Subgroups — Q₁₆×C₂²⋊Dic₄₇ #26232140

Order 12032.

1398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×Dic₄₇	C₂	1	2	yes	maximal, complemented
2	Q₈×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal
3	#20244250	C₂	1	2	yes	maximal, complemented
4	#20243731	C₂	1	4	yes	maximal, complemented
5	#20243417	C₂	1	1	yes	maximal, characteristic
6	#20243323	C₂	1	2	yes	maximal
7	C₈×C₂²⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
8	C₂³×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂×Q₈×Dic₄₇	C₂²	1	4	yes	—
10	Q₁₆×Dic₄₇	—	2	8	no	—
11	C₂×#13093958	C₂²	1	2	yes	—
12	C₂×#13093948	C₂²	1	4	yes	—
13	C₂×#13093948	C₂²	1	4	yes	—
14	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
16	#15689030	—	2	4	no	—
17	#15689030	C₂²	1	4	yes	—
18	#15688983	—	2	2	no	—
19	#15688983	C₂²	1	2	yes	—
20	C₄×C₂²⋊Dic₄₇	—	2	2	no	—
21	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
22	#15688886	C₂²	1	2	yes	—
23	#15688877	C₂²	1	2	yes	—
24	C₂³×Q₈×C₄₇	C₂²	1	2	yes	—
25	C₂²×Q₁₆×C₄₇	—	2	8	no	—
26	C₂²×Q₁₆×C₄₇	C₄	1	8	yes	complemented
27	C₂²×Q₁₆×C₄₇	C₂²	1	2	yes	—
28	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
30	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
32	Q₈×Dic₄₇	—	2	8	no	—
33	Q₈×Dic₄₇	—	4	4	no	—
34	C₂×C₄⋊Dic₄₇	—	2	4	no	—
35	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
36	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
37	C₂×C₂²⋊Dic₄₇	D₄	1	1	yes	characteristic
38	C₂×C₂²⋊Dic₄₇	D₄	1	1	yes	characteristic
39	C₂×C₄×Dic₄₇	—	2	4	no	—
40	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
41	#13093958	—	2	4	no	—
42	#13093948	—	2	8	no	—
43	#13093948	—	4	4	no	—
44	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
45	C₈×Dic₄₇	—	2	4	no	—
46	C₄₇⋊#95	—	2	2	no	—
47	C₄₇⋊#95	—	2	4	no	—
48	C₄₇⋊#95	—	2	4	no	—
49	C₄₇⋊#95	D₄	1	2	yes	—
50	C₂²×Q₈×C₄₇	—	2	2	no	—
51	C₂²×Q₈×C₄₇	—	2	4	no	—
52	C₂²×Q₈×C₄₇	—	2	8	no	—
53	C₂²×Q₈×C₄₇	—	4	4	no	—
54	C₂²×Q₈×C₄₇	C₂×C₄	1	8	yes	—
55	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
56	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
57	C₂³×C₄×C₄₇	—	2	2	no	—
58	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
59	C₂×Q₁₆×C₄₇	—	2	8	no	—
60	C₂×Q₁₆×C₄₇	—	2	32	no	—
61	C₂×Q₁₆×C₄₇	—	2	4	no	—
62	C₂×Q₁₆×C₄₇	C₂×C₄	1	8	yes	—
63	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	—
64	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	—
65	C₂×Q₁₆×C₄₇	D₄	1	8	yes	—
66	C₂²×C₈×C₄₇	—	2	4	no	—
67	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
68	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
70	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
71	C₂×Q₈×C₄₇	—	2	8	no	—
72	C₂×Q₈×C₄₇	—	2	2	no	—
73	C₂×Q₈×C₄₇	—	2	2	no	—
74	C₂×Q₈×C₄₇	—	2	4	no	—
75	C₂×Q₈×C₄₇	—	2	16	no	—
76	C₂×Q₈×C₄₇	—	2	4	no	—
77	C₂×Q₈×C₄₇	—	2	4	no	—
78	C₂×Q₈×C₄₇	—	4	8	no	—
79	C₂×Q₈×C₄₇	—	4	8	no	—
80	C₂×Q₈×C₄₇	—	4	16	no	—
81	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
82	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
83	C₂×Q₈×C₄₇	C₂×D₄	1	8	yes	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	8	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	4	8	no	—
90	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	#41	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₄₇	—	2	4	no	—
95	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
96	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
97	Q₁₆×C₄₇	—	2	16	no	—
98	Q₁₆×C₄₇	—	2	8	no	—
99	Q₁₆×C₄₇	C₂²⋊C₄	1	16	yes	complemented
100	C₂×C₈×C₄₇	—	2	2	no	—
101	C₂×C₈×C₄₇	—	2	8	no	—
102	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
103	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
105	C₂²⋊Dic₄₇	—	2	2	no	—
106	C₂²⋊Dic₄₇	—	4	4	no	—
107	C₂²⋊Dic₄₇	Q₁₆	1	4	yes	direct product factor
108	C₄⋊Dic₄₇	—	2	4	no	—
109	C₄⋊Dic₄₇	—	2	4	no	—
110	C₄⋊Dic₄₇	—	4	8	no	—
111	C₄×Dic₄₇	—	2	2	no	—
112	C₄×Dic₄₇	—	2	2	no	—
113	C₄×Dic₄₇	—	4	8	no	—
114	C₂×C₄₇⋊C₈	—	2	2	no	—
115	C₂×C₄₇⋊C₈	—	2	2	no	—
116	C₂×C₄₇⋊C₈	—	2	2	no	—
117	C₂³×C₄₇	—	2	2	no	—
118	C₂³×C₄₇	—	2	2	no	—
119	C₂³×C₄₇	C₄×D₄	1	2	yes	—
120	C₂³×C₄₇	C₂×Q₁₆	1	2	yes	—
121	C₂³×C₄₇	#135	1	2	yes	—
122	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
123	Q₈×C₄₇	—	2	4	no	—
124	Q₈×C₄₇	—	2	8	no	—
125	Q₈×C₄₇	—	2	4	no	—
126	Q₈×C₄₇	—	2	4	no	—
127	Q₈×C₄₇	—	4	16	no	—
128	Q₈×C₄₇	—	4	4	no	—
129	Q₈×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
130	C₂×C₄×C₄₇	—	2	4	no	—
131	C₂×C₄×C₄₇	—	2	8	no	—
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	2	4	no	—
136	C₂×C₄×C₄₇	—	2	4	no	—
137	C₂×C₄×C₄₇	—	4	16	no	—
138	C₂×C₄×C₄₇	—	4	4	no	—
139	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
140	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
141	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
142	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
143	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
144	C₂×Dic₄₇	—	2	2	no	—
145	C₂×Dic₄₇	—	2	2	no	—
146	C₂×Dic₄₇	—	2	2	no	—
147	C₂×Dic₄₇	—	2	2	no	—
148	C₂×Dic₄₇	—	2	2	no	—
149	C₂×Dic₄₇	—	4	4	no	—
150	C₂×Dic₄₇	—	4	4	no	—
151	C₂×Dic₄₇	—	4	4	no	—
152	C₂×Dic₄₇	C₂×Q₁₆	1	4	yes	complemented
153	C₈×C₄₇	—	2	2	no	—
154	C₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
155	C₄₇⋊C₈	—	4	2	no	—
156	C₂²⋊C₄×Q₁₆	—	47	1	no	maximal, Sylow
157	C₂²×C₄₇	—	2	2	no	—
158	C₂²×C₄₇	—	2	2	no	—
159	C₂²×C₄₇	—	2	4	no	—
160	C₂²×C₄₇	—	2	4	no	—
161	C₂²×C₄₇	C₄×Q₁₆	1	4	yes	complemented
162	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
163	C₂²×C₄₇	D₄²	1	2	yes	—
164	C₂²×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
165	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
166	C₂²×C₄₇	#578	1	2	yes	—
167	C₄×C₄₇	—	2	2	no	—
168	C₄×C₄₇	—	2	8	no	—
169	C₄×C₄₇	—	4	4	no	—
170	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
171	C₄×C₄₇	#518	1	1	yes	characteristic
172	C₄×C₄₇	#546	1	2	yes	—
173	Dic₄₇	—	2	4	no	—
174	Dic₄₇	—	4	2	no	—
175	Dic₄₇	—	8	4	no	—
176	C₂³×Q₁₆	D₄₇	1	1	yes	characteristic
177	C₂×C₄×Q₁₆	—	47	2	no	—
178	Q₈×C₂²⋊C₄	—	47	2	no	—
179	#1969	—	47	2	no	—
180	#1878	—	47	4	no	—
181	#1808	—	47	1	no	—
182	#1787	—	47	2	no	—
183	C₈×C₂²⋊C₄	—	47	1	no	—
184	C₂×C₄₇	—	2	4	no	—
185	C₂×C₄₇	D₄×C₂²⋊C₄	1	1	yes	characteristic
186	C₂×C₄₇	C₂×C₄×Q₁₆	1	1	yes	characteristic
187	C₂×C₄₇	#2950	1	1	yes	characteristic
188	C₂×C₄₇	#3285	1	2	yes	—
189	C₂×C₄₇	D₄×Q₁₆	1	2	yes	—
190	C₂³×Q₈	C₂×D₄₇	1	2	yes	—
191	C₂²×Q₁₆	—	2	8	no	—
192	C₂²×Q₁₆	Dic₄₇	1	8	yes	complemented
193	C₂²×Q₁₆	C₂×D₄₇	1	2	yes	—
194	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
195	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
196	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
197	C₂×C₄×Q₈	—	47	4	no	—
198	C₄×Q₁₆	—	94	8	no	—
199	C₂×#107	—	47	2	no	—
200	C₂×#103	—	47	4	no	—
201	C₂×#103	—	47	4	no	—
202	C₂×C₂²⋊C₈	—	47	1	no	—
203	C₂×C₄×C₈	—	47	2	no	—
204	#391	—	47	4	no	—
205	#391	—	94	4	no	—
206	#380	—	47	2	no	—
207	#380	—	94	2	no	—
208	C₄×C₂²⋊C₄	—	47	1	no	—
209	C₄×C₂²⋊C₄	—	94	2	no	—
210	#340	—	47	2	no	—
211	#336	—	47	2	no	—
212	C₄₇	C₂²⋊C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
213	C₂²×Q₈	—	2	2	no	—
214	C₂²×Q₈	—	2	4	no	—
215	C₂²×Q₈	—	2	8	no	—
216	C₂²×Q₈	—	4	4	no	—
217	C₂²×Q₈	C₂×Dic₄₇	1	8	yes	—
218	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
219	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
220	C₂³×C₄	—	2	2	no	—
221	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
222	C₂×Q₁₆	—	2	8	no	—
223	C₂×Q₁₆	—	2	32	no	—
224	C₂×Q₁₆	—	2	4	no	—
225	C₂×Q₁₆	C₂×Dic₄₇	1	8	yes	—
226	C₂×Q₁₆	C₂×Dic₄₇	1	4	yes	—
227	C₂×Q₁₆	C₂×Dic₄₇	1	4	yes	—
228	C₂×Q₁₆	C₂²⋊D₄₇	1	8	yes	—
229	C₂²×C₈	—	2	4	no	—
230	C₂²×C₈	—	47	2	no	—
231	C₂²×C₈	C₂×Dic₄₇	1	4	yes	—
232	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
233	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
234	C₄×Q₈	—	94	8	no	—
235	C₄×Q₈	—	188	4	no	—
236	C₂×C₄⋊C₄	—	47	4	no	—
237	C₂×C₄⋊C₄	—	94	4	no	—
238	C₂×C₂²⋊C₄	—	47	1	no	—
239	C₂×C₂²⋊C₄	—	47	1	no	—
240	C₂×C₂²⋊C₄	—	94	2	no	—
241	C₂×C₄²	—	47	2	no	—
242	C₂×C₄²	—	94	4	no	—
243	#107	—	94	4	no	—
244	#103	—	94	8	no	—
245	#103	—	188	4	no	—
246	C₂²⋊C₈	—	94	2	no	—
247	C₄×C₈	—	94	4	no	—
248	#95	—	47	2	no	—
249	#95	—	94	4	no	—
250	#95	—	94	4	no	—
251	#95	—	94	2	no	—
252	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
253	C₂×Q₈	—	2	8	no	—
254	C₂×Q₈	—	2	2	no	—
255	C₂×Q₈	—	2	2	no	—
256	C₂×Q₈	—	2	4	no	—
257	C₂×Q₈	—	2	16	no	—
258	C₂×Q₈	—	2	4	no	—
259	C₂×Q₈	—	2	4	no	—
260	C₂×Q₈	—	4	8	no	—
261	C₂×Q₈	—	4	8	no	—
262	C₂×Q₈	—	4	16	no	—
263	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
264	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
265	C₂×Q₈	C₂×C₂²⋊D₄₇	1	8	yes	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	8	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	4	8	no	—
272	C₂²×C₄	—	47	2	no	—
273	C₂²×C₄	—	47	2	no	—
274	C₂²×C₄	—	94	4	no	—
275	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
276	C₂²×C₄	#10625352	1	2	yes	—
277	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
278	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
279	Q₁₆	—	2	16	no	—
280	Q₁₆	—	2	8	no	—
281	Q₁₆	C₂²⋊Dic₄₇	1	16	yes	direct product factor
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	8	no	—
284	C₂×C₈	—	94	2	no	—
285	C₂×C₈	—	94	2	no	—
286	C₂×C₈	—	94	2	no	—
287	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
288	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
289	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
290	C₄⋊C₄	—	94	4	no	—
291	C₄⋊C₄	—	94	4	no	—
292	C₄⋊C₄	—	188	8	no	—
293	C₂²⋊C₄	—	47	4	no	—
294	C₂²⋊C₄	—	94	2	no	—
295	C₂²⋊C₄	—	188	4	no	—
296	C₄²	—	94	2	no	—
297	C₄²	—	94	2	no	—
298	C₄²	—	188	8	no	—
299	C₂³	—	2	2	no	—
300	C₂³	—	2	2	no	—
301	C₂³	D₄×Dic₄₇	1	2	yes	—
302	C₂³	Q₁₆×D₄₇	1	2	yes	—
303	C₂³	#13094047	1	2	yes	—
304	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
305	Q₈	—	2	8	no	—
306	Q₈	—	2	4	no	—
307	Q₈	—	2	4	no	—
308	Q₈	—	2	4	no	—
309	Q₈	—	4	16	no	—
310	Q₈	—	4	4	no	—
311	Q₈	C₂×C₂²⋊Dic₄₇	1	8	yes	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	4	16	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	47	4	no	—
322	C₂×C₄	—	94	2	no	—
323	C₂×C₄	—	94	2	no	—
324	C₂×C₄	—	94	2	no	—
325	C₂×C₄	—	94	2	no	—
326	C₂×C₄	—	94	2	no	—
327	C₂×C₄	—	188	4	no	—
328	C₂×C₄	—	188	4	no	—
329	C₂×C₄	—	188	4	no	—
330	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
331	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
332	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
333	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
334	C₂×C₄	#13094069	1	2	yes	—
335	C₈	—	2	2	no	—
336	C₈	—	188	2	no	—
337	C₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
338	C₂²	—	2	2	no	—
339	C₂²	—	2	4	no	—
340	C₂²	—	2	4	no	—
341	C₂²	—	2	2	no	—
342	C₂²	Q₁₆×Dic₄₇	1	4	yes	complemented
343	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
344	C₂²	D₄×C₂²⋊D₄₇	1	2	yes	—
345	C₂²	C₂×Q₁₆×D₄₇	1	1	yes	characteristic
346	C₂²	C₂×#13094047	1	1	yes	characteristic
347	C₂²	#15689936	1	2	yes	—
348	C₄	—	2	2	no	—
349	C₄	—	2	8	no	—
350	C₄	—	4	4	no	—
351	C₄	—	94	4	no	—
352	C₄	—	376	4	no	—
353	C₄	—	188	2	no	—
354	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
355	C₄	#15689598	1	1	yes	characteristic
356	C₄	#15689767	1	2	yes	—
357	C₂	—	2	4	no	—
358	C₂	D₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
359	C₂	C₂×Q₁₆×Dic₄₇	1	1	yes	characteristic
360	C₂	#20252256	1	1	yes	characteristic
361	C₂	#20255129	1	2	yes	—
362	C₂	Q₁₆×C₂²⋊D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂³×Q₁₆×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂³×Q₁₆	D₄₇
hypocenter	C₄₇	C₂²⋊C₄×Q₁₆
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×Q₁₆×Dic₄₇	C₂	semidirect
3. #20244250	C₂	semidirect
4. #20243731	C₂	semidirect
26. C₂²×Q₁₆×C₄₇	C₄	semidirect
99. Q₁₆×C₄₇	C₂²⋊C₄	semidirect
107. C₂²⋊Dic₄₇	Q₁₆	direct (N × H)
152. C₂×Dic₄₇	C₂×Q₁₆	semidirect
161. C₂²×C₄₇	C₄×Q₁₆	semidirect
192. C₂²×Q₁₆	Dic₄₇	semidirect
212. C₄₇	C₂²⋊C₄×Q₁₆	semidirect
281. Q₁₆	C₂²⋊Dic₄₇	direct (N × H)
342. C₂²	Q₁₆×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×Dic₄₇	2
Q₈×C₂²⋊Dic₄₇	2
#20244250	2
#20243731	2
#20243417	2
#20243323	2
C₈×C₂²⋊Dic₄₇	2
C₂³×Q₁₆×C₄₇	2
C₂²⋊C₄×Q₁₆	47

Subgroups — Q16×C22⋊Dic47 #26232140

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₁₆×C₂²⋊Dic₄₇ #26232140