	166	1	no	—
284	#431	—	2	1	no	—
285	#431	—	83	1	no	—
286	#431	C₂×D₈₃	1	1	yes	characteristic
287	#427	—	83	1	no	—
288	#423	—	166	1	no	—
289	C₂×C₄⋊C₈	—	2	1	no	—
290	C₂×C₄⋊C₈	—	83	1	no	—
291	C₂×C₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic
292	#416	—	83	1	no	—
293	#416	—	83	1	no	—
294	C₂×C₄×C₈	—	83	1	no	—
295	#335	—	83	2	no	—
296	#335	—	83	2	no	—
297	Q₈⋊C₈	—	83	2	no	—
298	Q₈⋊C₈	—	83	2	no	—
299	D₄⋊C₈	—	83	2	no	—
300	D₄⋊C₈	—	83	2	no	—
301	#322	—	83	2	no	—
302	#322	—	83	2	no	—
303	C₂×#41	—	83	1	no	—
304	C₂×#41	C₄×D₈₃	1	1	yes	characteristic
305	#135	—	166	4	no	—
306	C₂×Q₁₆	—	83	1	no	—
307	C₂×SD₁₆	—	83	1	no	—
308	C₂×SD₁₆	—	83	1	no	—
309	C₂×D₈	—	83	1	no	—
310	C₂×M₁₆	—	166	2	no	—
311	C₂²×C₈	—	2	1	no	—
312	C₂²×C₈	—	2	2	no	—
313	C₂²×C₈	—	83	1	no	—
314	C₂²×C₈	—	83	1	no	—
315	C₂²×C₈	—	166	1	no	—
316	C₄×Q₈	—	83	1	no	—
317	C₄×Q₈	—	83	1	no	—
318	C₄×Q₈	C₄×D₈₃	1	1	yes	characteristic
319	C₄×Q₈	C₂²×D₈₃	1	1	yes	characteristic
320	C₄×D₄	—	2	1	no	—
321	C₄×D₄	—	2	1	no	—
322	C₄×D₄	—	83	1	no	—
323	C₄×D₄	—	83	1	no	—
324	C₄×D₄	—	166	1	no	—
325	C₄×D₄	—	166	1	no	—
326	C₄×D₄	C₄×D₈₃	1	1	yes	characteristic
327	C₄×D₄	C₂²×D₈₃	1	1	yes	characteristic
328	#117	—	2	1	no	—
329	#117	—	83	1	no	—
330	#117	—	166	1	no	—
331	#117	C₄×D₈₃	1	1	yes	characteristic
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	166	1	no	—
334	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
335	#107	—	83	1	no	—
336	#107	—	83	1	no	—
337	#106	—	83	1	no	—
338	#106	—	83	1	no	—
339	C₄⋊C₈	—	2	2	no	—
340	C₄⋊C₈	—	2	1	no	—
341	C₄⋊C₈	—	83	2	no	—
342	C₄⋊C₈	—	166	2	no	—
343	C₄⋊C₈	—	166	1	no	—
344	C₄⋊C₈	—	166	1	no	—
345	C₄⋊C₈	C₂²⋊D₈₃	1	1	yes	characteristic
346	C₄⋊C₈	C₂²⋊D₈₃	1	1	yes	characteristic
347	C₄⋊C₈	C₂²×D₈₃	1	2	yes	—
348	#103	—	83	1	no	—
349	#103	—	83	1	no	—
350	#103	—	83	1	no	—
351	#103	—	83	1	no	—
352	#102	—	83	1	no	—
353	#102	—	83	1	no	—
354	#102	—	83	1	no	—
355	#102	—	83	1	no	—
356	C₂²⋊C₈	—	2	2	no	—
357	C₂²⋊C₈	—	166	1	no	—
358	C₂²⋊C₈	—	166	2	no	—
359	C₂²⋊C₈	C₂²⋊D₈₃	1	2	yes	—
360	#97	—	166	2	no	—
361	C₄×C₈	—	2	2	no	—
362	C₄×C₈	—	83	1	no	—
363	C₄×C₈	—	83	1	no	—
364	C₄×C₈	—	83	1	no	—
365	C₄×C₈	—	83	1	no	—
366	C₄×C₈	—	83	2	no	—
367	C₄×C₈	C₂²×D₈₃	1	2	yes	—
368	#41	—	2	2	no	—
369	#41	—	166	2	no	—
370	#41	—	166	2	no	—
371	#41	#13050573	1	4	yes	complemented
372	C₂×Q₈	—	83	1	no	—
373	C₂×Q₈	C₂×C₄×D₈₃	1	1	yes	characteristic
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	83	1	no	—
376	C₂×D₄	—	166	1	no	—
377	C₂×D₄	C₂×C₄×D₈₃	1	1	yes	characteristic
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	166	1	no	—
382	C₂²×C₄	—	166	1	no	—
383	C₂²×C₄	—	166	1	no	—
384	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
385	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
386	C₂²×C₄	#13050590	1	1	yes	characteristic
387	Q₁₆	—	166	2	no	—
388	SD₁₆	—	166	2	no	—
389	SD₁₆	—	166	2	no	—
390	D₈	—	166	2	no	—
391	M₁₆	—	664	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	8	2	no	—
394	C₂×C₈	—	8	1	no	—
395	C₂×C₈	—	83	1	no	—
396	C₂×C₈	—	83	1	no	—
397	C₂×C₈	—	83	1	no	—
398	C₂×C₈	—	83	1	no	—
399	C₂×C₈	—	664	1	no	—
400	C₂×C₈	—	166	2	no	—
401	C₂×C₈	—	166	2	no	—
402	C₂×C₈	—	166	2	no	—
403	C₂×C₈	—	166	2	no	—
404	C₂×C₈	C₂×C₂²⋊D₈₃	1	2	yes	—
405	C₂×C₈	C₂×C₂²⋊D₈₃	1	2	yes	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	83	1	no	—
409	C₄⋊C₄	—	83	1	no	—
410	C₄⋊C₄	—	166	1	no	—
411	C₄⋊C₄	—	166	1	no	—
412	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
413	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	166	1	no	—
418	C₂²⋊C₄	—	166	1	no	—
419	C₂²⋊C₄	—	166	1	no	—
420	C₄²	—	2	1	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	166	1	no	—
424	C₄²	—	166	1	no	—
425	C₄²	—	166	1	no	—
426	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
427	C₄²	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
428	C₄²	#13050590	1	1	yes	characteristic
429	C₄²	C₂³×D₈₃	1	1	yes	characteristic
430	C₂³	—	2	1	no	—
431	C₂³	—	166	1	no	—
432	C₂³	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
433	Q₈	—	2	1	no	—
434	Q₈	—	166	1	no	—
435	Q₈	—	166	1	no	—
436	Q₈	C₂×#13050573	1	2	yes	—
437	D₄	—	2	4	no	—
438	D₄	—	2	1	no	—
439	D₄	—	332	2	no	—
440	D₄	—	166	1	no	—
441	D₄	—	166	1	no	—
442	D₄	C₂×#13050573	1	2	yes	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	8	1	no	—
453	C₂×C₄	—	332	1	no	—
454	C₂×C₄	—	332	1	no	—
455	C₂×C₄	—	332	2	no	—
456	C₂×C₄	—	664	1	no	—
457	C₂×C₄	—	166	1	no	—
458	C₂×C₄	—	166	1	no	—
459	C₂×C₄	—	166	1	no	—
460	C₂×C₄	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
461	C₂×C₄	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
462	C₂×C₄	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
463	C₂×C₄	C₂×#13050573	1	2	yes	—
464	C₂×C₄	#14581798	1	2	yes	—
465	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
466	C₂×C₄	C₂²×C₂²⋊D₈₃	1	1	yes	characteristic
467	C₂×C₄	C₂×#13050590	1	1	yes	characteristic
468	C₈	—	2	2	no	—
469	C₈	—	2	2	no	—
470	C₈	—	4	2	no	—
471	C₈	—	332	2	no	—
472	C₈	—	332	2	no	—
473	C₈	—	166	1	no	—
474	C₈	—	166	1	no	—
475	C₈	—	166	1	no	—
476	C₈	—	166	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	—	332	1	no	—
483	C₂²	—	332	1	no	—
484	C₂²	—	332	1	no	—
485	C₂²	#19127772	1	2	yes	—
486	C₂²	C₂×C₄×C₂²⋊D₈₃	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	2	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	1	no	—
493	C₄	—	332	1	no	—
494	C₄	—	332	1	no	—
495	C₄	—	332	1	no	—
496	C₄	#19127772	1	2	yes	—
497	C₄	C₂²×#13050573	1	1	yes	characteristic
498	C₄	C₂×#14581798	1	1	yes	characteristic
499	C₄	#19128504	1	1	yes	characteristic
500	C₄	#19128516	1	1	yes	characteristic
501	C₂	—	2	2	no	—
502	C₂	—	4	2	no	—
503	C₂	—	664	1	no	—
504	C₂	C₂×#19127772	1	1	yes	characteristic
505	C₂	#24916336	1	1	yes	characteristic
506	C₂	#24916378	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₈₃
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₄²	C₂³×D₈₃
Fitting	C₈₃×#2988	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	C₂×#14581812	C₄
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	#2988	D₈₃
hypocenter	C₈₃	#17881
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2988

Complements

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

N	H ≅ G/N	type
1. #24916576	C₂	semidirect
3. #24906341	C₂	semidirect
4. #24906320	C₂	semidirect
5. #24906313	C₂	semidirect
6. #24906292	C₂	semidirect
7. C₂×#19127453	C₂	semidirect
8. #24905850	C₂	semidirect
9. #24905848	C₂	semidirect
10. #24905756	C₂	semidirect
11. C₈₃×#2988	C₂	semidirect
147. #41×C₈₃	M₁₆	semidirect
255. #2988	D₈₃	semidirect
265. C₈₃	#17881	semidirect
371. #41	#13050573	semidirect

Maximal subgroups

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

subgroup	index
#24916576	2
C₄×#14581812	2
#24906341	2
#24906320	2
#24906313	2
#24906292	2
C₂×#19127453	2
#24905850	2
#24905848	2
#24905756	2
C₈₃×#2988	2
#17881	83