Subgroups — #35228569

Order 20864.

1252 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782381	C₂	1	1	yes	maximal, characteristic, complemented
2	#23782368	C₂	1	2	yes	maximal, complemented
3	#23782363	C₂	1	2	yes	maximal, complemented
4	#23782337	C₂	1	1	yes	maximal, characteristic, complemented
5	#23782306	C₂	1	2	yes	maximal, complemented
6	#23782306	C₂	1	4	yes	maximal, complemented
7	D₄×D₆₅₂	C₂	1	2	yes	maximal, complemented
8	D₄×D₆₅₂	C₂	1	1	yes	maximal, characteristic, complemented
9	#23782271	C₂	1	2	yes	maximal, complemented
10	#23782255	C₂	1	4	yes	maximal, complemented
11	#23782216	C₂	1	1	yes	maximal, characteristic, complemented
12	#23782202	C₂	1	1	yes	maximal, characteristic, complemented
13	#23782178	C₂	1	2	yes	maximal, complemented
14	C₂×#19104710	C₂	1	2	yes	maximal, complemented
15	#23782137	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#554×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14579700	C₂²	1	2	yes	complemented
19	C₂×#14579700	C₂²	1	2	yes	complemented
20	C₂²×D₆₅₂	C₂²	1	2	yes	complemented
21	C₂²×D₆₅₂	C₂²	1	4	yes	complemented
22	C₂×D₄×D₁₆₃	C₂²	1	1	yes	characteristic
23	C₂×D₄×D₁₆₃	C₂²	1	2	yes	—
24	C₂²×C₄×D₁₆₃	C₂²	1	2	yes	complemented
25	#19104732	C₂²	1	1	yes	characteristic, complemented
26	#19104732	C₂²	1	2	yes	complemented
27	#19104730	C₂²	1	2	yes	complemented
28	#19104730	C₂²	1	4	yes	complemented
29	#19104726	C₂²	1	1	yes	characteristic, complemented
30	#19104724	C₂²	1	1	yes	characteristic, complemented
31	#19104724	C₂²	1	2	yes	complemented
32	#19104724	C₂²	1	4	yes	complemented
33	#19104720	C₂²	1	4	yes	complemented
34	#19104720	C₂²	1	2	yes	complemented
35	#19104720	C₂²	1	4	yes	complemented
36	#19104720	C₂²	1	4	yes	complemented
37	#19104711	C₂²	1	1	yes	characteristic, complemented
38	#19104710	C₂²	1	1	yes	characteristic
39	#19104710	C₂²	1	2	yes	complemented
40	#19104710	C₂²	1	4	yes	complemented
41	#19104710	C₂²	1	4	yes	complemented
42	#19104710	C₂²	1	2	yes	complemented
43	#19104710	C₂²	1	2	yes	complemented
44	#19104710	C₂²	1	2	yes	complemented
45	#19104710	C₂²	1	4	yes	complemented
46	#19104710	C₂²	1	2	yes	complemented
47	#19104710	C₂²	1	2	yes	complemented
48	#19104710	C₂²	1	4	yes	complemented
49	#19104709	C₂²	1	2	yes	complemented
50	#19104709	C₂²	1	4	yes	complemented
51	#19104705	C₂²	1	4	yes	complemented
52	#19104705	C₂²	1	4	yes	complemented
53	#19104705	C₂²	1	4	yes	complemented
54	C₄×D₆₅₂	C₂²	1	2	yes	complemented
55	C₄×D₆₅₂	C₂²	1	1	yes	characteristic, complemented
56	C₄×D₆₅₂	C₂²	1	2	yes	complemented
57	C₄×D₆₅₂	C₂²	1	1	yes	characteristic, complemented
58	D₄×Dic₁₆₃	C₂²	1	1	yes	characteristic
59	#19104697	C₂²	1	4	yes	complemented
60	#19104697	C₂²	1	2	yes	complemented
61	#19104697	C₂²	1	2	yes	complemented
62	#19104697	C₂²	1	1	yes	characteristic, complemented
63	C₄×C₂²⋊D₁₆₃	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊D₁₆₃	C₂²	1	4	yes	complemented
65	(C₂²⋊D₁₆₃)⋊C₄	C₂²	1	4	yes	complemented
66	(C₂²⋊D₁₆₃)⋊C₄	C₂²	1	2	yes	complemented
67	#19104693	C₂²	1	2	yes	complemented
68	#19104693	C₂²	1	2	yes	complemented
69	#19104692	C₂²	1	2	yes	complemented
70	C₄⋊C₄×D₁₆₃	C₂²	1	1	yes	characteristic, complemented
71	C₂×(C₂×D₁₆₃)⋊C₄	C₂²	1	4	yes	complemented
72	C₂²⋊C₄×D₁₆₃	C₂²	1	2	yes	complemented
73	C₂²⋊C₄×D₁₆₃	C₂²	1	4	yes	complemented
74	C₄²×D₁₆₃	C₂²	1	1	yes	characteristic, complemented
75	C₄⋊Q₈×C₁₆₃	C₂²	1	1	yes	characteristic, complemented
76	#125×C₁₆₃	C₂²	1	2	yes	complemented
77	C₂²⋊Q₈×C₁₆₃	C₂²	1	2	yes	complemented
78	C₂²⋊Q₈×C₁₆₃	C₂²	1	4	yes	complemented
79	C₄×Q₈×C₁₆₃	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₄×C₁₆₃	C₂²	1	1	yes	characteristic
81	C₄×D₄×C₁₆₃	C₂²	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₆₃	C₂²	1	2	yes	complemented
83	C₂³×D₁₆₃	C₂³	1	2	yes	—
84	C₂³×D₁₆₃	C₂³	1	4	yes	—
85	#14579700	—	4	4	no	—
86	#14579700	—	4	4	no	—
87	C₂×D₆₅₂	—	4	4	no	—
88	C₂×D₆₅₂	—	4	8	no	—
89	C₂×D₆₅₂	C₂³	1	1	yes	characteristic
90	C₂×D₆₅₂	C₂³	1	2	yes	—
91	C₂×D₆₅₂	C₂³	1	2	yes	—
92	C₂×D₆₅₂	C₂³	1	1	yes	characteristic
93	C₂×D₆₅₂	C₂³	1	4	yes	—
94	C₂×D₆₅₂	C₂³	1	2	yes	—
95	C₂×D₆₅₂	C₂³	1	4	yes	—
96	C₂×D₆₅₂	C₂³	1	4	yes	—
97	C₂×D₆₅₂	C₂³	1	4	yes	—
98	C₂×D₆₅₂	C₂³	1	4	yes	—
99	C₂×D₆₅₂	C₂³	1	2	yes	—
100	C₂×C₂²⋊D₁₆₃	C₂³	1	2	yes	—
101	C₂×C₂²⋊D₁₆₃	C₂³	1	4	yes	—
102	D₄×D₁₆₃	—	2	4	no	—
103	D₄×D₁₆₃	—	2	8	no	—
104	C₂²×Dic₁₆₃	C₂³	1	2	yes	—
105	C₂×C₄×D₁₆₃	—	4	4	no	—
106	C₂×C₄×D₁₆₃	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
108	C₂×C₄×D₁₆₃	C₂³	1	1	yes	characteristic
109	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
110	C₂×C₄×D₁₆₃	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
112	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
113	C₂×C₄×D₁₆₃	C₂³	1	4	yes	—
114	C₂×C₄×D₁₆₃	C₂³	1	4	yes	—
115	C₄⋊Dic₁₆₃	C₂³	1	1	yes	characteristic
116	C₄⋊Dic₁₆₃	C₂³	1	1	yes	characteristic
117	C₄⋊Dic₁₆₃	C₂³	1	2	yes	—
118	Dic₁₆₃⋊C₄	C₂³	1	2	yes	—
119	Dic₁₆₃⋊C₄	C₂³	1	2	yes	—
120	Dic₁₆₃⋊C₄	C₂³	1	2	yes	—
121	C₂²⋊Dic₁₆₃	C₂³	1	2	yes	—
122	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
123	(C₂×D₁₆₃)⋊C₄	C₂³	1	4	yes	—
124	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
125	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
126	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
127	(C₂×D₁₆₃)⋊C₄	C₂³	1	4	yes	—
128	(C₂×D₁₆₃)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₁₆₃)⋊C₄	C₂³	1	4	yes	—
130	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
131	(C₂×D₁₆₃)⋊C₄	C₂³	1	4	yes	—
132	(C₂×D₁₆₃)⋊C₄	C₂³	1	4	yes	—
133	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
134	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
135	C₄×Dic₁₆₃	C₂³	1	1	yes	characteristic
136	C₄×Dic₁₆₃	C₂³	1	1	yes	characteristic
137	C₄×Dic₁₆₃	C₂³	1	1	yes	characteristic
138	C₄×Dic₁₆₃	C₂³	1	4	yes	—
139	C₂×Q₈×C₁₆₃	C₂³	1	1	yes	characteristic
140	C₂×Q₈×C₁₆₃	C₂³	1	2	yes	—
141	C₂×D₄×C₁₆₃	C₂³	1	1	yes	characteristic
142	C₂²×C₄×C₁₆₃	C₂³	1	2	yes	—
143	C₂²×C₄×C₁₆₃	C₂³	1	4	yes	—
144	C₄⋊C₄×C₁₆₃	C₂³	1	1	yes	characteristic
145	C₄⋊C₄×C₁₆₃	C₂³	1	4	yes	—
146	C₄⋊C₄×C₁₆₃	C₂³	1	2	yes	—
147	C₄⋊C₄×C₁₆₃	C₂³	1	1	yes	characteristic
148	C₄⋊C₄×C₁₆₃	C₂³	1	2	yes	—
149	C₄⋊C₄×C₁₆₃	C₂³	1	2	yes	—
150	C₄⋊C₄×C₁₆₃	C₂³	1	4	yes	—
151	C₂²⋊C₄×C₁₆₃	C₂³	1	4	yes	—
152	C₂²⋊C₄×C₁₆₃	C₂³	1	2	yes	—
153	C₄²×C₁₆₃	C₂³	1	2	yes	—
154	C₄²×C₁₆₃	C₂³	1	1	yes	characteristic
155	C₂²×D₁₆₃	—	2	4	no	—
156	C₂²×D₁₆₃	—	2	8	no	—
157	C₂²×D₁₆₃	—	2	4	no	—
158	C₂²×D₁₆₃	—	4	2	no	—
159	C₂²×D₁₆₃	—	4	4	no	—
160	C₂²×D₁₆₃	—	4	4	no	—
161	C₂²×D₁₆₃	C₂⁴	1	2	yes	—
162	C₂²×D₁₆₃	C₂⁴	1	2	yes	—
163	C₂²×D₁₆₃	C₂⁴	1	4	yes	—
164	C₂²×D₁₆₃	C₂⁴	1	1	yes	characteristic
165	D₆₅₂	—	2	4	no	—
166	D₆₅₂	—	2	8	no	—
167	D₆₅₂	—	2	2	no	—
168	D₆₅₂	—	2	4	no	—
169	D₆₅₂	—	2	2	no	—
170	D₆₅₂	—	2	4	no	—
171	D₆₅₂	—	4	4	no	—
172	D₆₅₂	—	4	4	no	—
173	D₆₅₂	—	4	4	no	—
174	D₆₅₂	—	4	4	no	—
175	D₆₅₂	—	4	2	no	—
176	C₂²⋊D₁₆₃	—	2	4	no	—
177	C₂²⋊D₁₆₃	—	2	8	no	—
178	C₂×Dic₁₆₃	—	4	2	no	—
179	C₂×Dic₁₆₃	C₂⁴	1	1	yes	characteristic
180	C₂×Dic₁₆₃	C₂⁴	1	2	yes	—
181	C₂×Dic₁₆₃	C₂⁴	1	1	yes	characteristic
182	C₂×Dic₁₆₃	C₂⁴	1	2	yes	—
183	C₂×Dic₁₆₃	C₂⁴	1	1	yes	characteristic
184	C₄×D₁₆₃	—	2	2	no	—
185	C₄×D₁₆₃	—	2	2	no	—
186	C₄×D₁₆₃	—	2	4	no	—
187	C₄×D₁₆₃	—	2	2	no	—
188	C₄×D₁₆₃	—	2	4	no	—
189	C₄×D₁₆₃	—	4	2	no	—
190	C₄×D₁₆₃	—	4	2	no	—
191	C₄×D₁₆₃	—	4	4	no	—
192	C₄×D₁₆₃	—	4	4	no	—
193	C₂³×C₁₆₃	C₂⁴	1	2	yes	—
194	Q₈×C₁₆₃	—	2	2	no	—
195	Q₈×C₁₆₃	—	4	2	no	—
196	D₄×C₁₆₃	#41	1	4	yes	complemented
197	C₂×C₄×C₁₆₃	—	2	4	no	—
198	C₂×C₄×C₁₆₃	—	4	4	no	—
199	C₂×C₄×C₁₆₃	C₂⁴	1	2	yes	—
200	C₂×C₄×C₁₆₃	C₂⁴	1	1	yes	characteristic
201	C₂×C₄×C₁₆₃	C₂⁴	1	2	yes	—
202	C₂×C₄×C₁₆₃	C₂⁴	1	2	yes	—
203	C₂×C₄×C₁₆₃	C₂⁴	1	4	yes	—
204	C₂×C₄×C₁₆₃	C₂⁴	1	1	yes	characteristic
205	C₂×C₄×C₁₆₃	C₂⁴	1	1	yes	characteristic
206	C₂²×C₁₆₃	—	2	2	no	—
207	C₂²×C₁₆₃	—	2	2	no	—
208	C₂²×C₁₆₃	C₂×#41	1	4	yes	—
209	C₂²×C₁₆₃	C₂⁵	1	1	yes	characteristic
210	C₂×D₁₆₃	—	2	1	no	—
211	C₂×D₁₆₃	—	2	1	no	—
212	C₂×D₁₆₃	—	2	2	no	—
213	C₂×D₁₆₃	—	2	2	no	—
214	C₂×D₁₆₃	—	2	4	no	—
215	C₂×D₁₆₃	—	2	2	no	—
216	C₂×D₁₆₃	—	2	4	no	—
217	C₂×D₁₆₃	—	2	4	no	—
218	C₂×D₁₆₃	—	2	2	no	—
219	C₂×D₁₆₃	—	2	2	no	—
220	C₂×D₁₆₃	—	2	2	no	—
221	C₂×D₁₆₃	—	4	8	no	—
222	C₂×D₁₆₃	—	8	8	no	—
223	C₂×D₁₆₃	H(5,𝔽₂)	1	2	yes	—
224	C₄×C₁₆₃	—	2	2	no	—
225	C₄×C₁₆₃	—	2	2	no	—
226	C₄×C₁₆₃	—	2	4	no	—
227	C₄×C₁₆₃	—	2	2	no	—
228	C₄×C₁₆₃	—	2	1	no	—
229	C₄×C₁₆₃	C₂×#41	1	2	yes	—
230	C₄×C₁₆₃	H(5,𝔽₂)	1	2	yes	—
231	Dic₁₆₃	—	2	1	no	—
232	Dic₁₆₃	—	2	2	no	—
233	Dic₁₆₃	—	2	1	no	—
234	Dic₁₆₃	—	2	2	no	—
235	Dic₁₆₃	—	2	1	no	—
236	C₂×C₁₆₃	—	2	4	no	—
237	C₂×C₁₆₃	C₂²×#41	1	1	yes	characteristic
238	C₂×C₁₆₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
239	C₂×C₁₆₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
240	D₁₆₃	—	2	2	no	—
241	D₁₆₃	—	4	2	no	—
242	D₁₆₃	—	4	4	no	—
243	D₁₆₃	—	4	2	no	—
244	C₁₆₃	#3519	1	1	yes	characteristic, complemented, Sylow
245	#3519	—	163	1	no	maximal, Sylow
246	#555	—	163	1	no	—
247	#554	D₁₆₃	1	1	yes	characteristic, complemented
248	#553	—	163	2	no	—
249	#553	—	163	2	no	—
250	#550	—	163	1	no	—
251	#546	—	163	4	no	—
252	#546	—	163	2	no	—
253	D₄²	—	163	2	no	—
254	D₄²	—	163	1	no	—
255	#540	—	163	2	no	—
256	#538	—	163	4	no	—
257	#532	—	163	1	no	—
258	#529	—	163	1	no	—
259	#525	—	163	2	no	—
260	C₂×#121	—	163	2	no	—
261	#518	—	163	2	no	—
262	C₂×C₄×D₄	—	163	1	no	—
263	C₂×#41	—	163	2	no	—
264	C₂×#41	—	163	2	no	—
265	C₂²×D₄	—	163	1	no	—
266	C₂²×D₄	—	163	2	no	—
267	C₂²×D₄	—	163	2	no	—
268	C₂²×D₄	—	163	4	no	—
269	C₂³×C₄	—	163	2	no	—
270	C₄⋊Q₈	C₂×D₁₆₃	1	1	yes	characteristic, complemented
271	#127	—	163	1	no	—
272	#127	—	163	2	no	—
273	#126	—	163	2	no	—
274	#126	—	163	4	no	—
275	#125	—	163	1	no	—
276	#125	C₂×D₁₆₃	1	2	yes	complemented
277	#124	—	163	1	no	—
278	#124	—	163	2	no	—
279	#124	—	163	4	no	—
280	#123	—	163	4	no	—
281	#123	—	163	2	no	—
282	#123	—	163	4	no	—
283	#123	—	163	4	no	—
284	C₂²⋊Q₈	—	163	1	no	—
285	C₂²⋊Q₈	C₂×D₁₆₃	1	2	yes	complemented
286	C₂²⋊Q₈	C₂×D₁₆₃	1	4	yes	complemented
287	#121	—	163	2	no	—
288	#121	—	163	4	no	—
289	#121	—	163	1	no	—
290	#121	—	163	2	no	—
291	#121	—	163	4	no	—
292	#121	—	163	4	no	—
293	#121	—	163	2	no	—
294	#121	—	163	2	no	—
295	#121	—	163	2	no	—
296	#121	—	163	4	no	—
297	#121	—	163	2	no	—
298	#121	—	163	2	no	—
299	#121	—	163	4	no	—
300	#120	—	163	4	no	—
301	#120	—	163	4	no	—
302	#120	—	163	4	no	—
303	C₄×Q₈	C₂×D₁₆₃	1	1	yes	characteristic, complemented
304	C₄×D₄	—	163	1	no	—
305	C₄×D₄	—	163	2	no	—
306	C₄×D₄	—	163	4	no	—
307	C₄×D₄	—	163	1	no	—
308	C₄×D₄	—	163	2	no	—
309	C₄×D₄	—	163	4	no	—
310	C₄×D₄	—	163	2	no	—
311	C₄×D₄	—	163	2	no	—
312	C₄×D₄	—	163	4	no	—
313	C₄×D₄	—	163	1	no	—
314	C₄×D₄	—	163	2	no	—
315	C₄×D₄	—	163	2	no	—
316	C₄×D₄	—	163	1	no	—
317	C₄×D₄	C₂×D₁₆₃	1	1	yes	characteristic
318	C₄×D₄	C₂×D₁₆₃	1	2	yes	—
319	#117	—	163	2	no	—
320	#117	—	163	2	no	—
321	#117	—	163	2	no	—
322	C₂×C₄⋊C₄	—	163	1	no	—
323	C₂×C₄⋊C₄	C₂×D₁₆₃	1	2	yes	complemented
324	C₂×C₂²⋊C₄	—	163	4	no	—
325	C₂×C₂²⋊C₄	—	163	2	no	—
326	C₂×C₂²⋊C₄	—	163	4	no	—
327	C₂×C₄²	—	163	1	no	—
328	C₂⁴	—	163	2	no	—
329	C₂⁴	—	163	4	no	—
330	#41	—	652	4	no	—
331	#41	—	652	4	no	—
332	C₂×Q₈	C₂²×D₁₆₃	1	1	yes	characteristic
333	C₂×Q₈	C₂²×D₁₆₃	1	2	yes	—
334	C₂×D₄	—	326	8	no	—
335	C₂×D₄	—	326	4	no	—
336	C₂×D₄	—	652	4	no	—
337	C₂×D₄	—	652	8	no	—
338	C₂×D₄	—	163	2	no	—
339	C₂×D₄	—	163	4	no	—
340	C₂×D₄	—	163	1	no	—
341	C₂×D₄	—	163	2	no	—
342	C₂×D₄	—	163	4	no	—
343	C₂×D₄	—	163	2	no	—
344	C₂×D₄	—	163	1	no	—
345	C₂×D₄	—	163	2	no	—
346	C₂×D₄	—	163	4	no	—
347	C₂×D₄	—	163	2	no	—
348	C₂×D₄	—	163	4	no	—
349	C₂×D₄	—	163	4	no	—
350	C₂×D₄	—	163	4	no	—
351	C₂×D₄	C₂²×D₁₆₃	1	1	yes	characteristic
352	C₂²×C₄	—	652	4	no	—
353	C₂²×C₄	—	163	1	no	—
354	C₂²×C₄	—	163	1	no	—
355	C₂²×C₄	—	163	1	no	—
356	C₂²×C₄	—	163	2	no	—
357	C₂²×C₄	—	163	2	no	—
358	C₂²×C₄	—	163	2	no	—
359	C₂²×C₄	—	163	2	no	—
360	C₂²×C₄	—	163	4	no	—
361	C₂²×C₄	—	163	4	no	—
362	C₂²×C₄	—	163	2	no	—
363	C₂²×C₄	C₂²×D₁₆₃	1	2	yes	—
364	C₂²×C₄	C₂²×D₁₆₃	1	4	yes	—
365	C₄⋊C₄	—	163	1	no	—
366	C₄⋊C₄	—	163	2	no	—
367	C₄⋊C₄	—	163	1	no	—
368	C₄⋊C₄	—	163	2	no	—
369	C₄⋊C₄	—	163	2	no	—
370	C₄⋊C₄	—	163	2	no	—
371	C₄⋊C₄	C₂²×D₁₆₃	1	1	yes	characteristic
372	C₄⋊C₄	C₂²×D₁₆₃	1	1	yes	characteristic
373	C₄⋊C₄	C₂²×D₁₆₃	1	2	yes	—
374	C₄⋊C₄	C₂²×D₁₆₃	1	4	yes	—
375	C₄⋊C₄	C₂²×D₁₆₃	1	2	yes	—
376	C₄⋊C₄	C₂²×D₁₆₃	1	4	yes	—
377	C₄⋊C₄	C₂²×D₁₆₃	1	2	yes	—
378	C₂²⋊C₄	—	163	2	no	—
379	C₂²⋊C₄	—	163	2	no	—
380	C₂²⋊C₄	—	163	4	no	—
381	C₂²⋊C₄	—	163	2	no	—
382	C₂²⋊C₄	—	163	4	no	—
383	C₂²⋊C₄	—	163	2	no	—
384	C₂²⋊C₄	—	163	4	no	—
385	C₂²⋊C₄	—	163	2	no	—
386	C₂²⋊C₄	—	163	4	no	—
387	C₂²⋊C₄	—	163	2	no	—
388	C₂²⋊C₄	—	163	2	no	—
389	C₂²⋊C₄	—	163	2	no	—
390	C₂²⋊C₄	—	163	4	no	—
391	C₂²⋊C₄	—	163	4	no	—
392	C₂²⋊C₄	C₂²×D₁₆₃	1	2	yes	—
393	C₂²⋊C₄	C₂²×D₁₆₃	1	4	yes	—
394	C₄²	—	163	1	no	—
395	C₄²	—	163	1	no	—
396	C₄²	—	163	1	no	—
397	C₄²	—	163	4	no	—
398	C₄²	C₂²×D₁₆₃	1	1	yes	characteristic
399	C₄²	C₂²×D₁₆₃	1	2	yes	—
400	C₂³	—	326	4	no	—
401	C₂³	—	326	8	no	—
402	C₂³	—	326	4	no	—
403	C₂³	—	652	4	no	—
404	C₂³	—	652	4	no	—
405	C₂³	—	652	2	no	—
406	C₂³	—	163	2	no	—
407	C₂³	—	163	4	no	—
408	C₂³	—	163	2	no	—
409	C₂³	—	163	1	no	—
410	C₂³	C₂³×D₁₆₃	1	2	yes	—
411	Q₈	—	2	2	no	—
412	Q₈	—	4	2	no	—
413	D₄	—	326	4	no	—
414	D₄	—	326	8	no	—
415	D₄	—	326	8	no	—
416	D₄	—	326	4	no	—
417	D₄	—	326	4	no	—
418	D₄	—	326	2	no	—
419	D₄	—	326	2	no	—
420	D₄	—	326	4	no	—
421	D₄	—	652	4	no	—
422	D₄	—	652	4	no	—
423	D₄	—	652	4	no	—
424	D₄	—	652	2	no	—
425	D₄	—	652	4	no	—
426	D₄	#14579700	1	4	yes	complemented
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	326	2	no	—
430	C₂×C₄	—	326	2	no	—
431	C₂×C₄	—	326	4	no	—
432	C₂×C₄	—	326	2	no	—
433	C₂×C₄	—	326	4	no	—
434	C₂×C₄	—	652	2	no	—
435	C₂×C₄	—	652	2	no	—
436	C₂×C₄	—	652	4	no	—
437	C₂×C₄	—	652	4	no	—
438	C₂×C₄	—	652	2	no	—
439	C₂×C₄	—	163	1	no	—
440	C₂×C₄	—	163	2	no	—
441	C₂×C₄	—	163	1	no	—
442	C₂×C₄	—	163	1	no	—
443	C₂×C₄	—	163	2	no	—
444	C₂×C₄	C₂³×D₁₆₃	1	1	yes	characteristic
445	C₂×C₄	C₂³×D₁₆₃	1	4	yes	—
446	C₂×C₄	C₂³×D₁₆₃	1	2	yes	—
447	C₂×C₄	C₂³×D₁₆₃	1	2	yes	—
448	C₂×C₄	C₂³×D₁₆₃	1	2	yes	—
449	C₂×C₄	C₂³×D₁₆₃	1	1	yes	characteristic
450	C₂×C₄	C₂³×D₁₆₃	1	1	yes	characteristic
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	1304	8	no	—
454	C₂²	—	326	1	no	—
455	C₂²	—	326	1	no	—
456	C₂²	—	326	2	no	—
457	C₂²	—	326	4	no	—
458	C₂²	—	326	2	no	—
459	C₂²	—	326	4	no	—
460	C₂²	—	326	2	no	—
461	C₂²	—	326	2	no	—
462	C₂²	—	326	2	no	—
463	C₂²	—	326	4	no	—
464	C₂²	—	326	2	no	—
465	C₂²	—	652	8	no	—
466	C₂²	—	163	2	no	—
467	C₂²	C₂×#14579700	1	4	yes	—
468	C₂²	C₂⁴×D₁₆₃	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	2	4	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	326	1	no	—
475	C₄	—	326	2	no	—
476	C₄	—	326	1	no	—
477	C₄	—	326	1	no	—
478	C₄	—	326	2	no	—
479	C₄	C₂×#14579700	1	2	yes	—
480	C₄	#19104781	1	2	yes	—
481	C₂	—	2	4	no	—
482	C₂	—	326	2	no	—
483	C₂	—	652	2	no	—
484	C₂	—	652	4	no	—
485	C₂	—	652	2	no	—
486	C₂	C₂²×#14579700	1	1	yes	characteristic
487	C₂	H(5,𝔽₂)×D₁₆₃	1	1	yes	characteristic
488	C₂	C₂×#19104781	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	#3519
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. #23782381	C₂	semidirect
2. #23782368	C₂	semidirect
3. #23782363	C₂	semidirect
4. #23782337	C₂	semidirect
5. #23782306	C₂	semidirect
6. #23782306	C₂	semidirect
7. D₄×D₆₅₂	C₂	semidirect
8. D₄×D₆₅₂	C₂	semidirect
9. #23782271	C₂	semidirect
10. #23782255	C₂	semidirect
11. #23782216	C₂	semidirect
12. #23782202	C₂	semidirect
13. #23782178	C₂	semidirect
14. C₂×#19104710	C₂	semidirect
15. #23782137	C₂	semidirect
16. C₄×D₄×D₁₆₃	C₂	semidirect
17. #554×C₁₆₃	C₂	semidirect
18. C₂×#14579700	C₂²	semidirect
19. C₂×#14579700	C₂²	semidirect
20. C₂²×D₆₅₂	C₂²	semidirect
21. C₂²×D₆₅₂	C₂²	semidirect
24. C₂²×C₄×D₁₆₃	C₂²	semidirect
25. #19104732	C₂²	semidirect
26. #19104732	C₂²	semidirect
27. #19104730	C₂²	semidirect
28. #19104730	C₂²	semidirect
29. #19104726	C₂²	semidirect
30. #19104724	C₂²	semidirect
31. #19104724	C₂²	semidirect
32. #19104724	C₂²	semidirect
33. #19104720	C₂²	semidirect
34. #19104720	C₂²	semidirect
35. #19104720	C₂²	semidirect
36. #19104720	C₂²	semidirect
37. #19104711	C₂²	semidirect
39. #19104710	C₂²	semidirect
40. #19104710	C₂²	semidirect
41. #19104710	C₂²	semidirect
42. #19104710	C₂²	semidirect
43. #19104710	C₂²	semidirect
44. #19104710	C₂²	semidirect
45. #19104710	C₂²	semidirect
46. #19104710	C₂²	semidirect
47. #19104710	C₂²	semidirect
48. #19104710	C₂²	semidirect
49. #19104709	C₂²	semidirect
50. #19104709	C₂²	semidirect
51. #19104705	C₂²	semidirect
52. #19104705	C₂²	semidirect
53. #19104705	C₂²	semidirect
54. C₄×D₆₅₂	C₂²	semidirect
55. C₄×D₆₅₂	C₂²	semidirect
56. C₄×D₆₅₂	C₂²	semidirect
57. C₄×D₆₅₂	C₂²	semidirect
59. #19104697	C₂²	semidirect
60. #19104697	C₂²	semidirect
61. #19104697	C₂²	semidirect
62. #19104697	C₂²	semidirect
63. C₄×C₂²⋊D₁₆₃	C₂²	semidirect
64. C₄×C₂²⋊D₁₆₃	C₂²	semidirect
65. (C₂²⋊D₁₆₃)⋊C₄	C₂²	semidirect
66. (C₂²⋊D₁₆₃)⋊C₄	C₂²	semidirect
67. #19104693	C₂²	semidirect
68. #19104693	C₂²	semidirect
69. #19104692	C₂²	semidirect
70. C₄⋊C₄×D₁₆₃	C₂²	semidirect
71. C₂×(C₂×D₁₆₃)⋊C₄	C₂²	semidirect
72. C₂²⋊C₄×D₁₆₃	C₂²	semidirect
73. C₂²⋊C₄×D₁₆₃	C₂²	semidirect
74. C₄²×D₁₆₃	C₂²	semidirect
75. C₄⋊Q₈×C₁₆₃	C₂²	semidirect
76. #125×C₁₆₃	C₂²	semidirect
77. C₂²⋊Q₈×C₁₆₃	C₂²	semidirect
78. C₂²⋊Q₈×C₁₆₃	C₂²	semidirect
79. C₄×Q₈×C₁₆₃	C₂²	semidirect
82. C₂×C₄⋊C₄×C₁₆₃	C₂²	semidirect
196. D₄×C₁₆₃	#41	semidirect
244. C₁₆₃	#3519	semidirect
247. #554	D₁₆₃	semidirect
270. C₄⋊Q₈	C₂×D₁₆₃	semidirect
276. #125	C₂×D₁₆₃	semidirect
285. C₂²⋊Q₈	C₂×D₁₆₃	semidirect
286. C₂²⋊Q₈	C₂×D₁₆₃	semidirect
303. C₄×Q₈	C₂×D₁₆₃	semidirect
323. C₂×C₄⋊C₄	C₂×D₁₆₃	semidirect
426. D₄	#14579700	semidirect

Maximal subgroups

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

subgroup	index
#23782381	2
#23782368	2
#23782363	2
#23782337	2
#23782306	2
D₄×D₆₅₂	2
#23782271	2
#23782255	2
#23782216	2
#23782202	2
#23782178	2
C₂×#19104710	2
#23782137	2
C₄×D₄×D₁₆₃	2
#554×C₁₆₃	2
#3519	163