Subgroups — #35228581

Order 20864.

1124 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782387	C₂	1	1	yes	maximal, characteristic, complemented
2	#23782370	C₂	1	1	yes	maximal, characteristic, complemented
3	#23782347	C₂	1	2	yes	maximal, complemented
4	#23782344	C₂	1	2	yes	maximal, complemented
5	#23782342	C₂	1	2	yes	maximal, complemented
6	#23782330	C₂	1	1	yes	maximal, characteristic, complemented
7	#23782325	C₂	1	2	yes	maximal, complemented
8	#23782317	C₂	1	1	yes	maximal, characteristic, complemented
9	#23782316	C₂	1	1	yes	maximal, characteristic, complemented
10	#23782311	C₂	1	1	yes	maximal, characteristic, complemented
11	#23782306	C₂	1	1	yes	maximal, characteristic, complemented
12	#23782289	C₂	1	1	yes	maximal, characteristic, complemented
13	#23782288	C₂	1	1	yes	maximal, characteristic, complemented
14	#23782263	C₂	1	2	yes	maximal, complemented
15	#23782261	C₂	1	2	yes	maximal, complemented
16	#23782217	C₂	1	1	yes	maximal, characteristic, complemented
17	#23782195	C₂	1	1	yes	maximal, characteristic, complemented
18	#23782174	C₂	1	2	yes	maximal, complemented
19	C₂²⋊Q₈×D₁₆₃	C₂	1	2	yes	maximal, complemented
20	#23782147	C₂	1	1	yes	maximal, characteristic, complemented
21	#23782146	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#19104697	C₂	1	1	yes	maximal, characteristic, complemented
23	#554×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14579700	C₂²	1	1	yes	characteristic
25	C₂×#14579699	C₂²	1	1	yes	characteristic
26	C₂×#14579699	C₂²	1	2	yes	complemented
27	C₂×Q₈×D₁₆₃	C₂²	1	2	yes	complemented
28	C₂²×D₆₅₂	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₆₃	C₂²	1	2	yes	—
30	#19104734	C₂²	1	1	yes	characteristic, complemented
31	#19104734	C₂²	1	1	yes	characteristic, complemented
32	#19104733	C₂²	1	1	yes	characteristic, complemented
33	#19104730	C₂²	1	1	yes	characteristic, complemented
34	#19104730	C₂²	1	2	yes	complemented
35	#19104730	C₂²	1	2	yes	complemented
36	#19104730	C₂²	1	2	yes	complemented
37	#19104729	C₂²	1	2	yes	complemented
38	#19104728	C₂²	1	1	yes	characteristic, complemented
39	#19104725	C₂²	1	1	yes	characteristic, complemented
40	#19104725	C₂²	1	2	yes	complemented
41	#19104725	C₂²	1	2	yes	complemented
42	#19104724	C₂²	1	1	yes	characteristic
43	#19104724	C₂²	1	2	yes	complemented
44	#19104723	C₂²	1	1	yes	characteristic
45	#19104721	C₂²	1	1	yes	characteristic, complemented
46	#19104721	C₂²	1	2	yes	complemented
47	#19104720	C₂²	1	2	yes	—
48	#19104720	C₂²	1	2	yes	—
49	#19104720	C₂²	1	2	yes	complemented
50	#19104720	C₂²	1	2	yes	complemented
51	#19104720	C₂²	1	2	yes	complemented
52	#19104719	C₂²	1	1	yes	characteristic
53	#19104718	C₂²	1	2	yes	complemented
54	#19104717	C₂²	1	2	yes	complemented
55	#19104717	C₂²	1	2	yes	complemented
56	#19104716	C₂²	1	1	yes	characteristic
57	#19104715	C₂²	1	2	yes	complemented
58	#19104715	C₂²	1	1	yes	characteristic, complemented
59	#19104714	C₂²	1	2	yes	—
60	#19104714	C₂²	1	1	yes	characteristic
61	#19104713	C₂²	1	2	yes	complemented
62	#19104713	C₂²	1	2	yes	complemented
63	#19104713	C₂²	1	2	yes	complemented
64	#19104713	C₂²	1	2	yes	complemented
65	#19104713	C₂²	1	2	yes	complemented
66	#19104712	C₂²	1	1	yes	characteristic
67	#19104712	C₂²	1	2	yes	—
68	#19104711	C₂²	1	2	yes	complemented
69	#19104711	C₂²	1	2	yes	complemented
70	#19104710	C₂²	1	2	yes	—
71	#19104710	C₂²	1	1	yes	characteristic
72	#19104709	C₂²	1	1	yes	characteristic
73	#19104708	C₂²	1	2	yes	—
74	#19104708	C₂²	1	2	yes	complemented
75	#19104707	C₂²	1	1	yes	characteristic
76	#19104705	C₂²	1	2	yes	—
77	#19104703	C₂²	1	2	yes	—
78	Q₈×Dic₁₆₃	C₂²	1	1	yes	characteristic, complemented
79	C₄×Dic₃₂₆	C₂²	1	1	yes	characteristic, complemented
80	#19104700	C₂²	1	1	yes	characteristic, complemented
81	#19104700	C₂²	1	1	yes	characteristic, complemented
82	#19104700	C₂²	1	2	yes	complemented
83	C₄×D₆₅₂	C₂²	1	1	yes	characteristic
84	C₄×D₆₅₂	C₂²	1	2	yes	complemented
85	#19104697	C₂²	1	1	yes	characteristic
86	#19104697	C₂²	1	1	yes	characteristic
87	#19104697	C₂²	1	2	yes	—
88	#19104697	C₂²	1	1	yes	characteristic
89	#19104697	C₂²	1	1	yes	characteristic
90	#19104697	C₂²	1	1	yes	characteristic
91	#19104697	C₂²	1	2	yes	—
92	#19104697	C₂²	1	2	yes	complemented
93	C₄×C₂²⋊D₁₆₃	C₂²	1	2	yes	—
94	C₄×C₂²⋊D₁₆₃	C₂²	1	1	yes	characteristic
95	C₄×C₂²⋊D₁₆₃	C₂²	1	2	yes	complemented
96	C₄×C₂²⋊D₁₆₃	C₂²	1	2	yes	complemented
97	C₄×C₂²⋊D₁₆₃	C₂²	1	1	yes	characteristic, complemented
98	#19104694	C₂²	1	1	yes	characteristic, complemented
99	#19104693	C₂²	1	2	yes	complemented
100	#19104692	C₂²	1	1	yes	characteristic, complemented
101	#19104692	C₂²	1	2	yes	complemented
102	#19104692	C₂²	1	2	yes	complemented
103	#19104691	C₂²	1	2	yes	—
104	C₄⋊C₄×D₁₆₃	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₁₆₃	C₂²	1	2	yes	complemented
106	C₄⋊C₄×D₁₆₃	C₂²	1	1	yes	characteristic, complemented
107	C₄⋊C₄×D₁₆₃	C₂²	1	2	yes	complemented
108	C₂×(C₂×D₁₆₃)⋊C₄	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₁₆₃	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₁₆₃	C₂²	1	2	yes	—
111	C₂×C₄×Dic₁₆₃	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₁₆₃	C₂²	1	1	yes	characteristic, complemented
113	#125×C₁₆₃	C₂²	1	2	yes	complemented
114	C₂²⋊Q₈×C₁₆₃	C₂²	1	2	yes	—
115	C₂²⋊Q₈×C₁₆₃	C₂²	1	1	yes	characteristic
116	C₂²⋊Q₈×C₁₆₃	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₁₆₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₁₆₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₁₆₃	C₂²	1	2	yes	—
120	C₄×D₄×C₁₆₃	C₂²	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₆₃	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₆₃	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₆₃	C₂³	1	2	yes	—
124	#14579700	—	2	4	no	—
125	#14579699	—	2	4	no	—
126	#14579699	—	4	4	no	—
127	C₂×Dic₃₂₆	C₂³	1	1	yes	characteristic
128	C₂×Dic₃₂₆	C₂³	1	2	yes	—
129	C₂×Dic₃₂₆	C₂³	1	1	yes	characteristic
130	C₂×Dic₃₂₆	C₂³	1	2	yes	—
131	Q₈×D₁₆₃	—	4	4	no	—
132	C₂×D₆₅₂	—	2	4	no	—
133	C₂×D₆₅₂	C₂³	1	2	yes	—
134	C₂×D₆₅₂	C₂³	1	1	yes	characteristic
135	C₂×D₆₅₂	C₂³	1	2	yes	—
136	C₂×D₆₅₂	C₂³	1	2	yes	—
137	C₂×D₆₅₂	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₆₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₆₃	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₁₆₃	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₁₆₃	C₂³	1	2	yes	—
142	C₂²×Dic₁₆₃	C₂³	1	1	yes	characteristic
143	C₂²×Dic₁₆₃	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₆₃	—	4	4	no	—
145	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
146	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
147	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
148	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
149	C₂×C₄×D₁₆₃	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
151	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
152	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
153	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
154	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
155	C₄⋊Dic₁₆₃	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₁₆₃	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₁₆₃	C₂³	1	2	yes	—
158	C₄⋊Dic₁₆₃	C₂³	1	2	yes	—
159	C₄⋊Dic₁₆₃	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₁₆₃	C₂³	1	1	yes	characteristic
161	Dic₁₆₃⋊C₄	C₂³	1	1	yes	characteristic
162	Dic₁₆₃⋊C₄	C₂³	1	2	yes	—
163	Dic₁₆₃⋊C₄	C₂³	1	1	yes	characteristic
164	Dic₁₆₃⋊C₄	C₂³	1	2	yes	—
165	Dic₁₆₃⋊C₄	C₂³	1	2	yes	—
166	Dic₁₆₃⋊C₄	C₂³	1	2	yes	—
167	Dic₁₆₃⋊C₄	C₂³	1	2	yes	—
168	Dic₁₆₃⋊C₄	C₂³	1	2	yes	—
169	Dic₁₆₃⋊C₄	C₂³	1	1	yes	characteristic
170	Dic₁₆₃⋊C₄	C₂³	1	1	yes	characteristic
171	Dic₁₆₃⋊C₄	C₂³	1	2	yes	—
172	Dic₁₆₃⋊C₄	C₂³	1	1	yes	characteristic
173	Dic₁₆₃⋊C₄	C₂³	1	2	yes	—
174	Dic₁₆₃⋊C₄	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₁₆₃	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₆₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₆₃	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₆₃	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₆₃	C₂³	1	1	yes	characteristic
180	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₁₆₃)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₁₆₃)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₁₆₃)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₁₆₃)⋊C₄	C₂³	1	1	yes	characteristic
197	C₄×Dic₁₆₃	C₂³	1	1	yes	characteristic
198	C₄×Dic₁₆₃	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₆₃	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₆₃	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₆₃	C₂³	1	2	yes	—
202	C₄×Dic₁₆₃	C₂³	1	2	yes	—
203	C₄×Dic₁₆₃	C₂³	1	2	yes	—
204	C₄×Dic₁₆₃	C₂³	1	1	yes	characteristic
205	C₂×Q₈×C₁₆₃	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₁₆₃	C₂³	1	2	yes	—
207	C₂×D₄×C₁₆₃	C₂³	1	1	yes	characteristic
208	C₂²×C₄×C₁₆₃	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₁₆₃	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₆₃	C₂³	1	2	yes	—
211	C₂²×C₄×C₁₆₃	C₂³	1	2	yes	—
212	C₄⋊C₄×C₁₆₃	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₁₆₃	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₆₃	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₁₆₃	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₆₃	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₆₃	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₁₆₃	C₂³	1	2	yes	—
219	C₄⋊C₄×C₁₆₃	C₂³	1	2	yes	—
220	C₄⋊C₄×C₁₆₃	C₂³	1	2	yes	—
221	C₄⋊C₄×C₁₆₃	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₁₆₃	C₂³	1	1	yes	characteristic
223	C₂²⋊C₄×C₁₆₃	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₁₆₃	C₂³	1	1	yes	characteristic
225	C₂²⋊C₄×C₁₆₃	C₂³	1	2	yes	—
226	C₄²×C₁₆₃	C₂³	1	2	yes	—
227	C₄²×C₁₆₃	C₂³	1	1	yes	characteristic
228	C₂²×D₁₆₃	—	2	4	no	—
229	C₂²×D₁₆₃	—	2	4	no	—
230	C₂²×D₁₆₃	—	4	2	no	—
231	C₂²×D₁₆₃	C₂⁴	1	2	yes	—
232	C₂²×D₁₆₃	C₂⁴	1	1	yes	characteristic
233	C₂²×D₁₆₃	C₂⁴	1	2	yes	—
234	Dic₃₂₆	—	2	2	no	—
235	Dic₃₂₆	—	2	2	no	—
236	Dic₃₂₆	—	2	4	no	—
237	Dic₃₂₆	—	4	2	no	—
238	D₆₅₂	—	2	4	no	—
239	D₆₅₂	—	2	4	no	—
240	D₆₅₂	—	2	2	no	—
241	D₆₅₂	—	4	2	no	—
242	D₆₅₂	#41	1	4	yes	complemented
243	C₂²⋊D₁₆₃	—	2	2	no	—
244	C₂²⋊D₁₆₃	—	2	4	no	—
245	C₂²⋊D₁₆₃	—	2	2	no	—
246	C₂²⋊D₁₆₃	—	4	2	no	—
247	C₂×Dic₁₆₃	—	2	2	no	—
248	C₂×Dic₁₆₃	—	2	2	no	—
249	C₂×Dic₁₆₃	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₁₆₃	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₆₃	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₁₆₃	C₂⁴	1	2	yes	—
253	C₂×Dic₁₆₃	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₁₆₃	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₆₃	C₂⁴	1	2	yes	—
256	C₂×Dic₁₆₃	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₆₃	C₂⁴	1	1	yes	characteristic
258	C₄×D₁₆₃	—	2	4	no	—
259	C₄×D₁₆₃	—	2	4	no	—
260	C₄×D₁₆₃	—	2	2	no	—
261	C₄×D₁₆₃	—	2	4	no	—
262	C₄×D₁₆₃	—	2	4	no	—
263	C₄×D₁₆₃	—	4	2	no	—
264	C₄×D₁₆₃	—	4	2	no	—
265	C₄×D₁₆₃	—	4	2	no	—
266	C₄×D₁₆₃	—	4	2	no	—
267	C₄×D₁₆₃	—	4	2	no	—
268	C₂³×C₁₆₃	C₂⁴	1	1	yes	characteristic
269	C₂³×C₁₆₃	C₂⁴	1	1	yes	characteristic
270	Q₈×C₁₆₃	—	2	2	no	—
271	Q₈×C₁₆₃	—	4	2	no	—
272	D₄×C₁₆₃	—	2	2	no	—
273	C₂×C₄×C₁₆₃	—	2	2	no	—
274	C₂×C₄×C₁₆₃	—	2	2	no	—
275	C₂×C₄×C₁₆₃	—	4	2	no	—
276	C₂×C₄×C₁₆₃	—	4	2	no	—
277	C₂×C₄×C₁₆₃	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₁₆₃	C₂⁴	1	2	yes	—
279	C₂×C₄×C₁₆₃	C₂⁴	1	1	yes	characteristic
280	C₂×C₄×C₁₆₃	C₂⁴	1	2	yes	—
281	C₂×C₄×C₁₆₃	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₁₆₃	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₁₆₃	C₂⁴	1	2	yes	—
284	C₂×C₄×C₁₆₃	C₂⁴	1	2	yes	—
285	C₂×C₄×C₁₆₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₁₆₃	—	2	1	no	—
287	C₂²×C₁₆₃	—	2	1	no	—
288	C₂²×C₁₆₃	—	2	1	no	—
289	C₂²×C₁₆₃	—	2	1	no	—
290	C₂²×C₁₆₃	—	2	1	no	—
291	C₂²×C₁₆₃	2₋¹⁺⁴	1	2	yes	—
292	C₂²×C₁₆₃	C₂⁵	1	1	yes	characteristic
293	C₂×D₁₆₃	—	2	2	no	—
294	C₂×D₁₆₃	—	2	2	no	—
295	C₂×D₁₆₃	—	2	1	no	—
296	C₂×D₁₆₃	—	2	2	no	—
297	C₂×D₁₆₃	—	2	2	no	—
298	C₂×D₁₆₃	—	2	1	no	—
299	C₂×D₁₆₃	—	2	1	no	—
300	C₂×D₁₆₃	—	2	2	no	—
301	C₂×D₁₆₃	—	4	8	no	—
302	C₂×D₁₆₃	C₂×#41	1	4	yes	—
303	C₄×C₁₆₃	—	2	1	no	—
304	C₄×C₁₆₃	—	2	1	no	—
305	C₄×C₁₆₃	—	2	2	no	—
306	C₄×C₁₆₃	—	2	2	no	—
307	C₄×C₁₆₃	—	2	2	no	—
308	C₄×C₁₆₃	—	2	2	no	—
309	C₄×C₁₆₃	—	2	1	no	—
310	C₄×C₁₆₃	—	2	1	no	—
311	C₄×C₁₆₃	C₂×#41	1	2	yes	—
312	Dic₁₆₃	—	2	1	no	—
313	Dic₁₆₃	—	2	2	no	—
314	Dic₁₆₃	—	2	1	no	—
315	Dic₁₆₃	—	2	2	no	—
316	Dic₁₆₃	—	2	1	no	—
317	Dic₁₆₃	—	2	1	no	—
318	Dic₁₆₃	—	2	1	no	—
319	Dic₁₆₃	—	2	1	no	—
320	Dic₁₆₃	H(5,𝔽₂)	1	2	yes	—
321	C₂×C₁₆₃	—	2	2	no	—
322	C₂×C₁₆₃	—	4	1	no	—
323	C₂×C₁₆₃	C₂²×#41	1	1	yes	characteristic
324	C₂×C₁₆₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
325	C₂×C₁₆₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
326	D₁₆₃	—	2	4	no	—
327	D₁₆₃	—	4	1	no	—
328	D₁₆₃	—	4	2	no	—
329	C₁₆₃	#3520	1	1	yes	characteristic, complemented, Sylow
330	#3520	—	163	1	no	maximal, Sylow
331	#556	—	163	1	no	—
332	#554	—	163	1	no	—
333	#554	D₁₆₃	1	1	yes	characteristic, complemented
334	#552	—	163	2	no	—
335	#551	—	163	2	no	—
336	#551	—	163	2	no	—
337	D₄×Q₈	—	163	1	no	—
338	#548	—	163	2	no	—
339	#547	—	163	1	no	—
340	#547	—	163	1	no	—
341	#546	—	163	1	no	—
342	#546	—	163	1	no	—
343	#542	—	163	1	no	—
344	#542	—	163	1	no	—
345	#539	—	163	2	no	—
346	#539	—	163	2	no	—
347	#533	—	163	1	no	—
348	#529	—	163	1	no	—
349	#525	—	163	2	no	—
350	C₂×C₂²⋊Q₈	—	163	2	no	—
351	#520	—	163	1	no	—
352	#520	—	163	1	no	—
353	C₂×C₄×D₄	—	163	1	no	—
354	C₂×#41	—	163	1	no	—
355	C₂×#41	—	163	1	no	—
356	C₂×#41	—	163	2	no	—
357	C₂²×Q₈	—	163	2	no	—
358	C₂²×D₄	—	163	1	no	—
359	C₂³×C₄	—	163	2	no	—
360	C₄⋊Q₈	—	163	1	no	—
361	C₄⋊Q₈	—	163	1	no	—
362	C₄⋊Q₈	—	163	1	no	—
363	C₄⋊Q₈	C₂×D₁₆₃	1	1	yes	characteristic, complemented
364	#126	—	163	1	no	—
365	#126	—	163	2	no	—
366	#126	—	163	2	no	—
367	#126	—	163	2	no	—
368	#126	—	163	1	no	—
369	#126	—	163	2	no	—
370	#125	—	163	1	no	—
371	#125	—	163	2	no	—
372	#125	—	163	2	no	—
373	#125	C₂×D₁₆₃	1	2	yes	complemented
374	#124	—	163	1	no	—
375	#124	—	163	2	no	—
376	#124	—	163	1	no	—
377	#124	—	163	2	no	—
378	#124	—	163	1	no	—
379	#123	—	163	1	no	—
380	#123	—	163	2	no	—
381	#123	—	163	2	no	—
382	#123	—	163	2	no	—
383	#123	—	163	2	no	—
384	#123	—	163	2	no	—
385	#123	—	163	2	no	—
386	#123	—	163	2	no	—
387	#123	—	163	1	no	—
388	#123	—	163	2	no	—
389	C₂²⋊Q₈	—	163	2	no	—
390	C₂²⋊Q₈	—	163	2	no	—
391	C₂²⋊Q₈	—	163	2	no	—
392	C₂²⋊Q₈	—	163	1	no	—
393	C₂²⋊Q₈	—	163	2	no	—
394	C₂²⋊Q₈	—	163	2	no	—
395	C₂²⋊Q₈	—	163	2	no	—
396	C₂²⋊Q₈	—	163	2	no	—
397	C₂²⋊Q₈	—	163	2	no	—
398	C₂²⋊Q₈	—	163	2	no	—
399	C₂²⋊Q₈	—	163	1	no	—
400	C₂²⋊Q₈	—	163	1	no	—
401	C₂²⋊Q₈	—	163	2	no	—
402	C₂²⋊Q₈	C₂×D₁₆₃	1	2	yes	—
403	C₂²⋊Q₈	C₂×D₁₆₃	1	1	yes	characteristic
404	C₂²⋊Q₈	C₂×D₁₆₃	1	2	yes	complemented
405	C₂²⋊Q₈	C₂×D₁₆₃	1	1	yes	characteristic, complemented
406	#121	—	163	1	no	—
407	#121	—	163	1	no	—
408	#121	—	163	2	no	—
409	#121	—	163	1	no	—
410	#121	—	163	2	no	—
411	#121	—	163	2	no	—
412	#120	—	163	2	no	—
413	#120	—	163	2	no	—
414	C₄×Q₈	—	163	1	no	—
415	C₄×Q₈	—	163	1	no	—
416	C₄×Q₈	—	163	1	no	—
417	C₄×Q₈	—	163	2	no	—
418	C₄×Q₈	—	163	1	no	—
419	C₄×Q₈	C₂×D₁₆₃	1	1	yes	characteristic, complemented
420	C₄×D₄	—	163	2	no	—
421	C₄×D₄	—	163	2	no	—
422	C₄×D₄	—	163	2	no	—
423	C₄×D₄	—	163	1	no	—
424	C₄×D₄	—	163	1	no	—
425	C₄×D₄	—	163	1	no	—
426	C₄×D₄	—	163	2	no	—
427	C₄×D₄	—	163	1	no	—
428	C₄×D₄	—	163	1	no	—
429	C₄×D₄	—	163	1	no	—
430	C₄×D₄	—	163	2	no	—
431	C₄×D₄	—	163	1	no	—
432	C₄×D₄	—	163	2	no	—
433	C₄×D₄	—	163	2	no	—
434	C₄×D₄	—	163	1	no	—
435	C₄×D₄	C₂×D₁₆₃	1	2	yes	—
436	C₄×D₄	C₂×D₁₆₃	1	1	yes	characteristic
437	#117	—	163	1	no	—
438	#117	—	163	2	no	—
439	#117	—	163	2	no	—
440	#117	—	163	1	no	—
441	#117	—	163	2	no	—
442	#117	—	163	2	no	—
443	C₂×C₄⋊C₄	—	163	2	no	—
444	C₂×C₄⋊C₄	—	163	2	no	—
445	C₂×C₄⋊C₄	—	163	1	no	—
446	C₂×C₄⋊C₄	—	163	2	no	—
447	C₂×C₄⋊C₄	C₂×D₁₆₃	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂×D₁₆₃	1	1	yes	characteristic, complemented
449	C₂×C₂²⋊C₄	—	163	2	no	—
450	C₂×C₂²⋊C₄	—	163	2	no	—
451	C₂×C₂²⋊C₄	—	163	2	no	—
452	C₂×C₄²	—	163	1	no	—
453	C₂⁴	—	163	2	no	—
454	#41	—	326	4	no	—
455	#41	—	326	4	no	—
456	#41	—	652	4	no	—
457	C₂×Q₈	—	652	4	no	—
458	C₂×Q₈	—	163	1	no	—
459	C₂×Q₈	—	163	1	no	—
460	C₂×Q₈	—	163	2	no	—
461	C₂×Q₈	—	163	2	no	—
462	C₂×Q₈	C₂²×D₁₆₃	1	1	yes	characteristic
463	C₂×Q₈	C₂²×D₁₆₃	1	2	yes	—
464	C₂×D₄	—	326	4	no	—
465	C₂×D₄	—	163	1	no	—
466	C₂×D₄	—	163	2	no	—
467	C₂×D₄	—	163	1	no	—
468	C₂×D₄	—	163	2	no	—
469	C₂×D₄	—	163	2	no	—
470	C₂×D₄	—	163	2	no	—
471	C₂×D₄	—	163	1	no	—
472	C₂×D₄	—	163	2	no	—
473	C₂×D₄	—	163	1	no	—
474	C₂×D₄	C₂²×D₁₆₃	1	1	yes	characteristic
475	C₂²×C₄	—	652	4	no	—
476	C₂²×C₄	—	163	1	no	—
477	C₂²×C₄	—	163	1	no	—
478	C₂²×C₄	—	163	2	no	—
479	C₂²×C₄	—	163	2	no	—
480	C₂²×C₄	—	163	1	no	—
481	C₂²×C₄	—	163	2	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	C₂²×D₁₆₃	1	1	yes	characteristic
489	C₂²×C₄	C₂²×D₁₆₃	1	1	yes	characteristic
490	C₂²×C₄	C₂²×D₁₆₃	1	2	yes	—
491	C₂²×C₄	C₂²×D₁₆₃	1	2	yes	—
492	C₄⋊C₄	—	163	1	no	—
493	C₄⋊C₄	—	163	1	no	—
494	C₄⋊C₄	—	163	2	no	—
495	C₄⋊C₄	—	163	1	no	—
496	C₄⋊C₄	—	163	2	no	—
497	C₄⋊C₄	—	163	1	no	—
498	C₄⋊C₄	—	163	2	no	—
499	C₄⋊C₄	—	163	2	no	—
500	C₄⋊C₄	—	163	2	no	—
501	C₄⋊C₄	—	163	2	no	—
502	C₄⋊C₄	—	163	1	no	—
503	C₄⋊C₄	—	163	1	no	—
504	C₄⋊C₄	—	163	1	no	—
505	C₄⋊C₄	—	163	2	no	—
506	C₄⋊C₄	—	163	2	no	—
507	C₄⋊C₄	—	163	2	no	—
508	C₄⋊C₄	—	163	1	no	—
509	C₄⋊C₄	—	163	2	no	—
510	C₄⋊C₄	—	163	1	no	—
511	C₄⋊C₄	—	163	1	no	—
512	C₄⋊C₄	C₂²×D₁₆₃	1	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₁₆₃	1	2	yes	—
514	C₄⋊C₄	C₂²×D₁₆₃	1	2	yes	—
515	C₄⋊C₄	C₂²×D₁₆₃	1	2	yes	—
516	C₄⋊C₄	C₂²×D₁₆₃	1	2	yes	—
517	C₄⋊C₄	C₂²×D₁₆₃	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₁₆₃	1	1	yes	characteristic
519	C₄⋊C₄	C₂²×D₁₆₃	1	2	yes	—
520	C₄⋊C₄	C₂²×D₁₆₃	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₁₆₃	1	2	yes	—
522	C₂²⋊C₄	—	163	1	no	—
523	C₂²⋊C₄	—	163	2	no	—
524	C₂²⋊C₄	—	163	1	no	—
525	C₂²⋊C₄	—	163	1	no	—
526	C₂²⋊C₄	—	163	1	no	—
527	C₂²⋊C₄	—	163	2	no	—
528	C₂²⋊C₄	—	163	2	no	—
529	C₂²⋊C₄	—	163	2	no	—
530	C₂²⋊C₄	—	163	2	no	—
531	C₂²⋊C₄	—	163	2	no	—
532	C₂²⋊C₄	—	163	2	no	—
533	C₂²⋊C₄	—	163	2	no	—
534	C₂²⋊C₄	—	163	2	no	—
535	C₂²⋊C₄	—	163	2	no	—
536	C₂²⋊C₄	—	163	2	no	—
537	C₂²⋊C₄	—	163	1	no	—
538	C₂²⋊C₄	—	163	1	no	—
539	C₂²⋊C₄	—	163	2	no	—
540	C₂²⋊C₄	—	163	2	no	—
541	C₂²⋊C₄	—	163	1	no	—
542	C₂²⋊C₄	—	163	2	no	—
543	C₂²⋊C₄	—	163	1	no	—
544	C₂²⋊C₄	C₂²×D₁₆₃	1	1	yes	characteristic
545	C₂²⋊C₄	C₂²×D₁₆₃	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₁₆₃	1	1	yes	characteristic
547	C₂²⋊C₄	C₂²×D₁₆₃	1	2	yes	—
548	C₄²	—	163	1	no	—
549	C₄²	—	163	1	no	—
550	C₄²	—	163	1	no	—
551	C₄²	—	163	1	no	—
552	C₄²	—	163	2	no	—
553	C₄²	—	163	2	no	—
554	C₄²	—	163	2	no	—
555	C₄²	—	163	1	no	—
556	C₄²	C₂²×D₁₆₃	1	2	yes	—
557	C₄²	C₂²×D₁₆₃	1	1	yes	characteristic
558	C₂³	—	326	4	no	—
559	C₂³	—	326	4	no	—
560	C₂³	—	652	2	no	—
561	C₂³	—	163	2	no	—
562	C₂³	—	163	1	no	—
563	C₂³	—	163	2	no	—
564	C₂³	C₂³×D₁₆₃	1	1	yes	characteristic
565	C₂³	C₂³×D₁₆₃	1	1	yes	characteristic
566	Q₈	—	2	2	no	—
567	Q₈	—	4	2	no	—
568	Q₈	—	326	2	no	—
569	Q₈	—	326	4	no	—
570	Q₈	—	326	2	no	—
571	Q₈	—	652	2	no	—
572	D₄	—	2	2	no	—
573	D₄	—	326	4	no	—
574	D₄	—	326	4	no	—
575	D₄	—	326	4	no	—
576	D₄	—	326	2	no	—
577	D₄	—	326	2	no	—
578	D₄	—	326	2	no	—
579	D₄	—	652	2	no	—
580	D₄	—	652	2	no	—
581	D₄	—	163	4	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	326	4	no	—
587	C₂×C₄	—	326	4	no	—
588	C₂×C₄	—	326	4	no	—
589	C₂×C₄	—	326	4	no	—
590	C₂×C₄	—	326	2	no	—
591	C₂×C₄	—	326	2	no	—
592	C₂×C₄	—	326	2	no	—
593	C₂×C₄	—	652	2	no	—
594	C₂×C₄	—	652	2	no	—
595	C₂×C₄	—	652	2	no	—
596	C₂×C₄	—	652	2	no	—
597	C₂×C₄	—	652	2	no	—
598	C₂×C₄	—	163	1	no	—
599	C₂×C₄	—	163	1	no	—
600	C₂×C₄	—	163	1	no	—
601	C₂×C₄	—	163	2	no	—
602	C₂×C₄	—	163	1	no	—
603	C₂×C₄	—	163	1	no	—
604	C₂×C₄	—	163	2	no	—
605	C₂×C₄	—	163	1	no	—
606	C₂×C₄	—	163	1	no	—
607	C₂×C₄	C₂³×D₁₆₃	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₁₆₃	1	2	yes	—
609	C₂×C₄	C₂³×D₁₆₃	1	2	yes	—
610	C₂×C₄	C₂³×D₁₆₃	1	2	yes	—
611	C₂×C₄	C₂³×D₁₆₃	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₁₆₃	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₁₆₃	1	1	yes	characteristic
614	C₂×C₄	C₂³×D₁₆₃	1	2	yes	—
615	C₂×C₄	C₂³×D₁₆₃	1	1	yes	characteristic
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	326	2	no	—
622	C₂²	—	326	2	no	—
623	C₂²	—	326	1	no	—
624	C₂²	—	326	2	no	—
625	C₂²	—	326	2	no	—
626	C₂²	—	326	1	no	—
627	C₂²	—	326	1	no	—
628	C₂²	—	326	2	no	—
629	C₂²	—	652	8	no	—
630	C₂²	—	163	4	no	—
631	C₂²	#19104783	1	2	yes	—
632	C₂²	C₂⁴×D₁₆₃	1	1	yes	characteristic
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	2	no	—
639	C₄	—	2	1	no	—
640	C₄	—	2	1	no	—
641	C₄	—	326	1	no	—
642	C₄	—	326	2	no	—
643	C₄	—	326	1	no	—
644	C₄	—	326	2	no	—
645	C₄	—	326	1	no	—
646	C₄	—	326	1	no	—
647	C₄	—	326	1	no	—
648	C₄	—	326	1	no	—
649	C₄	—	163	2	no	—
650	C₄	#41×D₁₆₃	1	2	yes	—
651	C₂	—	2	2	no	—
652	C₂	—	4	1	no	—
653	C₂	—	326	4	no	—
654	C₂	—	652	2	no	—
655	C₂	—	652	1	no	—
656	C₂	C₂×#41×D₁₆₃	1	1	yes	characteristic
657	C₂	H(5,𝔽₂)×D₁₆₃	1	1	yes	characteristic
658	C₂	C₂×#19104783	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₆₃
commutator, socle, cosocle	C₂²×C₁₆₃	C₂⁵
Fitting	#554×C₁₆₃	C₂
hypercenter	#554	D₁₆₃
hypocenter	C₁₆₃	#3520
LCS	G ▷ C₂²×C₁₆₃ ▷ C₁₆₃
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #23782387	C₂	semidirect
2. #23782370	C₂	semidirect
3. #23782347	C₂	semidirect
4. #23782344	C₂	semidirect
5. #23782342	C₂	semidirect
6. #23782330	C₂	semidirect
7. #23782325	C₂	semidirect
8. #23782317	C₂	semidirect
9. #23782316	C₂	semidirect
10. #23782311	C₂	semidirect
11. #23782306	C₂	semidirect
12. #23782289	C₂	semidirect
13. #23782288	C₂	semidirect
14. #23782263	C₂	semidirect
15. #23782261	C₂	semidirect
16. #23782217	C₂	semidirect
17. #23782195	C₂	semidirect
18. #23782174	C₂	semidirect
19. C₂²⋊Q₈×D₁₆₃	C₂	semidirect
20. #23782147	C₂	semidirect
21. #23782146	C₂	semidirect
22. C₂×#19104697	C₂	semidirect
23. #554×C₁₆₃	C₂	semidirect
26. C₂×#14579699	C₂²	semidirect
27. C₂×Q₈×D₁₆₃	C₂²	semidirect
30. #19104734	C₂²	semidirect
31. #19104734	C₂²	semidirect
32. #19104733	C₂²	semidirect
33. #19104730	C₂²	semidirect
34. #19104730	C₂²	semidirect
35. #19104730	C₂²	semidirect
36. #19104730	C₂²	semidirect
37. #19104729	C₂²	semidirect
38. #19104728	C₂²	semidirect
39. #19104725	C₂²	semidirect
40. #19104725	C₂²	semidirect
41. #19104725	C₂²	semidirect
43. #19104724	C₂²	semidirect
45. #19104721	C₂²	semidirect
46. #19104721	C₂²	semidirect
49. #19104720	C₂²	semidirect
50. #19104720	C₂²	semidirect
51. #19104720	C₂²	semidirect
53. #19104718	C₂²	semidirect
54. #19104717	C₂²	semidirect
55. #19104717	C₂²	semidirect
57. #19104715	C₂²	semidirect
58. #19104715	C₂²	semidirect
61. #19104713	C₂²	semidirect
62. #19104713	C₂²	semidirect
63. #19104713	C₂²	semidirect
64. #19104713	C₂²	semidirect
65. #19104713	C₂²	semidirect
68. #19104711	C₂²	semidirect
69. #19104711	C₂²	semidirect
74. #19104708	C₂²	semidirect
78. Q₈×Dic₁₆₃	C₂²	semidirect
79. C₄×Dic₃₂₆	C₂²	semidirect
80. #19104700	C₂²	semidirect
81. #19104700	C₂²	semidirect
82. #19104700	C₂²	semidirect
84. C₄×D₆₅₂	C₂²	semidirect
92. #19104697	C₂²	semidirect
95. C₄×C₂²⋊D₁₆₃	C₂²	semidirect
96. C₄×C₂²⋊D₁₆₃	C₂²	semidirect
97. C₄×C₂²⋊D₁₆₃	C₂²	semidirect
98. #19104694	C₂²	semidirect
99. #19104693	C₂²	semidirect
100. #19104692	C₂²	semidirect
101. #19104692	C₂²	semidirect
102. #19104692	C₂²	semidirect
104. C₄⋊C₄×D₁₆₃	C₂²	semidirect
105. C₄⋊C₄×D₁₆₃	C₂²	semidirect
106. C₄⋊C₄×D₁₆₃	C₂²	semidirect
107. C₄⋊C₄×D₁₆₃	C₂²	semidirect
112. C₄⋊Q₈×C₁₆₃	C₂²	semidirect
113. #125×C₁₆₃	C₂²	semidirect
116. C₂²⋊Q₈×C₁₆₃	C₂²	semidirect
117. C₂²⋊Q₈×C₁₆₃	C₂²	semidirect
118. C₄×Q₈×C₁₆₃	C₂²	semidirect
122. C₂×C₄⋊C₄×C₁₆₃	C₂²	semidirect
242. D₆₅₂	#41	semidirect
329. C₁₆₃	#3520	semidirect
333. #554	D₁₆₃	semidirect
363. C₄⋊Q₈	C₂×D₁₆₃	semidirect
373. #125	C₂×D₁₆₃	semidirect
404. C₂²⋊Q₈	C₂×D₁₆₃	semidirect
405. C₂²⋊Q₈	C₂×D₁₆₃	semidirect
419. C₄×Q₈	C₂×D₁₆₃	semidirect
448. C₂×C₄⋊C₄	C₂×D₁₆₃	semidirect

Maximal subgroups

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

subgroup	index
#23782387	2
#23782370	2
#23782347	2
#23782344	2
#23782342	2
#23782330	2
#23782325	2
#23782317	2
#23782316	2
#23782311	2
#23782306	2
#23782289	2
#23782288	2
#23782263	2
#23782261	2
#23782217	2
#23782195	2
#23782174	2
C₂²⋊Q₈×D₁₆₃	2
#23782147	2
#23782146	2
C₂×#19104697	2
#554×C₁₆₃	2
#3520	163