Subgroups — C₄₇×#11205 #26050903

Order 12032.

918 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#2315	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#2315	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₇×#342	C₂	1	2	yes	maximal
4	C₂×C₄₇×#342	C₂	1	2	yes	maximal
5	C₂×C₄₇×#342	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
7	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
8	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
9	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
11	C₄₇×#385	—	2	2	no	—
12	C₄₇×#385	—	2	4	no	—
13	C₄₇×#385	C₄	1	4	yes	complemented
14	C₄₇×#380	—	2	2	no	—
15	C₄₇×#380	—	2	2	no	—
16	C₄₇×#342	—	2	2	no	—
17	C₄₇×#342	—	2	4	no	—
18	C₄₇×#342	—	2	4	no	—
19	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
20	C₂³×C₄×C₄₇	—	2	1	no	—
21	C₂³×C₄×C₄₇	—	2	2	no	—
22	C₂³×C₄×C₄₇	—	2	2	no	—
23	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
24	C₂³×C₄×C₄₇	D₄	1	2	yes	—
25	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
26	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
27	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
28	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
29	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
30	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
31	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
32	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
33	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
34	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
35	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
36	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
37	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
38	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
39	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
40	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
41	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
42	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
43	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
44	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
46	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
47	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
48	C₂×C₂²⋊C₄×C₄₇	D₄	1	4	yes	—
49	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
50	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
51	C₂×C₂²⋊C₄×C₄₇	Q₈	1	4	yes	—
52	C₂×C₂²⋊C₄×C₄₇	Q₈	1	2	yes	—
53	#95×C₄₇	—	2	4	no	—
54	#95×C₄₇	—	2	4	no	—
55	C₂⁴×C₄₇	—	8	2	no	—
56	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
57	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
58	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
59	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
60	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
61	C₂⁴×C₄₇	C₂×Q₈	1	1	yes	characteristic
62	C₂⁴×C₄₇	C₂×Q₈	1	2	yes	—
63	C₂⁴×C₄₇	#41	1	2	yes	—
64	C₂⁴×C₄₇	#41	1	1	yes	characteristic
65	C₂⁴×C₄₇	#41	1	1	yes	characteristic
66	C₂⁴×C₄₇	#41	1	2	yes	—
67	C₂²×C₄×C₄₇	—	2	2	no	—
68	C₂²×C₄×C₄₇	—	2	2	no	—
69	C₂²×C₄×C₄₇	—	2	2	no	—
70	C₂²×C₄×C₄₇	—	2	2	no	—
71	C₂²×C₄×C₄₇	—	2	2	no	—
72	C₂²×C₄×C₄₇	—	2	2	no	—
73	C₂²×C₄×C₄₇	—	2	4	no	—
74	C₂²×C₄×C₄₇	—	2	4	no	—
75	C₂²×C₄×C₄₇	—	2	4	no	—
76	C₂²×C₄×C₄₇	—	4	2	no	—
77	C₂²×C₄×C₄₇	—	4	2	no	—
78	C₂²×C₄×C₄₇	—	4	2	no	—
79	C₂²×C₄×C₄₇	—	4	2	no	—
80	C₂²×C₄×C₄₇	—	8	2	no	—
81	C₂²×C₄×C₄₇	—	8	2	no	—
82	C₂²×C₄×C₄₇	—	8	4	no	—
83	C₂²×C₄×C₄₇	—	8	2	no	—
84	C₂²×C₄×C₄₇	—	8	4	no	—
85	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
86	C₄⋊C₄×C₄₇	—	8	4	no	—
87	C₄⋊C₄×C₄₇	—	8	4	no	—
88	C₂²⋊C₄×C₄₇	—	2	2	no	—
89	C₂²⋊C₄×C₄₇	—	2	4	no	—
90	C₂²⋊C₄×C₄₇	—	2	2	no	—
91	C₂²⋊C₄×C₄₇	—	2	4	no	—
92	C₂²⋊C₄×C₄₇	—	2	2	no	—
93	C₂²⋊C₄×C₄₇	—	2	4	no	—
94	C₂²⋊C₄×C₄₇	—	2	4	no	—
95	C₂²⋊C₄×C₄₇	—	2	4	no	—
96	C₂²⋊C₄×C₄₇	—	2	4	no	—
97	C₂²⋊C₄×C₄₇	—	4	1	no	—
98	C₂²⋊C₄×C₄₇	—	4	2	no	—
99	C₂²⋊C₄×C₄₇	—	4	2	no	—
100	C₂²⋊C₄×C₄₇	—	4	2	no	—
101	C₂²⋊C₄×C₄₇	—	4	2	no	—
102	C₂²⋊C₄×C₄₇	—	4	1	no	—
103	C₂²⋊C₄×C₄₇	—	4	2	no	—
104	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	4	yes	complemented
105	C₂³×C₄₇	—	4	2	no	—
106	C₂³×C₄₇	—	4	2	no	—
107	C₂³×C₄₇	—	4	2	no	—
108	C₂³×C₄₇	—	4	4	no	—
109	C₂³×C₄₇	—	4	4	no	—
110	C₂³×C₄₇	—	8	1	no	—
111	C₂³×C₄₇	—	8	1	no	—
112	C₂³×C₄₇	—	8	2	no	—
113	C₂³×C₄₇	—	8	2	no	—
114	C₂³×C₄₇	—	8	1	no	—
115	C₂³×C₄₇	—	8	1	no	—
116	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
117	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
118	C₂³×C₄₇	#117	1	1	yes	characteristic
119	C₂³×C₄₇	C₄×D₄	1	2	yes	—
120	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
121	C₂³×C₄₇	#120	1	1	yes	characteristic
122	C₂³×C₄₇	#121	1	2	yes	—
123	C₂³×C₄₇	#121	1	1	yes	characteristic
124	C₂³×C₄₇	#121	1	1	yes	characteristic
125	C₂³×C₄₇	#121	1	2	yes	—
126	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
127	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
128	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
129	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
130	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
131	C₂³×C₄₇	#123	1	1	yes	characteristic
132	C₂³×C₄₇	#123	1	2	yes	—
133	C₂³×C₄₇	#124	1	1	yes	characteristic
134	C₂³×C₄₇	#125	1	2	yes	—
135	C₂³×C₄₇	#125	1	2	yes	—
136	C₂³×C₄₇	#126	1	2	yes	—
137	C₂³×C₄₇	C₄⋊Q₈	1	2	yes	—
138	C₂³×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
139	C₂×C₄×C₄₇	—	2	4	no	—
140	C₂×C₄×C₄₇	—	2	4	no	—
141	C₂×C₄×C₄₇	—	4	4	no	—
142	C₂×C₄×C₄₇	—	4	4	no	—
143	C₂×C₄×C₄₇	—	4	4	no	—
144	C₂×C₄×C₄₇	—	4	8	no	—
145	C₂×C₄×C₄₇	—	4	4	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	4	no	—
148	C₂×C₄×C₄₇	—	4	4	no	—
149	C₂×C₄×C₄₇	—	8	2	no	—
150	C₂×C₄×C₄₇	—	8	2	no	—
151	C₂×C₄×C₄₇	—	8	2	no	—
152	C₂×C₄×C₄₇	—	8	4	no	—
153	C₂×C₄×C₄₇	—	8	4	no	—
154	C₂×C₄×C₄₇	—	8	4	no	—
155	C₂×C₄×C₄₇	—	8	4	no	—
156	C₂×C₄×C₄₇	—	8	4	no	—
157	C₂×C₄×C₄₇	—	8	4	no	—
158	#11205	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂²×C₄₇	—	2	2	no	—
160	C₂²×C₄₇	—	2	2	no	—
161	C₂²×C₄₇	—	2	4	no	—
162	C₂²×C₄₇	—	2	4	no	—
163	C₂²×C₄₇	—	2	2	no	—
164	C₂²×C₄₇	—	4	1	no	—
165	C₂²×C₄₇	—	4	2	no	—
166	C₂²×C₄₇	—	4	1	no	—
167	C₂²×C₄₇	—	4	2	no	—
168	C₂²×C₄₇	—	4	2	no	—
169	C₂²×C₄₇	—	4	2	no	—
170	C₂²×C₄₇	—	4	1	no	—
171	C₂²×C₄₇	—	4	1	no	—
172	C₂²×C₄₇	—	4	2	no	—
173	C₂²×C₄₇	—	4	1	no	—
174	C₂²×C₄₇	—	4	1	no	—
175	C₂²×C₄₇	—	4	2	no	—
176	C₂²×C₄₇	—	4	2	no	—
177	C₂²×C₄₇	—	4	1	no	—
178	C₂²×C₄₇	—	4	2	no	—
179	C₂²×C₄₇	—	4	2	no	—
180	C₂²×C₄₇	—	4	2	no	—
181	C₂²×C₄₇	—	4	1	no	—
182	C₂²×C₄₇	#380	1	1	yes	characteristic
183	C₂²×C₄₇	#386	1	1	yes	characteristic
184	C₂²×C₄₇	#387	1	2	yes	—
185	C₂²×C₄₇	#389	1	2	yes	—
186	C₂²×C₄₇	#391	1	1	yes	characteristic
187	C₂²×C₄₇	#394	1	1	yes	characteristic
188	C₂²×C₄₇	#395	1	1	yes	characteristic
189	C₂²×C₄₇	#396	1	2	yes	—
190	C₂²×C₄₇	#398	1	2	yes	—
191	C₂²×C₄₇	#398	1	1	yes	characteristic
192	C₂²×C₄₇	#400	1	1	yes	characteristic
193	C₄×C₄₇	—	4	4	no	—
194	C₄×C₄₇	—	4	4	no	—
195	C₄×C₄₇	—	8	4	no	—
196	C₄×C₄₇	—	8	4	no	—
197	C₄×C₄₇	—	8	2	no	—
198	#2315	C₂×C₄₇	1	1	yes	characteristic
199	#2315	C₂×C₄₇	1	1	yes	characteristic
200	C₂×#342	C₂×C₄₇	1	2	yes	—
201	C₂×#342	C₂×C₄₇	1	2	yes	—
202	C₂×#342	C₂×C₄₇	1	1	yes	characteristic
203	C₂×C₄₇	—	2	1	no	—
204	C₂×C₄₇	—	2	1	no	—
205	C₂×C₄₇	—	2	2	no	—
206	C₂×C₄₇	—	2	2	no	—
207	C₂×C₄₇	—	2	2	no	—
208	C₂×C₄₇	—	2	1	no	—
209	C₂×C₄₇	—	2	1	no	—
210	C₂×C₄₇	—	2	2	no	—
211	C₂×C₄₇	—	2	1	no	—
212	C₂×C₄₇	—	2	1	no	—
213	C₂×C₄₇	#1441	1	1	yes	characteristic
214	C₂×C₄₇	#1913	1	2	yes	—
215	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
216	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
217	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
218	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
219	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
220	#385	—	2	2	no	—
221	#385	—	2	4	no	—
222	#385	C₄×C₄₇	1	4	yes	complemented
223	#380	—	2	2	no	—
224	#380	—	2	2	no	—
225	#342	—	2	2	no	—
226	#342	—	2	4	no	—
227	#342	—	2	4	no	—
228	C₄₇	#11205	1	1	yes	characteristic, direct product factor, Sylow
229	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
230	C₂³×C₄	—	2	1	no	—
231	C₂³×C₄	—	2	2	no	—
232	C₂³×C₄	—	2	2	no	—
233	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
234	C₂³×C₄	D₄×C₄₇	1	2	yes	—
235	C₂×C₄⋊C₄	—	2	4	no	—
236	C₂×C₄⋊C₄	—	2	4	no	—
237	C₂×C₂²⋊C₄	—	2	2	no	—
238	C₂×C₂²⋊C₄	—	2	1	no	—
239	C₂×C₂²⋊C₄	—	2	1	no	—
240	C₂×C₂²⋊C₄	—	2	1	no	—
241	C₂×C₂²⋊C₄	—	2	2	no	—
242	C₂×C₂²⋊C₄	—	2	2	no	—
243	C₂×C₂²⋊C₄	—	2	2	no	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₂²⋊C₄	—	2	2	no	—
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
257	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
258	C₂×C₂²⋊C₄	D₄×C₄₇	1	4	yes	—
259	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
260	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
261	C₂×C₂²⋊C₄	Q₈×C₄₇	1	4	yes	—
262	C₂×C₂²⋊C₄	Q₈×C₄₇	1	2	yes	—
263	#95	—	2	4	no	—
264	#95	—	2	4	no	—
265	C₂⁴	—	8	2	no	—
266	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
267	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
268	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
269	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
270	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
271	C₂⁴	C₂×Q₈×C₄₇	1	1	yes	characteristic
272	C₂⁴	C₂×Q₈×C₄₇	1	2	yes	—
273	C₂⁴	#41×C₄₇	1	2	yes	—
274	C₂⁴	#41×C₄₇	1	1	yes	characteristic
275	C₂⁴	#41×C₄₇	1	1	yes	characteristic
276	C₂⁴	#41×C₄₇	1	2	yes	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	8	2	no	—
291	C₂²×C₄	—	8	2	no	—
292	C₂²×C₄	—	8	4	no	—
293	C₂²×C₄	—	8	2	no	—
294	C₂²×C₄	—	8	4	no	—
295	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
296	C₄⋊C₄	—	8	4	no	—
297	C₄⋊C₄	—	8	4	no	—
298	C₂²⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	—	2	4	no	—
300	C₂²⋊C₄	—	2	2	no	—
301	C₂²⋊C₄	—	2	4	no	—
302	C₂²⋊C₄	—	2	2	no	—
303	C₂²⋊C₄	—	2	4	no	—
304	C₂²⋊C₄	—	2	4	no	—
305	C₂²⋊C₄	—	2	4	no	—
306	C₂²⋊C₄	—	2	4	no	—
307	C₂²⋊C₄	—	4	1	no	—
308	C₂²⋊C₄	—	4	2	no	—
309	C₂²⋊C₄	—	4	2	no	—
310	C₂²⋊C₄	—	4	2	no	—
311	C₂²⋊C₄	—	4	2	no	—
312	C₂²⋊C₄	—	4	1	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	C₄⋊C₄×C₄₇	1	4	yes	complemented
315	C₂³	—	4	2	no	—
316	C₂³	—	4	2	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	4	no	—
319	C₂³	—	4	4	no	—
320	C₂³	—	8	1	no	—
321	C₂³	—	8	1	no	—
322	C₂³	—	8	2	no	—
323	C₂³	—	8	2	no	—
324	C₂³	—	8	1	no	—
325	C₂³	—	8	1	no	—
326	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
327	C₂³	C₂×C₄⋊C₄×C₄₇	1	1	yes	characteristic
328	C₂³	#117×C₄₇	1	1	yes	characteristic
329	C₂³	C₄×D₄×C₄₇	1	2	yes	—
330	C₂³	C₄×Q₈×C₄₇	1	2	yes	—
331	C₂³	#120×C₄₇	1	1	yes	characteristic
332	C₂³	#121×C₄₇	1	2	yes	—
333	C₂³	#121×C₄₇	1	1	yes	characteristic
334	C₂³	#121×C₄₇	1	1	yes	characteristic
335	C₂³	#121×C₄₇	1	2	yes	—
336	C₂³	C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
337	C₂³	C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
338	C₂³	C₂²⋊Q₈×C₄₇	1	2	yes	—
339	C₂³	C₂²⋊Q₈×C₄₇	1	2	yes	—
340	C₂³	C₂²⋊Q₈×C₄₇	1	2	yes	—
341	C₂³	#123×C₄₇	1	1	yes	characteristic
342	C₂³	#123×C₄₇	1	2	yes	—
343	C₂³	#124×C₄₇	1	1	yes	characteristic
344	C₂³	#125×C₄₇	1	2	yes	—
345	C₂³	#125×C₄₇	1	2	yes	—
346	C₂³	#126×C₄₇	1	2	yes	—
347	C₂³	C₄⋊Q₈×C₄₇	1	2	yes	—
348	C₂³	C₄⋊Q₈×C₄₇	1	1	yes	characteristic
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	8	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	8	2	no	—
360	C₂×C₄	—	8	2	no	—
361	C₂×C₄	—	8	2	no	—
362	C₂×C₄	—	8	4	no	—
363	C₂×C₄	—	8	4	no	—
364	C₂×C₄	—	8	4	no	—
365	C₂×C₄	—	8	4	no	—
366	C₂×C₄	—	8	4	no	—
367	C₂×C₄	—	8	4	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	4	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	1	no	—
391	C₂²	C₄₇×#380	1	1	yes	characteristic
392	C₂²	C₄₇×#386	1	1	yes	characteristic
393	C₂²	C₄₇×#387	1	2	yes	—
394	C₂²	C₄₇×#389	1	2	yes	—
395	C₂²	C₄₇×#391	1	1	yes	characteristic
396	C₂²	C₄₇×#394	1	1	yes	characteristic
397	C₂²	C₄₇×#395	1	1	yes	characteristic
398	C₂²	C₄₇×#396	1	2	yes	—
399	C₂²	C₄₇×#398	1	2	yes	—
400	C₂²	C₄₇×#398	1	1	yes	characteristic
401	C₂²	C₄₇×#400	1	1	yes	characteristic
402	C₄	—	4	4	no	—
403	C₄	—	4	4	no	—
404	C₄	—	8	4	no	—
405	C₄	—	8	4	no	—
406	C₄	—	8	2	no	—
407	C₂	—	2	1	no	—
408	C₂	—	2	1	no	—
409	C₂	—	2	2	no	—
410	C₂	—	2	2	no	—
411	C₂	—	2	2	no	—
412	C₂	—	2	1	no	—
413	C₂	—	2	1	no	—
414	C₂	—	2	2	no	—
415	C₂	—	2	1	no	—
416	C₂	—	2	1	no	—
417	C₂	C₄₇×#1441	1	1	yes	characteristic
418	C₂	C₄₇×#1913	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₇	#386
commutator	C₂⁴	C₂²×C₄×C₄₇
Frattini, cosocle	C₂⁵	C₂³×C₄₇
prime radical	C₂⁵×C₄₇	C₂³
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂⁵×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₄₇×#385	C₄	semidirect
104. C₂²⋊C₄×C₄₇	C₄⋊C₄	semidirect
158. #11205	C₄₇	direct (N × H)
222. #385	C₄×C₄₇	semidirect
228. C₄₇	#11205	direct (N × H)
314. C₂²⋊C₄	C₄⋊C₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#2315	2
C₂×C₄₇×#342	2
#11205	47

Subgroups — C47×#11205 #26050903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#11205 #26050903