Subgroups — C₂×C₄₇×#2043 #26063201

Order 12032.

1542 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#103×C₄₇	C₂	1	2	yes	maximal
3	C₂²×#103×C₄₇	C₂	1	2	yes	maximal
4	C₂×C₄₇×#389	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#2043	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₇×#336	C₂	1	1	yes	maximal, characteristic
7	C₂³×Q₈×C₄₇	C₂²	1	2	yes	—
8	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
9	C₂×C₄⋊Q₈×C₄₇	—	2	8	no	—
10	C₂×C₄⋊Q₈×C₄₇	—	2	2	no	—
11	C₂×C₄⋊Q₈×C₄₇	C₂²	1	4	yes	—
12	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
13	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
14	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
15	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×#103×C₄₇	—	2	8	no	—
19	C₂×#103×C₄₇	—	2	8	no	—
20	C₂×#103×C₄₇	C₂²	1	8	yes	—
21	C₂×#103×C₄₇	C₂²	1	8	yes	—
22	C₄₇×#389	—	2	2	no	—
23	C₄₇×#389	C₂²	1	4	yes	—
24	C₂×#95×C₄₇	—	2	1	no	—
25	C₄₇×#336	C₂²	1	4	yes	—
26	C₂²×Q₈×C₄₇	—	2	4	no	—
27	C₂²×Q₈×C₄₇	—	2	2	no	—
28	C₂²×Q₈×C₄₇	—	2	4	no	—
29	C₂²×Q₈×C₄₇	—	2	4	no	—
30	C₂²×Q₈×C₄₇	—	2	4	no	—
31	C₂²×Q₈×C₄₇	—	2	4	no	—
32	C₂²×Q₈×C₄₇	D₄	1	8	yes	—
33	C₂²×Q₈×C₄₇	C₂³	1	4	yes	—
34	C₂³×C₄×C₄₇	—	2	2	no	—
35	C₂³×C₄×C₄₇	—	2	1	no	—
36	C₂³×C₄×C₄₇	—	2	1	no	—
37	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₄₇	—	2	4	no	—
41	C₂²×C₈×C₄₇	—	2	4	no	—
42	C₂²×C₈×C₄₇	—	2	4	no	—
43	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
44	C₄⋊Q₈×C₄₇	—	2	16	no	—
45	C₄⋊Q₈×C₄₇	—	2	16	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
49	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
50	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
51	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
53	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
56	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
57	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
59	C₂×C₄²×C₄₇	—	2	4	no	—
60	C₂×C₄²×C₄₇	D₄	1	2	yes	—
61	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
62	#103×C₄₇	—	2	16	no	—
63	#103×C₄₇	—	2	16	no	—
64	#95×C₄₇	—	2	4	no	—
65	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
66	C₂×Q₈×C₄₇	—	2	8	no	—
67	C₂×Q₈×C₄₇	—	2	4	no	—
68	C₂×Q₈×C₄₇	—	2	16	no	—
69	C₂×Q₈×C₄₇	—	2	16	no	—
70	C₂×Q₈×C₄₇	—	2	4	no	—
71	C₂×Q₈×C₄₇	—	2	4	no	—
72	C₂×Q₈×C₄₇	—	2	4	no	—
73	C₂×Q₈×C₄₇	—	2	4	no	—
74	C₂×Q₈×C₄₇	—	4	4	no	—
75	C₂×Q₈×C₄₇	—	4	8	no	—
76	C₂×Q₈×C₄₇	—	4	8	no	—
77	C₂×Q₈×C₄₇	—	4	4	no	—
78	C₂×Q₈×C₄₇	C₂×D₄	1	8	yes	—
79	C₂²×C₄×C₄₇	—	2	2	no	—
80	C₂²×C₄×C₄₇	—	2	2	no	—
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	—	2	8	no	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	4	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	4	4	no	—
89	C₂²×C₄×C₄₇	—	4	4	no	—
90	C₂²×C₄×C₄₇	—	4	2	no	—
91	C₂²×C₄×C₄₇	—	4	2	no	—
92	C₂²×C₄×C₄₇	—	4	2	no	—
93	C₂²×C₄×C₄₇	—	4	2	no	—
94	C₂²×C₄×C₄₇	—	4	2	no	—
95	C₂²×C₄×C₄₇	SD₁₆	1	4	yes	—
96	C₂²×C₄×C₄₇	Q₁₆	1	4	yes	—
97	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₇	#41	1	4	yes	—
103	C₂²×C₄×C₄₇	#41	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
105	C₂×C₈×C₄₇	—	2	4	no	—
106	C₂×C₈×C₄₇	—	2	4	no	—
107	C₂×C₈×C₄₇	—	2	4	no	—
108	C₂×C₈×C₄₇	—	4	8	no	—
109	C₄⋊C₄×C₄₇	—	2	16	no	—
110	C₄⋊C₄×C₄₇	—	2	16	no	—
111	C₄⋊C₄×C₄₇	—	2	4	no	—
112	C₄⋊C₄×C₄₇	—	2	2	no	—
113	C₄⋊C₄×C₄₇	—	2	4	no	—
114	C₄⋊C₄×C₄₇	—	4	2	no	—
115	C₄⋊C₄×C₄₇	—	4	8	no	—
116	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
117	C₄²×C₄₇	—	2	4	no	—
118	C₄²×C₄₇	—	2	4	no	—
119	C₂³×C₄₇	#120	1	2	yes	—
120	C₂³×C₄₇	#121	1	2	yes	—
121	C₂³×C₄₇	#124	1	2	yes	—
122	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
123	C₂³×C₄₇	C₂×Q₁₆	1	2	yes	—
124	C₂³×C₄₇	#137	1	2	yes	—
125	C₂³×C₄₇	#137	1	2	yes	—
126	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
127	Q₈×C₄₇	—	2	8	no	—
128	Q₈×C₄₇	—	2	8	no	—
129	Q₈×C₄₇	—	4	4	no	—
130	Q₈×C₄₇	—	4	4	no	—
131	Q₈×C₄₇	—	4	16	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	2	no	—
136	C₂×C₄×C₄₇	—	2	8	no	—
137	C₂×C₄×C₄₇	—	2	8	no	—
138	C₂×C₄×C₄₇	—	2	8	no	—
139	C₂×C₄×C₄₇	—	2	4	no	—
140	C₂×C₄×C₄₇	—	4	4	no	—
141	C₂×C₄×C₄₇	—	4	4	no	—
142	C₂×C₄×C₄₇	—	4	2	no	—
143	C₂×C₄×C₄₇	—	4	2	no	—
144	C₂×C₄×C₄₇	—	4	16	no	—
145	C₂×C₄×C₄₇	—	4	8	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	8	4	no	—
150	C₂×C₄×C₄₇	#120	1	2	yes	—
151	C₂×C₄×C₄₇	#121	1	8	yes	—
152	C₂×C₄×C₄₇	#121	1	2	yes	—
153	C₂×C₄×C₄₇	#123	1	8	yes	—
154	C₂×C₄×C₄₇	#124	1	2	yes	—
155	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
156	C₂×C₄×C₄₇	C₂×Q₁₆	1	4	yes	—
157	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
159	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
160	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
161	C₈×C₄₇	—	4	4	no	—
162	C₂×#2043	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂²×C₄₇	#394	1	4	yes	—
164	C₂²×C₄₇	#448	1	4	yes	—
165	C₂²×C₄₇	#451	1	4	yes	—
166	C₂²×C₄₇	#461	1	4	yes	—
167	C₂²×C₄₇	#462	1	4	yes	—
168	C₂²×C₄₇	#487	1	4	yes	—
169	C₂²×C₄₇	#491	1	4	yes	—
170	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
171	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
172	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
173	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
174	C₂²×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
175	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
176	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
177	C₄×C₄₇	—	2	4	no	—
178	C₄×C₄₇	—	2	4	no	—
179	C₄×C₄₇	—	4	8	no	—
180	C₄×C₄₇	—	4	4	no	—
181	C₄×C₄₇	—	8	2	no	—
182	C₄×C₄₇	#394	1	4	yes	—
183	C₄×C₄₇	C₂×#121	1	2	yes	—
184	C₄×C₄₇	C₂×#123	1	2	yes	—
185	C₂²×C₄⋊Q₈	C₂×C₄₇	1	1	yes	characteristic
186	C₂²×#103	C₂×C₄₇	1	2	yes	—
187	C₂²×#103	C₂×C₄₇	1	2	yes	—
188	C₂×#389	C₂×C₄₇	1	1	yes	characteristic
189	#2043	C₂×C₄₇	1	8	yes	direct product factor
190	C₂×#336	C₂×C₄₇	1	1	yes	characteristic
191	C₂×C₄₇	#2043	1	8	yes	direct product factor
192	C₂×C₄₇	C₂×#394	1	1	yes	characteristic
193	C₂×C₄₇	C₂×#448	1	1	yes	characteristic
194	C₂×C₄₇	C₂×#451	1	1	yes	characteristic
195	C₂×C₄₇	C₂×#461	1	1	yes	characteristic
196	C₂×C₄₇	C₂×#462	1	1	yes	characteristic
197	C₂×C₄₇	C₂×#487	1	1	yes	characteristic
198	C₂×C₄₇	C₂×#491	1	1	yes	characteristic
199	C₂³×Q₈	C₂²×C₄₇	1	2	yes	—
200	C₂³×C₈	C₂²×C₄₇	1	2	yes	—
201	C₂×C₄⋊Q₈	—	2	8	no	—
202	C₂×C₄⋊Q₈	—	2	2	no	—
203	C₂×C₄⋊Q₈	C₂²×C₄₇	1	4	yes	—
204	C₂²×C₄⋊C₄	—	2	1	no	—
205	C₂²×C₄⋊C₄	—	2	1	no	—
206	C₂²×C₄⋊C₄	—	2	1	no	—
207	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
208	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
209	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
210	C₂×#103	—	2	8	no	—
211	C₂×#103	—	2	8	no	—
212	C₂×#103	C₂²×C₄₇	1	8	yes	—
213	C₂×#103	C₂²×C₄₇	1	8	yes	—
214	#389	—	2	2	no	—
215	#389	C₂²×C₄₇	1	4	yes	—
216	C₂×#95	—	2	1	no	—
217	#336	C₂²×C₄₇	1	4	yes	—
218	C₄₇	C₂×#2043	1	1	yes	characteristic, direct product factor, Sylow
219	C₂²×Q₈	—	2	4	no	—
220	C₂²×Q₈	—	2	2	no	—
221	C₂²×Q₈	—	2	4	no	—
222	C₂²×Q₈	—	2	4	no	—
223	C₂²×Q₈	—	2	4	no	—
224	C₂²×Q₈	—	2	4	no	—
225	C₂²×Q₈	D₄×C₄₇	1	8	yes	—
226	C₂²×Q₈	C₂³×C₄₇	1	4	yes	—
227	C₂³×C₄	—	2	2	no	—
228	C₂³×C₄	—	2	1	no	—
229	C₂³×C₄	—	2	1	no	—
230	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
231	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
232	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
233	C₂²×C₈	—	2	4	no	—
234	C₂²×C₈	—	2	4	no	—
235	C₂²×C₈	—	2	4	no	—
236	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
237	C₄⋊Q₈	—	2	16	no	—
238	C₄⋊Q₈	—	2	16	no	—
239	C₂×C₄⋊C₄	—	2	8	no	—
240	C₂×C₄⋊C₄	—	2	8	no	—
241	C₂×C₄⋊C₄	—	2	4	no	—
242	C₂×C₄⋊C₄	—	2	4	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	4	no	—
246	C₂×C₄⋊C₄	—	2	4	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	4	4	no	—
249	C₂×C₄⋊C₄	D₄×C₄₇	1	4	yes	—
250	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
251	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
252	C₂×C₄²	—	2	4	no	—
253	C₂×C₄²	D₄×C₄₇	1	2	yes	—
254	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
255	#103	—	2	16	no	—
256	#103	—	2	16	no	—
257	#95	—	2	4	no	—
258	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
259	C₂×Q₈	—	2	8	no	—
260	C₂×Q₈	—	2	4	no	—
261	C₂×Q₈	—	2	16	no	—
262	C₂×Q₈	—	2	16	no	—
263	C₂×Q₈	—	2	4	no	—
264	C₂×Q₈	—	2	4	no	—
265	C₂×Q₈	—	2	4	no	—
266	C₂×Q₈	—	2	4	no	—
267	C₂×Q₈	—	4	4	no	—
268	C₂×Q₈	—	4	8	no	—
269	C₂×Q₈	—	4	8	no	—
270	C₂×Q₈	—	4	4	no	—
271	C₂×Q₈	C₂×D₄×C₄₇	1	8	yes	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	8	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	4	4	no	—
282	C₂²×C₄	—	4	4	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	SD₁₆×C₄₇	1	4	yes	—
289	C₂²×C₄	Q₁₆×C₄₇	1	4	yes	—
290	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
292	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
294	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
295	C₂²×C₄	#41×C₄₇	1	4	yes	—
296	C₂²×C₄	#41×C₄₇	1	2	yes	—
297	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	—	4	8	no	—
302	C₄⋊C₄	—	2	16	no	—
303	C₄⋊C₄	—	2	16	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄⋊C₄	—	4	8	no	—
309	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
310	C₄²	—	2	4	no	—
311	C₄²	—	2	4	no	—
312	C₂³	#120×C₄₇	1	2	yes	—
313	C₂³	#121×C₄₇	1	2	yes	—
314	C₂³	#124×C₄₇	1	2	yes	—
315	C₂³	C₂×SD₁₆×C₄₇	1	2	yes	—
316	C₂³	C₂×Q₁₆×C₄₇	1	2	yes	—
317	C₂³	#137×C₄₇	1	2	yes	—
318	C₂³	#137×C₄₇	1	2	yes	—
319	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
320	Q₈	—	2	8	no	—
321	Q₈	—	2	8	no	—
322	Q₈	—	4	4	no	—
323	Q₈	—	4	4	no	—
324	Q₈	—	4	16	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	4	8	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	16	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	8	4	no	—
343	C₂×C₄	#120×C₄₇	1	2	yes	—
344	C₂×C₄	#121×C₄₇	1	8	yes	—
345	C₂×C₄	#121×C₄₇	1	2	yes	—
346	C₂×C₄	#123×C₄₇	1	8	yes	—
347	C₂×C₄	#124×C₄₇	1	2	yes	—
348	C₂×C₄	C₂×SD₁₆×C₄₇	1	4	yes	—
349	C₂×C₄	C₂×Q₁₆×C₄₇	1	4	yes	—
350	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
351	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
352	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
353	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
354	C₈	—	4	4	no	—
355	C₂²	C₄₇×#394	1	4	yes	—
356	C₂²	C₄₇×#448	1	4	yes	—
357	C₂²	C₄₇×#451	1	4	yes	—
358	C₂²	C₄₇×#461	1	4	yes	—
359	C₂²	C₄₇×#462	1	4	yes	—
360	C₂²	C₄₇×#487	1	4	yes	—
361	C₂²	C₄₇×#491	1	4	yes	—
362	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
363	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
364	C₂²	C₂×#124×C₄₇	1	1	yes	characteristic
365	C₂²	C₂²×SD₁₆×C₄₇	1	1	yes	characteristic
366	C₂²	C₂²×Q₁₆×C₄₇	1	1	yes	characteristic
367	C₂²	C₂×#137×C₄₇	1	1	yes	characteristic
368	C₂²	C₂×#137×C₄₇	1	1	yes	characteristic
369	C₄	—	2	4	no	—
370	C₄	—	2	4	no	—
371	C₄	—	4	4	no	—
372	C₄	—	4	8	no	—
373	C₄	—	8	2	no	—
374	C₄	C₄₇×#394	1	4	yes	—
375	C₄	C₂×#121×C₄₇	1	2	yes	—
376	C₄	C₂×#123×C₄₇	1	2	yes	—
377	C₂	C₄₇×#2043	1	8	yes	direct product factor
378	C₂	C₂×C₄₇×#394	1	1	yes	characteristic
379	C₂	C₂×C₄₇×#448	1	1	yes	characteristic
380	C₂	C₂×C₄₇×#451	1	1	yes	characteristic
381	C₂	C₂×C₄₇×#461	1	1	yes	characteristic
382	C₂	C₂×C₄₇×#462	1	1	yes	characteristic
383	C₂	C₂×C₄₇×#487	1	1	yes	characteristic
384	C₂	C₂×C₄₇×#491	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
5. C₄₇×#2043	C₂	direct (N × H)
162. C₂×#2043	C₄₇	direct (N × H)
189. #2043	C₂×C₄₇	direct (N × H)
191. C₂×C₄₇	#2043	direct (N × H)
218. C₄₇	C₂×#2043	direct (N × H)
377. C₂	C₄₇×#2043	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊Q₈×C₄₇	2
C₂²×#103×C₄₇	2
C₂×C₄₇×#389	2
C₄₇×#2043	2
C₂×C₄₇×#336	2
C₂×#2043	47

Subgroups — C2×C47×#2043 #26063201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#2043 #26063201