Subgroups — #35423848

Order 21248.

740 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14581812	C₂	1	1	yes	maximal, characteristic
2	#24916129	C₂	1	1	yes	maximal, characteristic, complemented
3	#24916032	C₂	1	1	yes	maximal, characteristic, complemented
4	#24908171	C₂	1	2	yes	maximal, complemented
5	#24908060	C₂	1	2	yes	maximal, complemented
6	#24907787	C₂	1	2	yes	maximal
7	#24907600	C₂	1	1	yes	maximal, characteristic, complemented
8	#24907484	C₂	1	1	yes	maximal, characteristic, complemented
9	#24907332	C₂	1	1	yes	maximal, characteristic, complemented
10	#24907304	C₂	1	2	yes	maximal, complemented
11	C₈₃×#1806	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14581812	C₂²	1	1	yes	characteristic
13	C₂×#14581800	C₂²	1	2	yes	—
14	C₄×#13050590	C₂²	1	1	yes	characteristic
15	C₄×#13050580	C₄	1	1	yes	characteristic, complemented
16	C₄×#13050580	C₄	1	1	yes	characteristic, complemented
17	C₄×#13050577	C₄	1	1	yes	characteristic, complemented
18	C₄×#13050577	C₄	1	1	yes	characteristic, complemented
19	C₄×#13050578	C₄	1	1	yes	characteristic, complemented
20	C₄×#13050578	C₄	1	1	yes	characteristic, complemented
21	C₄×#13050575	C₄	1	1	yes	characteristic, complemented
22	C₄×#13050575	C₄	1	1	yes	characteristic, complemented
23	#19127762	—	2	2	no	—
24	#19127758	—	2	1	no	—
25	#19127754	—	2	1	no	—
26	#19127737	C₂²	1	1	yes	characteristic
27	#19127729	C₂²	1	2	yes	—
28	#19127726	—	2	2	no	—
29	#19127725	C₂²	1	1	yes	characteristic
30	#19127723	—	2	1	no	—
31	C₂×C₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
32	C₄⋊C₈×D₈₃	—	2	1	no	—
33	C₂×#14581720	C₂²	1	2	yes	—
34	#19127697	C₂²	1	1	yes	characteristic
35	#19127695	C₂²	1	1	yes	characteristic
36	#19127668	C₂²	1	2	yes	—
37	#19127657	C₂²	1	2	yes	—
38	C₂×#14581703	C₂²	1	2	yes	—
39	C₂×C₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
40	#19127465	C₂²	1	2	yes	—
41	#19127465	C₂²	1	2	yes	—
42	#19127461	C₂²	1	2	yes	—
43	#19127456	C₂²	1	2	yes	—
44	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
45	#423×C₈₃	C₂²	1	1	yes	characteristic
46	C₂×#104×C₈₃	C₂²	1	2	yes	—
47	C₄×C₄⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
48	#339×C₈₃	C₂²	1	2	yes	—
49	C₂×#13050590	C₂³	1	1	yes	characteristic
50	#14581812	—	2	2	no	—
51	#14581812	—	2	2	no	—
52	C₂×#13050580	C₂×C₄	1	1	yes	characteristic
53	C₂×#13050578	C₂×C₄	1	1	yes	characteristic
54	C₂×#13050577	C₂×C₄	1	1	yes	characteristic
55	C₂×#13050575	C₂×C₄	1	1	yes	characteristic
56	#14581800	—	2	4	no	—
57	#14581800	—	4	2	no	—
58	C₂×#13050574	C₂³	1	2	yes	—
59	C₂×#13050573	—	2	2	no	—
60	C₂²×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₈₃⋊C₈	C₂³	1	2	yes	—
63	C₂×C₈×D₈₃	—	2	2	no	—
64	C₄×Dic₁₆₆	C₂×C₄	1	1	yes	characteristic
65	C₄×Dic₁₆₆	C₂×C₄	1	1	yes	characteristic
66	C₄×D₃₃₂	C₂×C₄	1	1	yes	characteristic
67	C₄×D₃₃₂	C₂×C₄	1	1	yes	characteristic
68	C₄×C₂²⋊D₈₃	—	2	1	no	—
69	C₄×C₂²⋊D₈₃	—	2	1	no	—
70	#14581751	C₂³	1	1	yes	characteristic
71	#14581749	—	2	1	no	—
72	C₄²×D₈₃	—	2	1	no	—
73	#14581725	C₂×C₄	1	1	yes	characteristic
74	#14581725	C₂×C₄	1	1	yes	characteristic
75	#14581723	C₂×C₄	1	1	yes	characteristic
76	#14581723	C₂×C₄	1	1	yes	characteristic
77	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
78	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
79	C₄⋊(C₈₃⋊C₈)	D₄	1	1	yes	characteristic
80	C₄⋊(C₈₃⋊C₈)	D₄	1	1	yes	characteristic
81	C₄⋊(C₈₃⋊C₈)	D₄	1	2	yes	—
82	Dic₈₃⋊C₈	—	2	2	no	—
83	Dic₈₃⋊C₈	—	2	2	no	—
84	#14581720	—	2	4	no	—
85	#14581716	C₂×C₄	1	1	yes	characteristic
86	#14581716	C₂×C₄	1	1	yes	characteristic
87	#14581715	C₂×C₄	1	1	yes	characteristic
88	#14581715	C₂×C₄	1	1	yes	characteristic
89	#14581713	C₂×C₄	1	1	yes	characteristic
90	#14581713	C₂×C₄	1	1	yes	characteristic
91	#14581712	C₂×C₄	1	1	yes	characteristic
92	#14581712	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊(C₈₃⋊C₈)	—	2	2	no	—
94	C₂²⋊(C₈₃⋊C₈)	—	2	2	no	—
95	#14581703	—	2	2	no	—
96	#14581703	—	4	2	no	—
97	C₄×C₈₃⋊C₈	—	2	2	no	—
98	C₄×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₄×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
100	C₄×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
101	C₄×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
102	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
104	C₄×Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
105	C₄×Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
106	C₄×D₄×C₈₃	—	2	1	no	—
107	C₄×D₄×C₈₃	—	2	1	no	—
108	C₄×D₄×C₈₃	C₂×C₄	1	1	yes	characteristic
109	C₄×D₄×C₈₃	C₂×C₄	1	1	yes	characteristic
110	#117×C₈₃	—	2	1	no	—
111	#117×C₈₃	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
113	C₂×C₄²×C₈₃	—	2	1	no	—
114	C₂×C₄²×C₈₃	C₂³	1	2	yes	—
115	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
116	C₄⋊C₈×C₈₃	—	2	1	no	—
117	C₄⋊C₈×C₈₃	—	2	1	no	—
118	#104×C₈₃	—	4	2	no	—
119	#95×C₈₃	—	2	1	no	—
120	#13050590	—	2	1	no	—
121	#13050590	—	2	1	no	—
122	#13050590	#41	1	2	yes	—
123	#13050590	#41	1	2	yes	—
124	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
125	C₂×D₃₃₂	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₂²⋊D₈₃	—	2	1	no	—
127	C₂×C₄×D₈₃	—	2	1	no	—
128	C₂×C₄×D₈₃	—	2	1	no	—
129	C₂×C₄×D₈₃	—	2	1	no	—
130	#13050580	—	2	2	no	—
131	#13050578	—	2	2	no	—
132	#13050577	—	2	2	no	—
133	#13050575	—	2	2	no	—
134	#13050574	—	2	2	no	—
135	#13050574	—	2	2	no	—
136	#13050573	—	4	4	no	—
137	C₂×C₈₃⋊C₈	—	2	2	no	—
138	C₂×C₈₃⋊C₈	—	2	1	no	—
139	C₂×C₈₃⋊C₈	—	2	1	no	—
140	C₂×C₈₃⋊C₈	—	2	2	no	—
141	C₂×C₈₃⋊C₈	—	2	1	no	—
142	C₂×C₈₃⋊C₈	—	2	1	no	—
143	C₂×C₈₃⋊C₈	—	2	2	no	—
144	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈₃⋊C₈	C₂×D₄	1	2	yes	—
149	C₂×C₈₃⋊C₈	C₂×D₄	1	2	yes	—
150	C₈×D₈₃	—	4	4	no	—
151	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
152	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
153	Dic₈₃⋊C₄	—	2	1	no	—
154	Dic₈₃⋊C₄	—	2	1	no	—
155	C₂²⋊Dic₈₃	—	2	1	no	—
156	(C₂×D₈₃)⋊C₄	—	2	1	no	—
157	(C₂×D₈₃)⋊C₄	—	2	1	no	—
158	C₄×Dic₈₃	—	2	1	no	—
159	C₄×Dic₈₃	—	2	1	no	—
160	C₄×Dic₈₃	—	2	1	no	—
161	#41×C₈₃	—	2	1	no	—
162	#41×C₈₃	—	2	1	no	—
163	#41×C₈₃	—	2	1	no	—
164	#41×C₈₃	—	2	1	no	—
165	C₂×Q₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
166	C₂×D₄×C₈₃	—	2	1	no	—
167	C₂×D₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₈₃	—	2	1	no	—
169	C₂²×C₄×C₈₃	—	2	1	no	—
170	C₂²×C₄×C₈₃	—	2	1	no	—
171	C₂²×C₄×C₈₃	—	2	2	no	—
172	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
173	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
174	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
175	M₁₆×C₈₃	—	2	2	no	—
176	M₁₆×C₈₃	—	2	2	no	—
177	C₂×C₈×C₈₃	—	2	2	no	—
178	C₄⋊C₄×C₈₃	—	2	1	no	—
179	C₄⋊C₄×C₈₃	—	2	1	no	—
180	C₄⋊C₄×C₈₃	—	4	2	no	—
181	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
182	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
183	C₂²⋊C₄×C₈₃	—	2	1	no	—
184	C₂²⋊C₄×C₈₃	—	2	1	no	—
185	C₂²⋊C₄×C₈₃	—	2	1	no	—
186	C₄²×C₈₃	—	2	1	no	—
187	C₄²×C₈₃	—	2	1	no	—
188	C₄²×C₈₃	—	2	1	no	—
189	C₄²×C₈₃	—	2	2	no	—
190	C₄²×C₈₃	—	2	2	no	—
191	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
192	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
193	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
195	C₂³×C₈₃	—	2	1	no	—
196	C₂³×C₈₃	C₂×#41	1	1	yes	characteristic
197	C₂²×D₈₃	—	2	1	no	—
198	Q₈×C₈₃	—	2	1	no	—
199	Q₈×C₈₃	—	2	1	no	—
200	D₄×C₈₃	—	2	1	no	—
201	D₄×C₈₃	—	2	1	no	—
202	D₄×C₈₃	—	4	1	no	—
203	D₄×C₈₃	—	4	1	no	—
204	C₂×C₄×C₈₃	—	2	2	no	—
205	C₂×C₄×C₈₃	—	2	1	no	—
206	C₂×C₄×C₈₃	—	2	1	no	—
207	C₂×C₄×C₈₃	—	2	1	no	—
208	C₂×C₄×C₈₃	—	4	1	no	—
209	C₂×C₄×C₈₃	—	4	1	no	—
210	C₂×C₄×C₈₃	—	4	1	no	—
211	C₂×C₄×C₈₃	—	4	2	no	—
212	C₂×C₄×C₈₃	—	4	2	no	—
213	C₂×C₄×C₈₃	—	4	2	no	—
214	C₂×C₄×C₈₃	—	4	2	no	—
215	C₂×C₄×C₈₃	—	8	1	no	—
216	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
225	C₂×C₄×C₈₃	2₋¹⁺⁴	1	1	yes	characteristic
226	C₂²⋊D₈₃	—	2	2	no	—
227	C₂²⋊D₈₃	—	2	2	no	—
228	C₂×Dic₈₃	—	2	1	no	—
229	C₂×Dic₈₃	—	2	1	no	—
230	C₂×Dic₈₃	—	2	1	no	—
231	D₃₃₂	—	2	1	no	—
232	D₃₃₂	#117	1	2	yes	—
233	C₄×D₈₃	—	2	2	no	—
234	C₄×D₈₃	—	2	2	no	—
235	C₄×D₈₃	—	4	2	no	—
236	C₄×D₈₃	—	8	1	no	—
237	Dic₁₆₆	—	2	1	no	—
238	Dic₁₆₆	#117	1	2	yes	—
239	C₈×C₈₃	—	4	2	no	—
240	C₈₃⋊C₈	—	2	1	no	—
241	C₈₃⋊C₈	—	2	1	no	—
242	C₈₃⋊C₈	—	2	1	no	—
243	C₈₃⋊C₈	—	2	1	no	—
244	C₈₃⋊C₈	—	2	2	no	—
245	C₈₃⋊C₈	—	2	2	no	—
246	C₈₃⋊C₈	—	4	2	no	—
247	C₂²×C₈₃	—	2	1	no	—
248	C₂²×C₈₃	—	2	1	no	—
249	C₂²×C₈₃	—	4	1	no	—
250	C₂²×C₈₃	—	4	1	no	—
251	C₂²×C₈₃	—	4	1	no	—
252	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
253	C₂²×C₈₃	#552	1	1	yes	characteristic
254	C₂²×C₈₃	#553	1	1	yes	characteristic
255	C₂×D₈₃	—	2	2	no	—
256	C₂×D₈₃	—	4	1	no	—
257	C₂×D₈₃	—	4	1	no	—
258	C₄×C₈₃	—	2	1	no	—
259	C₄×C₈₃	—	2	1	no	—
260	C₄×C₈₃	—	2	1	no	—
261	C₄×C₈₃	—	4	1	no	—
262	C₄×C₈₃	—	4	1	no	—
263	C₄×C₈₃	—	4	1	no	—
264	C₄×C₈₃	—	8	2	no	—
265	C₄×C₈₃	#444	1	2	yes	—
266	C₄×C₈₃	C₂×#117	1	1	yes	characteristic
267	C₄×C₈₃	#520	1	1	yes	characteristic
268	C₄×C₈₃	#546	1	1	yes	characteristic
269	C₄×C₈₃	#548	1	1	yes	characteristic
270	Dic₈₃	—	2	2	no	—
271	Dic₈₃	—	4	1	no	—
272	Dic₈₃	—	4	1	no	—
273	#22782	—	83	1	no	maximal, Sylow
274	C₂×C₈₃	—	2	1	no	—
275	C₂×C₈₃	—	2	1	no	—
276	C₂×C₈₃	—	8	1	no	—
277	C₂×C₈₃	#2352	1	1	yes	characteristic
278	C₂×C₈₃	C₂×#444	1	1	yes	characteristic
279	C₂×C₈₃	#2957	1	1	yes	characteristic
280	D₈₃	—	4	2	no	—
281	C₄×#135	—	83	1	no	—
282	#2925	—	83	1	no	—
283	#2906	—	83	1	no	—
284	#1938	—	83	2	no	—
285	#1922	—	83	2	no	—
286	#1876	—	83	2	no	—
287	#1837	—	83	1	no	—
288	#1806	—	83	1	no	—
289	#1806	D₈₃	1	1	yes	characteristic, complemented
290	#1770	—	83	1	no	—
291	#1765	—	83	2	no	—
292	C₈₃	#22782	1	1	yes	characteristic, complemented, Sylow
293	C₂×#135	—	83	1	no	—
294	C₂×#131	—	83	2	no	—
295	C₄×#41	—	83	1	no	—
296	C₄×#41	C₂×D₈₃	1	1	yes	characteristic
297	C₄×Q₁₆	—	83	1	no	—
298	C₄×Q₁₆	—	83	1	no	—
299	C₄×SD₁₆	—	83	1	no	—
300	C₄×SD₁₆	—	83	1	no	—
301	C₄×SD₁₆	—	83	1	no	—
302	C₄×SD₁₆	—	83	1	no	—
303	C₄×D₈	—	83	1	no	—
304	C₄×D₈	—	83	1	no	—
305	#433	—	166	2	no	—
306	#432	—	166	1	no	—
307	#431	—	166	1	no	—
308	#427	—	83	1	no	—
309	#424	—	83	2	no	—
310	#424	—	166	2	no	—
311	#423	—	83	1	no	—
312	#423	—	166	1	no	—
313	#423	C₂×D₈₃	1	1	yes	characteristic
314	C₂×C₄⋊C₈	—	83	1	no	—
315	C₂×C₄⋊C₈	—	166	1	no	—
316	C₂×#104	—	83	2	no	—
317	C₂×#104	C₂×D₈₃	1	2	yes	—
318	#416	—	83	1	no	—
319	#416	—	83	1	no	—
320	#408	—	83	2	no	—
321	#405	—	83	2	no	—
322	C₂×#97	—	83	2	no	—
323	C₂×C₄×C₈	—	83	1	no	—
324	C₄×C₄⋊C₄	C₂×D₈₃	1	1	yes	characteristic
325	#341	—	83	2	no	—
326	#341	—	83	2	no	—
327	#339	—	83	2	no	—
328	#339	C₂×D₈₃	1	2	yes	—
329	#336	—	83	2	no	—
330	C₂×#41	—	83	1	no	—
331	C₂×#41	C₂²×D₈₃	1	1	yes	characteristic
332	#135	—	166	2	no	—
333	#135	—	166	2	no	—
334	C₂×Q₁₆	—	83	1	no	—
335	C₂×SD₁₆	—	83	1	no	—
336	C₂×SD₁₆	—	83	1	no	—
337	C₂×D₈	—	83	1	no	—
338	#131	—	332	2	no	—
339	#131	—	166	4	no	—
340	C₂×M₁₆	—	83	2	no	—
341	C₂×M₁₆	—	166	2	no	—
342	C₂×M₁₆	C₂²×D₈₃	1	2	yes	—
343	C₂²×C₈	—	83	2	no	—
344	C₂²×C₈	—	83	1	no	—
345	C₂²×C₈	—	83	1	no	—
346	C₂²×C₈	—	166	2	no	—
347	C₄×Q₈	—	83	1	no	—
348	C₄×Q₈	—	83	1	no	—
349	C₄×Q₈	C₄×D₈₃	1	1	yes	characteristic
350	C₄×Q₈	C₄×D₈₃	1	1	yes	characteristic
351	C₄×D₄	—	2	1	no	—
352	C₄×D₄	—	2	1	no	—
353	C₄×D₄	—	83	1	no	—
354	C₄×D₄	—	83	1	no	—
355	C₄×D₄	—	166	1	no	—
356	C₄×D₄	—	166	1	no	—
357	C₄×D₄	C₄×D₈₃	1	1	yes	characteristic
358	C₄×D₄	C₄×D₈₃	1	1	yes	characteristic
359	#117	—	2	1	no	—
360	#117	—	83	1	no	—
361	#117	—	166	1	no	—
362	#117	C₂²×D₈₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	—	166	1	no	—
366	C₂×C₄²	C₂²×D₈₃	1	2	yes	—
367	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
368	#107	—	83	1	no	—
369	#107	—	83	1	no	—
370	#106	—	83	1	no	—
371	#106	—	83	1	no	—
372	C₄⋊C₈	—	2	1	no	—
373	C₄⋊C₈	—	2	1	no	—
374	C₄⋊C₈	—	83	1	no	—
375	C₄⋊C₈	—	83	1	no	—
376	C₄⋊C₈	—	83	2	no	—
377	C₄⋊C₈	—	166	2	no	—
378	C₄⋊C₈	—	166	2	no	—
379	C₄⋊C₈	—	166	1	no	—
380	C₄⋊C₈	—	166	1	no	—
381	#104	—	4	2	no	—
382	#104	—	166	4	no	—
383	#103	—	83	1	no	—
384	#103	—	83	1	no	—
385	#103	—	83	1	no	—
386	#103	—	83	1	no	—
387	#102	—	83	1	no	—
388	#102	—	83	1	no	—
389	#102	—	83	1	no	—
390	#102	—	83	1	no	—
391	C₂²⋊C₈	—	166	2	no	—
392	C₂²⋊C₈	—	166	2	no	—
393	#97	—	332	2	no	—
394	#97	—	166	2	no	—
395	C₄×C₈	—	83	1	no	—
396	C₄×C₈	—	83	1	no	—
397	C₄×C₈	—	83	1	no	—
398	C₄×C₈	—	83	1	no	—
399	C₄×C₈	—	166	2	no	—
400	#95	—	2	1	no	—
401	#41	—	2	1	no	—
402	#41	—	2	1	no	—
403	#41	—	2	1	no	—
404	#41	—	2	1	no	—
405	#41	—	83	2	no	—
406	#41	—	83	2	no	—
407	#41	—	166	1	no	—
408	#41	—	166	1	no	—
409	C₂×Q₈	—	83	1	no	—
410	C₂×Q₈	C₂×C₄×D₈₃	1	1	yes	characteristic
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	83	1	no	—
413	C₂×D₄	—	166	1	no	—
414	C₂×D₄	C₂×C₄×D₈₃	1	1	yes	characteristic
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	166	1	no	—
420	C₂²×C₄	—	166	1	no	—
421	C₂²×C₄	—	166	1	no	—
422	C₂²×C₄	#13050589	1	1	yes	characteristic
423	C₂²×C₄	#13050589	1	1	yes	characteristic
424	C₂²×C₄	C₂³×D₈₃	1	1	yes	characteristic
425	Q₁₆	—	166	2	no	—
426	SD₁₆	—	166	2	no	—
427	SD₁₆	—	166	2	no	—
428	D₈	—	166	2	no	—
429	M₁₆	—	2	2	no	—
430	M₁₆	—	2	2	no	—
431	M₁₆	—	332	4	no	—
432	M₁₆	—	166	2	no	—
433	M₁₆	—	166	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	332	4	no	—
436	C₂×C₈	—	83	1	no	—
437	C₂×C₈	—	83	1	no	—
438	C₂×C₈	—	83	1	no	—
439	C₂×C₈	—	83	1	no	—
440	C₂×C₈	—	83	2	no	—
441	C₂×C₈	—	83	2	no	—
442	C₂×C₈	—	166	2	no	—
443	C₂×C₈	—	166	2	no	—
444	C₂×C₈	—	166	1	no	—
445	C₂×C₈	—	166	1	no	—
446	C₂×C₈	—	166	1	no	—
447	C₂×C₈	—	166	2	no	—
448	C₂×C₈	—	166	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	4	2	no	—
452	C₄⋊C₄	—	83	1	no	—
453	C₄⋊C₄	—	83	1	no	—
454	C₄⋊C₄	—	166	1	no	—
455	C₄⋊C₄	—	166	1	no	—
456	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
457	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	166	1	no	—
462	C₂²⋊C₄	—	166	1	no	—
463	C₂²⋊C₄	—	166	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	166	1	no	—
470	C₄²	—	166	1	no	—
471	C₄²	—	166	1	no	—
472	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
473	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
474	C₄²	D₄×D₈₃	1	1	yes	characteristic
475	C₄²	D₄×D₈₃	1	1	yes	characteristic
476	C₂³	—	2	1	no	—
477	C₂³	—	166	1	no	—
478	C₂³	C₂×#13050589	1	1	yes	characteristic
479	Q₈	—	2	1	no	—
480	Q₈	—	2	1	no	—
481	Q₈	—	83	2	no	—
482	Q₈	—	166	1	no	—
483	D₄	—	2	1	no	—
484	D₄	—	2	1	no	—
485	D₄	—	4	1	no	—
486	D₄	—	4	1	no	—
487	D₄	—	83	2	no	—
488	D₄	—	166	2	no	—
489	D₄	—	166	2	no	—
490	D₄	—	166	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	8	1	no	—
503	C₂×C₄	—	332	2	no	—
504	C₂×C₄	—	664	1	no	—
505	C₂×C₄	—	166	1	no	—
506	C₂×C₄	—	166	1	no	—
507	C₂×C₄	—	166	1	no	—
508	C₂×C₄	—	166	2	no	—
509	C₂×C₄	—	166	2	no	—
510	C₂×C₄	(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
511	C₂×C₄	(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
512	C₂×C₄	(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
513	C₂×C₄	(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
514	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
515	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
516	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
517	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
518	C₂×C₄	#14581837	1	1	yes	characteristic
519	C₂×C₄	#14581840	1	1	yes	characteristic
520	C₈	—	4	2	no	—
521	C₈	—	332	2	no	—
522	C₈	—	166	2	no	—
523	C₈	—	166	2	no	—
524	C₈	—	166	1	no	—
525	C₈	—	166	1	no	—
526	C₈	—	166	1	no	—
527	C₈	—	166	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	332	1	no	—
534	C₂²	—	332	1	no	—
535	C₂²	—	166	2	no	—
536	C₂²	C₂×(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
537	C₂²	#19128385	1	1	yes	characteristic
538	C₂²	#19128398	1	1	yes	characteristic
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	8	2	no	—
546	C₄	—	332	1	no	—
547	C₄	—	332	1	no	—
548	C₄	—	166	2	no	—
549	C₄	#19127820	1	2	yes	—
550	C₄	#117×D₈₃	1	1	yes	characteristic
551	C₄	#19128182	1	1	yes	characteristic
552	C₄	#19128348	1	1	yes	characteristic
553	C₄	#19128361	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	8	1	no	—
557	C₂	—	332	2	no	—
558	C₂	#24910385	1	1	yes	characteristic
559	C₂	C₂×#19127820	1	1	yes	characteristic
560	C₂	#24916376	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₃
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₃
Fitting	C₈₃×#1806	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	C₂×#14581812	C₂²
cosocle	C₂²×C₄×C₈₃	C₂⁴
hypercenter	#1806	D₈₃
hypocenter	C₈₃	#22782
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1806

Complements

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

N	H ≅ G/N	type
2. #24916129	C₂	semidirect
3. #24916032	C₂	semidirect
4. #24908171	C₂	semidirect
5. #24908060	C₂	semidirect
7. #24907600	C₂	semidirect
8. #24907484	C₂	semidirect
9. #24907332	C₂	semidirect
10. #24907304	C₂	semidirect
11. C₈₃×#1806	C₂	semidirect
15. C₄×#13050580	C₄	semidirect
16. C₄×#13050580	C₄	semidirect
17. C₄×#13050577	C₄	semidirect
18. C₄×#13050577	C₄	semidirect
19. C₄×#13050578	C₄	semidirect
20. C₄×#13050578	C₄	semidirect
21. C₄×#13050575	C₄	semidirect
22. C₄×#13050575	C₄	semidirect
289. #1806	D₈₃	semidirect
292. C₈₃	#22782	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14581812	2
#24916129	2
#24916032	2
#24908171	2
#24908060	2
#24907787	2
#24907600	2
#24907484	2
#24907332	2
#24907304	2
C₈₃×#1806	2
#22782	83