Subgroups — #35228580

Order 20864.

1124 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782389	C₂	1	1	yes	maximal, characteristic, complemented
2	#23782373	C₂	1	2	yes	maximal, complemented
3	#23782356	C₂	1	2	yes	maximal, complemented
4	#23782339	C₂	1	4	yes	maximal, complemented
5	#23782330	C₂	1	1	yes	maximal, characteristic, complemented
6	#23782327	C₂	1	2	yes	maximal, complemented
7	#23782318	C₂	1	1	yes	maximal, characteristic, complemented
8	#23782318	C₂	1	1	yes	maximal, characteristic, complemented
9	#23782306	C₂	1	2	yes	maximal, complemented
10	#23782287	C₂	1	2	yes	maximal, complemented
11	#23782263	C₂	1	4	yes	maximal, complemented
12	#23782199	C₂	1	1	yes	maximal, characteristic, complemented
13	#23782178	C₂	1	2	yes	maximal, complemented
14	C₂²⋊Q₈×D₁₆₃	C₂	1	2	yes	maximal, complemented
15	#23782147	C₂	1	2	yes	maximal, complemented
16	C₂×C₄×D₆₅₂	C₂	1	1	yes	maximal, characteristic, complemented
17	#533×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14579700	C₂²	1	2	yes	—
19	C₂×#14579700	C₂²	1	2	yes	complemented
20	C₂×Q₈×D₁₆₃	C₂²	1	2	yes	complemented
21	C₂²×D₆₅₂	C₂²	1	1	yes	characteristic
22	C₂²×C₄×D₁₆₃	C₂²	1	2	yes	—
23	#19104734	C₂²	1	2	yes	complemented
24	#19104730	C₂²	1	4	yes	complemented
25	#19104729	C₂²	1	2	yes	complemented
26	#19104729	C₂²	1	4	yes	complemented
27	#19104727	C₂²	1	1	yes	characteristic, complemented
28	#19104725	C₂²	1	4	yes	complemented
29	#19104724	C₂²	1	2	yes	—
30	#19104723	C₂²	1	1	yes	characteristic, complemented
31	#19104723	C₂²	1	4	yes	complemented
32	#19104720	C₂²	1	4	yes	—
33	#19104720	C₂²	1	4	yes	complemented
34	#19104720	C₂²	1	4	yes	complemented
35	#19104720	C₂²	1	4	yes	complemented
36	#19104718	C₂²	1	2	yes	—
37	#19104715	C₂²	1	2	yes	complemented
38	#19104715	C₂²	1	4	yes	complemented
39	#19104714	C₂²	1	1	yes	characteristic
40	#19104713	C₂²	1	4	yes	complemented
41	#19104713	C₂²	1	4	yes	complemented
42	#19104712	C₂²	1	4	yes	—
43	#19104711	C₂²	1	2	yes	complemented
44	#19104711	C₂²	1	2	yes	complemented
45	#19104711	C₂²	1	2	yes	complemented
46	#19104710	C₂²	1	4	yes	—
47	#19104710	C₂²	1	2	yes	—
48	#19104710	C₂²	1	2	yes	complemented
49	#19104709	C₂²	1	1	yes	characteristic
50	#19104705	C₂²	1	4	yes	—
51	Q₈×Dic₁₆₃	C₂²	1	2	yes	complemented
52	C₄×Dic₃₂₆	C₂²	1	1	yes	characteristic, complemented
53	C₄×D₆₅₂	C₂²	1	1	yes	characteristic
54	C₄×D₆₅₂	C₂²	1	2	yes	—
55	C₄×D₆₅₂	C₂²	1	1	yes	characteristic
56	C₄×D₆₅₂	C₂²	1	1	yes	characteristic
57	C₄×D₆₅₂	C₂²	1	1	yes	characteristic
58	C₄×D₆₅₂	C₂²	1	2	yes	—
59	C₄×D₆₅₂	C₂²	1	4	yes	complemented
60	C₄×D₆₅₂	C₂²	1	1	yes	characteristic, complemented
61	#19104697	C₂²	1	2	yes	—
62	#19104697	C₂²	1	4	yes	complemented
63	C₄×C₂²⋊D₁₆₃	C₂²	1	2	yes	—
64	(C₂²⋊D₁₆₃)⋊C₄	C₂²	1	4	yes	—
65	#19104693	C₂²	1	2	yes	complemented
66	#19104692	C₂²	1	2	yes	complemented
67	#19104692	C₂²	1	4	yes	complemented
68	C₂×C₄⋊Dic₁₆₃	C₂²	1	1	yes	characteristic
69	C₄⋊C₄×D₁₆₃	C₂²	1	4	yes	complemented
70	C₄⋊C₄×D₁₆₃	C₂²	1	2	yes	complemented
71	C₄⋊C₄×D₁₆₃	C₂²	1	2	yes	complemented
72	C₂×(C₂×D₁₆₃)⋊C₄	C₂²	1	2	yes	—
73	C₂²⋊C₄×D₁₆₃	C₂²	1	4	yes	—
74	C₄⋊Q₈×C₁₆₃	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	—
78	C₂²⋊Q₈×C₁₆₃	C₂²	1	2	yes	—
79	C₄×Q₈×C₁₆₃	C₂²	1	2	yes	complemented
80	C₄×Q₈×C₁₆₃	C₂²	1	2	yes	complemented
81	#117×C₁₆₃	C₂²	1	2	yes	—
82	C₂×C₄²×C₁₆₃	C₂²	1	1	yes	characteristic
83	C₂³×D₁₆₃	C₂³	1	2	yes	—
84	#14579700	—	2	8	no	—
85	#14579700	—	4	4	no	—
86	C₂×Dic₃₂₆	C₂³	1	1	yes	characteristic
87	C₂×Dic₃₂₆	C₂³	1	4	yes	—
88	Q₈×D₁₆₃	—	4	4	no	—
89	C₂×D₆₅₂	—	2	4	no	—
90	C₂×D₆₅₂	C₂³	1	2	yes	—
91	C₂×D₆₅₂	C₂³	1	1	yes	characteristic
92	C₂×D₆₅₂	C₂³	1	4	yes	—
93	C₂×D₆₅₂	C₂³	1	1	yes	characteristic
94	C₂×D₆₅₂	C₂³	1	4	yes	—
95	C₂×D₆₅₂	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊D₁₆₃	C₂³	1	2	yes	—
97	C₂²×Dic₁₆₃	C₂³	1	2	yes	—
98	C₂×C₄×D₁₆₃	—	4	4	no	—
99	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
100	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
101	C₂×C₄×D₁₆₃	C₂³	1	4	yes	—
102	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
103	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
104	C₂×C₄×D₁₆₃	C₂³	1	2	yes	—
105	C₂×C₄×D₁₆₃	C₂³	1	4	yes	—
106	C₂×C₄×D₁₆₃	C₂³	1	4	yes	—
107	C₄⋊Dic₁₆₃	C₂³	1	1	yes	characteristic
108	C₄⋊Dic₁₆₃	C₂³	1	1	yes	characteristic
109	C₄⋊Dic₁₆₃	C₂³	1	4	yes	—
110	C₄⋊Dic₁₆₃	C₂³	1	1	yes	characteristic
111	C₄⋊Dic₁₆₃	C₂³	1	2	yes	—
112	C₄⋊Dic₁₆₃	C₂³	1	1	yes	characteristic
113	Dic₁₆₃⋊C₄	C₂³	1	4	yes	—
114	Dic₁₆₃⋊C₄	C₂³	1	2	yes	—
115	Dic₁₆₃⋊C₄	C₂³	1	4	yes	—
116	Dic₁₆₃⋊C₄	C₂³	1	2	yes	—
117	Dic₁₆₃⋊C₄	C₂³	1	4	yes	—
118	Dic₁₆₃⋊C₄	C₂³	1	2	yes	—
119	Dic₁₆₃⋊C₄	C₂³	1	2	yes	—
120	C₂²⋊Dic₁₆₃	C₂³	1	2	yes	—
121	(C₂×D₁₆₃)⋊C₄	C₂³	1	4	yes	—
122	(C₂×D₁₆₃)⋊C₄	C₂³	1	4	yes	—
123	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	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	2	yes	—
129	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
130	(C₂×D₁₆₃)⋊C₄	C₂³	1	4	yes	—
131	(C₂×D₁₆₃)⋊C₄	C₂³	1	4	yes	—
132	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
133	(C₂×D₁₆₃)⋊C₄	C₂³	1	2	yes	—
134	C₄×Dic₁₆₃	C₂³	1	4	yes	—
135	C₄×Dic₁₆₃	C₂³	1	2	yes	—
136	C₂×Q₈×C₁₆₃	C₂³	1	2	yes	—
137	C₂×Q₈×C₁₆₃	C₂³	1	2	yes	—
138	C₂²×C₄×C₁₆₃	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₁₆₃	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₁₆₃	C₂³	1	1	yes	characteristic
141	C₄⋊C₄×C₁₆₃	C₂³	1	2	yes	—
142	C₄⋊C₄×C₁₆₃	C₂³	1	2	yes	—
143	C₄⋊C₄×C₁₆₃	C₂³	1	4	yes	—
144	C₄⋊C₄×C₁₆₃	C₂³	1	4	yes	—
145	C₄⋊C₄×C₁₆₃	C₂³	1	2	yes	—
146	C₄⋊C₄×C₁₆₃	C₂³	1	2	yes	—
147	C₂²⋊C₄×C₁₆₃	C₂³	1	4	yes	—
148	C₄²×C₁₆₃	C₂³	1	1	yes	characteristic
149	C₄²×C₁₆₃	C₂³	1	1	yes	characteristic
150	C₄²×C₁₆₃	C₂³	1	1	yes	characteristic
151	C₄²×C₁₆₃	C₂³	1	1	yes	characteristic
152	C₄²×C₁₆₃	C₂³	1	4	yes	—
153	C₂²×D₁₆₃	—	2	4	no	—
154	C₂²×D₁₆₃	—	2	4	no	—
155	C₂²×D₁₆₃	—	4	2	no	—
156	C₂²×D₁₆₃	C₂⁴	1	2	yes	—
157	C₂²×D₁₆₃	C₂⁴	1	2	yes	—
158	C₂²×D₁₆₃	C₂⁴	1	2	yes	—
159	Dic₃₂₆	—	2	2	no	—
160	Dic₃₂₆	—	4	4	no	—
161	D₆₅₂	—	2	4	no	—
162	D₆₅₂	—	2	8	no	—
163	D₆₅₂	—	2	2	no	—
164	D₆₅₂	—	2	2	no	—
165	D₆₅₂	—	4	4	no	—
166	D₆₅₂	#41	1	4	yes	complemented
167	C₂²⋊D₁₆₃	—	2	4	no	—
168	C₂×Dic₁₆₃	—	4	2	no	—
169	C₂×Dic₁₆₃	C₂⁴	1	2	yes	—
170	C₂×Dic₁₆₃	C₂⁴	1	2	yes	—
171	C₂×Dic₁₆₃	C₂⁴	1	2	yes	—
172	C₂×Dic₁₆₃	C₂⁴	1	2	yes	—
173	C₂×Dic₁₆₃	C₂⁴	1	2	yes	—
174	C₄×D₁₆₃	—	2	8	no	—
175	C₄×D₁₆₃	—	2	4	no	—
176	C₄×D₁₆₃	—	2	4	no	—
177	C₄×D₁₆₃	—	2	4	no	—
178	C₄×D₁₆₃	—	4	2	no	—
179	C₄×D₁₆₃	—	4	2	no	—
180	C₄×D₁₆₃	—	4	4	no	—
181	C₄×D₁₆₃	—	4	4	no	—
182	C₂³×C₁₆₃	C₂⁴	1	1	yes	characteristic
183	Q₈×C₁₆₃	—	2	4	no	—
184	Q₈×C₁₆₃	—	2	4	no	—
185	C₂×C₄×C₁₆₃	—	2	2	no	—
186	C₂×C₄×C₁₆₃	—	2	2	no	—
187	C₂×C₄×C₁₆₃	—	2	2	no	—
188	C₂×C₄×C₁₆₃	C₂⁴	1	1	yes	characteristic
189	C₂×C₄×C₁₆₃	C₂⁴	1	1	yes	characteristic
190	C₂×C₄×C₁₆₃	C₂⁴	1	1	yes	characteristic
191	C₂×C₄×C₁₆₃	C₂⁴	1	1	yes	characteristic
192	C₂×C₄×C₁₆₃	C₂⁴	1	4	yes	—
193	C₂×C₄×C₁₆₃	C₂⁴	1	4	yes	—
194	C₂×C₄×C₁₆₃	C₂⁴	1	1	yes	characteristic
195	C₂×C₄×C₁₆₃	C₂⁴	1	1	yes	characteristic
196	C₂²×C₁₆₃	—	2	1	no	—
197	C₂²×C₁₆₃	—	2	1	no	—
198	C₂²×C₁₆₃	2₋¹⁺⁴	1	2	yes	—
199	C₂²×C₁₆₃	C₂⁵	1	1	yes	characteristic
200	C₂×D₁₆₃	—	2	2	no	—
201	C₂×D₁₆₃	—	2	2	no	—
202	C₂×D₁₆₃	—	2	2	no	—
203	C₂×D₁₆₃	—	2	2	no	—
204	C₂×D₁₆₃	—	2	2	no	—
205	C₂×D₁₆₃	—	2	2	no	—
206	C₂×D₁₆₃	—	2	2	no	—
207	C₂×D₁₆₃	—	2	2	no	—
208	C₂×D₁₆₃	—	4	8	no	—
209	C₂×D₁₆₃	C₂×#41	1	4	yes	—
210	C₄×C₁₆₃	—	2	1	no	—
211	C₄×C₁₆₃	—	2	4	no	—
212	C₄×C₁₆₃	—	2	1	no	—
213	C₄×C₁₆₃	—	2	4	no	—
214	C₄×C₁₆₃	—	2	1	no	—
215	C₄×C₁₆₃	—	2	1	no	—
216	C₄×C₁₆₃	C₂×#41	1	2	yes	—
217	C₄×C₁₆₃	H(5,𝔽₂)	1	2	yes	—
218	Dic₁₆₃	—	2	2	no	—
219	Dic₁₆₃	—	2	2	no	—
220	Dic₁₆₃	—	2	2	no	—
221	Dic₁₆₃	—	2	2	no	—
222	Dic₁₆₃	—	2	2	no	—
223	C₂×C₁₆₃	—	2	2	no	—
224	C₂×C₁₆₃	C₂²×#41	1	1	yes	characteristic
225	C₂×C₁₆₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
226	C₂×C₁₆₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
227	D₁₆₃	—	2	4	no	—
228	D₁₆₃	—	4	2	no	—
229	D₁₆₃	—	4	2	no	—
230	C₁₆₃	#3520	1	1	yes	characteristic, complemented, Sylow
231	#3520	—	163	1	no	maximal, Sylow
232	#556	—	163	1	no	—
233	#554	—	163	2	no	—
234	#552	—	163	2	no	—
235	#551	—	163	4	no	—
236	D₄×Q₈	—	163	1	no	—
237	#548	—	163	2	no	—
238	#547	—	163	1	no	—
239	#547	—	163	1	no	—
240	#546	—	163	2	no	—
241	#542	—	163	2	no	—
242	#539	—	163	4	no	—
243	#533	D₁₆₃	1	1	yes	characteristic, complemented
244	#529	—	163	1	no	—
245	#525	—	163	2	no	—
246	C₂×C₂²⋊Q₈	—	163	2	no	—
247	#520	—	163	2	no	—
248	C₂×C₄×D₄	—	163	1	no	—
249	C₂×#41	—	163	2	no	—
250	C₂×#41	—	163	2	no	—
251	C₂²×Q₈	—	163	2	no	—
252	C₂²×D₄	—	163	1	no	—
253	C₂³×C₄	—	163	2	no	—
254	C₄⋊Q₈	—	163	2	no	—
255	C₄⋊Q₈	C₂×D₁₆₃	1	1	yes	characteristic, complemented
256	C₄⋊Q₈	C₂×D₁₆₃	1	1	yes	characteristic, complemented
257	#126	—	163	4	no	—
258	#126	—	163	2	no	—
259	#126	—	163	4	no	—
260	#125	—	163	4	no	—
261	#125	—	163	1	no	—
262	#125	C₂×D₁₆₃	1	2	yes	complemented
263	#124	—	163	2	no	—
264	#124	—	163	1	no	—
265	#124	—	163	4	no	—
266	#123	—	163	2	no	—
267	#123	—	163	4	no	—
268	#123	—	163	4	no	—
269	#123	—	163	4	no	—
270	#123	—	163	4	no	—
271	C₂²⋊Q₈	—	163	2	no	—
272	C₂²⋊Q₈	—	163	2	no	—
273	C₂²⋊Q₈	—	163	2	no	—
274	C₂²⋊Q₈	—	163	1	no	—
275	C₂²⋊Q₈	—	163	4	no	—
276	C₂²⋊Q₈	—	163	2	no	—
277	C₂²⋊Q₈	—	163	4	no	—
278	C₂²⋊Q₈	—	163	4	no	—
279	C₂²⋊Q₈	—	163	4	no	—
280	C₂²⋊Q₈	C₂×D₁₆₃	1	2	yes	—
281	C₂²⋊Q₈	C₂×D₁₆₃	1	2	yes	—
282	#121	—	163	1	no	—
283	#121	—	163	2	no	—
284	#121	—	163	4	no	—
285	#121	—	163	2	no	—
286	#120	—	163	4	no	—
287	C₄×Q₈	—	163	2	no	—
288	C₄×Q₈	—	163	1	no	—
289	C₄×Q₈	C₂×D₁₆₃	1	2	yes	complemented
290	C₄×Q₈	C₂×D₁₆₃	1	2	yes	complemented
291	C₄×D₄	—	163	2	no	—
292	C₄×D₄	—	163	4	no	—
293	C₄×D₄	—	163	2	no	—
294	C₄×D₄	—	163	4	no	—
295	C₄×D₄	—	163	1	no	—
296	C₄×D₄	—	163	2	no	—
297	C₄×D₄	—	163	1	no	—
298	C₄×D₄	—	163	1	no	—
299	C₄×D₄	—	163	1	no	—
300	C₄×D₄	—	163	2	no	—
301	C₄×D₄	—	163	4	no	—
302	C₄×D₄	—	163	1	no	—
303	#117	—	163	2	no	—
304	#117	—	163	2	no	—
305	#117	—	163	4	no	—
306	#117	C₂×D₁₆₃	1	2	yes	—
307	C₂×C₄⋊C₄	—	163	1	no	—
308	C₂×C₄⋊C₄	—	163	4	no	—
309	C₂×C₄⋊C₄	—	163	2	no	—
310	C₂×C₄⋊C₄	—	163	2	no	—
311	C₂×C₂²⋊C₄	—	163	2	no	—
312	C₂×C₂²⋊C₄	—	163	4	no	—
313	C₂×C₄²	C₂×D₁₆₃	1	1	yes	characteristic
314	C₂⁴	—	163	2	no	—
315	#41	—	326	8	no	—
316	#41	—	652	4	no	—
317	C₂×Q₈	—	652	4	no	—
318	C₂×Q₈	—	163	1	no	—
319	C₂×Q₈	—	163	4	no	—
320	C₂×Q₈	C₂²×D₁₆₃	1	2	yes	—
321	C₂×Q₈	C₂²×D₁₆₃	1	2	yes	—
322	C₂×D₄	—	326	4	no	—
323	C₂×D₄	—	163	2	no	—
324	C₂×D₄	—	163	4	no	—
325	C₂×D₄	—	163	2	no	—
326	C₂×D₄	—	163	1	no	—
327	C₂×D₄	—	163	1	no	—
328	C₂×D₄	—	163	4	no	—
329	C₂×D₄	—	163	1	no	—
330	C₂²×C₄	—	652	4	no	—
331	C₂²×C₄	—	163	4	no	—
332	C₂²×C₄	—	163	2	no	—
333	C₂²×C₄	—	163	2	no	—
334	C₂²×C₄	—	163	2	no	—
335	C₂²×C₄	—	163	2	no	—
336	C₂²×C₄	—	163	4	no	—
337	C₂²×C₄	—	163	2	no	—
338	C₂²×C₄	—	163	4	no	—
339	C₂²×C₄	—	163	2	no	—
340	C₂²×C₄	C₂²×D₁₆₃	1	1	yes	characteristic
341	C₂²×C₄	C₂²×D₁₆₃	1	1	yes	characteristic
342	C₂²×C₄	C₂²×D₁₆₃	1	1	yes	characteristic
343	C₄⋊C₄	—	163	1	no	—
344	C₄⋊C₄	—	163	2	no	—
345	C₄⋊C₄	—	163	4	no	—
346	C₄⋊C₄	—	163	1	no	—
347	C₄⋊C₄	—	163	2	no	—
348	C₄⋊C₄	—	163	1	no	—
349	C₄⋊C₄	—	163	4	no	—
350	C₄⋊C₄	—	163	4	no	—
351	C₄⋊C₄	—	163	2	no	—
352	C₄⋊C₄	—	163	1	no	—
353	C₄⋊C₄	—	163	4	no	—
354	C₄⋊C₄	—	163	2	no	—
355	C₄⋊C₄	—	163	2	no	—
356	C₄⋊C₄	C₂²×D₁₆₃	1	2	yes	—
357	C₄⋊C₄	C₂²×D₁₆₃	1	2	yes	—
358	C₄⋊C₄	C₂²×D₁₆₃	1	4	yes	—
359	C₄⋊C₄	C₂²×D₁₆₃	1	2	yes	—
360	C₄⋊C₄	C₂²×D₁₆₃	1	2	yes	—
361	C₄⋊C₄	C₂²×D₁₆₃	1	4	yes	—
362	C₂²⋊C₄	—	163	2	no	—
363	C₂²⋊C₄	—	163	2	no	—
364	C₂²⋊C₄	—	163	2	no	—
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	2	no	—
371	C₂²⋊C₄	—	163	2	no	—
372	C₂²⋊C₄	—	163	4	no	—
373	C₂²⋊C₄	—	163	2	no	—
374	C₂²⋊C₄	—	163	4	no	—
375	C₂²⋊C₄	—	163	2	no	—
376	C₂²⋊C₄	C₂²×D₁₆₃	1	4	yes	—
377	C₄²	—	163	4	no	—
378	C₄²	—	163	2	no	—
379	C₄²	C₂²×D₁₆₃	1	1	yes	characteristic
380	C₄²	C₂²×D₁₆₃	1	1	yes	characteristic
381	C₄²	C₂²×D₁₆₃	1	1	yes	characteristic
382	C₄²	C₂²×D₁₆₃	1	1	yes	characteristic
383	C₄²	C₂²×D₁₆₃	1	4	yes	—
384	C₂³	—	326	4	no	—
385	C₂³	—	326	4	no	—
386	C₂³	—	652	2	no	—
387	C₂³	—	163	2	no	—
388	C₂³	—	163	2	no	—
389	C₂³	—	163	2	no	—
390	C₂³	C₂³×D₁₆₃	1	1	yes	characteristic
391	Q₈	—	2	4	no	—
392	Q₈	—	2	4	no	—
393	Q₈	—	326	2	no	—
394	Q₈	—	652	4	no	—
395	D₄	—	326	4	no	—
396	D₄	—	326	8	no	—
397	D₄	—	326	4	no	—
398	D₄	—	326	2	no	—
399	D₄	—	326	2	no	—
400	D₄	—	652	4	no	—
401	D₄	—	163	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	326	8	no	—
406	C₂×C₄	—	326	4	no	—
407	C₂×C₄	—	326	4	no	—
408	C₂×C₄	—	326	4	no	—
409	C₂×C₄	—	652	2	no	—
410	C₂×C₄	—	652	2	no	—
411	C₂×C₄	—	652	4	no	—
412	C₂×C₄	—	652	4	no	—
413	C₂×C₄	—	652	2	no	—
414	C₂×C₄	—	163	2	no	—
415	C₂×C₄	—	163	2	no	—
416	C₂×C₄	—	163	2	no	—
417	C₂×C₄	—	163	2	no	—
418	C₂×C₄	—	163	2	no	—
419	C₂×C₄	C₂³×D₁₆₃	1	4	yes	—
420	C₂×C₄	C₂³×D₁₆₃	1	1	yes	characteristic
421	C₂×C₄	C₂³×D₁₆₃	1	1	yes	characteristic
422	C₂×C₄	C₂³×D₁₆₃	1	1	yes	characteristic
423	C₂×C₄	C₂³×D₁₆₃	1	1	yes	characteristic
424	C₂×C₄	C₂³×D₁₆₃	1	4	yes	—
425	C₂×C₄	C₂³×D₁₆₃	1	1	yes	characteristic
426	C₂×C₄	C₂³×D₁₆₃	1	1	yes	characteristic
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	326	2	no	—
430	C₂²	—	326	2	no	—
431	C₂²	—	326	2	no	—
432	C₂²	—	326	2	no	—
433	C₂²	—	326	2	no	—
434	C₂²	—	326	2	no	—
435	C₂²	—	326	2	no	—
436	C₂²	—	326	2	no	—
437	C₂²	—	652	8	no	—
438	C₂²	—	163	4	no	—
439	C₂²	#19104783	1	2	yes	—
440	C₂²	C₂⁴×D₁₆₃	1	1	yes	characteristic
441	C₄	—	2	1	no	—
442	C₄	—	2	4	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	4	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	326	2	no	—
448	C₄	—	326	2	no	—
449	C₄	—	326	2	no	—
450	C₄	—	326	2	no	—
451	C₄	—	326	2	no	—
452	C₄	#41×D₁₆₃	1	2	yes	—
453	C₄	#19104781	1	2	yes	—
454	C₂	—	2	2	no	—
455	C₂	—	326	4	no	—
456	C₂	—	652	2	no	—
457	C₂	—	652	2	no	—
458	C₂	C₂×#41×D₁₆₃	1	1	yes	characteristic
459	C₂	C₂×#19104781	1	1	yes	characteristic
460	C₂	C₂×#19104783	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₆₃
commutator, socle, cosocle	C₂²×C₁₆₃	C₂⁵
Fitting	#533×C₁₆₃	C₂
hypercenter	#533	D₁₆₃
hypocenter	C₁₆₃	#3520
LCS	G ▷ C₂²×C₁₆₃ ▷ C₁₆₃
UCS	C₁ ◁ C₂² ◁ #533

Complements

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

N	H ≅ G/N	type
1. #23782389	C₂	semidirect
2. #23782373	C₂	semidirect
3. #23782356	C₂	semidirect
4. #23782339	C₂	semidirect
5. #23782330	C₂	semidirect
6. #23782327	C₂	semidirect
7. #23782318	C₂	semidirect
8. #23782318	C₂	semidirect
9. #23782306	C₂	semidirect
10. #23782287	C₂	semidirect
11. #23782263	C₂	semidirect
12. #23782199	C₂	semidirect
13. #23782178	C₂	semidirect
14. C₂²⋊Q₈×D₁₆₃	C₂	semidirect
15. #23782147	C₂	semidirect
16. C₂×C₄×D₆₅₂	C₂	semidirect
17. #533×C₁₆₃	C₂	semidirect
19. C₂×#14579700	C₂²	semidirect
20. C₂×Q₈×D₁₆₃	C₂²	semidirect
23. #19104734	C₂²	semidirect
24. #19104730	C₂²	semidirect
25. #19104729	C₂²	semidirect
26. #19104729	C₂²	semidirect
27. #19104727	C₂²	semidirect
28. #19104725	C₂²	semidirect
30. #19104723	C₂²	semidirect
31. #19104723	C₂²	semidirect
33. #19104720	C₂²	semidirect
34. #19104720	C₂²	semidirect
35. #19104720	C₂²	semidirect
37. #19104715	C₂²	semidirect
38. #19104715	C₂²	semidirect
40. #19104713	C₂²	semidirect
41. #19104713	C₂²	semidirect
43. #19104711	C₂²	semidirect
44. #19104711	C₂²	semidirect
45. #19104711	C₂²	semidirect
48. #19104710	C₂²	semidirect
51. Q₈×Dic₁₆₃	C₂²	semidirect
52. C₄×Dic₃₂₆	C₂²	semidirect
59. C₄×D₆₅₂	C₂²	semidirect
60. C₄×D₆₅₂	C₂²	semidirect
62. #19104697	C₂²	semidirect
65. #19104693	C₂²	semidirect
66. #19104692	C₂²	semidirect
67. #19104692	C₂²	semidirect
69. C₄⋊C₄×D₁₆₃	C₂²	semidirect
70. C₄⋊C₄×D₁₆₃	C₂²	semidirect
71. C₄⋊C₄×D₁₆₃	C₂²	semidirect
74. C₄⋊Q₈×C₁₆₃	C₂²	semidirect
75. C₄⋊Q₈×C₁₆₃	C₂²	semidirect
76. #125×C₁₆₃	C₂²	semidirect
79. C₄×Q₈×C₁₆₃	C₂²	semidirect
80. C₄×Q₈×C₁₆₃	C₂²	semidirect
166. D₆₅₂	#41	semidirect
230. C₁₆₃	#3520	semidirect
243. #533	D₁₆₃	semidirect
255. C₄⋊Q₈	C₂×D₁₆₃	semidirect
256. C₄⋊Q₈	C₂×D₁₆₃	semidirect
262. #125	C₂×D₁₆₃	semidirect
289. C₄×Q₈	C₂×D₁₆₃	semidirect
290. C₄×Q₈	C₂×D₁₆₃	semidirect

Maximal subgroups

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

subgroup	index
#23782389	2
#23782373	2
#23782356	2
#23782339	2
#23782330	2
#23782327	2
#23782318	2
#23782306	2
#23782287	2
#23782263	2
#23782199	2
#23782178	2
C₂²⋊Q₈×D₁₆₃	2
#23782147	2
C₂×C₄×D₆₅₂	2
#533×C₁₆₃	2
#3520	163