Subgroups — D₄₇×#1566 #26185273

Order 12032.

854 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#423×D₄₇	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
3	#20242144	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242143	C₂	1	2	yes	maximal, complemented
5	#20242142	C₂	1	4	yes	maximal, complemented
6	#334×D₄₇	C₂	1	4	yes	maximal, complemented
7	C₄₇×#1566	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₄₇	—	2	2	no	—
9	C₂²×C₈×D₄₇	C₄	1	2	yes	—
10	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
11	#15689147	C₂²	1	2	yes	—
12	#15689146	—	2	2	no	—
13	#15689145	—	2	2	no	—
14	#15689145	C₂²	1	4	yes	—
15	C₄⋊C₈×D₄₇	—	2	2	no	—
16	C₄⋊C₈×D₄₇	C₂²	1	4	yes	—
17	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₈×Dic₄₇	C₄	1	2	yes	—
19	C₄×C₈×D₄₇	C₄	1	1	yes	characteristic
20	C₄×C₈×D₄₇	C₄	1	1	yes	characteristic
21	C₄×C₈×D₄₇	C₄	1	1	yes	characteristic
22	C₄×C₈×D₄₇	C₄	1	1	yes	characteristic
23	C₄×C₈×D₄₇	C₂²	1	2	yes	—
24	C₄×C₈×D₄₇	C₂²	1	2	yes	—
25	#15688874	C₂²	1	4	yes	complemented
26	#15688873	C₂²	1	8	yes	complemented
27	C₄₇×#423	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₄₇×#334	C₂²	1	4	yes	complemented
30	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
32	C₂²×C₄×D₄₇	Q₈	1	1	yes	characteristic
33	C₂×#10625329	—	2	2	no	—
34	C₂×#10625324	—	2	4	no	—
35	M₁₆×D₄₇	—	4	8	no	—
36	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
37	C₂×C₈×D₄₇	—	2	8	no	—
38	C₂×C₈×D₄₇	—	2	4	no	—
39	C₂×C₈×D₄₇	C₂×C₄	1	2	yes	—
40	C₂×C₈×D₄₇	C₂×C₄	1	2	yes	—
41	C₂×C₈×D₄₇	C₂×C₄	1	2	yes	—
42	C₂×C₈×D₄₇	C₂×C₄	1	2	yes	—
43	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
45	C₂×C₄×Dic₄₇	Q₈	1	1	yes	characteristic
46	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
47	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
48	C₄²×D₄₇	D₄	1	1	yes	characteristic
49	C₄²×D₄₇	D₄	1	1	yes	characteristic
50	C₄²×D₄₇	Q₈	1	1	yes	characteristic
51	C₄²×D₄₇	Q₈	1	1	yes	characteristic
52	C₄²×D₄₇	C₂³	1	1	yes	characteristic
53	C₄²×D₄₇	C₂³	1	1	yes	characteristic
54	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
55	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
56	Dic₄₇⋊C₈	—	2	4	no	—
57	Dic₄₇⋊C₈	—	2	4	no	—
58	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
59	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
60	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
61	C₈×Dic₄₇	C₂×C₄	1	2	yes	—
62	C₈×Dic₄₇	C₂×C₄	1	2	yes	—
63	C₈×Dic₄₇	C₂×C₄	1	2	yes	—
64	C₈×Dic₄₇	C₂×C₄	1	2	yes	—
65	C₂×M₁₆×C₄₇	—	2	2	no	—
66	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₄₇	—	2	2	no	—
69	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
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	C₂³×D₄₇	C₄⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
77	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
80	C₂×C₄×D₄₇	—	2	4	no	—
81	C₂×C₄×D₄₇	—	2	4	no	—
82	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
88	C₂×C₄×D₄₇	SD₁₆	1	8	yes	—
89	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂×C₄×D₄₇	C₂×Q₈	1	1	yes	characteristic
94	C₂×C₄×D₄₇	C₂×Q₈	1	1	yes	characteristic
95	M₁₆×C₄₇	—	4	4	no	—
96	C₂×C₈×C₄₇	—	2	4	no	—
97	C₂×C₈×C₄₇	—	2	4	no	—
98	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
100	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
103	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
104	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
105	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
106	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
107	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
108	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
109	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
110	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
113	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
114	C₄×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
115	C₄×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
116	#10625329	—	4	4	no	—
117	C₂×C₄₇⋊C₈	—	2	4	no	—
118	C₂×C₄₇⋊C₈	—	2	4	no	—
119	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
120	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
121	#10625324	—	4	8	no	—
122	C₈×D₄₇	—	2	4	no	—
123	C₈×D₄₇	—	2	4	no	—
124	C₈×D₄₇	—	2	4	no	—
125	C₈×D₄₇	—	4	8	no	—
126	C₈×D₄₇	M₁₆	1	8	yes	complemented
127	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂²×D₄₇	—	2	2	no	—
129	C₂²×D₄₇	—	2	2	no	—
130	C₂²×D₄₇	#106	1	4	yes	—
131	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
139	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
140	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
141	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
142	C₂×Dic₄₇	—	2	2	no	—
143	C₂×Dic₄₇	—	2	2	no	—
144	C₂×Dic₄₇	#106	1	4	yes	—
145	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₄×D₄₇	—	2	2	no	—
152	C₄×D₄₇	—	2	2	no	—
153	C₄×D₄₇	—	2	2	no	—
154	C₄×D₄₇	—	2	2	no	—
155	C₄×D₄₇	—	2	2	no	—
156	C₄×D₄₇	—	2	2	no	—
157	C₄×D₄₇	#106	1	4	yes	—
158	C₄×D₄₇	#106	1	4	yes	—
159	C₄×D₄₇	#108	1	4	yes	—
160	C₄×D₄₇	C₂×M₁₆	1	4	yes	—
161	C₄×D₄₇	C₂×SD₁₆	1	4	yes	—
162	C₄×D₄₇	C₂×SD₁₆	1	4	yes	—
163	C₈×C₄₇	—	2	2	no	—
164	C₈×C₄₇	—	4	4	no	—
165	C₈×C₄₇	C₂×M₁₆	1	4	yes	complemented
166	C₄₇⋊C₈	—	2	2	no	—
167	C₄₇⋊C₈	—	4	4	no	—
168	C₄₇⋊C₈	C₂×M₁₆	1	4	yes	complemented
169	C₂×#1566	—	47	1	no	maximal, Sylow
170	C₂²×C₄₇	—	2	1	no	—
171	C₂²×C₄₇	—	2	1	no	—
172	C₂²×C₄₇	C₂×#106	1	2	yes	—
173	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
174	C₂×D₄₇	—	2	1	no	—
175	C₂×D₄₇	—	2	1	no	—
176	C₂×D₄₇	—	2	8	no	—
177	C₂×D₄₇	#423	1	2	yes	—
178	C₂×D₄₇	C₂×#106	1	2	yes	—
179	C₂×D₄₇	C₂×#106	1	2	yes	—
180	C₂×D₄₇	C₂×#108	1	2	yes	—
181	C₄×C₄₇	—	2	1	no	—
182	C₄×C₄₇	—	2	1	no	—
183	C₄×C₄₇	C₂×#106	1	2	yes	—
184	C₄×C₄₇	C₂×#108	1	2	yes	—
185	C₄×C₄₇	C₂²×M₁₆	1	2	yes	—
186	C₄×C₄₇	C₂²×SD₁₆	1	2	yes	—
187	Dic₄₇	—	2	1	no	—
188	Dic₄₇	—	2	1	no	—
189	Dic₄₇	#423	1	2	yes	—
190	Dic₄₇	C₂×#106	1	2	yes	—
191	Dic₄₇	C₂×#106	1	2	yes	—
192	Dic₄₇	C₂×#108	1	2	yes	—
193	C₂×#423	—	47	2	no	—
194	C₂²×C₄×C₈	—	47	1	no	—
195	#1566	—	47	2	no	—
196	#1566	—	47	1	no	—
197	#1566	—	47	4	no	—
198	#1566	D₄₇	1	1	yes	characteristic, direct product factor
199	C₂×#334	—	47	4	no	—
200	C₂×C₄₇	—	2	2	no	—
201	C₂×C₄₇	C₂×#423	1	1	yes	characteristic
202	C₂×C₄₇	C₂²×#106	1	1	yes	characteristic
203	C₂×C₄₇	C₂²×#108	1	1	yes	characteristic
204	D₄₇	—	2	2	no	—
205	D₄₇	#1566	1	4	yes	direct product factor
206	C₂²×M₁₆	—	94	2	no	—
207	C₂³×C₈	—	47	2	no	—
208	C₂²×C₄²	—	47	1	no	—
209	#423	—	47	2	no	—
210	#423	—	47	4	no	—
211	#423	—	94	2	no	—
212	#423	—	94	2	no	—
213	#423	C₂×D₄₇	1	2	yes	—
214	C₂×C₄⋊C₈	—	47	4	no	—
215	C₂×C₄⋊C₈	—	94	2	no	—
216	C₂×C₄×C₈	—	47	2	no	—
217	C₂×C₄×C₈	—	47	1	no	—
218	C₂×C₄×C₈	—	47	1	no	—
219	C₂×C₄×C₈	—	47	1	no	—
220	C₂×C₄×C₈	—	47	1	no	—
221	C₂×C₄×C₈	—	47	1	no	—
222	C₂×C₄×C₈	—	47	2	no	—
223	C₂×C₄×C₈	—	47	2	no	—
224	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
225	#334	—	47	8	no	—
226	#334	—	47	4	no	—
227	#334	C₂×D₄₇	1	4	yes	complemented
228	C₄₇	C₂×#1566	1	1	yes	characteristic, complemented, Sylow
229	C₂³×C₄	—	47	1	no	—
230	C₂³×C₄	—	47	1	no	—
231	C₂³×C₄	—	47	1	no	—
232	C₂×M₁₆	—	2	2	no	—
233	C₂×M₁₆	—	94	4	no	—
234	C₂×M₁₆	—	94	2	no	—
235	C₂×M₁₆	—	188	8	no	—
236	C₂²×C₈	—	47	2	no	—
237	C₂²×C₈	—	47	2	no	—
238	C₂²×C₈	—	47	2	no	—
239	C₂²×C₈	—	47	2	no	—
240	C₂²×C₈	—	47	2	no	—
241	C₂²×C₈	—	94	8	no	—
242	C₂²×C₈	—	94	4	no	—
243	C₂²×C₈	C₄×D₄₇	1	2	yes	—
244	C₂×C₄²	—	47	1	no	—
245	C₂×C₄²	—	47	1	no	—
246	C₂×C₄²	—	47	1	no	—
247	C₂×C₄²	—	47	1	no	—
248	C₂×C₄²	—	47	1	no	—
249	C₂×C₄²	—	47	1	no	—
250	C₂×C₄²	—	47	1	no	—
251	C₂×C₄²	—	47	1	no	—
252	C₂×C₄²	—	47	1	no	—
253	C₂×C₄²	—	47	1	no	—
254	C₂×C₄²	—	47	1	no	—
255	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
256	C₄⋊C₈	—	2	2	no	—
257	C₄⋊C₈	—	47	4	no	—
258	C₄⋊C₈	—	94	4	no	—
259	C₄⋊C₈	—	94	4	no	—
260	C₄⋊C₈	—	94	2	no	—
261	C₄⋊C₈	C₂²×D₄₇	1	4	yes	—
262	C₄×C₈	—	47	2	no	—
263	C₄×C₈	—	47	2	no	—
264	C₄×C₈	—	47	2	no	—
265	C₄×C₈	—	47	2	no	—
266	C₄×C₈	—	47	1	no	—
267	C₄×C₈	—	47	1	no	—
268	C₄×C₈	—	47	2	no	—
269	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
270	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
271	C₄×C₈	C₂²×D₄₇	1	2	yes	—
272	C₂⁴	—	47	1	no	—
273	C₂²×C₄	—	47	1	no	—
274	C₂²×C₄	—	47	1	no	—
275	C₂²×C₄	—	47	1	no	—
276	C₂²×C₄	—	47	1	no	—
277	C₂²×C₄	—	47	8	no	—
278	C₂²×C₄	—	47	1	no	—
279	C₂²×C₄	—	47	1	no	—
280	C₂²×C₄	—	47	1	no	—
281	C₂²×C₄	—	47	1	no	—
282	C₂²×C₄	—	47	1	no	—
283	C₂²×C₄	—	47	1	no	—
284	C₂²×C₄	—	47	1	no	—
285	C₂²×C₄	—	47	1	no	—
286	C₂²×C₄	—	47	1	no	—
287	C₂²×C₄	—	47	1	no	—
288	C₂²×C₄	—	47	1	no	—
289	C₂²×C₄	—	94	4	no	—
290	C₂²×C₄	—	94	4	no	—
291	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
292	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
293	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
294	M₁₆	—	4	4	no	—
295	M₁₆	—	188	8	no	—
296	M₁₆	—	188	4	no	—
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	47	2	no	—
300	C₂×C₈	—	47	8	no	—
301	C₂×C₈	—	47	2	no	—
302	C₂×C₈	—	94	4	no	—
303	C₂×C₈	—	94	4	no	—
304	C₂×C₈	—	94	4	no	—
305	C₂×C₈	—	94	4	no	—
306	C₂×C₈	—	94	4	no	—
307	C₂×C₈	—	188	8	no	—
308	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
309	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
310	C₄²	—	47	1	no	—
311	C₄²	—	47	1	no	—
312	C₄²	—	47	1	no	—
313	C₄²	—	47	1	no	—
314	C₄²	—	47	1	no	—
315	C₄²	—	47	1	no	—
316	C₄²	—	47	1	no	—
317	C₄²	—	47	1	no	—
318	C₄²	—	47	1	no	—
319	C₄²	—	47	1	no	—
320	C₄²	—	47	1	no	—
321	C₄²	—	47	1	no	—
322	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
323	C₄²	D₄×D₄₇	1	1	yes	characteristic
324	C₄²	Q₈×D₄₇	1	1	yes	characteristic
325	C₄²	C₂³×D₄₇	1	1	yes	characteristic
326	C₂³	—	47	1	no	—
327	C₂³	—	47	1	no	—
328	C₂³	—	47	4	no	—
329	C₂³	—	94	2	no	—
330	C₂³	—	94	2	no	—
331	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	47	1	no	—
335	C₂×C₄	—	47	1	no	—
336	C₂×C₄	—	47	1	no	—
337	C₂×C₄	—	47	1	no	—
338	C₂×C₄	—	47	4	no	—
339	C₂×C₄	—	47	4	no	—
340	C₂×C₄	—	47	4	no	—
341	C₂×C₄	—	47	4	no	—
342	C₂×C₄	—	47	4	no	—
343	C₂×C₄	—	47	4	no	—
344	C₂×C₄	—	47	4	no	—
345	C₂×C₄	—	47	1	no	—
346	C₂×C₄	—	47	1	no	—
347	C₂×C₄	—	94	2	no	—
348	C₂×C₄	—	94	2	no	—
349	C₂×C₄	—	94	2	no	—
350	C₂×C₄	—	94	2	no	—
351	C₂×C₄	—	94	2	no	—
352	C₂×C₄	—	94	2	no	—
353	C₂×C₄	—	94	2	no	—
354	C₂×C₄	—	94	2	no	—
355	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
356	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
357	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
358	C₂×C₄	SD₁₆×D₄₇	1	4	yes	—
359	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
360	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
361	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
362	C₈	—	2	2	no	—
363	C₈	—	4	4	no	—
364	C₈	—	47	4	no	—
365	C₈	—	94	2	no	—
366	C₈	—	188	4	no	—
367	C₈	M₁₆×D₄₇	1	4	yes	complemented
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	47	2	no	—
371	C₂²	—	47	2	no	—
372	C₂²	—	47	2	no	—
373	C₂²	—	47	2	no	—
374	C₂²	—	94	8	no	—
375	C₂²	—	94	1	no	—
376	C₂²	—	94	1	no	—
377	C₂²	#106×D₄₇	1	2	yes	—
378	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	47	2	no	—
382	C₄	—	47	2	no	—
383	C₄	—	47	2	no	—
384	C₄	—	47	2	no	—
385	C₄	—	94	1	no	—
386	C₄	—	94	1	no	—
387	C₄	#106×D₄₇	1	2	yes	—
388	C₄	#108×D₄₇	1	2	yes	—
389	C₄	C₂×M₁₆×D₄₇	1	2	yes	—
390	C₄	C₂×SD₁₆×D₄₇	1	2	yes	—
391	C₂	—	2	2	no	—
392	C₂	—	47	4	no	—
393	C₂	—	94	2	no	—
394	C₂	#423×D₄₇	1	1	yes	characteristic
395	C₂	C₂×#106×D₄₇	1	1	yes	characteristic
396	C₂	C₂×#108×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×#1566	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂³×D₄₇	C₄⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1566	D₄₇
hypocenter	C₄₇	C₂×#1566
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1566

Complements

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

N	H ≅ G/N	type
3. #20242144	C₂	semidirect
4. #20242143	C₂	semidirect
5. #20242142	C₂	semidirect
6. #334×D₄₇	C₂	semidirect
7. C₄₇×#1566	C₂	semidirect
25. #15688874	C₂²	semidirect
26. #15688873	C₂²	semidirect
29. C₄₇×#334	C₂²	semidirect
126. C₈×D₄₇	M₁₆	semidirect
165. C₈×C₄₇	C₂×M₁₆	semidirect
168. C₄₇⋊C₈	C₂×M₁₆	semidirect
198. #1566	D₄₇	direct (N × H)
205. D₄₇	#1566	direct (N × H)
227. #334	C₂×D₄₇	semidirect
228. C₄₇	C₂×#1566	semidirect
367. C₈	M₁₆×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#423×D₄₇	2
C₂×C₄×C₈×D₄₇	2
#20242144	2
#20242143	2
#20242142	2
#334×D₄₇	2
C₄₇×#1566	2
C₂×#1566	47

Subgroups — D47×#1566 #26185273

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#1566 #26185273