Subgroups — C₄₇×#10937 #26050635

Order 12032.

1066 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#407	C₂	1	2	yes	maximal
2	C₄₇×#2873	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2280	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇×#344	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1742	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
8	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
9	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
10	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
11	C₄₇×#407	—	2	4	no	—
12	C₄₇×#407	C₄	1	8	yes	complemented
13	C₂×C₂²⋊C₈×C₄₇	—	2	4	no	—
14	C₄₇×#405	—	2	4	no	—
15	C₄×M₁₆×C₄₇	—	2	2	no	—
16	C₄₇×#381	C₄	1	2	yes	—
17	C₄₇×#380	—	2	2	no	—
18	C₄₇×#379	C₄	1	2	yes	—
19	C₄×C₂²⋊C₄×C₄₇	—	2	2	no	—
20	C₄₇×#344	—	2	4	no	—
21	C₄₇×#343	—	2	2	no	—
22	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₄₇	—	2	1	no	—
24	C₂³×C₄×C₄₇	—	2	1	no	—
25	C₂³×C₄×C₄₇	—	2	2	no	—
26	C₂³×C₄×C₄₇	—	2	2	no	—
27	C₂³×C₄×C₄₇	—	2	2	no	—
28	C₂³×C₄×C₄₇	—	2	2	no	—
29	C₂³×C₄×C₄₇	—	2	2	no	—
30	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
32	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
33	C₂×M₁₆×C₄₇	—	2	2	no	—
34	C₂×M₁₆×C₄₇	—	2	2	no	—
35	C₂×M₁₆×C₄₇	—	2	2	no	—
36	C₂×M₁₆×C₄₇	—	2	2	no	—
37	C₂×M₁₆×C₄₇	—	2	2	no	—
38	C₂×M₁₆×C₄₇	—	2	2	no	—
39	C₂×M₁₆×C₄₇	—	2	2	no	—
40	C₂×M₁₆×C₄₇	—	2	2	no	—
41	C₂×M₁₆×C₄₇	—	2	2	no	—
42	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
43	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
44	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
45	C₂²×C₈×C₄₇	—	2	2	no	—
46	C₂²×C₈×C₄₇	D₄	1	4	yes	—
47	#117×C₄₇	—	2	2	no	—
48	#117×C₄₇	—	2	2	no	—
49	#117×C₄₇	—	2	2	no	—
50	#117×C₄₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
52	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
53	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
54	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
55	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₄₇	—	2	1	no	—
57	C₂×C₄²×C₄₇	D₄	1	2	yes	—
58	C₂²⋊C₈×C₄₇	—	2	16	no	—
59	#97×C₄₇	—	2	4	no	—
60	C₄×C₈×C₄₇	—	2	4	no	—
61	#95×C₄₇	—	2	4	no	—
62	C₂⁴×C₄₇	—	2	1	no	—
63	C₂⁴×C₄₇	—	2	2	no	—
64	C₂⁴×C₄₇	—	2	1	no	—
65	C₂⁴×C₄₇	—	2	2	no	—
66	C₂⁴×C₄₇	—	4	4	no	—
67	C₂⁴×C₄₇	C₄²	1	2	yes	—
68	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₄₇	—	2	1	no	—
70	C₂²×C₄×C₄₇	—	2	1	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	—	2	4	no	—
77	C₂²×C₄×C₄₇	—	2	4	no	—
78	C₂²×C₄×C₄₇	—	2	4	no	—
79	C₂²×C₄×C₄₇	—	2	2	no	—
80	C₂²×C₄×C₄₇	—	4	1	no	—
81	C₂²×C₄×C₄₇	—	4	2	no	—
82	C₂²×C₄×C₄₇	—	4	2	no	—
83	C₂²×C₄×C₄₇	—	4	2	no	—
84	C₂²×C₄×C₄₇	—	4	1	no	—
85	C₂²×C₄×C₄₇	—	4	2	no	—
86	C₂²×C₄×C₄₇	—	4	2	no	—
87	C₂²×C₄×C₄₇	—	4	1	no	—
88	C₂²×C₄×C₄₇	—	4	2	no	—
89	C₂²×C₄×C₄₇	—	4	1	no	—
90	C₂²×C₄×C₄₇	C₄²	1	2	yes	—
91	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	#41	1	2	yes	—
98	C₂²×C₄×C₄₇	#41	1	2	yes	—
99	C₂²×C₄×C₄₇	#41	1	2	yes	—
100	M₁₆×C₄₇	—	2	4	no	—
101	M₁₆×C₄₇	—	2	4	no	—
102	M₁₆×C₄₇	—	2	4	no	—
103	M₁₆×C₄₇	—	2	4	no	—
104	M₁₆×C₄₇	—	2	4	no	—
105	M₁₆×C₄₇	—	2	4	no	—
106	M₁₆×C₄₇	—	4	2	no	—
107	M₁₆×C₄₇	—	4	2	no	—
108	C₂×C₈×C₄₇	—	2	4	no	—
109	C₂×C₈×C₄₇	—	2	4	no	—
110	C₂×C₈×C₄₇	—	2	4	no	—
111	C₂×C₈×C₄₇	—	4	2	no	—
112	C₂×C₈×C₄₇	—	4	2	no	—
113	C₂×C₈×C₄₇	C₂²⋊C₄	1	8	yes	complemented
114	C₄⋊C₄×C₄₇	—	2	4	no	—
115	C₄⋊C₄×C₄₇	—	4	1	no	—
116	C₄⋊C₄×C₄₇	—	4	1	no	—
117	C₂²⋊C₄×C₄₇	—	2	4	no	—
118	C₂²⋊C₄×C₄₇	—	2	4	no	—
119	C₂²⋊C₄×C₄₇	—	4	8	no	—
120	C₄²×C₄₇	—	2	2	no	—
121	C₄²×C₄₇	—	2	2	no	—
122	C₄²×C₄₇	—	4	2	no	—
123	C₂³×C₄₇	—	2	4	no	—
124	C₂³×C₄₇	—	2	8	no	—
125	C₂³×C₄₇	—	2	4	no	—
126	C₂³×C₄₇	—	2	2	no	—
127	C₂³×C₄₇	—	4	4	no	—
128	C₂³×C₄₇	—	4	2	no	—
129	C₂³×C₄₇	—	4	2	no	—
130	C₂³×C₄₇	—	4	4	no	—
131	C₂³×C₄₇	—	4	4	no	—
132	C₂³×C₄₇	—	4	8	no	—
133	C₂³×C₄₇	—	4	1	no	—
134	C₂³×C₄₇	—	4	2	no	—
135	C₂³×C₄₇	—	4	1	no	—
136	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
137	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂³×C₄₇	#117	1	1	yes	characteristic
139	C₂³×C₄₇	C₄×D₄	1	2	yes	—
140	C₂³×C₄₇	C₄×D₄	1	2	yes	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	4	1	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	1	no	—
147	C₂×C₄×C₄₇	—	4	4	no	—
148	C₂×C₄×C₄₇	—	4	4	no	—
149	C₂×C₄×C₄₇	—	4	4	no	—
150	C₂×C₄×C₄₇	—	4	4	no	—
151	C₂×C₄×C₄₇	—	4	4	no	—
152	C₂×C₄×C₄₇	—	4	4	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₄₇	#117	1	2	yes	—
156	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
157	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
158	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
159	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
160	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
161	C₂×C₄×C₄₇	#121	1	2	yes	—
162	C₂×C₄×C₄₇	#121	1	2	yes	—
163	C₂×C₄×C₄₇	#121	1	2	yes	—
164	C₂×C₄×C₄₇	#123	1	2	yes	—
165	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
166	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
167	C₂×C₄×C₄₇	#124	1	2	yes	—
168	C₂×C₄×C₄₇	#126	1	2	yes	—
169	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
170	C₈×C₄₇	—	2	8	no	—
171	C₈×C₄₇	—	4	4	no	—
172	#10937	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂²×C₄₇	—	2	2	no	—
174	C₂²×C₄₇	—	2	4	no	—
175	C₂²×C₄₇	—	2	4	no	—
176	C₂²×C₄₇	—	2	8	no	—
177	C₂²×C₄₇	—	4	1	no	—
178	C₂²×C₄₇	—	4	1	no	—
179	C₂²×C₄₇	—	4	2	no	—
180	C₂²×C₄₇	—	4	4	no	—
181	C₂²×C₄₇	—	4	2	no	—
182	C₂²×C₄₇	—	4	4	no	—
183	C₂²×C₄₇	—	4	8	no	—
184	C₂²×C₄₇	—	4	4	no	—
185	C₂²×C₄₇	—	4	2	no	—
186	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
187	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
188	C₂²×C₄₇	#386	1	1	yes	characteristic
189	C₂²×C₄₇	#388	1	2	yes	—
190	C₂²×C₄₇	#390	1	1	yes	characteristic
191	C₄×C₄₇	—	4	4	no	—
192	C₄×C₄₇	—	4	2	no	—
193	C₄×C₄₇	—	8	2	no	—
194	C₄×C₄₇	#386	1	2	yes	—
195	C₄×C₄₇	#388	1	2	yes	—
196	C₄×C₄₇	#388	1	2	yes	—
197	C₄×C₄₇	#390	1	2	yes	—
198	C₂×#407	C₂×C₄₇	1	2	yes	—
199	#2873	C₂×C₄₇	1	1	yes	characteristic, complemented
200	#2280	C₂×C₄₇	1	1	yes	characteristic
201	C₂×#344	C₂×C₄₇	1	2	yes	complemented
202	#1742	C₂×C₄₇	1	1	yes	characteristic, complemented
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	—	4	4	no	—
208	C₂×C₄₇	#1437	1	1	yes	characteristic
209	C₂×C₄₇	#1891	1	2	yes	—
210	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
211	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
212	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
213	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
214	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
215	#407	—	2	4	no	—
216	#407	C₄×C₄₇	1	8	yes	complemented
217	C₂×C₂²⋊C₈	—	2	4	no	—
218	#405	—	2	4	no	—
219	C₄×M₁₆	—	2	2	no	—
220	#381	C₄×C₄₇	1	2	yes	—
221	#380	—	2	2	no	—
222	#379	C₄×C₄₇	1	2	yes	—
223	C₄×C₂²⋊C₄	—	2	2	no	—
224	#344	—	2	4	no	—
225	#343	—	2	2	no	—
226	C₄₇	#10937	1	1	yes	characteristic, direct product factor, Sylow
227	C₂⁵	C₂×C₄×C₄₇	1	1	yes	characteristic
228	C₂³×C₄	—	2	1	no	—
229	C₂³×C₄	—	2	1	no	—
230	C₂³×C₄	—	2	2	no	—
231	C₂³×C₄	—	2	2	no	—
232	C₂³×C₄	—	2	2	no	—
233	C₂³×C₄	—	2	2	no	—
234	C₂³×C₄	—	2	2	no	—
235	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
236	C₂³×C₄	C₂×C₄×C₄₇	1	4	yes	—
237	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
238	C₂×M₁₆	—	2	2	no	—
239	C₂×M₁₆	—	2	2	no	—
240	C₂×M₁₆	—	2	2	no	—
241	C₂×M₁₆	—	2	2	no	—
242	C₂×M₁₆	—	2	2	no	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	2	2	no	—
245	C₂×M₁₆	—	2	2	no	—
246	C₂×M₁₆	—	2	2	no	—
247	C₂×M₁₆	C₂×C₄×C₄₇	1	4	yes	—
248	C₂×M₁₆	C₂×C₄×C₄₇	1	4	yes	—
249	C₂×M₁₆	D₄×C₄₇	1	4	yes	—
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	D₄×C₄₇	1	4	yes	—
252	#117	—	2	2	no	—
253	#117	—	2	2	no	—
254	#117	—	2	2	no	—
255	#117	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
258	C₂×C₂²⋊C₄	—	2	4	no	—
259	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
260	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
261	C₂×C₄²	—	2	1	no	—
262	C₂×C₄²	D₄×C₄₇	1	2	yes	—
263	C₂²⋊C₈	—	2	16	no	—
264	#97	—	2	4	no	—
265	C₄×C₈	—	2	4	no	—
266	#95	—	2	4	no	—
267	C₂⁴	—	2	1	no	—
268	C₂⁴	—	2	2	no	—
269	C₂⁴	—	2	1	no	—
270	C₂⁴	—	2	2	no	—
271	C₂⁴	—	4	4	no	—
272	C₂⁴	C₄²×C₄₇	1	2	yes	—
273	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	2	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	C₄²×C₄₇	1	2	yes	—
296	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
297	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
298	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
299	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
300	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
302	C₂²×C₄	#41×C₄₇	1	2	yes	—
303	C₂²×C₄	#41×C₄₇	1	2	yes	—
304	C₂²×C₄	#41×C₄₇	1	2	yes	—
305	M₁₆	—	2	4	no	—
306	M₁₆	—	2	4	no	—
307	M₁₆	—	2	4	no	—
308	M₁₆	—	2	4	no	—
309	M₁₆	—	2	4	no	—
310	M₁₆	—	2	4	no	—
311	M₁₆	—	4	2	no	—
312	M₁₆	—	4	2	no	—
313	C₂×C₈	—	2	4	no	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	—	2	4	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	—	4	2	no	—
318	C₂×C₈	C₂²⋊C₄×C₄₇	1	8	yes	complemented
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₂²⋊C₄	—	2	4	no	—
323	C₂²⋊C₄	—	2	4	no	—
324	C₂²⋊C₄	—	4	8	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	4	2	no	—
328	C₂³	—	2	4	no	—
329	C₂³	—	2	8	no	—
330	C₂³	—	2	4	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	4	4	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	4	no	—
336	C₂³	—	4	4	no	—
337	C₂³	—	4	8	no	—
338	C₂³	—	4	1	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	1	no	—
341	C₂³	C₂×C₄²×C₄₇	1	1	yes	characteristic
342	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
343	C₂³	#117×C₄₇	1	1	yes	characteristic
344	C₂³	C₄×D₄×C₄₇	1	2	yes	—
345	C₂³	C₄×D₄×C₄₇	1	2	yes	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
360	C₂×C₄	#117×C₄₇	1	2	yes	—
361	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
362	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
363	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
364	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
365	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
366	C₂×C₄	#121×C₄₇	1	2	yes	—
367	C₂×C₄	#121×C₄₇	1	2	yes	—
368	C₂×C₄	#121×C₄₇	1	2	yes	—
369	C₂×C₄	#123×C₄₇	1	2	yes	—
370	C₂×C₄	#123×C₄₇	1	1	yes	characteristic
371	C₂×C₄	#124×C₄₇	1	1	yes	characteristic
372	C₂×C₄	#124×C₄₇	1	2	yes	—
373	C₂×C₄	#126×C₄₇	1	2	yes	—
374	C₂×C₄	#127×C₄₇	1	1	yes	characteristic
375	C₈	—	2	8	no	—
376	C₈	—	4	4	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	4	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	8	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	4	no	—
387	C₂²	—	4	8	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	4	2	no	—
390	C₂²	C₄×C₂²⋊C₄×C₄₇	1	2	yes	—
391	C₂²	C₄×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
392	C₂²	C₄₇×#386	1	1	yes	characteristic
393	C₂²	C₄₇×#388	1	2	yes	—
394	C₂²	C₄₇×#390	1	1	yes	characteristic
395	C₄	—	4	4	no	—
396	C₄	—	4	2	no	—
397	C₄	—	8	2	no	—
398	C₄	C₄₇×#386	1	2	yes	—
399	C₄	C₄₇×#388	1	2	yes	—
400	C₄	C₄₇×#388	1	2	yes	—
401	C₄	C₄₇×#390	1	2	yes	—
402	C₂	—	2	1	no	—
403	C₂	—	2	1	no	—
404	C₂	—	2	2	no	—
405	C₂	—	2	2	no	—
406	C₂	—	4	4	no	—
407	C₂	C₄₇×#1437	1	1	yes	characteristic
408	C₂	C₄₇×#1891	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₇	#120
commutator	C₂³	C₂×C₄²×C₄₇
Frattini, cosocle	C₂³×C₄	C₂³×C₄₇
socle	C₂²×C₄₇	#386
prime radical	C₂⁵×C₄₇	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₇ ◁ C₂³×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#2873	C₂	semidirect
4. C₂×C₄₇×#344	C₂	semidirect
5. C₄₇×#1742	C₂	semidirect
12. C₄₇×#407	C₄	semidirect
113. C₂×C₈×C₄₇	C₂²⋊C₄	semidirect
172. #10937	C₄₇	direct (N × H)
199. #2873	C₂×C₄₇	semidirect
201. C₂×#344	C₂×C₄₇	semidirect
202. #1742	C₂×C₄₇	semidirect
216. #407	C₄×C₄₇	semidirect
226. C₄₇	#10937	direct (N × H)
318. C₂×C₈	C₂²⋊C₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#407	2
C₄₇×#2873	2
C₄₇×#2280	2
C₂×C₄₇×#344	2
C₄₇×#1742	2
#10937	47

Subgroups — C47×#10937 #26050635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#10937 #26050635