Subgroups — M₁₆×Q₁₆×C₄₇ #26057736

Order 12032.

638 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×M₁₆×C₄₇	C₂	1	2	yes	maximal
2	C₂×C₄×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#1591	C₂	1	2	yes	maximal, complemented
4	C₄₇×#1584	C₂	1	4	yes	maximal, complemented
5	C₈×Q₁₆×C₄₇	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1567	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#1487	C₂	1	2	yes	maximal
8	C₈×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×Q₁₆×C₄₇	C₄	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
11	C₄₇×#446	—	2	4	no	—
12	C₄₇×#446	C₂²	1	4	yes	—
13	C₈×Q₈×C₄₇	C₂²	1	4	yes	—
14	C₄×Q₁₆×C₄₇	C₄	1	1	yes	characteristic
15	C₄×Q₁₆×C₄₇	C₄	1	2	yes	—
16	C₄×Q₁₆×C₄₇	C₄	1	1	yes	characteristic
17	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
18	C₄×Q₁₆×C₄₇	C₂²	1	2	yes	—
19	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#431	C₂²	1	1	yes	characteristic
21	C₂×#107×C₄₇	C₄	1	1	yes	characteristic
22	C₄₇×#423	—	2	2	no	—
23	C₄₇×#423	C₂²	1	2	yes	—
24	C₂×#103×C₄₇	C₄	1	2	yes	—
25	C₄×M₁₆×C₄₇	—	2	2	no	—
26	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₄₇×#335	C₂²	1	2	yes	—
29	C₄₇×#335	C₂²	1	2	yes	—
30	C₄₇×Q₈⋊C₈	C₂²	1	4	yes	—
31	C₄₇×Q₈⋊C₈	C₂²	1	4	yes	—
32	C₄₇×#322	C₂²	1	2	yes	—
33	C₈²×C₄₇	C₂²	1	2	yes	—
34	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
35	C₂×Q₁₆×C₄₇	—	2	4	no	—
36	C₂×Q₁₆×C₄₇	C₂×C₄	1	2	yes	—
37	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
38	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
39	C₂×M₁₆×C₄₇	—	2	2	no	—
40	C₂×M₁₆×C₄₇	D₄	1	1	yes	characteristic
41	C₂×M₁₆×C₄₇	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
44	C₄×Q₈×C₄₇	—	2	2	no	—
45	C₄×Q₈×C₄₇	—	2	2	no	—
46	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
47	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
48	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
49	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
50	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₄₇	—	2	2	no	—
53	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
54	#107×C₄₇	C₂×C₄	1	2	yes	—
55	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
56	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
57	C₄⋊C₈×C₄₇	—	2	4	no	—
58	C₄⋊C₈×C₄₇	—	2	4	no	—
59	C₄⋊C₈×C₄₇	—	2	2	no	—
60	C₄⋊C₈×C₄₇	—	2	1	no	—
61	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
62	#103×C₄₇	C₂×C₄	1	2	yes	—
63	#103×C₄₇	C₂×C₄	1	2	yes	—
64	#103×C₄₇	C₂×C₄	1	2	yes	—
65	#103×C₄₇	C₂×C₄	1	2	yes	—
66	C₂²⋊C₈×C₄₇	—	2	1	no	—
67	#97×C₄₇	—	2	4	no	—
68	#97×C₄₇	D₄	1	2	yes	—
69	C₄×C₈×C₄₇	—	2	4	no	—
70	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
71	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
72	C₄×C₈×C₄₇	C₂³	1	2	yes	—
73	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₄₇	C₂³	1	2	yes	—
76	C₂×Q₈×C₄₇	—	2	2	no	—
77	C₂×Q₈×C₄₇	—	2	4	no	—
78	C₂×Q₈×C₄₇	—	4	2	no	—
79	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
80	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
86	Q₁₆×C₄₇	—	2	4	no	—
87	Q₁₆×C₄₇	—	2	2	no	—
88	Q₁₆×C₄₇	M₁₆	1	4	yes	direct product factor
89	M₁₆×C₄₇	—	2	2	no	—
90	M₁₆×C₄₇	—	4	4	no	—
91	M₁₆×C₄₇	Q₁₆	1	4	yes	direct product factor
92	C₂×C₈×C₄₇	—	2	2	no	—
93	C₂×C₈×C₄₇	—	2	4	no	—
94	C₂×C₈×C₄₇	—	2	2	no	—
95	C₂×C₈×C₄₇	—	4	1	no	—
96	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
101	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
102	C₄⋊C₄×C₄₇	—	2	2	no	—
103	C₄⋊C₄×C₄₇	—	2	2	no	—
104	C₄⋊C₄×C₄₇	—	2	2	no	—
105	C₄⋊C₄×C₄₇	—	2	2	no	—
106	C₄⋊C₄×C₄₇	—	2	2	no	—
107	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
108	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
109	C₄²×C₄₇	—	2	2	no	—
110	C₄²×C₄₇	—	2	2	no	—
111	C₄²×C₄₇	—	2	2	no	—
112	C₄²×C₄₇	—	2	2	no	—
113	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₄₇	#41	1	1	yes	characteristic
116	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
117	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
118	Q₈×C₄₇	—	2	2	no	—
119	Q₈×C₄₇	—	2	2	no	—
120	Q₈×C₄₇	—	2	2	no	—
121	Q₈×C₄₇	—	4	4	no	—
122	Q₈×C₄₇	C₂×M₁₆	1	4	yes	—
123	C₂×C₄×C₄₇	—	2	2	no	—
124	C₂×C₄×C₄₇	—	2	1	no	—
125	C₂×C₄×C₄₇	—	2	1	no	—
126	C₂×C₄×C₄₇	—	2	2	no	—
127	C₂×C₄×C₄₇	—	2	2	no	—
128	C₂×C₄×C₄₇	—	2	2	no	—
129	C₂×C₄×C₄₇	—	4	1	no	—
130	C₂×C₄×C₄₇	—	4	4	no	—
131	C₂×C₄×C₄₇	—	8	2	no	—
132	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
133	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
134	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
135	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
136	C₂×C₄×C₄₇	#135	1	2	yes	—
137	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
138	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
139	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
140	C₈×C₄₇	—	2	1	no	—
141	C₈×C₄₇	—	2	1	no	—
142	C₈×C₄₇	—	2	1	no	—
143	C₈×C₄₇	—	2	2	no	—
144	C₈×C₄₇	—	4	2	no	—
145	C₈×C₄₇	—	4	4	no	—
146	C₈×C₄₇	C₂×M₁₆	1	2	yes	—
147	C₈×C₄₇	C₂×Q₁₆	1	4	yes	complemented
148	M₁₆×Q₁₆	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂²×C₄₇	—	2	1	no	—
150	C₂²×C₄₇	—	2	1	no	—
151	C₂²×C₄₇	C₄×Q₁₆	1	2	yes	—
152	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
153	C₄×C₄₇	—	2	1	no	—
154	C₄×C₄₇	—	2	4	no	—
155	C₄×C₄₇	—	2	1	no	—
156	C₄×C₄₇	—	2	1	no	—
157	C₄×C₄₇	—	4	2	no	—
158	C₄×C₄₇	—	4	2	no	—
159	C₄×C₄₇	—	4	2	no	—
160	C₄×C₄₇	C₄×Q₁₆	1	2	yes	—
161	C₄×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
162	C₄×C₄₇	#568	1	1	yes	characteristic
163	C₄×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
164	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
165	Q₈×M₁₆	C₂×C₄₇	1	2	yes	—
166	C₂×C₄×Q₁₆	C₂×C₄₇	1	1	yes	characteristic
167	#1591	C₂×C₄₇	1	2	yes	complemented
168	#1584	C₂×C₄₇	1	4	yes	complemented
169	C₈×Q₁₆	C₂×C₄₇	1	2	yes	complemented
170	#1567	C₂×C₄₇	1	1	yes	characteristic
171	#1487	C₂×C₄₇	1	2	yes	—
172	C₈×M₁₆	C₂×C₄₇	1	1	yes	characteristic
173	C₂×C₄₇	—	2	2	no	—
174	C₂×C₄₇	D₄×M₁₆	1	1	yes	characteristic
175	C₂×C₄₇	C₂×C₄×Q₁₆	1	1	yes	characteristic
176	C₂×C₄₇	#2957	1	1	yes	characteristic
177	C₂²×Q₁₆	C₄×C₄₇	1	1	yes	characteristic
178	C₂×C₄×Q₈	C₂²×C₄₇	1	2	yes	—
179	#446	—	2	4	no	—
180	#446	C₂²×C₄₇	1	4	yes	—
181	C₈×Q₈	C₂²×C₄₇	1	4	yes	—
182	C₄×Q₁₆	C₄×C₄₇	1	2	yes	—
183	C₄×Q₁₆	C₄×C₄₇	1	1	yes	characteristic
184	C₄×Q₁₆	C₄×C₄₇	1	1	yes	characteristic
185	C₄×Q₁₆	C₂²×C₄₇	1	1	yes	characteristic
186	C₄×Q₁₆	C₂²×C₄₇	1	2	yes	—
187	C₄×Q₁₆	C₂²×C₄₇	1	1	yes	characteristic
188	#431	C₂²×C₄₇	1	1	yes	characteristic
189	C₂×#107	C₄×C₄₇	1	1	yes	characteristic
190	#423	—	2	2	no	—
191	#423	C₂²×C₄₇	1	2	yes	—
192	C₂×#103	C₄×C₄₇	1	2	yes	—
193	C₄×M₁₆	—	2	2	no	—
194	C₄×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
195	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
196	#335	C₂²×C₄₇	1	2	yes	—
197	#335	C₂²×C₄₇	1	2	yes	—
198	Q₈⋊C₈	C₂²×C₄₇	1	4	yes	—
199	Q₈⋊C₈	C₂²×C₄₇	1	4	yes	—
200	#322	C₂²×C₄₇	1	2	yes	—
201	C₈²	C₂²×C₄₇	1	2	yes	—
202	C₄₇	M₁₆×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
203	C₂²×Q₈	C₂×C₄×C₄₇	1	2	yes	—
204	C₂×Q₁₆	—	2	4	no	—
205	C₂×Q₁₆	C₂×C₄×C₄₇	1	2	yes	—
206	C₂×Q₁₆	C₂×C₄×C₄₇	1	1	yes	characteristic
207	C₂×Q₁₆	C₂×C₄×C₄₇	1	1	yes	characteristic
208	C₂×M₁₆	—	2	2	no	—
209	C₂×M₁₆	D₄×C₄₇	1	1	yes	characteristic
210	C₂×M₁₆	D₄×C₄₇	1	1	yes	characteristic
211	C₂²×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
212	C₂²×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
213	C₄×Q₈	—	2	2	no	—
214	C₄×Q₈	—	2	2	no	—
215	C₄×Q₈	C₂×C₄×C₄₇	1	2	yes	—
216	C₄×Q₈	C₂×C₄×C₄₇	1	2	yes	—
217	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
218	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
219	C₂×C₄⋊C₄	—	2	2	no	—
220	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
221	C₂×C₄²	—	2	2	no	—
222	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
223	#107	C₂×C₄×C₄₇	1	2	yes	—
224	#107	C₂×C₄×C₄₇	1	1	yes	characteristic
225	#107	C₂×C₄×C₄₇	1	1	yes	characteristic
226	C₄⋊C₈	—	2	4	no	—
227	C₄⋊C₈	—	2	4	no	—
228	C₄⋊C₈	—	2	2	no	—
229	C₄⋊C₈	—	2	1	no	—
230	C₄⋊C₈	C₂³×C₄₇	1	4	yes	—
231	#103	C₂×C₄×C₄₇	1	2	yes	—
232	#103	C₂×C₄×C₄₇	1	2	yes	—
233	#103	C₂×C₄×C₄₇	1	2	yes	—
234	#103	C₂×C₄×C₄₇	1	2	yes	—
235	C₂²⋊C₈	—	2	1	no	—
236	#97	—	2	4	no	—
237	#97	D₄×C₄₇	1	2	yes	—
238	C₄×C₈	—	2	4	no	—
239	C₄×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
240	C₄×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
241	C₄×C₈	C₂³×C₄₇	1	2	yes	—
242	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
243	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
244	C₄×C₈	C₂³×C₄₇	1	2	yes	—
245	C₂×Q₈	—	2	2	no	—
246	C₂×Q₈	—	2	4	no	—
247	C₂×Q₈	—	4	2	no	—
248	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	—
249	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
253	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
254	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
255	Q₁₆	—	2	4	no	—
256	Q₁₆	—	2	2	no	—
257	Q₁₆	M₁₆×C₄₇	1	4	yes	direct product factor
258	M₁₆	—	2	2	no	—
259	M₁₆	—	4	4	no	—
260	M₁₆	Q₁₆×C₄₇	1	4	yes	direct product factor
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	4	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	4	1	no	—
265	C₂×C₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
266	C₂×C₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
267	C₂×C₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
268	C₂×C₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
269	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
270	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
271	C₄⋊C₄	—	2	2	no	—
272	C₄⋊C₄	—	2	2	no	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	—	2	2	no	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
277	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
278	C₄²	—	2	2	no	—
279	C₄²	—	2	2	no	—
280	C₄²	—	2	2	no	—
281	C₄²	—	2	2	no	—
282	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
283	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
284	C₄²	#41×C₄₇	1	1	yes	characteristic
285	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
286	C₂³	C₄×D₄×C₄₇	1	1	yes	characteristic
287	Q₈	—	2	2	no	—
288	Q₈	—	2	2	no	—
289	Q₈	—	2	2	no	—
290	Q₈	—	4	4	no	—
291	Q₈	C₂×M₁₆×C₄₇	1	4	yes	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	4	1	no	—
299	C₂×C₄	—	4	4	no	—
300	C₂×C₄	—	8	2	no	—
301	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
302	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
303	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
304	C₂×C₄	C₂×Q₁₆×C₄₇	1	2	yes	—
305	C₂×C₄	#135×C₄₇	1	2	yes	—
306	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
307	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
308	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
309	C₈	—	2	1	no	—
310	C₈	—	2	1	no	—
311	C₈	—	2	1	no	—
312	C₈	—	2	2	no	—
313	C₈	—	4	2	no	—
314	C₈	—	4	4	no	—
315	C₈	C₂×M₁₆×C₄₇	1	2	yes	—
316	C₈	C₂×Q₁₆×C₄₇	1	4	yes	complemented
317	C₂²	—	2	1	no	—
318	C₂²	—	2	1	no	—
319	C₂²	C₄×Q₁₆×C₄₇	1	2	yes	—
320	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
321	C₄	—	2	1	no	—
322	C₄	—	2	4	no	—
323	C₄	—	2	1	no	—
324	C₄	—	2	1	no	—
325	C₄	—	4	2	no	—
326	C₄	—	4	2	no	—
327	C₄	—	4	2	no	—
328	C₄	C₄×Q₁₆×C₄₇	1	2	yes	—
329	C₄	C₂²×M₁₆×C₄₇	1	1	yes	characteristic
330	C₄	C₄₇×#568	1	1	yes	characteristic
331	C₄	C₂²×Q₁₆×C₄₇	1	1	yes	characteristic
332	C₄	C₂×#135×C₄₇	1	1	yes	characteristic
333	C₂	—	2	2	no	—
334	C₂	D₄×M₁₆×C₄₇	1	1	yes	characteristic
335	C₂	C₂×C₄×Q₁₆×C₄₇	1	1	yes	characteristic
336	C₂	C₄₇×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₄²	C₂⁴×C₄₇
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂³×C₄₇	C₄×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₇ ◁ C₄×M₁₆×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₇×#1591	C₂	semidirect
4. C₄₇×#1584	C₂	semidirect
5. C₈×Q₁₆×C₄₇	C₂	semidirect
88. Q₁₆×C₄₇	M₁₆	direct (N × H)
91. M₁₆×C₄₇	Q₁₆	direct (N × H)
147. C₈×C₄₇	C₂×Q₁₆	semidirect
148. M₁₆×Q₁₆	C₄₇	direct (N × H)
167. #1591	C₂×C₄₇	semidirect
168. #1584	C₂×C₄₇	semidirect
169. C₈×Q₁₆	C₂×C₄₇	semidirect
202. C₄₇	M₁₆×Q₁₆	direct (N × H)
257. Q₁₆	M₁₆×C₄₇	direct (N × H)
260. M₁₆	Q₁₆×C₄₇	direct (N × H)
316. C₈	C₂×Q₁₆×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
Q₈×M₁₆×C₄₇	2
C₂×C₄×Q₁₆×C₄₇	2
C₄₇×#1591	2
C₄₇×#1584	2
C₈×Q₁₆×C₄₇	2
C₄₇×#1567	2
C₄₇×#1487	2
C₈×M₁₆×C₄₇	2
M₁₆×Q₁₆	47

Subgroups — M16×Q16×C47 #26057736

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×Q₁₆×C₄₇ #26057736