Subgroups — #35228147

Order 20864.

1242 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782400	C₂	1	1	yes	maximal, characteristic, complemented
2	#23782376	C₂	1	1	yes	maximal, characteristic, complemented
3	#23782368	C₂	1	2	yes	maximal, complemented
4	#23782363	C₂	1	2	yes	maximal, complemented
5	#23782342	C₂	1	4	yes	maximal, complemented
6	#23782310	C₂	1	2	yes	maximal, complemented
7	#23782306	C₂	1	2	yes	maximal, complemented
8	D₄×D₆₅₂	C₂	1	1	yes	maximal, characteristic, complemented
9	#23782216	C₂	1	1	yes	maximal, characteristic, complemented
10	#23782201	C₂	1	2	yes	maximal, complemented
11	#23782200	C₂	1	2	yes	maximal, complemented
12	#23782178	C₂	1	4	yes	maximal, complemented
13	C₄×#14579700	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#14579698	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#19104697	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₁₆₃	C₂	1	2	yes	maximal, complemented
17	#554×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14579700	C₂²	1	1	yes	characteristic
19	C₂×#14579700	C₂²	1	2	yes	complemented
20	C₂×#14579698	C₂²	1	1	yes	characteristic
21	C₂²×D₆₅₂	C₂²	1	2	yes	—
22	C₂×D₄×D₁₆₃	C₂²	1	2	yes	—
23	C₂²×C₄×D₁₆₃	C₂²	1	4	yes	complemented
24	#19104732	C₂²	1	1	yes	characteristic
25	#19104730	C₂²	1	4	yes	complemented
26	#19104730	C₂²	1	4	yes	complemented
27	#19104726	C₂²	1	2	yes	complemented
28	#19104724	C₂²	1	2	yes	complemented
29	#19104724	C₂²	1	2	yes	complemented
30	#19104723	C₂²	1	2	yes	complemented
31	#19104720	C₂²	1	4	yes	complemented
32	#19104720	C₂²	1	4	yes	complemented
33	#19104720	C₂²	1	4	yes	complemented
34	#19104719	C₂²	1	4	yes	complemented
35	#19104715	C₂²	1	2	yes	complemented
36	#19104711	C₂²	1	4	yes	complemented
37	#19104710	C₂²	1	2	yes	—
38	#19104710	C₂²	1	4	yes	complemented
39	#19104710	C₂²	1	2	yes	complemented
40	#19104710	C₂²	1	2	yes	complemented
41	#19104709	C₂²	1	2	yes	—
42	#19104709	C₂²	1	4	yes	complemented
43	#19104705	C₂²	1	4	yes	—
44	#19104705	C₂²	1	4	yes	complemented
45	Q₈×Dic₁₆₃	C₂²	1	1	yes	characteristic, complemented
46	C₄×Dic₃₂₆	C₂²	1	1	yes	characteristic, complemented
47	#19104700	C₂²	1	1	yes	characteristic, complemented
48	C₄×D₆₅₂	C₂²	1	1	yes	characteristic
49	C₄×D₆₅₂	C₂²	1	2	yes	complemented
50	C₄×D₆₅₂	C₂²	1	2	yes	complemented
51	D₄×Dic₁₆₃	C₂²	1	1	yes	characteristic
52	#19104697	C₂²	1	2	yes	—
53	#19104697	C₂²	1	1	yes	characteristic
54	#19104697	C₂²	1	2	yes	complemented
55	#19104697	C₂²	1	2	yes	complemented
56	#19104697	C₂²	1	4	yes	complemented
57	#19104697	C₂²	1	2	yes	complemented
58	#19104697	C₂²	1	2	yes	complemented
59	#19104697	C₂²	1	4	yes	complemented
60	C₄×C₂²⋊D₁₆₃	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊D₁₆₃	C₂²	1	4	yes	complemented
62	(C₂²⋊D₁₆₃)⋊C₄	C₂²	1	2	yes	complemented
63	(C₂²⋊D₁₆₃)⋊C₄	C₂²	1	4	yes	complemented
64	#19104693	C₂²	1	4	yes	complemented
65	#19104693	C₂²	1	2	yes	complemented
66	#19104693	C₂²	1	1	yes	characteristic, complemented
67	#19104693	C₂²	1	1	yes	characteristic, complemented
68	#19104691	C₂²	1	2	yes	complemented
69	C₄⋊C₄×D₁₆₃	C₂²	1	2	yes	complemented
70	C₂×(C₂×D₁₆₃)⋊C₄	C₂²	1	4	yes	complemented
71	C₂²⋊C₄×D₁₆₃	C₂²	1	4	yes	complemented
72	C₂×C₄×Dic₁₆₃	C₂²	1	2	yes	complemented
73	C₄²×D₁₆₃	C₂²	1	2	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	4	yes	complemented
78	C₂²⋊Q₈×C₁₆₃	C₂²	1	2	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	4	yes	—
84	#14579700	—	2	4	no	—
85	#14579700	—	4	4	no	—
86	#14579698	—	2	4	no	—
87	C₂×Dic₃₂₆	C₂³	1	1	yes	characteristic
88	C₂×D₆₅₂	—	2	8	no	—
89	C₂×D₆₅₂	C₂³	1	2	yes	—
90	C₂×D₆₅₂	C₂³	1	4	yes	—
91	C₂×D₆₅₂	C₂³	1	2	yes	—
92	C₂×D₆₅₂	C₂³	1	2	yes	—
93	C₂×D₆₅₂	C₂³	1	2	yes	—
94	C₂×D₆₅₂	C₂³	1	4	yes	—
95	C₂×D₆₅₂	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊D₁₆₃	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₁₆₃	C₂³	1	2	yes	—
98	D₄×D₁₆₃	—	2	8	no	—
99	C₂²×Dic₁₆₃	C₂³	1	2	yes	—
100	C₂²×Dic₁₆₃	C₂³	1	2	yes	—
101	C₂×C₄×D₁₆₃	—	4	8	no	—
102	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
103	C₂×C₄×D₁₆₃	C₂³	1	4	yes	—
104	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
105	C₂×C₄×D₁₆₃	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
107	C₂×C₄×D₁₆₃	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₁₆₃	C₂³	1	1	yes	characteristic
109	C₂×C₄×D₁₆₃	C₂³	1	4	yes	—
110	C₂×C₄×D₁₆₃	C₂³	1	4	yes	—
111	C₄⋊Dic₁₆₃	C₂³	1	1	yes	characteristic
112	C₄⋊Dic₁₆₃	C₂³	1	1	yes	characteristic
113	C₄⋊Dic₁₆₃	C₂³	1	2	yes	—
114	C₄⋊Dic₁₆₃	C₂³	1	4	yes	—
115	Dic₁₆₃⋊C₄	C₂³	1	4	yes	—
116	Dic₁₆₃⋊C₄	C₂³	1	2	yes	—
117	Dic₁₆₃⋊C₄	C₂³	1	2	yes	—
118	C₂²⋊Dic₁₆₃	C₂³	1	2	yes	—
119	(C₂×D₁₆₃)⋊C₄	C₂³	1	4	yes	—
120	(C₂×D₁₆₃)⋊C₄	C₂³	1	4	yes	—
121	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
122	(C₂×D₁₆₃)⋊C₄	C₂³	1	4	yes	—
123	(C₂×D₁₆₃)⋊C₄	C₂³	1	4	yes	—
124	(C₂×D₁₆₃)⋊C₄	C₂³	1	4	yes	—
125	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
126	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
127	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
128	(C₂×D₁₆₃)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₁₆₃)⋊C₄	C₂³	1	4	yes	—
130	C₄×Dic₁₆₃	C₂³	1	1	yes	characteristic
131	C₄×Dic₁₆₃	C₂³	1	1	yes	characteristic
132	C₄×Dic₁₆₃	C₂³	1	1	yes	characteristic
133	C₄×Dic₁₆₃	C₂³	1	2	yes	—
134	C₄×Dic₁₆₃	C₂³	1	2	yes	—
135	C₄×Dic₁₆₃	C₂³	1	2	yes	—
136	C₄×Dic₁₆₃	C₂³	1	2	yes	—
137	C₄×Dic₁₆₃	C₂³	1	2	yes	—
138	C₂×Q₈×C₁₆₃	C₂³	1	1	yes	characteristic
139	C₂×Q₈×C₁₆₃	C₂³	1	2	yes	—
140	C₂×D₄×C₁₆₃	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₁₆₃	C₂³	1	2	yes	—
142	C₂²×C₄×C₁₆₃	C₂³	1	4	yes	—
143	C₄⋊C₄×C₁₆₃	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₁₆₃	C₂³	1	4	yes	—
145	C₄⋊C₄×C₁₆₃	C₂³	1	2	yes	—
146	C₄⋊C₄×C₁₆₃	C₂³	1	1	yes	characteristic
147	C₄⋊C₄×C₁₆₃	C₂³	1	2	yes	—
148	C₄⋊C₄×C₁₆₃	C₂³	1	2	yes	—
149	C₄⋊C₄×C₁₆₃	C₂³	1	4	yes	—
150	C₂²⋊C₄×C₁₆₃	C₂³	1	4	yes	—
151	C₂²⋊C₄×C₁₆₃	C₂³	1	2	yes	—
152	C₄²×C₁₆₃	C₂³	1	2	yes	—
153	C₄²×C₁₆₃	C₂³	1	1	yes	characteristic
154	C₂²×D₁₆₃	—	2	8	no	—
155	C₂²×D₁₆₃	—	2	8	no	—
156	C₂²×D₁₆₃	—	4	4	no	—
157	C₂²×D₁₆₃	C₂⁴	1	4	yes	—
158	C₂²×D₁₆₃	C₂⁴	1	1	yes	characteristic
159	C₂²×D₁₆₃	C₂⁴	1	2	yes	—
160	Dic₃₂₆	—	2	2	no	—
161	D₆₅₂	—	2	8	no	—
162	D₆₅₂	—	2	4	no	—
163	D₆₅₂	—	2	4	no	—
164	D₆₅₂	—	2	4	no	—
165	D₆₅₂	—	4	4	no	—
166	D₆₅₂	—	4	2	no	—
167	D₆₅₂	#41	1	4	yes	complemented
168	C₂²⋊D₁₆₃	—	2	8	no	—
169	C₂²⋊D₁₆₃	—	2	4	no	—
170	C₂×Dic₁₆₃	—	2	4	no	—
171	C₂×Dic₁₆₃	—	2	4	no	—
172	C₂×Dic₁₆₃	C₂⁴	1	1	yes	characteristic
173	C₂×Dic₁₆₃	C₂⁴	1	1	yes	characteristic
174	C₂×Dic₁₆₃	C₂⁴	1	2	yes	—
175	C₂×Dic₁₆₃	C₂⁴	1	2	yes	—
176	C₂×Dic₁₆₃	C₂⁴	1	2	yes	—
177	C₂×Dic₁₆₃	C₂⁴	1	1	yes	characteristic
178	C₄×D₁₆₃	—	2	4	no	—
179	C₄×D₁₆₃	—	2	4	no	—
180	C₄×D₁₆₃	—	2	2	no	—
181	C₄×D₁₆₃	—	2	2	no	—
182	C₄×D₁₆₃	—	2	4	no	—
183	C₄×D₁₆₃	—	2	8	no	—
184	C₄×D₁₆₃	—	2	2	no	—
185	C₄×D₁₆₃	—	4	4	no	—
186	C₄×D₁₆₃	—	4	4	no	—
187	C₂³×C₁₆₃	C₂⁴	1	2	yes	—
188	Q₈×C₁₆₃	—	2	2	no	—
189	Q₈×C₁₆₃	—	4	2	no	—
190	D₄×C₁₆₃	#41	1	4	yes	complemented
191	C₂×C₄×C₁₆₃	—	2	4	no	—
192	C₂×C₄×C₁₆₃	—	4	4	no	—
193	C₂×C₄×C₁₆₃	C₂⁴	1	2	yes	—
194	C₂×C₄×C₁₆₃	C₂⁴	1	1	yes	characteristic
195	C₂×C₄×C₁₆₃	C₂⁴	1	2	yes	—
196	C₂×C₄×C₁₆₃	C₂⁴	1	2	yes	—
197	C₂×C₄×C₁₆₃	C₂⁴	1	4	yes	—
198	C₂×C₄×C₁₆₃	C₂⁴	1	1	yes	characteristic
199	C₂×C₄×C₁₆₃	C₂⁴	1	1	yes	characteristic
200	C₂²×C₁₆₃	—	2	2	no	—
201	C₂²×C₁₆₃	—	2	2	no	—
202	C₂²×C₁₆₃	C₂×#41	1	4	yes	—
203	C₂²×C₁₆₃	C₂⁵	1	1	yes	characteristic
204	C₂×D₁₆₃	—	2	2	no	—
205	C₂×D₁₆₃	—	2	2	no	—
206	C₂×D₁₆₃	—	2	1	no	—
207	C₂×D₁₆₃	—	2	1	no	—
208	C₂×D₁₆₃	—	2	4	no	—
209	C₂×D₁₆₃	—	2	4	no	—
210	C₂×D₁₆₃	—	2	4	no	—
211	C₂×D₁₆₃	—	2	1	no	—
212	C₂×D₁₆₃	—	4	16	no	—
213	C₂×D₁₆₃	C₂×#41	1	4	yes	—
214	C₄×C₁₆₃	—	2	2	no	—
215	C₄×C₁₆₃	—	2	2	no	—
216	C₄×C₁₆₃	—	2	2	no	—
217	C₄×C₁₆₃	—	2	4	no	—
218	C₄×C₁₆₃	—	2	1	no	—
219	C₄×C₁₆₃	C₂×#41	1	2	yes	—
220	C₄×C₁₆₃	C₂×#41	1	2	yes	—
221	Dic₁₆₃	—	2	1	no	—
222	Dic₁₆₃	—	2	1	no	—
223	Dic₁₆₃	—	2	2	no	—
224	Dic₁₆₃	—	2	2	no	—
225	Dic₁₆₃	—	2	2	no	—
226	Dic₁₆₃	H(5,𝔽₂)	1	2	yes	—
227	C₂×C₁₆₃	—	2	4	no	—
228	C₂×C₁₆₃	C₂²×#41	1	1	yes	characteristic
229	C₂×C₁₆₃	C₂²×#41	1	1	yes	characteristic
230	C₂×C₁₆₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
231	D₁₆₃	—	2	4	no	—
232	D₁₆₃	—	4	1	no	—
233	D₁₆₃	—	4	4	no	—
234	C₁₆₃	#3481	1	1	yes	characteristic, complemented, Sylow
235	#3481	—	163	1	no	maximal, Sylow
236	#559	—	163	1	no	—
237	#554	—	163	1	no	—
238	#554	D₁₆₃	1	1	yes	characteristic, complemented
239	#553	—	163	2	no	—
240	#553	—	163	2	no	—
241	#551	—	163	4	no	—
242	#546	—	163	2	no	—
243	#546	—	163	2	no	—
244	D₄²	—	163	1	no	—
245	#532	—	163	1	no	—
246	#529	—	163	2	no	—
247	#529	—	163	2	no	—
248	#525	—	163	4	no	—
249	C₄×#41	—	163	1	no	—
250	C₄×#41	—	163	1	no	—
251	C₂×C₄×D₄	—	163	2	no	—
252	C₂×C₄×D₄	—	163	2	no	—
253	C₂×#41	—	163	1	no	—
254	C₂×#41	—	163	2	no	—
255	C₂×#41	—	163	1	no	—
256	C₂²×D₄	—	163	2	no	—
257	C₂²×D₄	—	163	2	no	—
258	C₂³×C₄	—	163	4	no	—
259	C₄⋊Q₈	C₂×D₁₆₃	1	1	yes	characteristic, complemented
260	#127	—	163	1	no	—
261	#126	—	163	4	no	—
262	#126	—	163	4	no	—
263	#125	—	163	2	no	—
264	#125	C₂×D₁₆₃	1	2	yes	complemented
265	#124	—	163	2	no	—
266	#124	—	163	2	no	—
267	#124	—	163	2	no	—
268	#123	—	163	4	no	—
269	#123	—	163	4	no	—
270	#123	—	163	4	no	—
271	#123	—	163	4	no	—
272	C₂²⋊Q₈	—	163	4	no	—
273	C₂²⋊Q₈	—	163	2	no	—
274	C₂²⋊Q₈	C₂×D₁₆₃	1	4	yes	complemented
275	C₂²⋊Q₈	C₂×D₁₆₃	1	2	yes	complemented
276	#121	—	163	4	no	—
277	#121	—	163	2	no	—
278	#121	—	163	4	no	—
279	#121	—	163	2	no	—
280	#121	—	163	2	no	—
281	#121	—	163	2	no	—
282	#120	—	163	4	no	—
283	#120	—	163	4	no	—
284	C₄×Q₈	—	163	1	no	—
285	C₄×Q₈	—	163	1	no	—
286	C₄×Q₈	—	163	1	no	—
287	C₄×Q₈	C₂×D₁₆₃	1	1	yes	characteristic, complemented
288	C₄×D₄	—	163	1	no	—
289	C₄×D₄	—	163	4	no	—
290	C₄×D₄	—	163	2	no	—
291	C₄×D₄	—	163	1	no	—
292	C₄×D₄	—	163	4	no	—
293	C₄×D₄	—	163	2	no	—
294	C₄×D₄	—	163	2	no	—
295	C₄×D₄	—	163	2	no	—
296	C₄×D₄	—	163	4	no	—
297	C₄×D₄	—	163	2	no	—
298	C₄×D₄	—	163	2	no	—
299	C₄×D₄	—	163	4	no	—
300	C₄×D₄	—	163	2	no	—
301	C₄×D₄	—	163	2	no	—
302	C₄×D₄	—	163	1	no	—
303	C₄×D₄	—	163	2	no	—
304	C₄×D₄	C₂×D₁₆₃	1	2	yes	—
305	C₄×D₄	C₂×D₁₆₃	1	1	yes	characteristic
306	#117	—	163	2	no	—
307	#117	—	163	1	no	—
308	#117	—	163	1	no	—
309	#117	—	163	4	no	—
310	#117	—	163	2	no	—
311	C₂×C₄⋊C₄	—	163	2	no	—
312	C₂×C₄⋊C₄	C₂×D₁₆₃	1	2	yes	complemented
313	C₂×C₂²⋊C₄	—	163	4	no	—
314	C₂×C₂²⋊C₄	—	163	4	no	—
315	C₂×C₄²	—	163	2	no	—
316	C₂×C₄²	—	163	2	no	—
317	C₂×C₄²	—	163	1	no	—
318	C₂⁴	—	163	4	no	—
319	#41	—	326	4	no	—
320	#41	—	326	4	no	—
321	#41	—	652	4	no	—
322	C₂×Q₈	—	163	1	no	—
323	C₂×Q₈	C₂²×D₁₆₃	1	1	yes	characteristic
324	C₂×Q₈	C₂²×D₁₆₃	1	2	yes	—
325	C₂×D₄	—	326	8	no	—
326	C₂×D₄	—	326	8	no	—
327	C₂×D₄	—	163	2	no	—
328	C₂×D₄	—	163	4	no	—
329	C₂×D₄	—	163	2	no	—
330	C₂×D₄	—	163	4	no	—
331	C₂×D₄	—	163	2	no	—
332	C₂×D₄	—	163	2	no	—
333	C₂×D₄	—	163	2	no	—
334	C₂×D₄	—	163	4	no	—
335	C₂×D₄	—	163	1	no	—
336	C₂×D₄	C₂²×D₁₆₃	1	1	yes	characteristic
337	C₂²×C₄	—	652	8	no	—
338	C₂²×C₄	—	163	2	no	—
339	C₂²×C₄	—	163	2	no	—
340	C₂²×C₄	—	163	2	no	—
341	C₂²×C₄	—	163	2	no	—
342	C₂²×C₄	—	163	1	no	—
343	C₂²×C₄	—	163	1	no	—
344	C₂²×C₄	—	163	2	no	—
345	C₂²×C₄	—	163	1	no	—
346	C₂²×C₄	—	163	4	no	—
347	C₂²×C₄	—	163	4	no	—
348	C₂²×C₄	—	163	4	no	—
349	C₂²×C₄	C₂²×D₁₆₃	1	2	yes	—
350	C₂²×C₄	C₂²×D₁₆₃	1	4	yes	—
351	C₄⋊C₄	—	163	1	no	—
352	C₄⋊C₄	—	163	4	no	—
353	C₄⋊C₄	—	163	1	no	—
354	C₄⋊C₄	—	163	2	no	—
355	C₄⋊C₄	—	163	2	no	—
356	C₄⋊C₄	—	163	2	no	—
357	C₄⋊C₄	—	163	4	no	—
358	C₄⋊C₄	C₂²×D₁₆₃	1	2	yes	—
359	C₄⋊C₄	C₂²×D₁₆₃	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×D₁₆₃	1	2	yes	—
361	C₄⋊C₄	C₂²×D₁₆₃	1	4	yes	—
362	C₄⋊C₄	C₂²×D₁₆₃	1	2	yes	—
363	C₄⋊C₄	C₂²×D₁₆₃	1	1	yes	characteristic
364	C₄⋊C₄	C₂²×D₁₆₃	1	4	yes	—
365	C₂²⋊C₄	—	163	2	no	—
366	C₂²⋊C₄	—	163	2	no	—
367	C₂²⋊C₄	—	163	4	no	—
368	C₂²⋊C₄	—	163	4	no	—
369	C₂²⋊C₄	—	163	4	no	—
370	C₂²⋊C₄	—	163	4	no	—
371	C₂²⋊C₄	—	163	4	no	—
372	C₂²⋊C₄	—	163	2	no	—
373	C₂²⋊C₄	—	163	2	no	—
374	C₂²⋊C₄	—	163	2	no	—
375	C₂²⋊C₄	—	163	4	no	—
376	C₂²⋊C₄	—	163	4	no	—
377	C₂²⋊C₄	C₂²×D₁₆₃	1	4	yes	—
378	C₂²⋊C₄	C₂²×D₁₆₃	1	2	yes	—
379	C₄²	—	163	1	no	—
380	C₄²	—	163	1	no	—
381	C₄²	—	163	1	no	—
382	C₄²	—	163	2	no	—
383	C₄²	—	163	2	no	—
384	C₄²	—	163	2	no	—
385	C₄²	—	163	2	no	—
386	C₄²	—	163	2	no	—
387	C₄²	C₂²×D₁₆₃	1	2	yes	—
388	C₄²	C₂²×D₁₆₃	1	1	yes	characteristic
389	C₂³	—	326	8	no	—
390	C₂³	—	326	8	no	—
391	C₂³	—	652	4	no	—
392	C₂³	—	163	4	no	—
393	C₂³	—	163	1	no	—
394	C₂³	—	163	2	no	—
395	C₂³	C₂³×D₁₆₃	1	2	yes	—
396	Q₈	—	2	2	no	—
397	Q₈	—	4	2	no	—
398	Q₈	—	326	2	no	—
399	D₄	—	326	8	no	—
400	D₄	—	326	4	no	—
401	D₄	—	326	8	no	—
402	D₄	—	326	4	no	—
403	D₄	—	326	4	no	—
404	D₄	—	326	4	no	—
405	D₄	—	652	4	no	—
406	D₄	—	652	2	no	—
407	D₄	—	163	4	no	—
408	D₄	#14579700	1	4	yes	complemented
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	326	4	no	—
412	C₂×C₄	—	326	4	no	—
413	C₂×C₄	—	326	8	no	—
414	C₂×C₄	—	326	2	no	—
415	C₂×C₄	—	326	4	no	—
416	C₂×C₄	—	326	4	no	—
417	C₂×C₄	—	326	2	no	—
418	C₂×C₄	—	326	4	no	—
419	C₂×C₄	—	326	2	no	—
420	C₂×C₄	—	652	4	no	—
421	C₂×C₄	—	652	4	no	—
422	C₂×C₄	—	163	1	no	—
423	C₂×C₄	—	163	1	no	—
424	C₂×C₄	—	163	2	no	—
425	C₂×C₄	—	163	2	no	—
426	C₂×C₄	—	163	2	no	—
427	C₂×C₄	—	163	1	no	—
428	C₂×C₄	C₂³×D₁₆₃	1	2	yes	—
429	C₂×C₄	C₂³×D₁₆₃	1	2	yes	—
430	C₂×C₄	C₂³×D₁₆₃	1	2	yes	—
431	C₂×C₄	C₂³×D₁₆₃	1	1	yes	characteristic
432	C₂×C₄	C₂³×D₁₆₃	1	4	yes	—
433	C₂×C₄	C₂³×D₁₆₃	1	1	yes	characteristic
434	C₂×C₄	C₂³×D₁₆₃	1	1	yes	characteristic
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	326	2	no	—
438	C₂²	—	326	2	no	—
439	C₂²	—	326	1	no	—
440	C₂²	—	326	4	no	—
441	C₂²	—	326	1	no	—
442	C₂²	—	326	4	no	—
443	C₂²	—	326	4	no	—
444	C₂²	—	326	1	no	—
445	C₂²	—	652	16	no	—
446	C₂²	—	163	4	no	—
447	C₂²	C₂×#14579700	1	4	yes	—
448	C₂²	C₂⁴×D₁₆₃	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	2	4	no	—
453	C₄	—	2	1	no	—
454	C₄	—	326	1	no	—
455	C₄	—	326	1	no	—
456	C₄	—	326	2	no	—
457	C₄	—	326	2	no	—
458	C₄	—	326	2	no	—
459	C₄	—	163	2	no	—
460	C₄	#41×D₁₆₃	1	2	yes	—
461	C₄	C₂×#14579700	1	2	yes	—
462	C₂	—	2	4	no	—
463	C₂	—	326	4	no	—
464	C₂	—	652	4	no	—
465	C₂	—	652	1	no	—
466	C₂	C₂×#41×D₁₆₃	1	1	yes	characteristic
467	C₂	C₂²×#14579700	1	1	yes	characteristic
468	C₂	H(5,𝔽₂)×D₁₆₃	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	#3481
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. #23782400	C₂	semidirect
2. #23782376	C₂	semidirect
3. #23782368	C₂	semidirect
4. #23782363	C₂	semidirect
5. #23782342	C₂	semidirect
6. #23782310	C₂	semidirect
7. #23782306	C₂	semidirect
8. D₄×D₆₅₂	C₂	semidirect
9. #23782216	C₂	semidirect
10. #23782201	C₂	semidirect
11. #23782200	C₂	semidirect
12. #23782178	C₂	semidirect
13. C₄×#14579700	C₂	semidirect
14. C₄×#14579698	C₂	semidirect
15. C₂×#19104697	C₂	semidirect
16. C₄×D₄×D₁₆₃	C₂	semidirect
17. #554×C₁₆₃	C₂	semidirect
19. C₂×#14579700	C₂²	semidirect
23. C₂²×C₄×D₁₆₃	C₂²	semidirect
25. #19104730	C₂²	semidirect
26. #19104730	C₂²	semidirect
27. #19104726	C₂²	semidirect
28. #19104724	C₂²	semidirect
29. #19104724	C₂²	semidirect
30. #19104723	C₂²	semidirect
31. #19104720	C₂²	semidirect
32. #19104720	C₂²	semidirect
33. #19104720	C₂²	semidirect
34. #19104719	C₂²	semidirect
35. #19104715	C₂²	semidirect
36. #19104711	C₂²	semidirect
38. #19104710	C₂²	semidirect
39. #19104710	C₂²	semidirect
40. #19104710	C₂²	semidirect
42. #19104709	C₂²	semidirect
44. #19104705	C₂²	semidirect
45. Q₈×Dic₁₆₃	C₂²	semidirect
46. C₄×Dic₃₂₆	C₂²	semidirect
47. #19104700	C₂²	semidirect
49. C₄×D₆₅₂	C₂²	semidirect
50. C₄×D₆₅₂	C₂²	semidirect
54. #19104697	C₂²	semidirect
55. #19104697	C₂²	semidirect
56. #19104697	C₂²	semidirect
57. #19104697	C₂²	semidirect
58. #19104697	C₂²	semidirect
59. #19104697	C₂²	semidirect
60. C₄×C₂²⋊D₁₆₃	C₂²	semidirect
61. C₄×C₂²⋊D₁₆₃	C₂²	semidirect
62. (C₂²⋊D₁₆₃)⋊C₄	C₂²	semidirect
63. (C₂²⋊D₁₆₃)⋊C₄	C₂²	semidirect
64. #19104693	C₂²	semidirect
65. #19104693	C₂²	semidirect
66. #19104693	C₂²	semidirect
67. #19104693	C₂²	semidirect
68. #19104691	C₂²	semidirect
69. C₄⋊C₄×D₁₆₃	C₂²	semidirect
70. C₂×(C₂×D₁₆₃)⋊C₄	C₂²	semidirect
71. C₂²⋊C₄×D₁₆₃	C₂²	semidirect
72. C₂×C₄×Dic₁₆₃	C₂²	semidirect
73. C₄²×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
167. D₆₅₂	#41	semidirect
190. D₄×C₁₆₃	#41	semidirect
234. C₁₆₃	#3481	semidirect
238. #554	D₁₆₃	semidirect
259. C₄⋊Q₈	C₂×D₁₆₃	semidirect
264. #125	C₂×D₁₆₃	semidirect
274. C₂²⋊Q₈	C₂×D₁₆₃	semidirect
275. C₂²⋊Q₈	C₂×D₁₆₃	semidirect
287. C₄×Q₈	C₂×D₁₆₃	semidirect
312. C₂×C₄⋊C₄	C₂×D₁₆₃	semidirect
408. D₄	#14579700	semidirect

Maximal subgroups

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

subgroup	index
#23782400	2
#23782376	2
#23782368	2
#23782363	2
#23782342	2
#23782310	2
#23782306	2
D₄×D₆₅₂	2
#23782216	2
#23782201	2
#23782200	2
#23782178	2
C₄×#14579700	2
C₄×#14579698	2
C₂×#19104697	2
C₄×D₄×D₁₆₃	2
#554×C₁₆₃	2
#3481	163