Subgroups — #35294657

Order 21248.

598 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24916096	C₂	1	1	yes	maximal, characteristic
2	#24916096	C₂	1	1	yes	maximal, characteristic
3	#24905360	C₂	1	4	yes	maximal, complemented
4	C₂²×C₄⋊C₈×C₈₃	C₂	1	1	yes	maximal, characteristic
5	#19127758	—	2	1	no	—
6	#19127758	—	2	1	no	—
7	#19127758	C₄	1	2	yes	—
8	#19127758	C₄	1	2	yes	—
9	#19127754	—	2	1	no	—
10	#19127754	—	2	1	no	—
11	#19127754	C₄	1	2	yes	—
12	#19127754	C₂²	1	2	yes	—
13	#19127725	—	2	1	no	—
14	#19127725	C₂²	1	2	yes	—
15	#19127665	—	2	1	no	—
16	#19127665	C₄	1	2	yes	—
17	C₄×#13050574	—	2	1	no	—
18	C₄×#13050574	—	2	1	no	—
19	C₂³×C₈×C₈₃	—	2	1	no	—
20	C₂²×C₄²×C₈₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₈₃	—	2	1	no	—
22	C₂×C₄⋊C₈×C₈₃	—	2	1	no	—
23	C₂×C₄⋊C₈×C₈₃	—	2	1	no	—
24	C₂×C₄⋊C₈×C₈₃	C₄	1	2	yes	—
25	C₂×C₄⋊C₈×C₈₃	C₄	1	2	yes	—
26	C₂×C₄⋊C₈×C₈₃	C₂²	1	2	yes	—
27	C₂×#13050574	—	2	2	no	—
28	C₂×#13050574	—	2	2	no	—
29	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
30	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
31	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
32	C₄⋊(C₈₃⋊C₈)	C₂×C₄	1	4	yes	—
33	C₂²⋊(C₈₃⋊C₈)	—	2	2	no	—
34	C₂²⋊(C₈₃⋊C₈)	—	2	2	no	—
35	C₂²⋊(C₈₃⋊C₈)	—	2	2	no	—
36	C₂²⋊(C₈₃⋊C₈)	C₂×C₄	1	4	yes	—
37	#14581703	—	2	2	no	—
38	#14581703	—	2	2	no	—
39	C₄×C₈₃⋊C₈	—	2	2	no	—
40	C₄×C₈₃⋊C₈	—	2	2	no	—
41	C₂³×C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₈₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₈₃	Q₈	1	1	yes	characteristic
44	C₂²×C₈×C₈₃	—	2	2	no	—
45	C₂²×C₈×C₈₃	—	2	2	no	—
46	C₂²×C₈×C₈₃	—	2	2	no	—
47	C₂²×C₈×C₈₃	—	4	4	no	—
48	C₂×C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₈₃	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₈₃	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₈₃	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₈₃	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₈₃	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₈₃	Q₈	1	1	yes	characteristic
59	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
60	C₄⋊C₈×C₈₃	—	2	2	no	—
61	C₄⋊C₈×C₈₃	—	2	2	no	—
62	C₄⋊C₈×C₈₃	—	2	2	no	—
63	C₄⋊C₈×C₈₃	C₂×C₄	1	4	yes	—
64	#13050574	—	4	4	no	—
65	#13050574	—	4	2	no	—
66	#13050574	—	4	2	no	—
67	C₂×C₈₃⋊C₈	—	2	4	no	—
68	C₂×C₈₃⋊C₈	—	2	4	no	—
69	C₂⁴×C₈₃	C₄⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₈₃	—	2	4	no	—
71	C₂²×C₄×C₈₃	—	2	2	no	—
72	C₂²×C₄×C₈₃	—	2	2	no	—
73	C₂²×C₄×C₈₃	—	4	2	no	—
74	C₂²×C₄×C₈₃	C₄²	1	1	yes	characteristic
75	C₂²×C₄×C₈₃	C₄²	1	1	yes	characteristic
76	C₂²×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₈₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₈₃	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₈₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₈₃	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₈₃	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₈₃	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₈₃	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₈₃	C₂×Q₈	1	1	yes	characteristic
92	C₂×C₈×C₈₃	—	2	4	no	—
93	C₂×C₈×C₈₃	—	4	4	no	—
94	C₂×C₈×C₈₃	—	4	4	no	—
95	C₂×C₈×C₈₃	—	4	4	no	—
96	C₄²×C₈₃	C₄²	1	1	yes	characteristic
97	C₄²×C₈₃	C₄²	1	1	yes	characteristic
98	C₄²×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₈₃	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₈₃	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₈₃	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₈₃	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
112	C₂³×C₈₃	—	2	2	no	—
113	C₂³×C₈₃	—	2	2	no	—
114	C₂³×C₈₃	—	2	2	no	—
115	C₂³×C₈₃	#95	1	1	yes	characteristic
116	C₂³×C₈₃	#95	1	1	yes	characteristic
117	C₂³×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₄×C₈₃	—	2	2	no	—
119	C₂×C₄×C₈₃	—	2	2	no	—
120	C₂×C₄×C₈₃	—	2	2	no	—
121	C₂×C₄×C₈₃	—	2	2	no	—
122	C₂×C₄×C₈₃	—	2	2	no	—
123	C₂×C₄×C₈₃	—	2	2	no	—
124	C₂×C₄×C₈₃	—	2	2	no	—
125	C₂×C₄×C₈₃	—	2	2	no	—
126	C₂×C₄×C₈₃	—	2	1	no	—
127	C₂×C₄×C₈₃	—	2	1	no	—
128	C₂×C₄×C₈₃	—	2	1	no	—
129	C₂×C₄×C₈₃	—	2	1	no	—
130	C₂×C₄×C₈₃	—	2	2	no	—
131	C₂×C₄×C₈₃	—	2	2	no	—
132	C₂×C₄×C₈₃	—	4	1	no	—
133	C₂×C₄×C₈₃	—	4	1	no	—
134	C₂×C₄×C₈₃	—	4	1	no	—
135	C₂×C₄×C₈₃	—	4	1	no	—
136	C₂×C₄×C₈₃	#95	1	1	yes	characteristic
137	C₂×C₄×C₈₃	#95	1	1	yes	characteristic
138	C₂×C₄×C₈₃	#95	1	1	yes	characteristic
139	C₂×C₄×C₈₃	#95	1	1	yes	characteristic
140	C₂×C₄×C₈₃	#95	1	1	yes	characteristic
141	C₂×C₄×C₈₃	#95	1	1	yes	characteristic
142	C₂×C₄×C₈₃	#108	1	4	yes	—
143	C₂×C₄×C₈₃	C₂×C₄²	1	1	yes	characteristic
144	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₈₃	AGL(1,ℤ/8)	1	2	yes	—
150	C₂×C₄×C₈₃	#137	1	2	yes	—
151	C₈×C₈₃	—	4	4	no	—
152	C₈₃⋊C₈	—	4	4	no	—
153	C₈₃⋊C₈	—	4	4	no	—
154	C₂²×C₈₃	—	2	8	no	—
155	C₂²×C₈₃	—	2	1	no	—
156	C₂²×C₈₃	—	2	1	no	—
157	C₂²×C₈₃	—	2	1	no	—
158	C₂²×C₈₃	—	2	1	no	—
159	C₂²×C₈₃	—	2	1	no	—
160	C₂²×C₈₃	—	2	1	no	—
161	C₂²×C₈₃	#341	1	2	yes	—
162	C₂²×C₈₃	#344	1	2	yes	—
163	C₂²×C₈₃	C₂×#95	1	1	yes	characteristic
164	C₂²×C₈₃	#428	1	2	yes	—
165	C₄×C₈₃	—	2	1	no	—
166	C₄×C₈₃	—	2	1	no	—
167	C₄×C₈₃	—	2	1	no	—
168	C₄×C₈₃	—	2	1	no	—
169	C₄×C₈₃	—	2	1	no	—
170	C₄×C₈₃	—	2	1	no	—
171	C₄×C₈₃	—	2	1	no	—
172	C₄×C₈₃	—	2	1	no	—
173	C₄×C₈₃	#341	1	2	yes	—
174	C₄×C₈₃	#417	1	2	yes	—
175	C₄×C₈₃	#418	1	1	yes	characteristic
176	C₄×C₈₃	#419	1	1	yes	characteristic
177	C₄×C₈₃	C₂×#108	1	2	yes	—
178	#8082	—	83	1	no	maximal, Sylow
179	C₂×C₈₃	—	2	2	no	—
180	C₂×C₈₃	—	2	2	no	—
181	C₂×C₈₃	—	2	2	no	—
182	C₂×C₈₃	#1736	1	1	yes	characteristic
183	C₂×C₈₃	C₂×#341	1	1	yes	characteristic
184	C₂×C₈₃	C₂×#344	1	1	yes	characteristic
185	#2920	—	83	1	no	—
186	#2920	—	83	1	no	—
187	C₂²×C₄⋊C₈	D₈₃	1	1	yes	characteristic
188	#1301	—	83	4	no	—
189	C₈₃	#8082	1	1	yes	characteristic, complemented, Sylow
190	C₂³×C₈	—	2	1	no	—
191	C₂²×C₄²	C₂×D₈₃	1	1	yes	characteristic
192	#432	—	83	2	no	—
193	#432	—	83	2	no	—
194	#432	—	166	1	no	—
195	#432	—	166	1	no	—
196	#431	—	83	2	no	—
197	#431	—	83	2	no	—
198	#431	—	166	1	no	—
199	#431	—	166	1	no	—
200	#423	—	83	2	no	—
201	#423	—	166	1	no	—
202	C₂×C₄⋊C₈	—	2	1	no	—
203	C₂×C₄⋊C₈	—	2	1	no	—
204	C₂×C₄⋊C₈	—	2	1	no	—
205	C₂×C₄⋊C₈	Dic₈₃	1	2	yes	—
206	C₂×C₄⋊C₈	Dic₈₃	1	2	yes	—
207	C₂×C₄⋊C₈	C₂×D₈₃	1	2	yes	—
208	#407	—	83	2	no	—
209	#407	—	166	1	no	—
210	C₄×M₁₆	—	166	1	no	—
211	C₄×M₁₆	—	166	1	no	—
212	C₂³×C₄	Dic₁₆₆	1	1	yes	characteristic
213	C₂³×C₄	C₄×D₈₃	1	1	yes	characteristic
214	C₂³×C₄	C₂²⋊D₈₃	1	1	yes	characteristic
215	C₂×M₁₆	—	166	2	no	—
216	C₂×M₁₆	—	166	2	no	—
217	C₂²×C₈	—	2	2	no	—
218	C₂²×C₈	—	2	2	no	—
219	C₂²×C₈	—	2	2	no	—
220	C₂²×C₈	—	4	4	no	—
221	C₂×C₄²	Dic₁₆₆	1	1	yes	characteristic
222	C₂×C₄²	C₄×D₈₃	1	1	yes	characteristic
223	C₂×C₄²	C₄×D₈₃	1	1	yes	characteristic
224	C₂×C₄²	C₄×D₈₃	1	1	yes	characteristic
225	C₂×C₄²	D₃₃₂	1	1	yes	characteristic
226	C₂×C₄²	D₃₃₂	1	1	yes	characteristic
227	C₂×C₄²	C₂×Dic₈₃	1	1	yes	characteristic
228	C₂×C₄²	C₂×Dic₈₃	1	1	yes	characteristic
229	C₂×C₄²	C₂²⋊D₈₃	1	1	yes	characteristic
230	C₂×C₄²	C₂²⋊D₈₃	1	1	yes	characteristic
231	C₂×C₄²	C₂²⋊D₈₃	1	1	yes	characteristic
232	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
233	C₄⋊C₈	—	2	2	no	—
234	C₄⋊C₈	—	2	2	no	—
235	C₄⋊C₈	—	2	2	no	—
236	C₄⋊C₈	—	83	4	no	—
237	C₄⋊C₈	—	166	2	no	—
238	C₄⋊C₈	—	166	2	no	—
239	C₄⋊C₈	—	166	2	no	—
240	C₄⋊C₈	C₂×Dic₈₃	1	4	yes	—
241	C₂²⋊C₈	—	83	4	no	—
242	C₂²⋊C₈	—	166	2	no	—
243	C₂²⋊C₈	—	166	2	no	—
244	C₂²⋊C₈	—	166	2	no	—
245	#97	—	166	2	no	—
246	#97	—	166	2	no	—
247	C₄×C₈	—	166	2	no	—
248	C₄×C₈	—	166	2	no	—
249	C₂⁴	Dic₈₃⋊C₄	1	1	yes	characteristic
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	C₄×Dic₈₃	1	1	yes	characteristic
255	C₂²×C₄	C₄×Dic₈₃	1	1	yes	characteristic
256	C₂²×C₄	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
257	C₂²×C₄	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
258	C₂²×C₄	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
259	C₂²×C₄	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
260	C₂²×C₄	C₂²⋊Dic₈₃	1	1	yes	characteristic
261	C₂²×C₄	C₂²⋊Dic₈₃	1	1	yes	characteristic
262	C₂²×C₄	Dic₈₃⋊C₄	1	1	yes	characteristic
263	C₂²×C₄	Dic₈₃⋊C₄	1	1	yes	characteristic
264	C₂²×C₄	Dic₈₃⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	Dic₈₃⋊C₄	1	1	yes	characteristic
266	C₂²×C₄	Dic₈₃⋊C₄	1	1	yes	characteristic
267	C₂²×C₄	C₄⋊Dic₈₃	1	1	yes	characteristic
268	C₂²×C₄	C₄⋊Dic₈₃	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
271	C₂²×C₄	C₂×Dic₁₆₆	1	1	yes	characteristic
272	M₁₆	—	332	4	no	—
273	M₁₆	—	332	2	no	—
274	M₁₆	—	332	2	no	—
275	C₂×C₈	—	2	4	no	—
276	C₂×C₈	—	4	4	no	—
277	C₂×C₈	—	4	4	no	—
278	C₂×C₈	—	4	4	no	—
279	C₂×C₈	—	166	4	no	—
280	C₂×C₈	—	166	4	no	—
281	C₄²	C₄×Dic₈₃	1	1	yes	characteristic
282	C₄²	C₄×Dic₈₃	1	1	yes	characteristic
283	C₄²	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
284	C₄²	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
285	C₄²	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
286	C₄²	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
287	C₄²	C₂²⋊Dic₈₃	1	1	yes	characteristic
288	C₄²	C₂²⋊Dic₈₃	1	1	yes	characteristic
289	C₄²	Dic₈₃⋊C₄	1	1	yes	characteristic
290	C₄²	Dic₈₃⋊C₄	1	1	yes	characteristic
291	C₄²	C₄⋊Dic₈₃	1	1	yes	characteristic
292	C₄²	C₄⋊Dic₈₃	1	1	yes	characteristic
293	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
294	C₄²	C₂²×Dic₈₃	1	1	yes	characteristic
295	C₄²	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
296	C₄²	C₂×D₃₃₂	1	1	yes	characteristic
297	C₂³	—	2	2	no	—
298	C₂³	—	2	2	no	—
299	C₂³	—	2	2	no	—
300	C₂³	C₈₃⋊#95	1	1	yes	characteristic
301	C₂³	C₈₃⋊#95	1	1	yes	characteristic
302	C₂³	C₂×Dic₈₃⋊C₄	1	1	yes	characteristic
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	C₈₃⋊#95	1	1	yes	characteristic
322	C₂×C₄	C₈₃⋊#95	1	1	yes	characteristic
323	C₂×C₄	C₈₃⋊#95	1	1	yes	characteristic
324	C₂×C₄	C₈₃⋊#95	1	1	yes	characteristic
325	C₂×C₄	C₈₃⋊#95	1	1	yes	characteristic
326	C₂×C₄	C₈₃⋊#95	1	1	yes	characteristic
327	C₂×C₄	#14581728	1	4	yes	—
328	C₂×C₄	C₂×C₄×Dic₈₃	1	1	yes	characteristic
329	C₂×C₄	C₂×(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
330	C₂×C₄	C₂×(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
331	C₂×C₄	C₂×C₂²⋊Dic₈₃	1	1	yes	characteristic
332	C₂×C₄	C₂×Dic₈₃⋊C₄	1	1	yes	characteristic
333	C₂×C₄	C₂×C₄⋊Dic₈₃	1	1	yes	characteristic
334	C₂×C₄	#14581818	1	2	yes	—
335	C₂×C₄	#14581823	1	2	yes	—
336	C₈	—	4	4	no	—
337	C₈	—	332	4	no	—
338	C₈	—	332	4	no	—
339	C₂²	—	2	8	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	#19127466	1	2	yes	—
347	C₂²	#19127473	1	2	yes	—
348	C₂²	C₂×C₈₃⋊#95	1	1	yes	characteristic
349	C₂²	#19127741	1	2	yes	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	#19127466	1	2	yes	—
359	C₄	#19127700	1	2	yes	—
360	C₄	#19127706	1	1	yes	characteristic
361	C₄	#19127710	1	1	yes	characteristic
362	C₄	C₂×#14581728	1	2	yes	—
363	C₂	—	2	2	no	—
364	C₂	—	2	2	no	—
365	C₂	—	2	2	no	—
366	C₂	#24907182	1	1	yes	characteristic
367	C₂	C₂×#19127466	1	1	yes	characteristic
368	C₂	C₂×#19127473	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₈₃)⋊C₄
commutator	C₂×C₄×C₈₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₈₃
Fitting	C₂²×C₄⋊C₈×C₈₃	C₂
socle	C₂²×C₈₃	C₂×#95
prime radical	C₂⁴×C₈₃	C₄⋊C₄
cosocle	C₂×C₄²×C₈₃	C₂³
hypercenter	C₂²×C₄⋊C₈	D₈₃
hypocenter	C₈₃	#8082
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. #24905360	C₂	semidirect
189. C₈₃	#8082	semidirect

Maximal subgroups

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

subgroup	index
#24916096	2
#24905360	2
C₂²×C₄⋊C₈×C₈₃	2
#8082	83