Subgroups — #3489×C₁₆₃ #35212247

Order 20864.

1522 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×2₋¹⁺⁴×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#41×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Q₈×C₁₆₃	C₂	1	2	yes	maximal, complemented
4	#548×C₁₆₃	C₂	1	2	yes	maximal, complemented
5	#547×C₁₆₃	C₂	1	6	yes	maximal, complemented
6	#546×C₁₆₃	C₂	1	6	yes	maximal, complemented
7	#537×C₁₆₃	C₂	1	3	yes	maximal, complemented
8	#536×C₁₆₃	C₂	1	3	yes	maximal, complemented
9	#525×C₁₆₃	C₂	1	3	yes	maximal, complemented
10	C₂×C₂²⋊Q₈×C₁₆₃	C₂	1	3	yes	maximal, complemented
11	#520×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
12	2₋¹⁺⁴×C₁₆₃	—	2	8	no	—
13	C₂×#41×C₁₆₃	—	2	8	no	—
14	C₂×#41×C₁₆₃	C₂²	1	3	yes	—
15	C₂×#41×C₁₆₃	C₂²	1	3	yes	—
16	C₂×#41×C₁₆₃	C₂²	1	1	yes	characteristic
17	C₂×#41×C₁₆₃	C₂²	1	1	yes	characteristic
18	C₂×#41×C₁₆₃	C₂²	1	3	yes	complemented
19	C₂×#41×C₁₆₃	C₂²	1	6	yes	complemented
20	C₂²×Q₈×C₁₆₃	C₂²	1	1	yes	characteristic
21	C₂²×Q₈×C₁₆₃	C₂²	1	3	yes	complemented
22	C₂²×Q₈×C₁₆₃	C₂²	1	2	yes	complemented
23	C₂²×D₄×C₁₆₃	C₂²	1	3	yes	—
24	C₂³×C₄×C₁₆₃	C₂²	1	3	yes	—
25	C₄⋊Q₈×C₁₆₃	C₂²	1	6	yes	complemented
26	#124×C₁₆₃	C₂²	1	6	yes	complemented
27	#123×C₁₆₃	C₂²	1	6	yes	complemented
28	#123×C₁₆₃	C₂²	1	12	yes	complemented
29	C₂²⋊Q₈×C₁₆₃	C₂²	1	3	yes	—
30	C₂²⋊Q₈×C₁₆₃	C₂²	1	6	yes	—
31	C₂²⋊Q₈×C₁₆₃	C₂²	1	6	yes	complemented
32	C₂²⋊Q₈×C₁₆₃	C₂²	1	6	yes	complemented
33	C₂²⋊Q₈×C₁₆₃	C₂²	1	3	yes	complemented
34	C₂²⋊Q₈×C₁₆₃	C₂²	1	6	yes	complemented
35	#121×C₁₆₃	C₂²	1	1	yes	characteristic
36	#121×C₁₆₃	C₂²	1	3	yes	complemented
37	#121×C₁₆₃	C₂²	1	12	yes	complemented
38	#121×C₁₆₃	C₂²	1	6	yes	complemented
39	#120×C₁₆₃	C₂²	1	6	yes	—
40	C₄×Q₈×C₁₆₃	C₂²	1	2	yes	complemented
41	C₄×D₄×C₁₆₃	C₂²	1	6	yes	—
42	C₄×D₄×C₁₆₃	C₂²	1	6	yes	complemented
43	C₄×D₄×C₁₆₃	C₂²	1	6	yes	complemented
44	#117×C₁₆₃	C₂²	1	3	yes	complemented
45	C₂×C₄⋊C₄×C₁₆₃	C₂²	1	3	yes	complemented
46	C₂×C₄⋊C₄×C₁₆₃	C₂²	1	6	yes	complemented
47	C₂×C₂²⋊C₄×C₁₆₃	C₂²	1	6	yes	—
48	C₂⁴×C₁₆₃	C₂³	1	3	yes	—
49	#41×C₁₆₃	—	2	4	no	—
50	#41×C₁₆₃	—	2	12	no	—
51	#41×C₁₆₃	—	2	24	no	—
52	#41×C₁₆₃	—	2	12	no	—
53	#41×C₁₆₃	—	2	12	no	—
54	#41×C₁₆₃	D₄	1	8	yes	complemented
55	C₂×Q₈×C₁₆₃	—	2	4	no	—
56	C₂×Q₈×C₁₆₃	—	2	8	no	—
57	C₂×Q₈×C₁₆₃	—	2	12	no	—
58	C₂×Q₈×C₁₆₃	C₂³	1	3	yes	—
59	C₂×Q₈×C₁₆₃	C₂³	1	6	yes	—
60	C₂×Q₈×C₁₆₃	C₂³	1	3	yes	—
61	C₂×Q₈×C₁₆₃	C₂³	1	1	yes	characteristic
62	C₂×D₄×C₁₆₃	—	2	12	no	—
63	C₂×D₄×C₁₆₃	C₂³	1	2	yes	—
64	C₂×D₄×C₁₆₃	C₂³	1	6	yes	—
65	C₂×D₄×C₁₆₃	C₂³	1	1	yes	characteristic
66	C₂×D₄×C₁₆₃	C₂³	1	6	yes	—
67	C₂×D₄×C₁₆₃	C₂³	1	3	yes	—
68	C₂×D₄×C₁₆₃	C₂³	1	6	yes	—
69	C₂×D₄×C₁₆₃	C₂³	1	3	yes	—
70	C₂²×C₄×C₁₆₃	—	2	12	no	—
71	C₂²×C₄×C₁₆₃	C₂³	1	6	yes	—
72	C₂²×C₄×C₁₆₃	C₂³	1	3	yes	—
73	C₂²×C₄×C₁₆₃	C₂³	1	3	yes	—
74	C₂²×C₄×C₁₆₃	C₂³	1	6	yes	—
75	C₂²×C₄×C₁₆₃	C₂³	1	3	yes	—
76	C₂²×C₄×C₁₆₃	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₁₆₃	C₂³	1	3	yes	—
78	C₂²×C₄×C₁₆₃	C₂³	1	6	yes	—
79	C₂²×C₄×C₁₆₃	C₂³	1	3	yes	—
80	C₄⋊C₄×C₁₆₃	C₂³	1	3	yes	—
81	C₄⋊C₄×C₁₆₃	C₂³	1	6	yes	—
82	C₄⋊C₄×C₁₆₃	C₂³	1	6	yes	—
83	C₄⋊C₄×C₁₆₃	C₂³	1	12	yes	—
84	C₄⋊C₄×C₁₆₃	C₂³	1	1	yes	characteristic
85	C₄⋊C₄×C₁₆₃	C₂³	1	6	yes	—
86	C₂²⋊C₄×C₁₆₃	C₂³	1	6	yes	—
87	C₂²⋊C₄×C₁₆₃	C₂³	1	12	yes	—
88	C₂²⋊C₄×C₁₆₃	C₂³	1	6	yes	—
89	C₂²⋊C₄×C₁₆₃	C₂³	1	6	yes	—
90	C₂²⋊C₄×C₁₆₃	C₂³	1	2	yes	—
91	C₂²⋊C₄×C₁₆₃	C₂³	1	6	yes	—
92	C₄²×C₁₆₃	C₂³	1	6	yes	—
93	C₂³×C₁₆₃	—	2	6	no	—
94	C₂³×C₁₆₃	—	2	6	no	—
95	C₂³×C₁₆₃	—	4	3	no	—
96	C₂³×C₁₆₃	C₂⁴	1	3	yes	—
97	C₂³×C₁₆₃	C₂⁴	1	2	yes	—
98	C₂³×C₁₆₃	C₂⁴	1	3	yes	—
99	C₂³×C₁₆₃	C₂⁴	1	1	yes	characteristic
100	Q₈×C₁₆₃	—	2	6	no	—
101	Q₈×C₁₆₃	—	2	12	no	—
102	Q₈×C₁₆₃	—	2	6	no	—
103	Q₈×C₁₆₃	C₂×D₄	1	4	yes	—
104	D₄×C₁₆₃	—	2	12	no	—
105	D₄×C₁₆₃	—	2	12	no	—
106	D₄×C₁₆₃	—	2	4	no	—
107	D₄×C₁₆₃	—	2	6	no	—
108	D₄×C₁₆₃	—	2	2	no	—
109	D₄×C₁₆₃	—	4	6	no	—
110	D₄×C₁₆₃	C₂×D₄	1	12	yes	—
111	C₂×C₄×C₁₆₃	—	2	6	no	—
112	C₂×C₄×C₁₆₃	—	2	12	no	—
113	C₂×C₄×C₁₆₃	—	2	2	no	—
114	C₂×C₄×C₁₆₃	—	2	6	no	—
115	C₂×C₄×C₁₆₃	—	2	6	no	—
116	C₂×C₄×C₁₆₃	—	2	6	no	—
117	C₂×C₄×C₁₆₃	—	2	12	no	—
118	C₂×C₄×C₁₆₃	—	4	6	no	—
119	C₂×C₄×C₁₆₃	C₂×D₄	1	12	yes	—
120	C₂×C₄×C₁₆₃	C₂⁴	1	2	yes	—
121	C₂×C₄×C₁₆₃	C₂⁴	1	6	yes	—
122	C₂×C₄×C₁₆₃	C₂⁴	1	6	yes	—
123	C₂×C₄×C₁₆₃	C₂⁴	1	1	yes	characteristic
124	C₂×C₄×C₁₆₃	C₂⁴	1	3	yes	—
125	C₂×C₄×C₁₆₃	C₂⁴	1	3	yes	—
126	C₂×C₄×C₁₆₃	C₂⁴	1	1	yes	characteristic
127	C₂²×C₁₆₃	—	2	1	no	—
128	C₂²×C₁₆₃	—	2	3	no	—
129	C₂²×C₁₆₃	—	2	3	no	—
130	C₂²×C₁₆₃	—	2	1	no	—
131	C₂²×C₁₆₃	—	2	2	no	—
132	C₂²×C₁₆₃	—	2	3	no	—
133	C₂²×C₁₆₃	—	2	2	no	—
134	C₂²×C₁₆₃	—	2	3	no	—
135	C₂²×C₁₆₃	—	2	2	no	—
136	C₂²×C₁₆₃	—	2	3	no	—
137	C₂²×C₁₆₃	—	4	12	no	—
138	C₂²×C₁₆₃	C₂²×D₄	1	6	yes	—
139	C₂²×C₁₆₃	2₋¹⁺⁴	1	2	yes	complemented
140	C₂²×C₁₆₃	C₂⁵	1	1	yes	characteristic
141	C₄×C₁₆₃	—	2	1	no	—
142	C₄×C₁₆₃	—	2	3	no	—
143	C₄×C₁₆₃	—	2	6	no	—
144	C₄×C₁₆₃	—	2	2	no	—
145	C₄×C₁₆₃	—	2	6	no	—
146	C₄×C₁₆₃	C₂²×D₄	1	2	yes	—
147	C₄×C₁₆₃	C₂²×D₄	1	6	yes	—
148	C₂×C₁₆₃	—	2	2	no	—
149	C₂×C₁₆₃	—	2	6	no	—
150	C₂×C₁₆₃	—	4	2	no	—
151	C₂×C₁₆₃	—	4	3	no	—
152	C₂×C₁₆₃	C₂³×D₄	1	1	yes	characteristic
153	C₂×C₁₆₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
154	C₂×C₁₆₃	#585	1	1	yes	characteristic
155	C₁₆₃	#3489	1	1	yes	characteristic, direct product factor, Sylow
156	#3489	C₁₆₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂×2₋¹⁺⁴	C₂×C₁₆₃	1	1	yes	characteristic, complemented
158	C₂²×#41	C₂×C₁₆₃	1	1	yes	characteristic, complemented
159	D₄×Q₈	C₂×C₁₆₃	1	2	yes	complemented
160	#548	C₂×C₁₆₃	1	2	yes	complemented
161	#547	C₂×C₁₆₃	1	6	yes	complemented
162	#546	C₂×C₁₆₃	1	6	yes	complemented
163	#537	C₂×C₁₆₃	1	3	yes	complemented
164	#536	C₂×C₁₆₃	1	3	yes	complemented
165	#525	C₂×C₁₆₃	1	3	yes	complemented
166	C₂×C₂²⋊Q₈	C₂×C₁₆₃	1	3	yes	complemented
167	#520	C₂×C₁₆₃	1	1	yes	characteristic, complemented
168	2₋¹⁺⁴	—	2	8	no	—
169	C₂×#41	—	2	8	no	—
170	C₂×#41	C₂²×C₁₆₃	1	3	yes	—
171	C₂×#41	C₂²×C₁₆₃	1	3	yes	—
172	C₂×#41	C₂²×C₁₆₃	1	1	yes	characteristic
173	C₂×#41	C₂²×C₁₆₃	1	1	yes	characteristic
174	C₂×#41	C₂²×C₁₆₃	1	3	yes	complemented
175	C₂×#41	C₂²×C₁₆₃	1	6	yes	complemented
176	C₂²×Q₈	C₂²×C₁₆₃	1	1	yes	characteristic
177	C₂²×Q₈	C₂²×C₁₆₃	1	3	yes	complemented
178	C₂²×Q₈	C₂²×C₁₆₃	1	2	yes	complemented
179	C₂²×D₄	C₂²×C₁₆₃	1	3	yes	—
180	C₂³×C₄	C₂²×C₁₆₃	1	3	yes	—
181	C₄⋊Q₈	C₂²×C₁₆₃	1	6	yes	complemented
182	#124	C₂²×C₁₆₃	1	6	yes	complemented
183	#123	C₂²×C₁₆₃	1	6	yes	complemented
184	#123	C₂²×C₁₆₃	1	12	yes	complemented
185	C₂²⋊Q₈	C₂²×C₁₆₃	1	3	yes	—
186	C₂²⋊Q₈	C₂²×C₁₆₃	1	6	yes	—
187	C₂²⋊Q₈	C₂²×C₁₆₃	1	6	yes	complemented
188	C₂²⋊Q₈	C₂²×C₁₆₃	1	6	yes	complemented
189	C₂²⋊Q₈	C₂²×C₁₆₃	1	3	yes	complemented
190	C₂²⋊Q₈	C₂²×C₁₆₃	1	6	yes	complemented
191	#121	C₂²×C₁₆₃	1	1	yes	characteristic
192	#121	C₂²×C₁₆₃	1	3	yes	complemented
193	#121	C₂²×C₁₆₃	1	12	yes	complemented
194	#121	C₂²×C₁₆₃	1	6	yes	complemented
195	#120	C₂²×C₁₆₃	1	6	yes	—
196	C₄×Q₈	C₂²×C₁₆₃	1	2	yes	complemented
197	C₄×D₄	C₂²×C₁₆₃	1	6	yes	—
198	C₄×D₄	C₂²×C₁₆₃	1	6	yes	complemented
199	C₄×D₄	C₂²×C₁₆₃	1	6	yes	complemented
200	#117	C₂²×C₁₆₃	1	3	yes	complemented
201	C₂×C₄⋊C₄	C₂²×C₁₆₃	1	3	yes	complemented
202	C₂×C₄⋊C₄	C₂²×C₁₆₃	1	6	yes	complemented
203	C₂×C₂²⋊C₄	C₂²×C₁₆₃	1	6	yes	—
204	C₂⁴	C₂³×C₁₆₃	1	3	yes	—
205	#41	—	2	4	no	—
206	#41	—	2	12	no	—
207	#41	—	2	24	no	—
208	#41	—	2	12	no	—
209	#41	—	2	12	no	—
210	#41	D₄×C₁₆₃	1	8	yes	complemented
211	C₂×Q₈	—	2	4	no	—
212	C₂×Q₈	—	2	8	no	—
213	C₂×Q₈	—	2	12	no	—
214	C₂×Q₈	C₂³×C₁₆₃	1	3	yes	—
215	C₂×Q₈	C₂³×C₁₆₃	1	6	yes	—
216	C₂×Q₈	C₂³×C₁₆₃	1	3	yes	—
217	C₂×Q₈	C₂³×C₁₆₃	1	1	yes	characteristic
218	C₂×D₄	—	2	12	no	—
219	C₂×D₄	C₂³×C₁₆₃	1	2	yes	—
220	C₂×D₄	C₂³×C₁₆₃	1	6	yes	—
221	C₂×D₄	C₂³×C₁₆₃	1	1	yes	characteristic
222	C₂×D₄	C₂³×C₁₆₃	1	6	yes	—
223	C₂×D₄	C₂³×C₁₆₃	1	3	yes	—
224	C₂×D₄	C₂³×C₁₆₃	1	6	yes	—
225	C₂×D₄	C₂³×C₁₆₃	1	3	yes	—
226	C₂²×C₄	—	2	12	no	—
227	C₂²×C₄	C₂³×C₁₆₃	1	6	yes	—
228	C₂²×C₄	C₂³×C₁₆₃	1	3	yes	—
229	C₂²×C₄	C₂³×C₁₆₃	1	3	yes	—
230	C₂²×C₄	C₂³×C₁₆₃	1	6	yes	—
231	C₂²×C₄	C₂³×C₁₆₃	1	3	yes	—
232	C₂²×C₄	C₂³×C₁₆₃	1	1	yes	characteristic
233	C₂²×C₄	C₂³×C₁₆₃	1	3	yes	—
234	C₂²×C₄	C₂³×C₁₆₃	1	6	yes	—
235	C₂²×C₄	C₂³×C₁₆₃	1	3	yes	—
236	C₄⋊C₄	C₂³×C₁₆₃	1	3	yes	—
237	C₄⋊C₄	C₂³×C₁₆₃	1	6	yes	—
238	C₄⋊C₄	C₂³×C₁₆₃	1	6	yes	—
239	C₄⋊C₄	C₂³×C₁₆₃	1	12	yes	—
240	C₄⋊C₄	C₂³×C₁₆₃	1	1	yes	characteristic
241	C₄⋊C₄	C₂³×C₁₆₃	1	6	yes	—
242	C₂²⋊C₄	C₂³×C₁₆₃	1	6	yes	—
243	C₂²⋊C₄	C₂³×C₁₆₃	1	12	yes	—
244	C₂²⋊C₄	C₂³×C₁₆₃	1	6	yes	—
245	C₂²⋊C₄	C₂³×C₁₆₃	1	6	yes	—
246	C₂²⋊C₄	C₂³×C₁₆₃	1	2	yes	—
247	C₂²⋊C₄	C₂³×C₁₆₃	1	6	yes	—
248	C₄²	C₂³×C₁₆₃	1	6	yes	—
249	C₂³	—	2	6	no	—
250	C₂³	—	2	6	no	—
251	C₂³	—	4	3	no	—
252	C₂³	C₂⁴×C₁₆₃	1	3	yes	—
253	C₂³	C₂⁴×C₁₆₃	1	2	yes	—
254	C₂³	C₂⁴×C₁₆₃	1	3	yes	—
255	C₂³	C₂⁴×C₁₆₃	1	1	yes	characteristic
256	Q₈	—	2	6	no	—
257	Q₈	—	2	12	no	—
258	Q₈	—	2	6	no	—
259	Q₈	C₂×D₄×C₁₆₃	1	4	yes	—
260	D₄	—	2	12	no	—
261	D₄	—	2	12	no	—
262	D₄	—	2	4	no	—
263	D₄	—	2	6	no	—
264	D₄	—	2	2	no	—
265	D₄	—	4	6	no	—
266	D₄	C₂×D₄×C₁₆₃	1	12	yes	—
267	C₂×C₄	—	2	6	no	—
268	C₂×C₄	—	2	12	no	—
269	C₂×C₄	—	2	2	no	—
270	C₂×C₄	—	2	6	no	—
271	C₂×C₄	—	2	6	no	—
272	C₂×C₄	—	2	6	no	—
273	C₂×C₄	—	2	12	no	—
274	C₂×C₄	—	4	6	no	—
275	C₂×C₄	C₂×D₄×C₁₆₃	1	12	yes	—
276	C₂×C₄	C₂⁴×C₁₆₃	1	2	yes	—
277	C₂×C₄	C₂⁴×C₁₆₃	1	6	yes	—
278	C₂×C₄	C₂⁴×C₁₆₃	1	6	yes	—
279	C₂×C₄	C₂⁴×C₁₆₃	1	1	yes	characteristic
280	C₂×C₄	C₂⁴×C₁₆₃	1	3	yes	—
281	C₂×C₄	C₂⁴×C₁₆₃	1	3	yes	—
282	C₂×C₄	C₂⁴×C₁₆₃	1	1	yes	characteristic
283	C₂²	—	2	1	no	—
284	C₂²	—	2	3	no	—
285	C₂²	—	2	3	no	—
286	C₂²	—	2	1	no	—
287	C₂²	—	2	2	no	—
288	C₂²	—	2	3	no	—
289	C₂²	—	2	2	no	—
290	C₂²	—	2	3	no	—
291	C₂²	—	2	2	no	—
292	C₂²	—	2	3	no	—
293	C₂²	—	4	12	no	—
294	C₂²	C₂²×D₄×C₁₆₃	1	6	yes	—
295	C₂²	2₋¹⁺⁴×C₁₆₃	1	2	yes	complemented
296	C₂²	C₂⁵×C₁₆₃	1	1	yes	characteristic
297	C₄	—	2	1	no	—
298	C₄	—	2	3	no	—
299	C₄	—	2	6	no	—
300	C₄	—	2	2	no	—
301	C₄	—	2	6	no	—
302	C₄	C₂²×D₄×C₁₆₃	1	2	yes	—
303	C₄	C₂²×D₄×C₁₆₃	1	6	yes	—
304	C₂	—	2	2	no	—
305	C₂	—	2	6	no	—
306	C₂	—	4	3	no	—
307	C₂	—	4	2	no	—
308	C₂	C₂³×D₄×C₁₆₃	1	1	yes	characteristic
309	C₂	C₂×2₋¹⁺⁴×C₁₆₃	1	1	yes	characteristic
310	C₂	#585×C₁₆₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₆₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₆₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₆₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×2₋¹⁺⁴×C₁₆₃	C₂	semidirect
2. C₂²×#41×C₁₆₃	C₂	semidirect
3. D₄×Q₈×C₁₆₃	C₂	semidirect
4. #548×C₁₆₃	C₂	semidirect
5. #547×C₁₆₃	C₂	semidirect
6. #546×C₁₆₃	C₂	semidirect
7. #537×C₁₆₃	C₂	semidirect
8. #536×C₁₆₃	C₂	semidirect
9. #525×C₁₆₃	C₂	semidirect
10. C₂×C₂²⋊Q₈×C₁₆₃	C₂	semidirect
11. #520×C₁₆₃	C₂	semidirect
18. C₂×#41×C₁₆₃	C₂²	semidirect
19. C₂×#41×C₁₆₃	C₂²	semidirect
21. C₂²×Q₈×C₁₆₃	C₂²	semidirect
22. C₂²×Q₈×C₁₆₃	C₂²	semidirect
25. C₄⋊Q₈×C₁₆₃	C₂²	semidirect
26. #124×C₁₆₃	C₂²	semidirect
27. #123×C₁₆₃	C₂²	semidirect
28. #123×C₁₆₃	C₂²	semidirect
31. C₂²⋊Q₈×C₁₆₃	C₂²	semidirect
32. C₂²⋊Q₈×C₁₆₃	C₂²	semidirect
33. C₂²⋊Q₈×C₁₆₃	C₂²	semidirect
34. C₂²⋊Q₈×C₁₆₃	C₂²	semidirect
36. #121×C₁₆₃	C₂²	semidirect
37. #121×C₁₆₃	C₂²	semidirect
38. #121×C₁₆₃	C₂²	semidirect
40. C₄×Q₈×C₁₆₃	C₂²	semidirect
42. C₄×D₄×C₁₆₃	C₂²	semidirect
43. C₄×D₄×C₁₆₃	C₂²	semidirect
44. #117×C₁₆₃	C₂²	semidirect
45. C₂×C₄⋊C₄×C₁₆₃	C₂²	semidirect
46. C₂×C₄⋊C₄×C₁₆₃	C₂²	semidirect
54. #41×C₁₆₃	D₄	semidirect
139. C₂²×C₁₆₃	2₋¹⁺⁴	semidirect
155. C₁₆₃	#3489	direct (N × H)
156. #3489	C₁₆₃	direct (N × H)
157. C₂×2₋¹⁺⁴	C₂×C₁₆₃	semidirect
158. C₂²×#41	C₂×C₁₆₃	semidirect
159. D₄×Q₈	C₂×C₁₆₃	semidirect
160. #548	C₂×C₁₆₃	semidirect
161. #547	C₂×C₁₆₃	semidirect
162. #546	C₂×C₁₆₃	semidirect
163. #537	C₂×C₁₆₃	semidirect
164. #536	C₂×C₁₆₃	semidirect
165. #525	C₂×C₁₆₃	semidirect
166. C₂×C₂²⋊Q₈	C₂×C₁₆₃	semidirect
167. #520	C₂×C₁₆₃	semidirect
174. C₂×#41	C₂²×C₁₆₃	semidirect
175. C₂×#41	C₂²×C₁₆₃	semidirect
177. C₂²×Q₈	C₂²×C₁₆₃	semidirect
178. C₂²×Q₈	C₂²×C₁₆₃	semidirect
181. C₄⋊Q₈	C₂²×C₁₆₃	semidirect
182. #124	C₂²×C₁₆₃	semidirect
183. #123	C₂²×C₁₆₃	semidirect
184. #123	C₂²×C₁₆₃	semidirect
187. C₂²⋊Q₈	C₂²×C₁₆₃	semidirect
188. C₂²⋊Q₈	C₂²×C₁₆₃	semidirect
189. C₂²⋊Q₈	C₂²×C₁₆₃	semidirect
190. C₂²⋊Q₈	C₂²×C₁₆₃	semidirect
192. #121	C₂²×C₁₆₃	semidirect
193. #121	C₂²×C₁₆₃	semidirect
194. #121	C₂²×C₁₆₃	semidirect
196. C₄×Q₈	C₂²×C₁₆₃	semidirect
198. C₄×D₄	C₂²×C₁₆₃	semidirect
199. C₄×D₄	C₂²×C₁₆₃	semidirect
200. #117	C₂²×C₁₆₃	semidirect
201. C₂×C₄⋊C₄	C₂²×C₁₆₃	semidirect
202. C₂×C₄⋊C₄	C₂²×C₁₆₃	semidirect
210. #41	D₄×C₁₆₃	semidirect
295. C₂²	2₋¹⁺⁴×C₁₆₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×2₋¹⁺⁴×C₁₆₃	2
C₂²×#41×C₁₆₃	2
D₄×Q₈×C₁₆₃	2
#548×C₁₆₃	2
#547×C₁₆₃	2
#546×C₁₆₃	2
#537×C₁₆₃	2
#536×C₁₆₃	2
#525×C₁₆₃	2
C₂×C₂²⋊Q₈×C₁₆₃	2
#520×C₁₆₃	2
#3489	163

Subgroups — #3489×C163 #35212247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3489×C₁₆₃ #35212247