Subgroups — #551×D₁₆₃ #35228029

Order 20864.

1328 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782346	C₂	1	1	yes	maximal, characteristic, complemented
2	#23782345	C₂	1	1	yes	maximal, characteristic, complemented
3	#23782344	C₂	1	2	yes	maximal, complemented
4	#23782343	C₂	1	1	yes	maximal, characteristic, complemented
5	#23782342	C₂	1	2	yes	maximal, complemented
6	#23782341	C₂	1	2	yes	maximal, complemented
7	#23782340	C₂	1	2	yes	maximal, complemented
8	#23782339	C₂	1	2	yes	maximal, complemented
9	#23782338	C₂	1	2	yes	maximal, complemented
10	#126×D₁₆₃	C₂	1	2	yes	maximal, complemented
11	#124×D₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#123×D₁₆₃	C₂	1	2	yes	maximal, complemented
13	#123×D₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊Q₈×D₁₆₃	C₂	1	2	yes	maximal, complemented
15	#120×D₁₆₃	C₂	1	1	yes	maximal, characteristic
16	C₄×D₄×D₁₆₃	C₂	1	2	yes	maximal, complemented
17	#117×D₁₆₃	C₂	1	2	yes	maximal, complemented
18	C₂×C₂²⋊C₄×D₁₆₃	C₂	1	2	yes	maximal, complemented
19	#551×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×D₁₆₃	C₂²	1	1	yes	characteristic
21	C₂×Q₈×D₁₆₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×D₄×D₁₆₃	C₂²	1	2	yes	—
23	C₂×D₄×D₁₆₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₁₆₃	C₂²	1	2	yes	—
25	C₂²×C₄×D₁₆₃	C₂²	1	2	yes	—
26	C₂²×C₄×D₁₆₃	C₂²	1	1	yes	characteristic, complemented
27	#19104730	C₂²	1	2	yes	complemented
28	#19104730	C₂²	1	2	yes	complemented
29	#19104730	C₂²	1	2	yes	complemented
30	#19104729	C₂²	1	2	yes	complemented
31	#19104728	C₂²	1	2	yes	complemented
32	#19104728	C₂²	1	2	yes	complemented
33	#19104728	C₂²	1	2	yes	complemented
34	#19104724	C₂²	1	1	yes	characteristic, complemented
35	#19104723	C₂²	1	1	yes	characteristic, complemented
36	#19104722	C₂²	1	1	yes	characteristic, complemented
37	#19104721	C₂²	1	2	yes	complemented
38	#19104721	C₂²	1	2	yes	complemented
39	#19104720	C₂²	1	2	yes	complemented
40	#19104720	C₂²	1	2	yes	complemented
41	#19104720	C₂²	1	2	yes	complemented
42	#19104719	C₂²	1	2	yes	complemented
43	#19104719	C₂²	1	1	yes	characteristic, complemented
44	#19104718	C₂²	1	2	yes	complemented
45	#19104718	C₂²	1	1	yes	characteristic, complemented
46	#19104717	C₂²	1	2	yes	complemented
47	#19104717	C₂²	1	2	yes	complemented
48	#19104717	C₂²	1	2	yes	complemented
49	#19104716	C₂²	1	1	yes	characteristic, complemented
50	#19104716	C₂²	1	2	yes	complemented
51	#19104715	C₂²	1	2	yes	complemented
52	#19104714	C₂²	1	2	yes	complemented
53	#19104713	C₂²	1	2	yes	complemented
54	#19104713	C₂²	1	2	yes	complemented
55	#19104712	C₂²	1	2	yes	complemented
56	#19104712	C₂²	1	2	yes	complemented
57	#19104711	C₂²	1	2	yes	complemented
58	#19104705	C₂²	1	2	yes	—
59	#19104705	C₂²	1	1	yes	characteristic
60	#19104704	C₂²	1	1	yes	characteristic
61	#19104703	C₂²	1	2	yes	—
62	#19104703	C₂²	1	1	yes	characteristic
63	C₄×D₆₅₂	C₂²	1	2	yes	complemented
64	D₄×Dic₁₆₃	C₂²	1	2	yes	complemented
65	#19104697	C₂²	1	2	yes	complemented
66	C₄×C₂²⋊D₁₆₃	C₂²	1	2	yes	complemented
67	C₄×C₂²⋊D₁₆₃	C₂²	1	2	yes	complemented
68	(C₂²⋊D₁₆₃)⋊C₄	C₂²	1	2	yes	complemented
69	(C₂²⋊D₁₆₃)⋊C₄	C₂²	1	2	yes	complemented
70	#19104694	C₂²	1	2	yes	complemented
71	#19104693	C₂²	1	2	yes	complemented
72	#19104693	C₂²	1	2	yes	complemented
73	#19104692	C₂²	1	2	yes	complemented
74	#19104692	C₂²	1	2	yes	complemented
75	#19104691	C₂²	1	2	yes	complemented
76	#19104691	C₂²	1	2	yes	complemented
77	C₄⋊C₄×D₁₆₃	C₂²	1	2	yes	complemented
78	C₄⋊C₄×D₁₆₃	C₂²	1	2	yes	complemented
79	C₄⋊C₄×D₁₆₃	C₂²	1	2	yes	complemented
80	C₄⋊C₄×D₁₆₃	C₂²	1	2	yes	complemented
81	C₂×C₂²⋊Dic₁₆₃	C₂²	1	2	yes	complemented
82	C₂×(C₂×D₁₆₃)⋊C₄	C₂²	1	2	yes	complemented
83	C₂×(C₂×D₁₆₃)⋊C₄	C₂²	1	2	yes	complemented
84	C₂²⋊C₄×D₁₆₃	C₂²	1	2	yes	—
85	C₂²⋊C₄×D₁₆₃	C₂²	1	1	yes	characteristic
86	C₂²⋊C₄×D₁₆₃	C₂²	1	2	yes	—
87	C₂²⋊C₄×D₁₆₃	C₂²	1	2	yes	—
88	C₂²⋊C₄×D₁₆₃	C₂²	1	2	yes	—
89	C₂²⋊C₄×D₁₆₃	C₂²	1	2	yes	—
90	C₂²⋊C₄×D₁₆₃	C₂²	1	2	yes	complemented
91	C₂²⋊C₄×D₁₆₃	C₂²	1	2	yes	complemented
92	C₂²⋊C₄×D₁₆₃	C₂²	1	2	yes	complemented
93	C₂²⋊C₄×D₁₆₃	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₁₆₃	C₂²	1	1	yes	characteristic, complemented
95	C₂²⋊C₄×D₁₆₃	C₂²	1	2	yes	complemented
96	C₄²×D₁₆₃	C₂²	1	1	yes	characteristic, complemented
97	C₄²×D₁₆₃	C₂²	1	2	yes	complemented
98	#126×C₁₆₃	C₂²	1	2	yes	complemented
99	#124×C₁₆₃	C₂²	1	1	yes	characteristic, complemented
100	#123×C₁₆₃	C₂²	1	1	yes	characteristic, complemented
101	#123×C₁₆₃	C₂²	1	2	yes	complemented
102	C₂²⋊Q₈×C₁₆₃	C₂²	1	2	yes	complemented
103	#120×C₁₆₃	C₂²	1	1	yes	characteristic
104	C₄×D₄×C₁₆₃	C₂²	1	2	yes	complemented
105	#117×C₁₆₃	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊C₄×C₁₆₃	C₂²	1	2	yes	complemented
107	C₂³×D₁₆₃	—	2	8	no	—
108	C₂³×D₁₆₃	—	4	2	no	—
109	C₂³×D₁₆₃	C₂³	1	1	yes	characteristic
110	C₂³×D₁₆₃	C₂³	1	1	yes	characteristic
111	C₂³×D₁₆₃	C₂³	1	1	yes	characteristic
112	C₂³×D₁₆₃	C₂³	1	2	yes	—
113	C₂³×D₁₆₃	C₂³	1	2	yes	—
114	C₂×Dic₃₂₆	C₂³	1	1	yes	characteristic, complemented
115	C₂×Dic₃₂₆	C₂³	1	2	yes	complemented
116	Q₈×D₁₆₃	—	4	2	no	—
117	C₂×D₆₅₂	C₂³	1	2	yes	—
118	C₂×D₆₅₂	C₂³	1	1	yes	characteristic
119	C₂×C₂²⋊D₁₆₃	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₁₆₃	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₁₆₃	C₂³	1	1	yes	characteristic
122	C₂×C₂²⋊D₁₆₃	C₂³	1	1	yes	characteristic
123	D₄×D₁₆₃	—	2	8	no	—
124	D₄×D₁₆₃	—	4	2	no	—
125	C₂²×Dic₁₆₃	C₂³	1	2	yes	—
126	C₂²×Dic₁₆₃	C₂³	1	2	yes	—
127	C₂²×Dic₁₆₃	C₂³	1	1	yes	characteristic, complemented
128	C₂×C₄×D₁₆₃	—	2	8	no	—
129	C₂×C₄×D₁₆₃	—	4	4	no	—
130	C₂×C₄×D₁₆₃	—	4	2	no	—
131	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
132	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
133	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
134	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
135	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
136	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
137	C₂×C₄×D₁₆₃	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
139	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
140	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
141	C₂×C₄×D₁₆₃	C₂³	1	2	yes	complemented
142	C₄⋊Dic₁₆₃	C₂³	1	2	yes	complemented
143	C₄⋊Dic₁₆₃	C₂³	1	2	yes	complemented
144	C₄⋊Dic₁₆₃	C₂³	1	2	yes	complemented
145	C₄⋊Dic₁₆₃	C₂³	1	2	yes	complemented
146	Dic₁₆₃⋊C₄	C₂³	1	2	yes	complemented
147	Dic₁₆₃⋊C₄	C₂³	1	2	yes	complemented
148	Dic₁₆₃⋊C₄	C₂³	1	2	yes	complemented
149	Dic₁₆₃⋊C₄	C₂³	1	2	yes	complemented
150	Dic₁₆₃⋊C₄	C₂³	1	2	yes	complemented
151	Dic₁₆₃⋊C₄	C₂³	1	2	yes	complemented
152	Dic₁₆₃⋊C₄	C₂³	1	2	yes	complemented
153	Dic₁₆₃⋊C₄	C₂³	1	2	yes	complemented
154	C₂²⋊Dic₁₆₃	C₂³	1	2	yes	—
155	C₂²⋊Dic₁₆₃	C₂³	1	2	yes	—
156	C₂²⋊Dic₁₆₃	C₂³	1	2	yes	—
157	C₂²⋊Dic₁₆₃	C₂³	1	2	yes	—
158	C₂²⋊Dic₁₆₃	C₂³	1	2	yes	—
159	C₂²⋊Dic₁₆₃	C₂³	1	1	yes	characteristic
160	C₂²⋊Dic₁₆₃	C₂³	1	2	yes	complemented
161	C₂²⋊Dic₁₆₃	C₂³	1	1	yes	characteristic, complemented
162	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
163	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
164	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
165	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
166	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
167	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
168	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
169	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
170	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
171	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
172	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
173	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	complemented
174	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	complemented
175	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	complemented
176	C₄×Dic₁₆₃	C₂³	1	1	yes	characteristic, complemented
177	C₄×Dic₁₆₃	C₂³	1	2	yes	complemented
178	C₄×Dic₁₆₃	C₂³	1	2	yes	complemented
179	C₄×Dic₁₆₃	C₂³	1	2	yes	complemented
180	C₄×Dic₁₆₃	C₂³	1	2	yes	complemented
181	C₂⁴×C₁₆₃	C₂³	1	1	yes	characteristic
182	C₂×Q₈×C₁₆₃	C₂³	1	1	yes	characteristic, complemented
183	C₂×D₄×C₁₆₃	C₂³	1	2	yes	—
184	C₂×D₄×C₁₆₃	C₂³	1	1	yes	characteristic
185	C₂²×C₄×C₁₆₃	C₂³	1	2	yes	—
186	C₂²×C₄×C₁₆₃	C₂³	1	2	yes	—
187	C₂²×C₄×C₁₆₃	C₂³	1	1	yes	characteristic, complemented
188	C₄⋊C₄×C₁₆₃	C₂³	1	2	yes	complemented
189	C₄⋊C₄×C₁₆₃	C₂³	1	2	yes	complemented
190	C₄⋊C₄×C₁₆₃	C₂³	1	2	yes	complemented
191	C₄⋊C₄×C₁₆₃	C₂³	1	2	yes	complemented
192	C₂²⋊C₄×C₁₆₃	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₁₆₃	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₁₆₃	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₁₆₃	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₁₆₃	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₁₆₃	C₂³	1	1	yes	characteristic
198	C₂²⋊C₄×C₁₆₃	C₂³	1	2	yes	complemented
199	C₂²⋊C₄×C₁₆₃	C₂³	1	1	yes	characteristic, complemented
200	C₄²×C₁₆₃	C₂³	1	1	yes	characteristic, complemented
201	C₄²×C₁₆₃	C₂³	1	2	yes	complemented
202	C₂²×D₁₆₃	—	2	4	no	—
203	C₂²×D₁₆₃	—	2	4	no	—
204	C₂²×D₁₆₃	—	2	4	no	—
205	C₂²×D₁₆₃	—	2	4	no	—
206	C₂²×D₁₆₃	—	2	4	no	—
207	C₂²×D₁₆₃	—	2	4	no	—
208	C₂²×D₁₆₃	—	2	4	no	—
209	C₂²×D₁₆₃	—	2	2	no	—
210	C₂²×D₁₆₃	—	2	2	no	—
211	C₂²×D₁₆₃	—	4	1	no	—
212	C₂²×D₁₆₃	—	4	2	no	—
213	C₂²×D₁₆₃	—	4	16	no	—
214	C₂²×D₁₆₃	#41	1	8	yes	—
215	C₂²×D₁₆₃	C₂⁴	1	1	yes	characteristic
216	C₂²×D₁₆₃	C₂⁴	1	1	yes	characteristic
217	C₂²×D₁₆₃	C₂⁴	1	2	yes	—
218	C₂²×D₁₆₃	C₂⁴	1	1	yes	characteristic
219	Dic₃₂₆	—	4	1	no	—
220	Dic₃₂₆	—	4	2	no	—
221	D₆₅₂	—	2	4	no	—
222	D₆₅₂	—	4	1	no	—
223	C₂²⋊D₁₆₃	—	2	4	no	—
224	C₂²⋊D₁₆₃	—	2	4	no	—
225	C₂²⋊D₁₆₃	—	4	1	no	—
226	C₂²⋊D₁₆₃	—	4	1	no	—
227	C₂×Dic₁₆₃	—	2	4	no	—
228	C₂×Dic₁₆₃	—	4	2	no	—
229	C₂×Dic₁₆₃	—	4	1	no	—
230	C₂×Dic₁₆₃	C₂⁴	1	2	yes	—
231	C₂×Dic₁₆₃	C₂⁴	1	2	yes	—
232	C₂×Dic₁₆₃	C₂⁴	1	2	yes	—
233	C₂×Dic₁₆₃	C₂⁴	1	1	yes	characteristic
234	C₂×Dic₁₆₃	C₂⁴	1	2	yes	—
235	C₂×Dic₁₆₃	C₂⁴	1	2	yes	—
236	C₄×D₁₆₃	—	2	4	no	—
237	C₄×D₁₆₃	—	2	4	no	—
238	C₄×D₁₆₃	—	2	4	no	—
239	C₄×D₁₆₃	—	2	4	no	—
240	C₄×D₁₆₃	—	2	4	no	—
241	C₄×D₁₆₃	—	2	4	no	—
242	C₄×D₁₆₃	—	2	4	no	—
243	C₄×D₁₆₃	—	2	2	no	—
244	C₄×D₁₆₃	—	4	2	no	—
245	C₄×D₁₆₃	—	4	2	no	—
246	C₄×D₁₆₃	—	4	2	no	—
247	C₂³×C₁₆₃	—	2	4	no	—
248	C₂³×C₁₆₃	—	4	1	no	—
249	C₂³×C₁₆₃	C₂⁴	1	1	yes	characteristic
250	C₂³×C₁₆₃	C₂⁴	1	1	yes	characteristic
251	C₂³×C₁₆₃	C₂⁴	1	2	yes	—
252	Q₈×C₁₆₃	—	4	1	no	—
253	D₄×C₁₆₃	—	2	4	no	—
254	D₄×C₁₆₃	—	4	1	no	—
255	C₂×C₄×C₁₆₃	—	2	4	no	—
256	C₂×C₄×C₁₆₃	—	4	2	no	—
257	C₂×C₄×C₁₆₃	—	4	1	no	—
258	C₂×C₄×C₁₆₃	C₂⁴	1	2	yes	—
259	C₂×C₄×C₁₆₃	C₂⁴	1	2	yes	—
260	C₂×C₄×C₁₆₃	C₂⁴	1	2	yes	—
261	C₂×C₄×C₁₆₃	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₁₆₃	C₂⁴	1	2	yes	—
263	C₂×C₄×C₁₆₃	C₂⁴	1	2	yes	—
264	C₂²×C₁₆₃	—	2	2	no	—
265	C₂²×C₁₆₃	—	2	2	no	—
266	C₂²×C₁₆₃	—	2	2	no	—
267	C₂²×C₁₆₃	—	2	2	no	—
268	C₂²×C₁₆₃	—	2	1	no	—
269	C₂²×C₁₆₃	—	2	1	no	—
270	C₂²×C₁₆₃	—	4	4	no	—
271	C₂²×C₁₆₃	C₂×#41	1	4	yes	—
272	C₂²×C₁₆₃	C₂⁵	1	1	yes	characteristic
273	C₂×D₁₆₃	—	2	2	no	—
274	C₂×D₁₆₃	—	2	2	no	—
275	C₂×D₁₆₃	—	2	16	no	—
276	C₂×D₁₆₃	—	2	2	no	—
277	C₂×D₁₆₃	—	2	2	no	—
278	C₂×D₁₆₃	—	2	1	no	—
279	C₂×D₁₆₃	—	2	1	no	—
280	C₂×D₁₆₃	—	4	4	no	—
281	C₂×D₁₆₃	—	4	8	no	—
282	C₂×D₁₆₃	—	4	4	no	—
283	C₂×D₁₆₃	—	4	4	no	—
284	C₂×D₁₆₃	C₂×#41	1	4	yes	—
285	C₂×D₁₆₃	C₂×#41	1	4	yes	—
286	C₂×D₁₆₃	H(5,𝔽₂)	1	2	yes	—
287	C₄×C₁₆₃	—	2	2	no	—
288	C₄×C₁₆₃	—	2	2	no	—
289	C₄×C₁₆₃	—	2	2	no	—
290	C₄×C₁₆₃	—	2	2	no	—
291	C₄×C₁₆₃	—	2	2	no	—
292	C₄×C₁₆₃	—	2	1	no	—
293	Dic₁₆₃	—	2	2	no	—
294	Dic₁₆₃	—	2	2	no	—
295	Dic₁₆₃	—	2	2	no	—
296	Dic₁₆₃	—	2	2	no	—
297	Dic₁₆₃	—	2	2	no	—
298	Dic₁₆₃	—	2	1	no	—
299	C₂×C₁₆₃	—	2	4	no	—
300	C₂×C₁₆₃	—	4	1	no	—
301	C₂×C₁₆₃	—	4	1	no	—
302	C₂×C₁₆₃	C₂²×#41	1	2	yes	—
303	C₂×C₁₆₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
304	D₁₆₃	—	2	4	no	—
305	D₁₆₃	—	4	1	no	—
306	D₁₆₃	—	4	1	no	—
307	D₁₆₃	#551	1	4	yes	direct product factor
308	C₁₆₃	C₂×#551	1	1	yes	characteristic, complemented, Sylow
309	C₂×#551	—	163	1	no	maximal, Sylow
310	#551	—	163	2	no	—
311	#551	—	163	1	no	—
312	#551	—	163	2	no	—
313	#551	—	163	1	no	—
314	#551	—	163	2	no	—
315	#551	—	163	1	no	—
316	#551	—	163	2	no	—
317	#551	—	163	2	no	—
318	#551	—	163	2	no	—
319	#551	D₁₆₃	1	1	yes	characteristic, direct product factor
320	C₂×#126	—	163	2	no	—
321	C₂×#124	—	163	1	no	—
322	C₂×#123	—	163	2	no	—
323	C₂×#123	—	163	1	no	—
324	C₂×C₂²⋊Q₈	—	163	2	no	—
325	C₂×#120	—	163	1	no	—
326	C₂×C₄×D₄	—	163	2	no	—
327	C₂×#117	—	163	2	no	—
328	C₂²×C₂²⋊C₄	—	163	2	no	—
329	C₂⁵	—	163	1	no	—
330	C₂²×Q₈	—	163	1	no	—
331	C₂²×D₄	—	163	2	no	—
332	C₂²×D₄	—	163	1	no	—
333	C₂³×C₄	—	163	2	no	—
334	C₂³×C₄	—	163	2	no	—
335	C₂³×C₄	—	163	1	no	—
336	#126	—	163	2	no	—
337	#126	—	163	2	no	—
338	#126	—	163	2	no	—
339	#126	—	163	2	no	—
340	#126	—	163	2	no	—
341	#126	—	163	2	no	—
342	#126	—	163	2	no	—
343	#126	C₂×D₁₆₃	1	2	yes	complemented
344	#124	—	163	1	no	—
345	#124	—	163	1	no	—
346	#124	—	163	2	no	—
347	#124	—	163	2	no	—
348	#124	—	163	1	no	—
349	#124	C₂×D₁₆₃	1	1	yes	characteristic, complemented
350	#123	—	163	2	no	—
351	#123	—	163	1	no	—
352	#123	—	163	2	no	—
353	#123	—	163	1	no	—
354	#123	—	163	2	no	—
355	#123	—	163	2	no	—
356	#123	—	163	2	no	—
357	#123	—	163	2	no	—
358	#123	—	163	2	no	—
359	#123	—	163	2	no	—
360	#123	—	163	2	no	—
361	#123	—	163	1	no	—
362	#123	C₂×D₁₆₃	1	1	yes	characteristic, complemented
363	#123	C₂×D₁₆₃	1	2	yes	complemented
364	C₂²⋊Q₈	—	163	2	no	—
365	C₂²⋊Q₈	—	163	2	no	—
366	C₂²⋊Q₈	—	163	2	no	—
367	C₂²⋊Q₈	—	163	2	no	—
368	C₂²⋊Q₈	—	163	2	no	—
369	C₂²⋊Q₈	—	163	2	no	—
370	C₂²⋊Q₈	—	163	2	no	—
371	C₂²⋊Q₈	C₂×D₁₆₃	1	2	yes	complemented
372	#120	—	163	1	no	—
373	#120	—	163	2	no	—
374	#120	—	163	1	no	—
375	#120	—	163	1	no	—
376	#120	—	163	2	no	—
377	#120	C₂×D₁₆₃	1	1	yes	characteristic
378	C₄×D₄	—	163	2	no	—
379	C₄×D₄	—	163	2	no	—
380	C₄×D₄	—	163	2	no	—
381	C₄×D₄	—	163	2	no	—
382	C₄×D₄	—	163	2	no	—
383	C₄×D₄	—	163	2	no	—
384	C₄×D₄	—	163	2	no	—
385	C₄×D₄	C₂×D₁₆₃	1	2	yes	complemented
386	#117	—	163	2	no	—
387	#117	—	163	2	no	—
388	#117	—	163	2	no	—
389	#117	—	163	2	no	—
390	#117	—	163	2	no	—
391	#117	—	163	2	no	—
392	#117	—	163	2	no	—
393	#117	C₂×D₁₆₃	1	2	yes	complemented
394	C₂×C₄⋊C₄	—	163	2	no	—
395	C₂×C₄⋊C₄	—	163	2	no	—
396	C₂×C₄⋊C₄	—	163	2	no	—
397	C₂×C₄⋊C₄	—	163	2	no	—
398	C₂×C₂²⋊C₄	—	163	2	no	—
399	C₂×C₂²⋊C₄	—	163	2	no	—
400	C₂×C₂²⋊C₄	—	163	2	no	—
401	C₂×C₂²⋊C₄	—	163	2	no	—
402	C₂×C₂²⋊C₄	—	163	2	no	—
403	C₂×C₂²⋊C₄	—	163	2	no	—
404	C₂×C₂²⋊C₄	—	163	2	no	—
405	C₂×C₂²⋊C₄	—	163	2	no	—
406	C₂×C₂²⋊C₄	—	163	2	no	—
407	C₂×C₂²⋊C₄	—	163	2	no	—
408	C₂×C₂²⋊C₄	—	163	2	no	—
409	C₂×C₂²⋊C₄	—	163	2	no	—
410	C₂×C₂²⋊C₄	—	163	1	no	—
411	C₂×C₂²⋊C₄	—	163	2	no	—
412	C₂×C₂²⋊C₄	—	163	1	no	—
413	C₂×C₂²⋊C₄	C₂×D₁₆₃	1	2	yes	complemented
414	C₂×C₄²	—	163	1	no	—
415	C₂×C₄²	—	163	2	no	—
416	C₂⁴	—	326	8	no	—
417	C₂⁴	—	652	2	no	—
418	C₂⁴	—	163	1	no	—
419	C₂⁴	—	163	1	no	—
420	C₂⁴	—	163	1	no	—
421	C₂⁴	—	163	2	no	—
422	C₂⁴	—	163	2	no	—
423	C₂⁴	C₂²×D₁₆₃	1	1	yes	characteristic
424	C₂×Q₈	—	652	2	no	—
425	C₂×Q₈	—	163	2	no	—
426	C₂×Q₈	—	163	1	no	—
427	C₂×Q₈	C₂²×D₁₆₃	1	1	yes	characteristic, complemented
428	C₂×D₄	—	326	8	no	—
429	C₂×D₄	—	652	2	no	—
430	C₂×D₄	—	163	2	no	—
431	C₂×D₄	—	163	2	no	—
432	C₂×D₄	—	163	1	no	—
433	C₂×D₄	—	163	1	no	—
434	C₂×D₄	—	163	2	no	—
435	C₂×D₄	—	163	1	no	—
436	C₂×D₄	C₂²×D₁₆₃	1	2	yes	—
437	C₂×D₄	C₂²×D₁₆₃	1	1	yes	characteristic
438	C₂²×C₄	—	326	8	no	—
439	C₂²×C₄	—	652	4	no	—
440	C₂²×C₄	—	652	2	no	—
441	C₂²×C₄	—	163	2	no	—
442	C₂²×C₄	—	163	2	no	—
443	C₂²×C₄	—	163	2	no	—
444	C₂²×C₄	—	163	2	no	—
445	C₂²×C₄	—	163	1	no	—
446	C₂²×C₄	—	163	2	no	—
447	C₂²×C₄	—	163	2	no	—
448	C₂²×C₄	—	163	2	no	—
449	C₂²×C₄	—	163	2	no	—
450	C₂²×C₄	—	163	2	no	—
451	C₂²×C₄	—	163	1	no	—
452	C₂²×C₄	—	163	2	no	—
453	C₂²×C₄	—	163	2	no	—
454	C₂²×C₄	—	163	2	no	—
455	C₂²×C₄	C₂²×D₁₆₃	1	2	yes	—
456	C₂²×C₄	C₂²×D₁₆₃	1	2	yes	—
457	C₂²×C₄	C₂²×D₁₆₃	1	1	yes	characteristic, complemented
458	C₄⋊C₄	—	163	2	no	—
459	C₄⋊C₄	—	163	2	no	—
460	C₄⋊C₄	—	163	2	no	—
461	C₄⋊C₄	—	163	2	no	—
462	C₄⋊C₄	—	163	2	no	—
463	C₄⋊C₄	—	163	2	no	—
464	C₄⋊C₄	—	163	2	no	—
465	C₄⋊C₄	—	163	2	no	—
466	C₄⋊C₄	—	163	2	no	—
467	C₄⋊C₄	—	163	2	no	—
468	C₄⋊C₄	—	163	2	no	—
469	C₄⋊C₄	—	163	2	no	—
470	C₄⋊C₄	C₂²×D₁₆₃	1	2	yes	complemented
471	C₄⋊C₄	C₂²×D₁₆₃	1	2	yes	complemented
472	C₄⋊C₄	C₂²×D₁₆₃	1	2	yes	complemented
473	C₄⋊C₄	C₂²×D₁₆₃	1	2	yes	complemented
474	C₂²⋊C₄	—	163	2	no	—
475	C₂²⋊C₄	—	163	2	no	—
476	C₂²⋊C₄	—	163	2	no	—
477	C₂²⋊C₄	—	163	2	no	—
478	C₂²⋊C₄	—	163	2	no	—
479	C₂²⋊C₄	—	163	2	no	—
480	C₂²⋊C₄	—	163	1	no	—
481	C₂²⋊C₄	—	163	1	no	—
482	C₂²⋊C₄	—	163	2	no	—
483	C₂²⋊C₄	—	163	2	no	—
484	C₂²⋊C₄	—	163	2	no	—
485	C₂²⋊C₄	—	163	2	no	—
486	C₂²⋊C₄	—	163	2	no	—
487	C₂²⋊C₄	—	163	2	no	—
488	C₂²⋊C₄	—	163	2	no	—
489	C₂²⋊C₄	—	163	2	no	—
490	C₂²⋊C₄	—	163	2	no	—
491	C₂²⋊C₄	—	163	2	no	—
492	C₂²⋊C₄	—	163	2	no	—
493	C₂²⋊C₄	—	163	2	no	—
494	C₂²⋊C₄	—	163	2	no	—
495	C₂²⋊C₄	—	163	2	no	—
496	C₂²⋊C₄	C₂²×D₁₆₃	1	2	yes	—
497	C₂²⋊C₄	C₂²×D₁₆₃	1	2	yes	—
498	C₂²⋊C₄	C₂²×D₁₆₃	1	2	yes	—
499	C₂²⋊C₄	C₂²×D₁₆₃	1	2	yes	—
500	C₂²⋊C₄	C₂²×D₁₆₃	1	2	yes	—
501	C₂²⋊C₄	C₂²×D₁₆₃	1	1	yes	characteristic
502	C₂²⋊C₄	C₂²×D₁₆₃	1	2	yes	complemented
503	C₂²⋊C₄	C₂²×D₁₆₃	1	1	yes	characteristic, complemented
504	C₄²	—	163	1	no	—
505	C₄²	—	163	2	no	—
506	C₄²	—	163	2	no	—
507	C₄²	—	163	2	no	—
508	C₄²	—	163	2	no	—
509	C₄²	C₂²×D₁₆₃	1	1	yes	characteristic, complemented
510	C₄²	C₂²×D₁₆₃	1	2	yes	complemented
511	C₂³	—	2	4	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	326	4	no	—
514	C₂³	—	326	4	no	—
515	C₂³	—	326	2	no	—
516	C₂³	—	326	4	no	—
517	C₂³	—	326	2	no	—
518	C₂³	—	326	4	no	—
519	C₂³	—	326	4	no	—
520	C₂³	—	326	4	no	—
521	C₂³	—	326	4	no	—
522	C₂³	—	652	2	no	—
523	C₂³	—	652	1	no	—
524	C₂³	—	652	16	no	—
525	C₂³	—	163	1	no	—
526	C₂³	—	163	1	no	—
527	C₂³	—	163	8	no	—
528	C₂³	—	163	2	no	—
529	C₂³	—	163	1	no	—
530	C₂³	C₂³×D₁₆₃	1	1	yes	characteristic
531	C₂³	C₂³×D₁₆₃	1	1	yes	characteristic
532	C₂³	C₂³×D₁₆₃	1	2	yes	—
533	Q₈	—	4	1	no	—
534	Q₈	—	652	2	no	—
535	Q₈	—	652	1	no	—
536	D₄	—	2	4	no	—
537	D₄	—	4	1	no	—
538	D₄	—	326	4	no	—
539	D₄	—	326	4	no	—
540	D₄	—	326	4	no	—
541	D₄	—	652	1	no	—
542	D₄	—	652	1	no	—
543	D₄	—	652	1	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	326	4	no	—
548	C₂×C₄	—	326	4	no	—
549	C₂×C₄	—	326	4	no	—
550	C₂×C₄	—	326	4	no	—
551	C₂×C₄	—	326	4	no	—
552	C₂×C₄	—	326	4	no	—
553	C₂×C₄	—	326	4	no	—
554	C₂×C₄	—	326	2	no	—
555	C₂×C₄	—	326	4	no	—
556	C₂×C₄	—	652	2	no	—
557	C₂×C₄	—	652	2	no	—
558	C₂×C₄	—	652	2	no	—
559	C₂×C₄	—	652	1	no	—
560	C₂×C₄	—	652	2	no	—
561	C₂×C₄	—	163	2	no	—
562	C₂×C₄	—	163	2	no	—
563	C₂×C₄	—	163	2	no	—
564	C₂×C₄	—	163	1	no	—
565	C₂×C₄	—	163	2	no	—
566	C₂×C₄	—	163	2	no	—
567	C₂×C₄	C₂³×D₁₆₃	1	2	yes	—
568	C₂×C₄	C₂³×D₁₆₃	1	2	yes	—
569	C₂×C₄	C₂³×D₁₆₃	1	2	yes	—
570	C₂×C₄	C₂³×D₁₆₃	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₁₆₃	1	2	yes	—
572	C₂×C₄	C₂³×D₁₆₃	1	2	yes	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	4	4	no	—
580	C₂²	—	326	16	no	—
581	C₂²	—	326	2	no	—
582	C₂²	—	326	2	no	—
583	C₂²	—	326	2	no	—
584	C₂²	—	326	2	no	—
585	C₂²	—	326	1	no	—
586	C₂²	—	326	1	no	—
587	C₂²	—	652	8	no	—
588	C₂²	—	652	4	no	—
589	C₂²	—	652	4	no	—
590	C₂²	—	652	4	no	—
591	C₂²	—	163	4	no	—
592	C₂²	—	163	4	no	—
593	C₂²	—	163	2	no	—
594	C₂²	#41×D₁₆₃	1	4	yes	—
595	C₂²	C₂⁴×D₁₆₃	1	1	yes	characteristic
596	C₄	—	2	2	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	2	no	—
600	C₄	—	2	2	no	—
601	C₄	—	2	1	no	—
602	C₄	—	326	2	no	—
603	C₄	—	326	2	no	—
604	C₄	—	326	2	no	—
605	C₄	—	326	2	no	—
606	C₄	—	326	2	no	—
607	C₄	—	326	1	no	—
608	C₂	—	2	4	no	—
609	C₂	—	4	1	no	—
610	C₂	—	4	1	no	—
611	C₂	—	326	4	no	—
612	C₂	—	652	1	no	—
613	C₂	—	652	1	no	—
614	C₂	—	163	4	no	—
615	C₂	C₂×#41×D₁₆₃	1	2	yes	—
616	C₂	H(5,𝔽₂)×D₁₆₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₆₃
commutator, socle, cosocle	C₂²×C₁₆₃	C₂⁵
Fitting	#551×C₁₆₃	C₂
prime radical	#120×D₁₆₃	C₂
hypercenter	#551	D₁₆₃
hypocenter	C₁₆₃	C₂×#551
LCS	G ▷ C₂²×C₁₆₃ ▷ C₁₆₃
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. #23782346	C₂	semidirect
2. #23782345	C₂	semidirect
3. #23782344	C₂	semidirect
4. #23782343	C₂	semidirect
5. #23782342	C₂	semidirect
6. #23782341	C₂	semidirect
7. #23782340	C₂	semidirect
8. #23782339	C₂	semidirect
9. #23782338	C₂	semidirect
10. #126×D₁₆₃	C₂	semidirect
11. #124×D₁₆₃	C₂	semidirect
12. #123×D₁₆₃	C₂	semidirect
13. #123×D₁₆₃	C₂	semidirect
14. C₂²⋊Q₈×D₁₆₃	C₂	semidirect
16. C₄×D₄×D₁₆₃	C₂	semidirect
17. #117×D₁₆₃	C₂	semidirect
18. C₂×C₂²⋊C₄×D₁₆₃	C₂	semidirect
19. #551×C₁₆₃	C₂	semidirect
21. C₂×Q₈×D₁₆₃	C₂²	semidirect
26. C₂²×C₄×D₁₆₃	C₂²	semidirect
27. #19104730	C₂²	semidirect
28. #19104730	C₂²	semidirect
29. #19104730	C₂²	semidirect
30. #19104729	C₂²	semidirect
31. #19104728	C₂²	semidirect
32. #19104728	C₂²	semidirect
33. #19104728	C₂²	semidirect
34. #19104724	C₂²	semidirect
35. #19104723	C₂²	semidirect
36. #19104722	C₂²	semidirect
37. #19104721	C₂²	semidirect
38. #19104721	C₂²	semidirect
39. #19104720	C₂²	semidirect
40. #19104720	C₂²	semidirect
41. #19104720	C₂²	semidirect
42. #19104719	C₂²	semidirect
43. #19104719	C₂²	semidirect
44. #19104718	C₂²	semidirect
45. #19104718	C₂²	semidirect
46. #19104717	C₂²	semidirect
47. #19104717	C₂²	semidirect
48. #19104717	C₂²	semidirect
49. #19104716	C₂²	semidirect
50. #19104716	C₂²	semidirect
51. #19104715	C₂²	semidirect
52. #19104714	C₂²	semidirect
53. #19104713	C₂²	semidirect
54. #19104713	C₂²	semidirect
55. #19104712	C₂²	semidirect
56. #19104712	C₂²	semidirect
57. #19104711	C₂²	semidirect
63. C₄×D₆₅₂	C₂²	semidirect
64. D₄×Dic₁₆₃	C₂²	semidirect
65. #19104697	C₂²	semidirect
66. C₄×C₂²⋊D₁₆₃	C₂²	semidirect
67. C₄×C₂²⋊D₁₆₃	C₂²	semidirect
68. (C₂²⋊D₁₆₃)⋊C₄	C₂²	semidirect
69. (C₂²⋊D₁₆₃)⋊C₄	C₂²	semidirect
70. #19104694	C₂²	semidirect
71. #19104693	C₂²	semidirect
72. #19104693	C₂²	semidirect
73. #19104692	C₂²	semidirect
74. #19104692	C₂²	semidirect
75. #19104691	C₂²	semidirect
76. #19104691	C₂²	semidirect
77. C₄⋊C₄×D₁₆₃	C₂²	semidirect
78. C₄⋊C₄×D₁₆₃	C₂²	semidirect
79. C₄⋊C₄×D₁₆₃	C₂²	semidirect
80. C₄⋊C₄×D₁₆₃	C₂²	semidirect
81. C₂×C₂²⋊Dic₁₆₃	C₂²	semidirect
82. C₂×(C₂×D₁₆₃)⋊C₄	C₂²	semidirect
83. C₂×(C₂×D₁₆₃)⋊C₄	C₂²	semidirect
90. C₂²⋊C₄×D₁₆₃	C₂²	semidirect
91. C₂²⋊C₄×D₁₆₃	C₂²	semidirect
92. C₂²⋊C₄×D₁₆₃	C₂²	semidirect
93. C₂²⋊C₄×D₁₆₃	C₂²	semidirect
94. C₂²⋊C₄×D₁₆₃	C₂²	semidirect
95. C₂²⋊C₄×D₁₆₃	C₂²	semidirect
96. C₄²×D₁₆₃	C₂²	semidirect
97. C₄²×D₁₆₃	C₂²	semidirect
98. #126×C₁₆₃	C₂²	semidirect
99. #124×C₁₆₃	C₂²	semidirect
100. #123×C₁₆₃	C₂²	semidirect
101. #123×C₁₆₃	C₂²	semidirect
102. C₂²⋊Q₈×C₁₆₃	C₂²	semidirect
104. C₄×D₄×C₁₆₃	C₂²	semidirect
105. #117×C₁₆₃	C₂²	semidirect
106. C₂×C₂²⋊C₄×C₁₆₃	C₂²	semidirect
114. C₂×Dic₃₂₆	C₂³	semidirect
115. C₂×Dic₃₂₆	C₂³	semidirect
127. C₂²×Dic₁₆₃	C₂³	semidirect
141. C₂×C₄×D₁₆₃	C₂³	semidirect
142. C₄⋊Dic₁₆₃	C₂³	semidirect
143. C₄⋊Dic₁₆₃	C₂³	semidirect
144. C₄⋊Dic₁₆₃	C₂³	semidirect
145. C₄⋊Dic₁₆₃	C₂³	semidirect
146. Dic₁₆₃⋊C₄	C₂³	semidirect
147. Dic₁₆₃⋊C₄	C₂³	semidirect
148. Dic₁₆₃⋊C₄	C₂³	semidirect
149. Dic₁₆₃⋊C₄	C₂³	semidirect
150. Dic₁₆₃⋊C₄	C₂³	semidirect
151. Dic₁₆₃⋊C₄	C₂³	semidirect
152. Dic₁₆₃⋊C₄	C₂³	semidirect
153. Dic₁₆₃⋊C₄	C₂³	semidirect
160. C₂²⋊Dic₁₆₃	C₂³	semidirect
161. C₂²⋊Dic₁₆₃	C₂³	semidirect
173. (C₂×D₁₆₃)⋊C₄	C₂³	semidirect
174. (C₂×D₁₆₃)⋊C₄	C₂³	semidirect
175. (C₂×D₁₆₃)⋊C₄	C₂³	semidirect
176. C₄×Dic₁₆₃	C₂³	semidirect
177. C₄×Dic₁₆₃	C₂³	semidirect
178. C₄×Dic₁₆₃	C₂³	semidirect
179. C₄×Dic₁₆₃	C₂³	semidirect
180. C₄×Dic₁₆₃	C₂³	semidirect
182. C₂×Q₈×C₁₆₃	C₂³	semidirect
187. C₂²×C₄×C₁₆₃	C₂³	semidirect
188. C₄⋊C₄×C₁₆₃	C₂³	semidirect
189. C₄⋊C₄×C₁₆₃	C₂³	semidirect
190. C₄⋊C₄×C₁₆₃	C₂³	semidirect
191. C₄⋊C₄×C₁₆₃	C₂³	semidirect
198. C₂²⋊C₄×C₁₆₃	C₂³	semidirect
199. C₂²⋊C₄×C₁₆₃	C₂³	semidirect
200. C₄²×C₁₆₃	C₂³	semidirect
201. C₄²×C₁₆₃	C₂³	semidirect
307. D₁₆₃	#551	direct (N × H)
308. C₁₆₃	C₂×#551	semidirect
319. #551	D₁₆₃	direct (N × H)
343. #126	C₂×D₁₆₃	semidirect
349. #124	C₂×D₁₆₃	semidirect
362. #123	C₂×D₁₆₃	semidirect
363. #123	C₂×D₁₆₃	semidirect
371. C₂²⋊Q₈	C₂×D₁₆₃	semidirect
385. C₄×D₄	C₂×D₁₆₃	semidirect
393. #117	C₂×D₁₆₃	semidirect
413. C₂×C₂²⋊C₄	C₂×D₁₆₃	semidirect
427. C₂×Q₈	C₂²×D₁₆₃	semidirect
457. C₂²×C₄	C₂²×D₁₆₃	semidirect
470. C₄⋊C₄	C₂²×D₁₆₃	semidirect
471. C₄⋊C₄	C₂²×D₁₆₃	semidirect
472. C₄⋊C₄	C₂²×D₁₆₃	semidirect
473. C₄⋊C₄	C₂²×D₁₆₃	semidirect
502. C₂²⋊C₄	C₂²×D₁₆₃	semidirect
503. C₂²⋊C₄	C₂²×D₁₆₃	semidirect
509. C₄²	C₂²×D₁₆₃	semidirect
510. C₄²	C₂²×D₁₆₃	semidirect

Maximal subgroups

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

subgroup	index
#23782346	2
#23782345	2
#23782344	2
#23782343	2
#23782342	2
#23782341	2
#23782340	2
#23782339	2
#23782338	2
#126×D₁₆₃	2
#124×D₁₆₃	2
#123×D₁₆₃	2
C₂²⋊Q₈×D₁₆₃	2
#120×D₁₆₃	2
C₄×D₄×D₁₆₃	2
#117×D₁₆₃	2
C₂×C₂²⋊C₄×D₁₆₃	2
#551×C₁₆₃	2
C₂×#551	163

Subgroups — #551×D163 #35228029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #551×D₁₆₃ #35228029