Subgroups — D₄₇×#1567 #26185277

Order 12032.

854 conjugacy classes of subgroups.

The subgroup lattice has 408 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	#20242147	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242146	C₂	1	2	yes	maximal, complemented
5	#20242145	C₂	1	4	yes	maximal, complemented
6	#335×D₄₇	C₂	1	4	yes	maximal, complemented
7	C₄₇×#1567	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	#15688876	C₂²	1	4	yes	complemented
26	#15688875	C₂²	1	8	yes	complemented
27	C₄₇×#423	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₄₇×#335	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	D₈	1	4	yes	—
89	C₂×C₄×D₄₇	Q₁₆	1	4	yes	—
90	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂×C₄×D₄₇	C₂×Q₈	1	1	yes	characteristic
95	C₂×C₄×D₄₇	C₂×Q₈	1	1	yes	characteristic
96	M₁₆×C₄₇	—	4	4	no	—
97	C₂×C₈×C₄₇	—	2	4	no	—
98	C₂×C₈×C₄₇	—	2	4	no	—
99	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
100	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
101	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
104	C₄²×C₄₇	C₂⁴	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	C₄⋊C₄	1	1	yes	characteristic
111	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
114	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
115	C₄×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
116	C₄×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
117	#10625329	—	4	4	no	—
118	C₂×C₄₇⋊C₈	—	2	4	no	—
119	C₂×C₄₇⋊C₈	—	2	4	no	—
120	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
121	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
122	#10625324	—	4	8	no	—
123	C₈×D₄₇	—	2	4	no	—
124	C₈×D₄₇	—	2	4	no	—
125	C₈×D₄₇	—	2	4	no	—
126	C₈×D₄₇	—	4	8	no	—
127	C₈×D₄₇	M₁₆	1	8	yes	complemented
128	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂²×D₄₇	—	2	2	no	—
130	C₂²×D₄₇	—	2	2	no	—
131	C₂²×D₄₇	#107	1	4	yes	—
132	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	2	2	no	—
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×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
140	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
141	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
142	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
144	C₂×Dic₄₇	—	2	2	no	—
145	C₂×Dic₄₇	—	2	2	no	—
146	C₂×Dic₄₇	#107	1	4	yes	—
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	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
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	—	2	2	no	—
158	C₄×D₄₇	—	2	2	no	—
159	C₄×D₄₇	#107	1	4	yes	—
160	C₄×D₄₇	#107	1	4	yes	—
161	C₄×D₄₇	#108	1	4	yes	—
162	C₄×D₄₇	C₂×M₁₆	1	4	yes	—
163	C₄×D₄₇	C₂×D₈	1	2	yes	—
164	C₄×D₄₇	C₂×D₈	1	2	yes	—
165	C₄×D₄₇	C₂×Q₁₆	1	2	yes	—
166	C₄×D₄₇	C₂×Q₁₆	1	2	yes	—
167	C₈×C₄₇	—	2	2	no	—
168	C₈×C₄₇	—	4	4	no	—
169	C₈×C₄₇	C₂×M₁₆	1	4	yes	complemented
170	C₄₇⋊C₈	—	2	2	no	—
171	C₄₇⋊C₈	—	4	4	no	—
172	C₄₇⋊C₈	C₂×M₁₆	1	4	yes	complemented
173	C₂×#1567	—	47	1	no	maximal, Sylow
174	C₂²×C₄₇	—	2	1	no	—
175	C₂²×C₄₇	—	2	1	no	—
176	C₂²×C₄₇	C₂×#107	1	2	yes	—
177	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
178	C₂×D₄₇	—	2	1	no	—
179	C₂×D₄₇	—	2	1	no	—
180	C₂×D₄₇	—	2	8	no	—
181	C₂×D₄₇	#423	1	2	yes	—
182	C₂×D₄₇	C₂×#107	1	2	yes	—
183	C₂×D₄₇	C₂×#107	1	2	yes	—
184	C₂×D₄₇	C₂×#108	1	2	yes	—
185	C₄×C₄₇	—	2	1	no	—
186	C₄×C₄₇	—	2	1	no	—
187	C₄×C₄₇	C₂×#107	1	2	yes	—
188	C₄×C₄₇	C₂×#108	1	2	yes	—
189	C₄×C₄₇	C₂²×M₁₆	1	2	yes	—
190	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
191	C₄×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
192	Dic₄₇	—	2	1	no	—
193	Dic₄₇	—	2	1	no	—
194	Dic₄₇	#423	1	2	yes	—
195	Dic₄₇	C₂×#107	1	2	yes	—
196	Dic₄₇	C₂×#107	1	2	yes	—
197	Dic₄₇	C₂×#108	1	2	yes	—
198	C₂×#423	—	47	2	no	—
199	C₂²×C₄×C₈	—	47	1	no	—
200	#1567	—	47	2	no	—
201	#1567	—	47	1	no	—
202	#1567	—	47	4	no	—
203	#1567	D₄₇	1	1	yes	characteristic, direct product factor
204	C₂×#335	—	47	4	no	—
205	C₂×C₄₇	—	2	2	no	—
206	C₂×C₄₇	C₂×#423	1	1	yes	characteristic
207	C₂×C₄₇	C₂²×#107	1	1	yes	characteristic
208	C₂×C₄₇	C₂²×#108	1	1	yes	characteristic
209	D₄₇	—	2	2	no	—
210	D₄₇	#1567	1	4	yes	direct product factor
211	C₂²×M₁₆	—	94	2	no	—
212	C₂³×C₈	—	47	2	no	—
213	C₂²×C₄²	—	47	1	no	—
214	#423	—	47	2	no	—
215	#423	—	47	4	no	—
216	#423	—	94	2	no	—
217	#423	—	94	2	no	—
218	#423	C₂×D₄₇	1	2	yes	—
219	C₂×C₄⋊C₈	—	47	4	no	—
220	C₂×C₄⋊C₈	—	94	2	no	—
221	C₂×C₄×C₈	—	47	2	no	—
222	C₂×C₄×C₈	—	47	1	no	—
223	C₂×C₄×C₈	—	47	1	no	—
224	C₂×C₄×C₈	—	47	1	no	—
225	C₂×C₄×C₈	—	47	1	no	—
226	C₂×C₄×C₈	—	47	1	no	—
227	C₂×C₄×C₈	—	47	2	no	—
228	C₂×C₄×C₈	—	47	2	no	—
229	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
230	#335	—	47	8	no	—
231	#335	—	47	4	no	—
232	#335	C₂×D₄₇	1	4	yes	complemented
233	C₄₇	C₂×#1567	1	1	yes	characteristic, complemented, Sylow
234	C₂³×C₄	—	47	1	no	—
235	C₂³×C₄	—	47	1	no	—
236	C₂³×C₄	—	47	1	no	—
237	C₂×M₁₆	—	2	2	no	—
238	C₂×M₁₆	—	94	4	no	—
239	C₂×M₁₆	—	94	2	no	—
240	C₂×M₁₆	—	188	8	no	—
241	C₂²×C₈	—	47	2	no	—
242	C₂²×C₈	—	47	2	no	—
243	C₂²×C₈	—	47	2	no	—
244	C₂²×C₈	—	47	2	no	—
245	C₂²×C₈	—	47	2	no	—
246	C₂²×C₈	—	94	8	no	—
247	C₂²×C₈	—	94	4	no	—
248	C₂²×C₈	C₄×D₄₇	1	2	yes	—
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	—	47	1	no	—
256	C₂×C₄²	—	47	1	no	—
257	C₂×C₄²	—	47	1	no	—
258	C₂×C₄²	—	47	1	no	—
259	C₂×C₄²	—	47	1	no	—
260	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
261	C₄⋊C₈	—	2	2	no	—
262	C₄⋊C₈	—	47	4	no	—
263	C₄⋊C₈	—	94	4	no	—
264	C₄⋊C₈	—	94	4	no	—
265	C₄⋊C₈	—	94	2	no	—
266	C₄⋊C₈	C₂²×D₄₇	1	4	yes	—
267	C₄×C₈	—	47	2	no	—
268	C₄×C₈	—	47	2	no	—
269	C₄×C₈	—	47	2	no	—
270	C₄×C₈	—	47	2	no	—
271	C₄×C₈	—	47	1	no	—
272	C₄×C₈	—	47	1	no	—
273	C₄×C₈	—	47	2	no	—
274	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
275	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
276	C₄×C₈	C₂²×D₄₇	1	2	yes	—
277	C₂⁴	—	47	1	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	4	no	—
283	C₂²×C₄	—	47	4	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	—	47	1	no	—
290	C₂²×C₄	—	47	1	no	—
291	C₂²×C₄	—	47	1	no	—
292	C₂²×C₄	—	47	1	no	—
293	C₂²×C₄	—	47	1	no	—
294	C₂²×C₄	—	47	1	no	—
295	C₂²×C₄	—	94	4	no	—
296	C₂²×C₄	—	94	4	no	—
297	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
298	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
299	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
300	M₁₆	—	4	4	no	—
301	M₁₆	—	188	8	no	—
302	M₁₆	—	188	4	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	2	4	no	—
305	C₂×C₈	—	47	2	no	—
306	C₂×C₈	—	47	8	no	—
307	C₂×C₈	—	47	2	no	—
308	C₂×C₈	—	94	4	no	—
309	C₂×C₈	—	94	4	no	—
310	C₂×C₈	—	94	4	no	—
311	C₂×C₈	—	94	4	no	—
312	C₂×C₈	—	94	4	no	—
313	C₂×C₈	—	188	8	no	—
314	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
315	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
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	—	47	1	no	—
323	C₄²	—	47	1	no	—
324	C₄²	—	47	1	no	—
325	C₄²	—	47	1	no	—
326	C₄²	—	47	1	no	—
327	C₄²	—	47	1	no	—
328	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
329	C₄²	D₄×D₄₇	1	1	yes	characteristic
330	C₄²	Q₈×D₄₇	1	1	yes	characteristic
331	C₄²	C₂³×D₄₇	1	1	yes	characteristic
332	C₂³	—	47	1	no	—
333	C₂³	—	47	1	no	—
334	C₂³	—	47	4	no	—
335	C₂³	—	94	2	no	—
336	C₂³	—	94	2	no	—
337	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	47	1	no	—
341	C₂×C₄	—	47	1	no	—
342	C₂×C₄	—	47	1	no	—
343	C₂×C₄	—	47	1	no	—
344	C₂×C₄	—	47	4	no	—
345	C₂×C₄	—	47	4	no	—
346	C₂×C₄	—	47	2	no	—
347	C₂×C₄	—	47	2	no	—
348	C₂×C₄	—	47	2	no	—
349	C₂×C₄	—	47	2	no	—
350	C₂×C₄	—	47	4	no	—
351	C₂×C₄	—	47	4	no	—
352	C₂×C₄	—	47	4	no	—
353	C₂×C₄	—	47	1	no	—
354	C₂×C₄	—	47	1	no	—
355	C₂×C₄	—	94	2	no	—
356	C₂×C₄	—	94	2	no	—
357	C₂×C₄	—	94	2	no	—
358	C₂×C₄	—	94	2	no	—
359	C₂×C₄	—	94	2	no	—
360	C₂×C₄	—	94	2	no	—
361	C₂×C₄	—	94	2	no	—
362	C₂×C₄	—	94	2	no	—
363	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
364	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
365	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
366	C₂×C₄	D₈×D₄₇	1	2	yes	—
367	C₂×C₄	Q₁₆×D₄₇	1	2	yes	—
368	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
369	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
370	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
371	C₈	—	2	2	no	—
372	C₈	—	4	4	no	—
373	C₈	—	47	4	no	—
374	C₈	—	94	2	no	—
375	C₈	—	188	4	no	—
376	C₈	M₁₆×D₄₇	1	4	yes	complemented
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	47	2	no	—
380	C₂²	—	47	2	no	—
381	C₂²	—	47	2	no	—
382	C₂²	—	47	2	no	—
383	C₂²	—	94	8	no	—
384	C₂²	—	94	1	no	—
385	C₂²	—	94	1	no	—
386	C₂²	#107×D₄₇	1	2	yes	—
387	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	47	2	no	—
391	C₄	—	47	2	no	—
392	C₄	—	47	2	no	—
393	C₄	—	47	2	no	—
394	C₄	—	94	1	no	—
395	C₄	—	94	1	no	—
396	C₄	#107×D₄₇	1	2	yes	—
397	C₄	#108×D₄₇	1	2	yes	—
398	C₄	C₂×M₁₆×D₄₇	1	2	yes	—
399	C₄	C₂×D₈×D₄₇	1	1	yes	characteristic
400	C₄	C₂×Q₁₆×D₄₇	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	47	4	no	—
403	C₂	—	94	2	no	—
404	C₂	#423×D₄₇	1	1	yes	characteristic
405	C₂	C₂×#107×D₄₇	1	1	yes	characteristic
406	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×#1567	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂³×D₄₇	C₄⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1567	D₄₇
hypocenter	C₄₇	C₂×#1567
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

Complements

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

N	H ≅ G/N	type
3. #20242147	C₂	semidirect
4. #20242146	C₂	semidirect
5. #20242145	C₂	semidirect
6. #335×D₄₇	C₂	semidirect
7. C₄₇×#1567	C₂	semidirect
25. #15688876	C₂²	semidirect
26. #15688875	C₂²	semidirect
29. C₄₇×#335	C₂²	semidirect
127. C₈×D₄₇	M₁₆	semidirect
169. C₈×C₄₇	C₂×M₁₆	semidirect
172. C₄₇⋊C₈	C₂×M₁₆	semidirect
203. #1567	D₄₇	direct (N × H)
210. D₄₇	#1567	direct (N × H)
232. #335	C₂×D₄₇	semidirect
233. C₄₇	C₂×#1567	semidirect
376. 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
#20242147	2
#20242146	2
#20242145	2
#335×D₄₇	2
C₄₇×#1567	2
C₂×#1567	47

Subgroups — D47×#1567 #26185277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#1567 #26185277