Subgroups — #35374999

Order 21248.

594 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24918063	C₂	1	1	yes	maximal, characteristic
2	#24916438	C₂	1	1	yes	maximal, characteristic
3	#24906370	C₂	1	2	yes	maximal, complemented
4	#24906363	C₂	1	2	yes	maximal, complemented
5	C₈×#13050580	C₂	1	2	yes	maximal, complemented
6	C₈×#13050577	C₂	1	2	yes	maximal, complemented
7	#24906228	C₂	1	1	yes	maximal, characteristic, complemented
8	#24905936	C₂	1	1	yes	maximal, characteristic, complemented
9	#24905926	C₂	1	1	yes	maximal, characteristic
10	C₈×#13050574	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
12	#19128235	C₂²	1	1	yes	characteristic
13	#19128107	C₄	1	1	yes	characteristic
14	#19128093	C₄	1	1	yes	characteristic
15	#19128069	C₄	1	1	yes	characteristic
16	#19128063	C₄	1	1	yes	characteristic
17	#19127957	C₄	1	2	yes	—
18	#19127949	C₄	1	2	yes	—
19	#19127831	C₂²	1	1	yes	characteristic
20	C₈×Dic₁₆₆	C₂²	1	1	yes	characteristic
21	C₄×#13050580	C₂²	1	2	yes	—
22	C₄×#13050577	C₂²	1	2	yes	—
23	#19127780	C₂²	1	1	yes	characteristic
24	#19127772	—	2	1	no	—
25	C₈×D₃₃₂	C₂²	1	1	yes	characteristic
26	C₈×C₂²⋊D₈₃	—	2	1	no	—
27	#19127760	—	2	1	no	—
28	#19127758	C₂²	1	1	yes	characteristic
29	#19127754	C₂²	1	1	yes	characteristic
30	#19127655	—	2	1	no	—
31	C₄×#13050574	C₂²	1	1	yes	characteristic
32	#19127453	C₂²	1	2	yes	—
33	#19127451	C₂²	1	2	yes	—
34	Q₈⋊(C₈₃⋊C₈)	C₂²	1	2	yes	—
35	Q₈⋊(C₈₃⋊C₈)	C₂²	1	2	yes	—
36	#19127431	C₂²	1	2	yes	—
37	#19127428	C₂²	1	2	yes	—
38	#19127423	C₂²	1	2	yes	—
39	C₈×C₈₃⋊C₈	C₂²	1	2	yes	—
40	#533×C₈₃	C₂²	1	1	yes	characteristic
41	#446×C₈₃	—	2	1	no	—
42	#446×C₈₃	C₂²	1	2	yes	—
43	C₈×Q₈×C₈₃	—	2	1	no	—
44	C₈×Q₈×C₈₃	C₂²	1	2	yes	—
45	#424×C₈₃	—	2	1	no	—
46	#423×C₈₃	C₂²	1	1	yes	characteristic
47	#405×C₈₃	—	2	1	no	—
48	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
49	C₂×#13050580	C₂×C₄	1	2	yes	—
50	C₂×#13050577	C₂×C₄	1	2	yes	—
51	C₂×#13050574	C₂×C₄	1	2	yes	—
52	C₂×#13050573	—	2	1	no	—
53	C₂×C₈×D₈₃	—	2	1	no	—
54	#14581786	—	2	1	no	—
55	#14581784	C₂×C₄	1	1	yes	characteristic
56	#14581780	C₂×C₄	1	1	yes	characteristic
57	#14581775	—	2	1	no	—
58	#14581771	C₂×C₄	1	1	yes	characteristic
59	#14581766	C₂×C₄	1	1	yes	characteristic
60	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
61	C₄×D₃₃₂	C₂³	1	1	yes	characteristic
62	C₄×C₂²⋊D₈₃	—	2	1	no	—
63	#14581749	—	2	1	no	—
64	#14581725	C₂×C₄	1	2	yes	—
65	#14581723	C₂×C₄	1	2	yes	—
66	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
67	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
68	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
69	Dic₈₃⋊C₈	—	2	1	no	—
70	Dic₈₃⋊C₈	—	2	1	no	—
71	#14581716	C₂×C₄	1	2	yes	—
72	#14581716	C₂×C₄	1	2	yes	—
73	#14581715	C₂×C₄	1	2	yes	—
74	#14581712	C₂×C₄	1	2	yes	—
75	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
76	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
77	(C₂×D₈₃)⋊C₈	—	2	1	no	—
78	(C₂×D₈₃)⋊C₈	—	2	1	no	—
79	#14581703	—	2	1	no	—
80	#14581703	C₂×C₄	1	1	yes	characteristic
81	#14581703	C₂×C₄	1	1	yes	characteristic
82	#14581702	—	2	1	no	—
83	C₄×C₈₃⋊C₈	C₂³	1	2	yes	—
84	C₄×C₈₃⋊C₈	C₂³	1	2	yes	—
85	C₈×Dic₈₃	—	2	1	no	—
86	C₂×M₁₆×C₈₃	—	2	1	no	—
87	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
88	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
89	C₄⋊Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
90	C₄⋊Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
91	#125×C₈₃	—	2	1	no	—
92	C₂²⋊Q₈×C₈₃	—	2	1	no	—
93	C₂²⋊Q₈×C₈₃	C₂×C₄	1	2	yes	—
94	C₄×Q₈×C₈₃	—	2	1	no	—
95	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
96	#117×C₈₃	—	2	1	no	—
97	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₈₃	—	2	2	no	—
99	C₄⋊C₈×C₈₃	—	2	2	no	—
100	C₄⋊C₈×C₈₃	—	2	1	no	—
101	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
102	#97×C₈₃	—	2	2	no	—
103	C₄×C₈×C₈₃	—	2	2	no	—
104	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
105	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
106	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
108	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
109	C₂×D₃₃₂	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₂²⋊D₈₃	—	2	1	no	—
111	C₂×C₄×D₈₃	—	2	1	no	—
112	#13050580	—	2	4	no	—
113	#13050577	—	2	4	no	—
114	#13050574	—	2	4	no	—
115	#13050573	—	4	2	no	—
116	C₂×C₈₃⋊C₈	—	2	1	no	—
117	C₂×C₈₃⋊C₈	—	2	1	no	—
118	C₂×C₈₃⋊C₈	—	2	2	no	—
119	C₂×C₈₃⋊C₈	C₂²×C₄	1	2	yes	—
120	C₂×C₈₃⋊C₈	C₂²×C₄	1	2	yes	—
121	C₈×D₈₃	—	4	2	no	—
122	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
123	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
124	Dic₈₃⋊C₄	—	2	1	no	—
125	Dic₈₃⋊C₄	—	2	1	no	—
126	Dic₈₃⋊C₄	—	2	1	no	—
127	Dic₈₃⋊C₄	—	2	1	no	—
128	C₂²⋊Dic₈₃	—	2	1	no	—
129	(C₂×D₈₃)⋊C₄	—	2	1	no	—
130	(C₂×D₈₃)⋊C₄	—	2	1	no	—
131	(C₂×D₈₃)⋊C₄	—	2	1	no	—
132	(C₂×D₈₃)⋊C₄	—	2	1	no	—
133	C₄×Dic₈₃	—	2	1	no	—
134	C₂×Q₈×C₈₃	—	2	1	no	—
135	C₂×Q₈×C₈₃	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
139	M₁₆×C₈₃	—	4	2	no	—
140	C₂×C₈×C₈₃	—	2	2	no	—
141	C₂×C₈×C₈₃	—	2	2	no	—
142	C₂×C₈×C₈₃	—	4	1	no	—
143	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
147	C₄⋊C₄×C₈₃	—	2	1	no	—
148	C₄⋊C₄×C₈₃	—	2	1	no	—
149	C₄⋊C₄×C₈₃	—	2	1	no	—
150	C₄⋊C₄×C₈₃	—	2	2	no	—
151	C₄⋊C₄×C₈₃	—	2	2	no	—
152	C₄⋊C₄×C₈₃	C₂²×C₄	1	2	yes	—
153	C₂²⋊C₄×C₈₃	—	2	2	no	—
154	C₄²×C₈₃	—	2	2	no	—
155	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₈₃	#41	1	1	yes	characteristic
158	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
159	C₂³×C₈₃	C₄×D₄	1	1	yes	characteristic
160	C₂²×D₈₃	—	2	1	no	—
161	Q₈×C₈₃	—	2	2	no	—
162	Q₈×C₈₃	—	2	2	no	—
163	Q₈×C₈₃	—	4	2	no	—
164	C₂×C₄×C₈₃	—	2	2	no	—
165	C₂×C₄×C₈₃	—	2	1	no	—
166	C₂×C₄×C₈₃	—	2	1	no	—
167	C₂×C₄×C₈₃	—	2	2	no	—
168	C₂×C₄×C₈₃	—	2	2	no	—
169	C₂×C₄×C₈₃	—	4	1	no	—
170	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
176	C₂²⋊D₈₃	—	4	2	no	—
177	C₂×Dic₈₃	—	2	1	no	—
178	C₂×Dic₈₃	—	2	1	no	—
179	C₂×Dic₈₃	—	2	1	no	—
180	D₃₃₂	—	2	2	no	—
181	C₄×D₈₃	—	4	1	no	—
182	C₄×D₈₃	—	4	1	no	—
183	Dic₁₆₆	—	2	2	no	—
184	C₈×C₈₃	—	2	1	no	—
185	C₈×C₈₃	—	2	1	no	—
186	C₈×C₈₃	—	2	1	no	—
187	C₈×C₈₃	—	4	2	no	—
188	C₈×C₈₃	#137	1	2	yes	—
189	C₈₃⋊C₈	—	2	2	no	—
190	C₈₃⋊C₈	—	4	2	no	—
191	C₈₃⋊C₈	—	4	1	no	—
192	C₈₃⋊C₈	—	4	1	no	—
193	C₈₃⋊C₈	#131	1	4	yes	—
194	C₂²×C₈₃	—	2	1	no	—
195	C₂²×C₈₃	—	2	1	no	—
196	C₂²×C₈₃	—	2	1	no	—
197	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂×D₈₃	—	4	1	no	—
199	C₂×D₈₃	—	4	1	no	—
200	C₂×D₈₃	—	4	1	no	—
201	C₄×C₈₃	—	2	1	no	—
202	C₄×C₈₃	—	2	1	no	—
203	C₄×C₈₃	—	2	1	no	—
204	C₄×C₈₃	—	2	1	no	—
205	C₄×C₈₃	—	4	2	no	—
206	C₄×C₈₃	—	4	2	no	—
207	C₄×C₈₃	C₂×#131	1	2	yes	—
208	C₄×C₈₃	C₂×#137	1	1	yes	characteristic
209	C₄×C₈₃	#575	1	1	yes	characteristic
210	Dic₈₃	—	4	1	no	—
211	Dic₈₃	—	4	1	no	—
212	Dic₈₃	—	4	1	no	—
213	#17965	—	83	1	no	maximal, Sylow
214	C₂×C₈₃	—	4	1	no	—
215	C₂×C₈₃	#2931	1	1	yes	characteristic
216	C₂×C₈₃	C₄×#137	1	1	yes	characteristic
217	C₂×C₈₃	#2955	1	1	yes	characteristic
218	D₈₃	—	8	1	no	—
219	#3172	—	83	1	no	—
220	#2966	—	83	1	no	—
221	#2960	D₈₃	1	1	yes	characteristic, complemented
222	#1593	—	83	2	no	—
223	#1592	—	83	2	no	—
224	C₈×Q₁₆	—	83	2	no	—
225	C₈×SD₁₆	—	83	2	no	—
226	#1569	—	83	1	no	—
227	#1497	—	83	1	no	—
228	#1495	—	83	1	no	—
229	C₈×M₁₆	—	83	1	no	—
230	C₈₃	#17965	1	1	yes	characteristic, complemented, Sylow
231	#533	C₂×D₈₃	1	1	yes	characteristic
232	#529	—	83	1	no	—
233	#501	—	83	1	no	—
234	#497	—	83	1	no	—
235	#491	—	83	1	no	—
236	#489	—	83	1	no	—
237	#470	—	83	2	no	—
238	#468	—	83	2	no	—
239	#446	—	2	1	no	—
240	#446	—	83	1	no	—
241	#446	C₂×D₈₃	1	2	yes	—
242	C₈×Q₈	—	2	1	no	—
243	C₈×Q₈	—	83	1	no	—
244	C₈×Q₈	C₂×D₈₃	1	2	yes	—
245	C₄×Q₁₆	—	83	2	no	—
246	C₄×SD₁₆	—	83	2	no	—
247	#436	—	83	1	no	—
248	#435	—	166	1	no	—
249	C₈×D₄	—	83	1	no	—
250	C₈×D₄	—	166	1	no	—
251	#433	—	166	1	no	—
252	#432	—	83	1	no	—
253	#431	—	83	1	no	—
254	#424	—	2	1	no	—
255	#423	C₂×D₈₃	1	1	yes	characteristic
256	#405	—	2	1	no	—
257	#405	—	166	1	no	—
258	C₄×M₁₆	—	83	1	no	—
259	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
260	#335	—	83	2	no	—
261	#334	—	83	2	no	—
262	Q₈⋊C₈	—	83	2	no	—
263	Q₈⋊C₈	—	83	2	no	—
264	Q₈⋊C₈	—	83	2	no	—
265	D₄⋊C₈	—	83	2	no	—
266	#322	—	83	2	no	—
267	C₈²	—	83	2	no	—
268	C₂×Q₁₆	—	83	2	no	—
269	C₂×SD₁₆	—	83	2	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	83	2	no	—
272	C₂×M₁₆	—	166	1	no	—
273	C₂²×C₈	—	166	1	no	—
274	C₂²×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
275	C₂²×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
276	C₄⋊Q₈	C₄×D₈₃	1	1	yes	characteristic
277	C₄⋊Q₈	C₄×D₈₃	1	1	yes	characteristic
278	#126	—	166	1	no	—
279	#125	—	2	1	no	—
280	#125	—	83	1	no	—
281	#124	—	83	1	no	—
282	#123	—	166	1	no	—
283	C₂²⋊Q₈	—	2	1	no	—
284	C₂²⋊Q₈	—	83	1	no	—
285	C₂²⋊Q₈	C₄×D₈₃	1	2	yes	—
286	#121	—	83	1	no	—
287	C₄×Q₈	—	2	1	no	—
288	C₄×Q₈	—	83	1	no	—
289	C₄×Q₈	C₂²×D₈₃	1	2	yes	—
290	C₄×D₄	—	83	1	no	—
291	C₄×D₄	—	166	1	no	—
292	#117	—	2	1	no	—
293	#117	—	166	1	no	—
294	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
295	#107	—	83	2	no	—
296	#106	—	83	2	no	—
297	C₄⋊C₈	—	2	2	no	—
298	C₄⋊C₈	—	2	2	no	—
299	C₄⋊C₈	—	2	1	no	—
300	C₄⋊C₈	—	83	1	no	—
301	C₄⋊C₈	—	83	1	no	—
302	C₄⋊C₈	—	166	1	no	—
303	C₄⋊C₈	—	166	1	no	—
304	C₄⋊C₈	—	166	1	no	—
305	C₄⋊C₈	C₂²×D₈₃	1	2	yes	—
306	#103	—	83	2	no	—
307	#103	—	83	2	no	—
308	#103	—	83	2	no	—
309	#102	—	83	2	no	—
310	C₂²⋊C₈	—	166	1	no	—
311	C₂²⋊C₈	—	166	1	no	—
312	C₂²⋊C₈	—	166	1	no	—
313	C₂²⋊C₈	—	166	1	no	—
314	#97	—	2	2	no	—
315	#97	—	83	1	no	—
316	#97	—	83	1	no	—
317	#97	—	166	1	no	—
318	#97	—	166	1	no	—
319	C₄×C₈	—	2	2	no	—
320	C₄×C₈	—	83	2	no	—
321	C₄×C₈	—	83	2	no	—
322	C₄×C₈	—	166	1	no	—
323	C₄×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
324	C₄×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
325	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	83	1	no	—
329	C₂×Q₈	C₂×C₄×D₈₃	1	2	yes	—
330	C₂×D₄	—	83	1	no	—
331	C₂×D₄	—	166	1	no	—
332	C₂²×C₄	—	166	1	no	—
333	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
335	C₂²×C₄	#13050590	1	1	yes	characteristic
336	Q₁₆	—	166	4	no	—
337	SD₁₆	—	166	4	no	—
338	M₁₆	—	4	2	no	—
339	M₁₆	—	332	2	no	—
340	M₁₆	—	166	4	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	332	2	no	—
345	C₂×C₈	—	83	2	no	—
346	C₂×C₈	—	83	2	no	—
347	C₂×C₈	—	166	1	no	—
348	C₂×C₈	—	166	1	no	—
349	C₂×C₈	—	166	2	no	—
350	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
351	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
352	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
353	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	83	1	no	—
360	C₄⋊C₄	—	83	1	no	—
361	C₄⋊C₄	—	166	1	no	—
362	C₄⋊C₄	—	166	1	no	—
363	C₄⋊C₄	—	166	1	no	—
364	C₄⋊C₄	—	166	1	no	—
365	C₄⋊C₄	C₂×C₄×D₈₃	1	2	yes	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	166	1	no	—
368	C₂²⋊C₄	—	166	1	no	—
369	C₂²⋊C₄	—	166	1	no	—
370	C₂²⋊C₄	—	166	1	no	—
371	C₂²⋊C₄	—	166	1	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	166	1	no	—
374	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
375	C₄²	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
376	C₄²	#13050590	1	1	yes	characteristic
377	C₄²	C₂³×D₈₃	1	1	yes	characteristic
378	C₂³	—	166	1	no	—
379	C₂³	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	166	2	no	—
384	D₄	—	332	2	no	—
385	D₄	—	166	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	332	1	no	—
393	C₂×C₄	—	332	1	no	—
394	C₂×C₄	—	166	1	no	—
395	C₂×C₄	—	166	1	no	—
396	C₂×C₄	—	166	1	no	—
397	C₂×C₄	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
398	C₂×C₄	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
399	C₂×C₄	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
401	C₂×C₄	C₂²×C₂²⋊D₈₃	1	1	yes	characteristic
402	C₂×C₄	C₂×#13050590	1	1	yes	characteristic
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	2	1	no	—
406	C₈	—	4	2	no	—
407	C₈	—	332	2	no	—
408	C₈	—	332	1	no	—
409	C₈	—	332	1	no	—
410	C₈	—	83	4	no	—
411	C₈	—	166	2	no	—
412	C₈	#14581823	1	2	yes	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	332	1	no	—
417	C₂²	—	332	1	no	—
418	C₂²	—	332	1	no	—
419	C₂²	C₂×C₄×C₂²⋊D₈₃	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	332	1	no	—
427	C₄	—	332	1	no	—
428	C₄	—	332	1	no	—
429	C₄	#131×D₈₃	1	2	yes	—
430	C₄	C₂×#14581823	1	1	yes	characteristic
431	C₄	#19128499	1	1	yes	characteristic
432	C₂	—	4	1	no	—
433	C₂	—	664	1	no	—
434	C₂	#24916173	1	1	yes	characteristic
435	C₂	C₄×#14581823	1	1	yes	characteristic
436	C₂	#24916364	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₈₃
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₄²	C₂³×D₈₃
Fitting	C₈₃×#2960	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	#14581766	C₂×C₄
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	#2960	D₈₃
hypocenter	C₈₃	#17965
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2960

Complements

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

N	H ≅ G/N	type
3. #24906370	C₂	semidirect
4. #24906363	C₂	semidirect
5. C₈×#13050580	C₂	semidirect
6. C₈×#13050577	C₂	semidirect
7. #24906228	C₂	semidirect
8. #24905936	C₂	semidirect
10. C₈×#13050574	C₂	semidirect
11. C₈₃×#2960	C₂	semidirect
221. #2960	D₈₃	semidirect
230. C₈₃	#17965	semidirect

Maximal subgroups

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

subgroup	index
#24918063	2
#24916438	2
#24906370	2
#24906363	2
C₈×#13050580	2
C₈×#13050577	2
#24906228	2
#24905936	2
#24905926	2
C₈×#13050574	2
C₈₃×#2960	2
#17965	83