Subgroups — #24916163

Order 10624.

492 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14581800	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₁₆×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#19128210	C₂	1	1	yes	maximal, characteristic
4	#19127780	C₂	1	1	yes	maximal, characteristic, complemented
5	#19127777	C₂	1	1	yes	maximal, characteristic, complemented
6	#19127777	C₂	1	1	yes	maximal, characteristic, complemented
7	#19127775	C₂	1	1	yes	maximal, characteristic, complemented
8	#19127773	C₂	1	1	yes	maximal, characteristic, complemented
9	#19127771	C₂	1	1	yes	maximal, characteristic, complemented
10	#19127769	C₂	1	1	yes	maximal, characteristic, complemented
11	#19127726	C₂	1	1	yes	maximal, characteristic, complemented
12	#19127666	C₂	1	1	yes	maximal, characteristic, complemented
13	#19127663	C₂	1	1	yes	maximal, characteristic, complemented
14	#19127655	C₂	1	1	yes	maximal, characteristic, complemented
15	#436×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13050590	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₈₃	C₂²	1	1	yes	characteristic
18	#14581800	—	2	4	no	—
19	C₂×#13050574	C₂²	1	1	yes	characteristic
20	C₂×#13050573	C₂²	1	1	yes	characteristic
21	C₂×#13050573	C₂²	1	1	yes	characteristic
22	C₂×#13050573	C₂²	1	1	yes	characteristic
23	C₂×#13050573	C₂²	1	1	yes	characteristic
24	C₂×#13050573	C₂²	1	1	yes	characteristic, complemented
25	M₁₆×D₈₃	—	2	4	no	—
26	C₂²×C₈₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₈×D₈₃	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₈₃	C₂²	1	1	yes	characteristic
29	C₂×C₈×D₈₃	C₂²	1	1	yes	characteristic, complemented
30	#14581777	C₄	1	1	yes	characteristic
31	#14581774	C₄	1	1	yes	characteristic
32	#14581770	C₄	1	1	yes	characteristic
33	#14581769	C₄	1	1	yes	characteristic
34	#14581765	C₄	1	1	yes	characteristic
35	#14581764	C₄	1	1	yes	characteristic
36	#14581762	C₄	1	1	yes	characteristic
37	#14581760	C₄	1	1	yes	characteristic
38	C₄×D₃₃₂	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
41	#14581749	C₂²	1	1	yes	characteristic
42	C₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
43	Dic₈₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	Dic₈₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
45	C₂²⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
46	C₂²⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
47	(C₂×D₈₃)⋊C₈	C₂²	1	1	yes	characteristic
48	(C₂×D₈₃)⋊C₈	C₂²	1	1	yes	characteristic
49	(C₂×D₈₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
50	(C₂×D₈₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	#14581703	C₂²	1	1	yes	characteristic, complemented
52	#14581702	C₂²	1	1	yes	characteristic, complemented
53	C₈×Dic₈₃	C₂²	1	1	yes	characteristic, complemented
54	C₂×M₁₆×C₈₃	C₂²	1	1	yes	characteristic
55	C₂×M₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
56	C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
57	C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
58	C₂²⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
59	C₂²⋊C₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₈₃	C₂×C₄	1	1	yes	characteristic
62	#13050590	—	2	2	no	—
63	#13050590	—	2	2	no	—
64	C₂×Dic₁₆₆	C₂×C₄	1	1	yes	characteristic
65	C₂×D₃₃₂	C₂×C₄	1	1	yes	characteristic
66	C₂×D₃₃₂	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊D₈₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₂²⋊D₈₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₂²⋊D₈₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊D₈₃	C₂×C₄	1	1	yes	characteristic
71	C₂²×Dic₈₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×D₈₃	—	2	2	no	—
73	C₂×C₄×D₈₃	—	2	2	no	—
74	C₂×C₄×D₈₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₈₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
77	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
78	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
79	#13050574	—	2	2	no	—
80	#13050573	—	2	2	no	—
81	#13050573	—	2	2	no	—
82	#13050573	—	2	2	no	—
83	#13050573	—	2	2	no	—
84	#13050573	—	2	2	no	—
85	C₂×C₈₃⋊C₈	—	2	2	no	—
86	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
87	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
88	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
89	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
90	C₈×D₈₃	—	2	2	no	—
91	C₈×D₈₃	—	2	2	no	—
92	C₈×D₈₃	D₄	1	4	yes	complemented
93	C₄⋊Dic₈₃	C₂×C₄	1	1	yes	characteristic
94	Dic₈₃⋊C₄	C₂×C₄	1	1	yes	characteristic
95	Dic₈₃⋊C₄	C₂×C₄	1	1	yes	characteristic
96	Dic₈₃⋊C₄	C₂×C₄	1	1	yes	characteristic
97	Dic₈₃⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₂²⋊Dic₈₃	C₂×C₄	1	1	yes	characteristic
99	C₂²⋊Dic₈₃	C₂×C₄	1	1	yes	characteristic
100	(C₂×D₈₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
101	(C₂×D₈₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
102	(C₂×D₈₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
103	(C₂×D₈₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
104	(C₂×D₈₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
105	(C₂×D₈₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
107	C₂×D₄×C₈₃	C₂×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
109	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
110	M₁₆×C₈₃	—	2	2	no	—
111	M₁₆×C₈₃	—	2	2	no	—
112	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
113	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
114	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
119	C₄²×C₈₃	C₂³	1	1	yes	characteristic
120	C₂³×C₈₃	C₂²×C₄	1	1	yes	characteristic
121	C₂³×C₈₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×D₈₃	—	2	2	no	—
123	C₂²×D₈₃	—	4	1	no	—
124	C₂²×D₈₃	—	4	1	no	—
125	C₂²×D₈₃	C₂²×C₄	1	1	yes	characteristic
126	C₂²×D₈₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×D₈₃	C₂²×C₄	1	1	yes	characteristic
128	D₄×C₈₃	—	4	1	no	—
129	C₂×C₄×C₈₃	—	2	1	no	—
130	C₂×C₄×C₈₃	—	2	1	no	—
131	C₂×C₄×C₈₃	—	2	1	no	—
132	C₂×C₄×C₈₃	—	2	1	no	—
133	C₂×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
138	C₂²⋊D₈₃	—	2	2	no	—
139	C₂²⋊D₈₃	—	2	2	no	—
140	C₂²⋊D₈₃	—	4	1	no	—
141	C₂²⋊D₈₃	—	4	1	no	—
142	C₂×Dic₈₃	—	2	2	no	—
143	C₂×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
144	C₂×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
146	C₂×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
148	D₃₃₂	—	2	2	no	—
149	D₃₃₂	—	4	1	no	—
150	C₄×D₈₃	—	2	2	no	—
151	C₄×D₈₃	—	2	1	no	—
152	C₄×D₈₃	—	2	1	no	—
153	C₄×D₈₃	—	2	1	no	—
154	C₄×D₈₃	—	2	1	no	—
155	C₄×D₈₃	—	2	2	no	—
156	C₄×D₈₃	C₂×D₄	1	2	yes	—
157	C₄×D₈₃	#41	1	2	yes	—
158	Dic₁₆₆	—	2	2	no	—
159	C₈×C₈₃	—	2	1	no	—
160	C₈×C₈₃	—	2	1	no	—
161	C₈×C₈₃	—	2	1	no	—
162	C₈×C₈₃	C₂×D₄	1	2	yes	—
163	C₈₃⋊C₈	—	2	1	no	—
164	C₈₃⋊C₈	—	2	1	no	—
165	C₈₃⋊C₈	—	2	1	no	—
166	C₈₃⋊C₈	C₂×D₄	1	2	yes	—
167	C₂²×C₈₃	—	2	1	no	—
168	C₂²×C₈₃	—	2	1	no	—
169	C₂²×C₈₃	—	2	1	no	—
170	C₂²×C₈₃	—	2	1	no	—
171	C₂²×C₈₃	—	2	1	no	—
172	C₂²×C₈₃	—	2	1	no	—
173	C₂²×C₈₃	C₂³×C₄	1	1	yes	characteristic
174	C₂×D₈₃	—	2	1	no	—
175	C₂×D₈₃	—	2	1	no	—
176	C₂×D₈₃	—	2	1	no	—
177	C₂×D₈₃	—	2	1	no	—
178	C₂×D₈₃	—	2	1	no	—
179	C₂×D₈₃	—	2	1	no	—
180	C₂×D₈₃	—	2	1	no	—
181	C₂×D₈₃	—	2	1	no	—
182	C₂×D₈₃	—	4	4	no	—
183	C₂×D₈₃	C₄×D₄	1	2	yes	—
184	C₄×C₈₃	—	2	1	no	—
185	C₄×C₈₃	—	2	1	no	—
186	C₄×C₈₃	—	2	1	no	—
187	C₄×C₈₃	—	2	1	no	—
188	C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
189	C₄×C₈₃	C₂×#41	1	1	yes	characteristic
190	Dic₈₃	—	2	1	no	—
191	Dic₈₃	—	2	1	no	—
192	Dic₈₃	—	2	1	no	—
193	Dic₈₃	—	2	1	no	—
194	Dic₈₃	C₄×D₄	1	2	yes	—
195	C₂×C₈₃	—	4	1	no	—
196	C₂×C₈₃	—	4	1	no	—
197	C₂×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂×C₈₃	#568	1	1	yes	characteristic
199	C₂×C₈₃	#568	1	1	yes	characteristic
200	D₈₃	—	2	2	no	—
201	D₈₃	—	4	1	no	—
202	D₈₃	—	4	1	no	—
203	#2930	—	83	1	no	maximal, Sylow
204	C₈₃	#2930	1	1	yes	characteristic, complemented, Sylow
205	C₂×#131	—	83	1	no	—
206	C₂²×M₁₆	—	83	1	no	—
207	#525	—	83	1	no	—
208	#436	—	83	1	no	—
209	#436	—	83	1	no	—
210	#436	—	83	1	no	—
211	#436	D₈₃	1	1	yes	characteristic, complemented
212	#435	—	83	1	no	—
213	#435	—	83	1	no	—
214	#435	—	83	1	no	—
215	#435	—	83	1	no	—
216	#424	—	83	1	no	—
217	#408	—	83	1	no	—
218	#407	—	83	1	no	—
219	#405	—	83	1	no	—
220	C₂×#41	—	83	1	no	—
221	C₂³×C₄	—	83	1	no	—
222	#131	—	166	4	no	—
223	C₂×M₁₆	—	83	1	no	—
224	C₂×M₁₆	—	83	1	no	—
225	C₂×M₁₆	—	83	1	no	—
226	C₂×M₁₆	—	83	1	no	—
227	C₂×M₁₆	—	83	1	no	—
228	C₂×M₁₆	—	83	1	no	—
229	C₂×M₁₆	—	166	4	no	—
230	C₂×M₁₆	C₂×D₈₃	1	1	yes	characteristic
231	C₂×M₁₆	C₂×D₈₃	1	1	yes	characteristic, complemented
232	C₂²×C₈	—	83	1	no	—
233	C₂²×C₈	—	83	1	no	—
234	C₂²×C₈	—	83	1	no	—
235	C₂²×C₈	—	83	1	no	—
236	#123	—	83	1	no	—
237	#123	—	83	1	no	—
238	C₂²⋊Q₈	—	83	1	no	—
239	C₂²⋊Q₈	—	83	1	no	—
240	#121	—	83	1	no	—
241	#121	—	83	1	no	—
242	#120	—	83	1	no	—
243	#120	—	83	1	no	—
244	C₄×D₄	—	83	1	no	—
245	C₄×D₄	—	83	1	no	—
246	C₄×D₄	—	83	1	no	—
247	C₄×D₄	C₂×D₈₃	1	1	yes	characteristic
248	#117	—	83	1	no	—
249	C₄⋊C₈	—	83	1	no	—
250	C₄⋊C₈	—	83	1	no	—
251	C₄⋊C₈	—	83	1	no	—
252	C₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic, complemented
253	C₂²⋊C₈	—	83	1	no	—
254	C₂²⋊C₈	—	83	1	no	—
255	C₂²⋊C₈	—	83	1	no	—
256	C₂²⋊C₈	—	83	1	no	—
257	C₂²⋊C₈	—	83	1	no	—
258	C₂²⋊C₈	—	83	1	no	—
259	C₂²⋊C₈	C₂×D₈₃	1	1	yes	characteristic
260	C₂²⋊C₈	C₂×D₈₃	1	1	yes	characteristic, complemented
261	#97	—	83	1	no	—
262	#97	—	83	1	no	—
263	C₄×C₈	—	83	1	no	—
264	C₄×C₈	C₂×D₈₃	1	1	yes	characteristic, complemented
265	C₂⁴	—	83	1	no	—
266	#41	—	166	2	no	—
267	#41	—	166	2	no	—
268	C₂×Q₈	—	83	1	no	—
269	C₂×D₄	—	83	1	no	—
270	C₂×D₄	—	83	1	no	—
271	C₂×D₄	—	83	1	no	—
272	C₂×D₄	—	83	1	no	—
273	C₂×D₄	—	83	1	no	—
274	C₂×D₄	—	83	1	no	—
275	C₂×D₄	C₄×D₈₃	1	1	yes	characteristic
276	C₂²×C₄	—	83	1	no	—
277	C₂²×C₄	—	83	1	no	—
278	C₂²×C₄	—	83	1	no	—
279	C₂²×C₄	—	83	1	no	—
280	C₂²×C₄	—	83	1	no	—
281	C₂²×C₄	—	83	1	no	—
282	C₂²×C₄	—	166	2	no	—
283	C₂²×C₄	—	166	2	no	—
284	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
285	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
286	M₁₆	—	2	2	no	—
287	M₁₆	—	2	2	no	—
288	M₁₆	—	166	2	no	—
289	M₁₆	—	166	2	no	—
290	M₁₆	—	166	2	no	—
291	M₁₆	—	166	2	no	—
292	M₁₆	—	166	2	no	—
293	M₁₆	—	166	2	no	—
294	C₂×C₈	—	83	1	no	—
295	C₂×C₈	—	83	4	no	—
296	C₂×C₈	—	83	1	no	—
297	C₂×C₈	—	83	1	no	—
298	C₂×C₈	—	83	1	no	—
299	C₂×C₈	—	166	2	no	—
300	C₂×C₈	—	166	2	no	—
301	C₂×C₈	—	166	2	no	—
302	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
303	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
304	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
305	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
306	C₄⋊C₄	—	83	1	no	—
307	C₄⋊C₄	—	83	1	no	—
308	C₄⋊C₄	—	83	1	no	—
309	C₄⋊C₄	—	83	1	no	—
310	C₄⋊C₄	—	83	1	no	—
311	C₄⋊C₄	C₄×D₈₃	1	1	yes	characteristic
312	C₂²⋊C₄	—	83	1	no	—
313	C₂²⋊C₄	—	83	1	no	—
314	C₂²⋊C₄	—	83	1	no	—
315	C₂²⋊C₄	—	83	1	no	—
316	C₂²⋊C₄	—	83	1	no	—
317	C₂²⋊C₄	—	83	1	no	—
318	C₂²⋊C₄	—	83	1	no	—
319	C₂²⋊C₄	—	83	1	no	—
320	C₂²⋊C₄	C₄×D₈₃	1	1	yes	characteristic
321	C₂²⋊C₄	C₄×D₈₃	1	1	yes	characteristic
322	C₄²	—	83	1	no	—
323	C₄²	C₂²×D₈₃	1	1	yes	characteristic
324	C₂³	—	332	1	no	—
325	C₂³	—	332	1	no	—
326	C₂³	—	83	1	no	—
327	C₂³	—	83	1	no	—
328	C₂³	—	83	1	no	—
329	C₂³	—	166	2	no	—
330	C₂³	C₂×C₄×D₈₃	1	1	yes	characteristic
331	C₂³	C₂×C₄×D₈₃	1	1	yes	characteristic
332	Q₈	—	166	2	no	—
333	D₄	—	4	1	no	—
334	D₄	—	332	1	no	—
335	D₄	—	332	1	no	—
336	D₄	—	332	1	no	—
337	D₄	—	166	2	no	—
338	D₄	—	166	2	no	—
339	D₄	—	166	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	83	1	no	—
345	C₂×C₄	—	83	2	no	—
346	C₂×C₄	—	83	2	no	—
347	C₂×C₄	—	83	1	no	—
348	C₂×C₄	—	83	1	no	—
349	C₂×C₄	—	83	1	no	—
350	C₂×C₄	—	83	1	no	—
351	C₂×C₄	—	166	2	no	—
352	C₂×C₄	—	166	2	no	—
353	C₂×C₄	—	166	2	no	—
354	C₂×C₄	—	166	1	no	—
355	C₂×C₄	—	166	1	no	—
356	C₂×C₄	—	166	1	no	—
357	C₂×C₄	—	166	1	no	—
358	C₂×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
361	C₂×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
362	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	83	2	no	—
367	C₈	—	166	1	no	—
368	C₈	—	166	1	no	—
369	C₈	—	166	1	no	—
370	C₈	D₄×D₈₃	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	332	4	no	—
378	C₂²	—	83	2	no	—
379	C₂²	—	166	1	no	—
380	C₂²	—	166	1	no	—
381	C₂²	—	166	1	no	—
382	C₂²	—	166	1	no	—
383	C₂²	—	166	1	no	—
384	C₂²	—	166	1	no	—
385	C₂²	—	166	1	no	—
386	C₂²	—	166	1	no	—
387	C₂²	C₂²×C₄×D₈₃	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	83	2	no	—
393	C₄	—	166	1	no	—
394	C₄	—	166	1	no	—
395	C₄	—	166	1	no	—
396	C₄	—	166	1	no	—
397	C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
398	C₄	#41×D₈₃	1	1	yes	characteristic
399	C₂	—	4	1	no	—
400	C₂	—	4	1	no	—
401	C₂	—	332	1	no	—
402	C₂	—	332	1	no	—
403	C₂	—	166	2	no	—
404	C₂	C₄×D₄×D₈₃	1	1	yes	characteristic
405	C₂	#19128466	1	1	yes	characteristic
406	C₂	#19128467	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₈₃
commutator, socle	C₂²×C₈₃	C₂³×C₄
Fitting	#436×C₈₃	C₂
prime radical	#19128210	C₂
cosocle	C₂×C₄×C₈₃	C₂⁴
hypercenter	#436	D₈₃
hypocenter	C₈₃	#2930
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ #436

Complements

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

N	H ≅ G/N	type
1. C₂×#14581800	C₂	semidirect
2. C₂×M₁₆×D₈₃	C₂	semidirect
4. #19127780	C₂	semidirect
5. #19127777	C₂	semidirect
6. #19127777	C₂	semidirect
7. #19127775	C₂	semidirect
8. #19127773	C₂	semidirect
9. #19127771	C₂	semidirect
10. #19127769	C₂	semidirect
11. #19127726	C₂	semidirect
12. #19127666	C₂	semidirect
13. #19127663	C₂	semidirect
14. #19127655	C₂	semidirect
15. #436×C₈₃	C₂	semidirect
24. C₂×#13050573	C₂²	semidirect
26. C₂²×C₈₃⋊C₈	C₂²	semidirect
29. C₂×C₈×D₈₃	C₂²	semidirect
42. C₄⋊(C₈₃⋊C₈)	C₂²	semidirect
43. Dic₈₃⋊C₈	C₂²	semidirect
44. Dic₈₃⋊C₈	C₂²	semidirect
46. C₂²⋊(C₈₃⋊C₈)	C₂²	semidirect
49. (C₂×D₈₃)⋊C₈	C₂²	semidirect
50. (C₂×D₈₃)⋊C₈	C₂²	semidirect
51. #14581703	C₂²	semidirect
52. #14581702	C₂²	semidirect
53. C₈×Dic₈₃	C₂²	semidirect
55. C₂×M₁₆×C₈₃	C₂²	semidirect
57. C₄⋊C₈×C₈₃	C₂²	semidirect
59. C₂²⋊C₈×C₈₃	C₂²	semidirect
60. C₄×C₈×C₈₃	C₂²	semidirect
92. C₈×D₈₃	D₄	semidirect
204. C₈₃	#2930	semidirect
211. #436	D₈₃	semidirect
231. C₂×M₁₆	C₂×D₈₃	semidirect
252. C₄⋊C₈	C₂×D₈₃	semidirect
260. C₂²⋊C₈	C₂×D₈₃	semidirect
264. C₄×C₈	C₂×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14581800	2
C₂×M₁₆×D₈₃	2
#19128210	2
#19127780	2
#19127777	2
#19127775	2
#19127773	2
#19127771	2
#19127769	2
#19127726	2
#19127666	2
#19127663	2
#19127655	2
#436×C₈₃	2
#2930	83