Subgroups — D₄₇×#1591 #26186016

Order 12032.

670 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#446×D₄₇	C₂	1	2	yes	maximal
2	C₄×Q₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic
3	#20242286	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242285	C₂	1	1	yes	maximal, characteristic, complemented
5	#20242284	C₂	1	1	yes	maximal, characteristic, complemented
6	#20242283	C₂	1	2	yes	maximal, complemented
7	#20242282	C₂	1	2	yes	maximal, complemented
8	#335×D₄₇	C₂	1	1	yes	maximal, characteristic
9	Q₈⋊C₈×D₄₇	C₂	1	2	yes	maximal
10	C₈²×D₄₇	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1591	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₄₇	C₄	1	1	yes	characteristic
13	C₄×Q₈×D₄₇	C₂²	1	2	yes	—
14	#15689254	C₂²	1	2	yes	—
15	#15689253	C₂²	1	2	yes	—
16	#15689252	—	2	2	no	—
17	#15689251	—	2	2	no	—
18	#15689250	C₂²	1	2	yes	—
19	C₄×Dic₁₈₈	C₂²	1	1	yes	characteristic
20	Q₁₆×Dic₄₇	C₄	1	1	yes	characteristic
21	#15689217	C₄	1	1	yes	characteristic
22	C₄×#10625337	C₂²	1	2	yes	—
23	#15689215	C₄	1	2	yes	—
24	#107×D₄₇	C₄	1	1	yes	characteristic
25	C₄⋊C₈×D₄₇	—	2	2	no	—
26	C₄⋊C₈×D₄₇	C₂²	1	2	yes	—
27	#103×D₄₇	C₄	1	2	yes	—
28	#97×D₄₇	—	2	2	no	—
29	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
32	#15688876	C₂²	1	1	yes	characteristic
33	#15688875	C₂²	1	2	yes	—
34	#15688855	C₂²	1	2	yes	—
35	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
36	#15688853	C₂²	1	2	yes	—
37	C₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
38	C₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
39	C₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
40	C₄₇×#446	C₂²	1	2	yes	—
41	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#335	C₂²	1	1	yes	characteristic
43	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₄₇	C₂²	1	1	yes	characteristic
45	C₂×Q₈×D₄₇	C₂×C₄	1	2	yes	—
46	C₂×Dic₁₈₈	C₂×C₄	1	1	yes	characteristic
47	C₂×#10625337	C₂×C₄	1	2	yes	—
48	Q₁₆×D₄₇	—	2	4	no	—
49	C₂×C₈×D₄₇	—	2	1	no	—
50	C₂×C₈×D₄₇	—	2	2	no	—
51	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
54	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
55	Q₈×Dic₄₇	C₂×C₄	1	2	yes	—
56	C₄×Dic₉₄	—	2	2	no	—
57	C₄×Dic₉₄	C₂³	1	2	yes	—
58	#13093989	—	2	2	no	—
59	#13093989	C₂×C₄	1	2	yes	—
60	C₄⋊C₄×D₄₇	—	2	2	no	—
61	C₄⋊C₄×D₄₇	C₂×C₄	1	2	yes	—
62	C₄²×D₄₇	—	2	2	no	—
63	C₄²×D₄₇	C₂³	1	1	yes	characteristic
64	#13093958	C₂×C₄	1	1	yes	characteristic
65	#13093957	C₂×C₄	1	2	yes	—
66	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
67	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
68	Dic₄₇⋊C₈	—	2	2	no	—
69	Dic₄₇⋊C₈	—	2	2	no	—
70	Dic₄₇⋊C₈	—	2	2	no	—
71	#13093949	C₂×C₄	1	2	yes	—
72	#13093948	C₂×C₄	1	2	yes	—
73	#13093947	C₂×C₄	1	2	yes	—
74	#13093935	—	2	2	no	—
75	#13093934	—	2	2	no	—
76	#13093934	—	2	2	no	—
77	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
78	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
79	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
80	C₈×Dic₄₇	—	2	1	no	—
81	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₄₇	D₄	1	1	yes	characteristic
84	C₈×Dic₄₇	D₄	1	1	yes	characteristic
85	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
87	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₈×C₄₇	—	2	2	no	—
89	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
90	#103×C₄₇	C₂×C₄	1	2	yes	—
91	#97×C₄₇	—	2	2	no	—
92	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
95	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
96	Q₈×D₄₇	—	2	4	no	—
97	Q₈×D₄₇	—	2	4	no	—
98	C₂×C₄×D₄₇	—	2	2	no	—
99	C₂×C₄×D₄₇	—	2	2	no	—
100	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂×C₄×D₄₇	#41	1	1	yes	characteristic
103	C₂×Dic₉₄	—	2	2	no	—
104	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
105	Q₁₆×C₄₇	—	2	2	no	—
106	C₂×C₈×C₄₇	—	2	1	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₄⋊C₄×C₄₇	—	2	2	no	—
113	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
114	C₄²×C₄₇	—	2	2	no	—
115	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
116	#10625337	—	2	4	no	—
117	C₄⋊Dic₄₇	—	2	2	no	—
118	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
119	Dic₄₇⋊C₄	—	2	2	no	—
120	Dic₄₇⋊C₄	—	2	2	no	—
121	Dic₄₇⋊C₄	—	2	2	no	—
122	C₄×Dic₄₇	—	2	2	no	—
123	C₄×Dic₄₇	—	2	2	no	—
124	C₄×Dic₄₇	—	2	2	no	—
125	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
126	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
127	C₄×Dic₄₇	#41	1	1	yes	characteristic
128	C₂×C₄₇⋊C₈	—	2	1	no	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
133	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
134	Dic₁₈₈	—	2	2	no	—
135	C₈×D₄₇	—	2	4	no	—
136	C₈×D₄₇	—	2	2	no	—
137	C₈×D₄₇	—	2	2	no	—
138	C₈×D₄₇	—	4	4	no	—
139	C₈×D₄₇	M₁₆	1	4	yes	—
140	C₈×D₄₇	Q₁₆	1	4	yes	complemented
141	C₂²×D₄₇	C₄×D₄	1	1	yes	characteristic
142	Q₈×C₄₇	—	2	2	no	—
143	Q₈×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
149	C₂×Dic₄₇	—	2	2	no	—
150	C₂×Dic₄₇	—	2	2	no	—
151	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
152	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
153	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
154	C₄×D₄₇	—	2	2	no	—
155	C₄×D₄₇	—	4	4	no	—
156	C₄×D₄₇	—	4	4	no	—
157	C₄×D₄₇	C₂×M₁₆	1	2	yes	—
158	C₄×D₄₇	#131	1	2	yes	—
159	C₄×D₄₇	C₂×Q₁₆	1	2	yes	—
160	C₄×D₄₇	#135	1	2	yes	—
161	Dic₉₄	—	2	2	no	—
162	Dic₉₄	—	2	2	no	—
163	Dic₉₄	—	4	4	no	—
164	C₈×C₄₇	—	2	2	no	—
165	C₈×C₄₇	—	2	1	no	—
166	C₈×C₄₇	—	2	1	no	—
167	C₈×C₄₇	—	4	2	no	—
168	C₈×C₄₇	C₂×M₁₆	1	2	yes	—
169	C₈×C₄₇	C₂×Q₁₆	1	2	yes	complemented
170	C₄₇⋊C₈	—	2	2	no	—
171	C₄₇⋊C₈	—	2	1	no	—
172	C₄₇⋊C₈	—	2	1	no	—
173	C₄₇⋊C₈	—	4	2	no	—
174	C₄₇⋊C₈	C₂×M₁₆	1	2	yes	—
175	C₄₇⋊C₈	C₂×Q₁₆	1	2	yes	complemented
176	C₂×#1591	—	47	1	no	maximal, Sylow
177	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
178	C₂×D₄₇	#436	1	2	yes	—
179	C₂×D₄₇	C₄×Q₁₆	1	2	yes	—
180	C₂×D₄₇	#443	1	2	yes	—
181	C₄×C₄₇	—	2	1	no	—
182	C₄×C₄₇	—	4	2	no	—
183	C₄×C₄₇	—	4	2	no	—
184	C₄×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
185	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
186	C₄×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
187	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
188	Dic₄₇	—	2	1	no	—
189	Dic₄₇	—	4	2	no	—
190	Dic₄₇	—	4	2	no	—
191	Dic₄₇	#436	1	2	yes	—
192	Dic₄₇	C₄×Q₁₆	1	2	yes	—
193	C₂×#446	—	47	2	no	—
194	C₂×C₄×Q₁₆	—	47	1	no	—
195	#1591	—	47	2	no	—
196	#1591	—	47	1	no	—
197	#1591	—	47	1	no	—
198	#1591	—	47	2	no	—
199	#1591	—	47	1	no	—
200	#1591	D₄₇	1	1	yes	characteristic, direct product factor
201	C₂×#335	—	47	1	no	—
202	C₂×Q₈⋊C₈	—	47	2	no	—
203	C₂×C₈²	—	47	1	no	—
204	C₂×C₄₇	C₂×#436	1	1	yes	characteristic
205	C₂×C₄₇	C₂×C₄×Q₁₆	1	1	yes	characteristic
206	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
207	D₄₇	#1591	1	4	yes	direct product factor
208	C₂²×Q₁₆	—	47	1	no	—
209	C₂×C₄×Q₈	—	47	2	no	—
210	#446	—	47	2	no	—
211	#446	—	47	2	no	—
212	#446	—	47	2	no	—
213	#446	—	94	2	no	—
214	#446	—	94	2	no	—
215	#446	C₂×D₄₇	1	2	yes	—
216	C₄×Q₁₆	—	47	1	no	—
217	C₄×Q₁₆	—	47	2	no	—
218	C₄×Q₁₆	—	47	1	no	—
219	C₄×Q₁₆	—	47	2	no	—
220	C₄×Q₁₆	—	47	1	no	—
221	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
222	C₂×#107	—	47	1	no	—
223	C₂×C₄⋊C₈	—	47	2	no	—
224	C₂×C₄⋊C₈	—	94	2	no	—
225	C₂×#103	—	47	2	no	—
226	C₂×#97	—	94	2	no	—
227	C₂×C₄×C₈	—	47	1	no	—
228	C₂×C₄×C₈	—	47	1	no	—
229	C₂×C₄×C₈	—	47	1	no	—
230	#335	—	47	2	no	—
231	#335	—	47	1	no	—
232	#335	C₂×D₄₇	1	1	yes	characteristic
233	Q₈⋊C₈	—	47	2	no	—
234	Q₈⋊C₈	—	47	2	no	—
235	Q₈⋊C₈	—	47	2	no	—
236	Q₈⋊C₈	C₂×D₄₇	1	2	yes	—
237	C₈²	—	47	1	no	—
238	C₈²	—	47	1	no	—
239	C₈²	—	47	1	no	—
240	C₈²	C₂×D₄₇	1	1	yes	characteristic
241	C₄₇	C₂×#1591	1	1	yes	characteristic, complemented, Sylow
242	C₂²×Q₈	—	47	2	no	—
243	C₂×Q₁₆	—	47	2	no	—
244	C₂×Q₁₆	—	47	1	no	—
245	C₂×Q₁₆	—	94	4	no	—
246	C₂×Q₁₆	C₄×D₄₇	1	1	yes	characteristic
247	C₂²×C₈	—	47	1	no	—
248	C₂²×C₈	—	47	1	no	—
249	C₂²×C₈	—	47	1	no	—
250	C₂²×C₈	—	47	1	no	—
251	C₂²×C₈	—	94	1	no	—
252	C₂²×C₈	—	94	2	no	—
253	C₄×Q₈	—	47	2	no	—
254	C₄×Q₈	—	47	2	no	—
255	C₄×Q₈	—	47	2	no	—
256	C₄×Q₈	—	94	2	no	—
257	C₄×Q₈	—	94	2	no	—
258	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
259	C₂×C₄⋊C₄	—	47	2	no	—
260	C₂×C₄⋊C₄	—	94	2	no	—
261	C₂×C₄²	—	47	1	no	—
262	C₂×C₄²	—	94	2	no	—
263	#107	—	47	1	no	—
264	#107	—	47	2	no	—
265	#107	C₄×D₄₇	1	1	yes	characteristic
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	—	47	2	no	—
268	C₄⋊C₈	—	94	2	no	—
269	C₄⋊C₈	—	94	2	no	—
270	C₄⋊C₈	—	94	2	no	—
271	C₄⋊C₈	—	94	2	no	—
272	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
273	#103	—	47	2	no	—
274	#103	—	47	2	no	—
275	#103	—	47	2	no	—
276	#103	C₄×D₄₇	1	2	yes	—
277	#97	—	2	2	no	—
278	#97	—	94	2	no	—
279	#97	—	94	2	no	—
280	#97	—	94	2	no	—
281	C₄×C₈	—	47	1	no	—
282	C₄×C₈	—	47	1	no	—
283	C₄×C₈	—	47	1	no	—
284	C₄×C₈	—	47	1	no	—
285	C₄×C₈	—	47	1	no	—
286	C₄×C₈	—	47	1	no	—
287	C₄×C₈	—	47	1	no	—
288	C₄×C₈	—	94	1	no	—
289	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
290	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
291	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
292	C₂×Q₈	—	47	2	no	—
293	C₂×Q₈	—	94	2	no	—
294	C₂×Q₈	—	94	4	no	—
295	C₂×Q₈	—	94	4	no	—
296	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
297	C₂²×C₄	—	47	1	no	—
298	C₂²×C₄	—	47	1	no	—
299	C₂²×C₄	—	47	1	no	—
300	C₂²×C₄	—	94	2	no	—
301	C₂²×C₄	—	94	2	no	—
302	Q₁₆	—	2	2	no	—
303	Q₁₆	—	94	4	no	—
304	Q₁₆	—	94	2	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	47	1	no	—
308	C₂×C₈	—	47	1	no	—
309	C₂×C₈	—	47	4	no	—
310	C₂×C₈	—	47	4	no	—
311	C₂×C₈	—	47	1	no	—
312	C₂×C₈	—	47	1	no	—
313	C₂×C₈	—	94	2	no	—
314	C₂×C₈	—	94	2	no	—
315	C₂×C₈	—	94	4	no	—
316	C₂×C₈	—	94	1	no	—
317	C₂×C₈	—	94	2	no	—
318	C₂×C₈	—	188	4	no	—
319	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
320	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
321	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
322	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	47	2	no	—
325	C₄⋊C₄	—	94	2	no	—
326	C₄⋊C₄	—	94	2	no	—
327	C₄⋊C₄	—	94	2	no	—
328	C₄⋊C₄	—	94	2	no	—
329	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
330	C₄²	—	2	2	no	—
331	C₄²	—	47	1	no	—
332	C₄²	—	47	1	no	—
333	C₄²	—	47	1	no	—
334	C₄²	—	94	2	no	—
335	C₄²	—	94	2	no	—
336	C₄²	—	94	2	no	—
337	C₄²	C₂³×D₄₇	1	1	yes	characteristic
338	C₂³	—	47	1	no	—
339	Q₈	—	2	2	no	—
340	Q₈	—	2	2	no	—
341	Q₈	—	94	2	no	—
342	Q₈	—	94	2	no	—
343	Q₈	—	188	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	47	1	no	—
347	C₂×C₄	—	47	1	no	—
348	C₂×C₄	—	47	2	no	—
349	C₂×C₄	—	47	2	no	—
350	C₂×C₄	—	47	2	no	—
351	C₂×C₄	—	47	2	no	—
352	C₂×C₄	—	47	1	no	—
353	C₂×C₄	—	94	2	no	—
354	C₂×C₄	—	94	2	no	—
355	C₂×C₄	—	94	2	no	—
356	C₂×C₄	—	188	4	no	—
357	C₂×C₄	—	188	4	no	—
358	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
359	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
360	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
361	C₈	—	2	2	no	—
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	4	2	no	—
365	C₈	—	47	2	no	—
366	C₈	—	47	2	no	—
367	C₈	—	94	2	no	—
368	C₈	—	94	1	no	—
369	C₈	—	94	1	no	—
370	C₈	—	188	2	no	—
371	C₈	M₁₆×D₄₇	1	2	yes	—
372	C₈	Q₁₆×D₄₇	1	2	yes	complemented
373	C₂²	—	47	2	no	—
374	C₂²	—	47	2	no	—
375	C₂²	—	47	2	no	—
376	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
377	C₄	—	2	1	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	2	no	—
380	C₄	—	47	2	no	—
381	C₄	—	47	2	no	—
382	C₄	—	94	1	no	—
383	C₄	—	188	2	no	—
384	C₄	—	188	2	no	—
385	C₄	C₂×M₁₆×D₄₇	1	1	yes	characteristic
386	C₄	#131×D₄₇	1	1	yes	characteristic
387	C₄	C₂×Q₁₆×D₄₇	1	1	yes	characteristic
388	C₄	#135×D₄₇	1	1	yes	characteristic
389	C₂	—	47	4	no	—
390	C₂	#436×D₄₇	1	1	yes	characteristic
391	C₂	C₄×Q₁₆×D₄₇	1	1	yes	characteristic
392	C₂	#443×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1591	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂²×D₄₇	C₄×D₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1591	D₄₇
hypocenter	C₄₇	C₂×#1591
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1591

Complements

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

N	H ≅ G/N	type
3. #20242286	C₂	semidirect
4. #20242285	C₂	semidirect
5. #20242284	C₂	semidirect
6. #20242283	C₂	semidirect
7. #20242282	C₂	semidirect
11. C₄₇×#1591	C₂	semidirect
140. C₈×D₄₇	Q₁₆	semidirect
169. C₈×C₄₇	C₂×Q₁₆	semidirect
175. C₄₇⋊C₈	C₂×Q₁₆	semidirect
200. #1591	D₄₇	direct (N × H)
207. D₄₇	#1591	direct (N × H)
241. C₄₇	C₂×#1591	semidirect
372. C₈	Q₁₆×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#446×D₄₇	2
C₄×Q₁₆×D₄₇	2
#20242286	2
#20242285	2
#20242284	2
#20242283	2
#20242282	2
#335×D₄₇	2
Q₈⋊C₈×D₄₇	2
C₈²×D₄₇	2
C₄₇×#1591	2
C₂×#1591	47

Subgroups — D47×#1591 #26186016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#1591 #26186016