Subgroups — C₄₇×#10949 #26050647

Order 12032.

990 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#421	C₂	1	2	yes	maximal
2	C₄₇×#2311	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2274	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₇×#343	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₇×H(3,ℤ/4)	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
8	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
9	C₂×#117×C₄₇	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
11	C₄₇×#421	—	2	4	no	—
12	C₄₇×#421	C₄	1	8	yes	complemented
13	C₂×#104×C₄₇	—	2	4	no	—
14	C₄₇×#391	C₄	1	2	yes	complemented
15	C₄₇×#390	C₄	1	2	yes	complemented
16	C₄₇×#386	—	2	2	no	—
17	C₄₇×#380	—	2	2	no	—
18	C₄×C₄⋊C₄×C₄₇	—	2	4	no	—
19	C₄×C₂²⋊C₄×C₄₇	—	2	2	no	—
20	C₄₇×#343	—	2	2	no	—
21	C₄₇×H(3,ℤ/4)	—	2	4	no	—
22	C₂×#41×C₄₇	—	2	2	no	—
23	C₂×#41×C₄₇	—	2	2	no	—
24	C₂×#41×C₄₇	—	2	2	no	—
25	C₂×#41×C₄₇	—	2	2	no	—
26	C₂×#41×C₄₇	—	2	2	no	—
27	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
28	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
29	C₂²×D₄×C₄₇	—	2	1	no	—
30	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₄₇	—	2	1	no	—
32	C₂³×C₄×C₄₇	D₄	1	2	yes	—
33	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
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	C₂×C₄	1	4	yes	—
40	C₂²×C₈×C₄₇	—	2	2	no	—
41	#117×C₄₇	—	2	2	no	—
42	#117×C₄₇	—	2	2	no	—
43	#117×C₄₇	—	2	2	no	—
44	#117×C₄₇	—	2	2	no	—
45	#117×C₄₇	C₂×C₄	1	4	yes	—
46	#117×C₄₇	D₄	1	4	yes	—
47	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
51	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
53	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
54	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
55	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
56	C₂×C₄²×C₄₇	—	2	4	no	—
57	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₄₇	D₄	1	4	yes	—
59	#104×C₄₇	—	2	16	no	—
60	#95×C₄₇	—	2	4	no	—
61	#95×C₄₇	—	2	4	no	—
62	C₂⁴×C₄₇	—	2	1	no	—
63	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
64	#41×C₄₇	—	2	4	no	—
65	#41×C₄₇	—	2	4	no	—
66	#41×C₄₇	—	2	4	no	—
67	#41×C₄₇	—	2	4	no	—
68	#41×C₄₇	—	4	2	no	—
69	#41×C₄₇	—	4	2	no	—
70	#41×C₄₇	—	4	2	no	—
71	#41×C₄₇	—	4	2	no	—
72	C₂×Q₈×C₄₇	—	2	1	no	—
73	C₂×Q₈×C₄₇	—	2	2	no	—
74	C₂×Q₈×C₄₇	—	2	2	no	—
75	C₂×Q₈×C₄₇	C₄²	1	2	yes	complemented
76	C₂×D₄×C₄₇	—	2	4	no	—
77	C₂×D₄×C₄₇	—	2	1	no	—
78	C₂×D₄×C₄₇	—	2	2	no	—
79	C₂×D₄×C₄₇	—	2	2	no	—
80	C₂×D₄×C₄₇	—	4	1	no	—
81	C₂×D₄×C₄₇	—	4	2	no	—
82	C₂×D₄×C₄₇	—	4	1	no	—
83	C₂×D₄×C₄₇	C₄²	1	2	yes	complemented
84	C₂²×C₄×C₄₇	—	2	1	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	—	2	4	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	4	2	no	—
91	C₂²×C₄×C₄₇	—	4	1	no	—
92	C₂²×C₄×C₄₇	—	4	1	no	—
93	C₂²×C₄×C₄₇	—	8	2	no	—
94	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
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	#41	1	2	yes	—
101	C₂²×C₄×C₄₇	#41	1	2	yes	—
102	C₂²×C₄×C₄₇	#41	1	2	yes	—
103	M₁₆×C₄₇	—	2	4	no	—
104	M₁₆×C₄₇	—	2	4	no	—
105	M₁₆×C₄₇	—	4	2	no	—
106	M₁₆×C₄₇	—	4	2	no	—
107	C₂×C₈×C₄₇	—	2	4	no	—
108	C₂×C₈×C₄₇	—	4	2	no	—
109	C₂×C₈×C₄₇	—	4	2	no	—
110	C₄⋊C₄×C₄₇	—	2	4	no	—
111	C₄⋊C₄×C₄₇	—	2	4	no	—
112	C₄⋊C₄×C₄₇	—	2	4	no	—
113	C₄⋊C₄×C₄₇	—	2	4	no	—
114	C₄⋊C₄×C₄₇	—	4	1	no	—
115	C₄⋊C₄×C₄₇	—	4	1	no	—
116	C₂²⋊C₄×C₄₇	—	2	4	no	—
117	C₂²⋊C₄×C₄₇	—	2	4	no	—
118	C₂²⋊C₄×C₄₇	—	4	2	no	—
119	C₂²⋊C₄×C₄₇	—	8	4	no	—
120	C₄²×C₄₇	—	2	4	no	—
121	C₄²×C₄₇	—	2	4	no	—
122	C₄²×C₄₇	—	8	4	no	—
123	C₄²×C₄₇	C₂²⋊C₄	1	8	yes	complemented
124	C₂³×C₄₇	—	2	2	no	—
125	C₂³×C₄₇	—	4	1	no	—
126	C₂³×C₄₇	—	4	1	no	—
127	C₂³×C₄₇	—	4	2	no	—
128	C₂³×C₄₇	—	4	2	no	—
129	C₂³×C₄₇	—	4	1	no	—
130	C₂³×C₄₇	—	4	1	no	—
131	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂³×C₄₇	C₄×D₄	1	2	yes	—
133	C₂³×C₄₇	#120	1	1	yes	characteristic
134	C₂³×C₄₇	#121	1	2	yes	—
135	C₂³×C₄₇	#123	1	1	yes	characteristic
136	Q₈×C₄₇	—	2	4	no	—
137	Q₈×C₄₇	—	4	2	no	—
138	D₄×C₄₇	—	2	4	no	—
139	D₄×C₄₇	—	4	4	no	—
140	D₄×C₄₇	—	4	4	no	—
141	D₄×C₄₇	—	4	2	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	8	no	—
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	—	4	4	no	—
146	C₂×C₄×C₄₇	—	4	4	no	—
147	C₂×C₄×C₄₇	—	4	4	no	—
148	C₂×C₄×C₄₇	—	4	1	no	—
149	C₂×C₄×C₄₇	—	4	1	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	—	4	2	no	—
155	C₂×C₄×C₄₇	—	4	2	no	—
156	C₂×C₄×C₄₇	—	8	2	no	—
157	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂×C₄×C₄₇	#117	1	2	yes	—
160	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
162	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
163	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
164	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
165	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
166	C₂×C₄×C₄₇	#121	1	2	yes	—
167	C₂×C₄×C₄₇	#121	1	2	yes	—
168	C₂×C₄×C₄₇	#123	1	2	yes	—
169	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
170	C₂×C₄×C₄₇	#124	1	2	yes	—
171	C₂×C₄×C₄₇	#126	1	2	yes	—
172	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
173	C₈×C₄₇	—	4	4	no	—
174	#10949	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂²×C₄₇	—	2	1	no	—
176	C₂²×C₄₇	—	2	1	no	—
177	C₂²×C₄₇	—	2	1	no	—
178	C₂²×C₄₇	—	2	1	no	—
179	C₂²×C₄₇	—	2	1	no	—
180	C₂²×C₄₇	—	2	1	no	—
181	C₂²×C₄₇	—	4	2	no	—
182	C₂²×C₄₇	—	4	2	no	—
183	C₂²×C₄₇	—	4	4	no	—
184	C₂²×C₄₇	—	4	2	no	—
185	C₂²×C₄₇	—	8	2	no	—
186	C₂²×C₄₇	—	8	1	no	—
187	C₂²×C₄₇	—	8	1	no	—
188	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
189	C₂²×C₄₇	#386	1	2	yes	—
190	C₂²×C₄₇	#386	1	1	yes	characteristic
191	C₂²×C₄₇	#388	1	2	yes	—
192	C₂²×C₄₇	#390	1	1	yes	characteristic
193	C₄×C₄₇	—	4	8	no	—
194	C₄×C₄₇	—	4	4	no	—
195	C₄×C₄₇	—	4	2	no	—
196	C₄×C₄₇	—	8	2	no	—
197	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
198	C₄×C₄₇	#388	1	2	yes	—
199	C₄×C₄₇	#388	1	2	yes	—
200	C₄×C₄₇	#390	1	2	yes	—
201	C₂×#421	C₂×C₄₇	1	2	yes	—
202	#2311	C₂×C₄₇	1	1	yes	characteristic
203	#2274	C₂×C₄₇	1	1	yes	characteristic, complemented
204	C₂×#343	C₂×C₄₇	1	1	yes	characteristic, complemented
205	C₂×H(3,ℤ/4)	C₂×C₄₇	1	2	yes	complemented
206	C₂×C₄₇	—	2	2	no	—
207	C₂×C₄₇	—	2	1	no	—
208	C₂×C₄₇	—	2	1	no	—
209	C₂×C₄₇	—	2	2	no	—
210	C₂×C₄₇	—	8	2	no	—
211	C₂×C₄₇	#1437	1	1	yes	characteristic
212	C₂×C₄₇	#1911	1	1	yes	characteristic
213	C₂×C₄₇	#1912	1	1	yes	characteristic
214	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
215	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
216	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
217	C₂×#117	C₂²×C₄₇	1	2	yes	—
218	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
219	#421	—	2	4	no	—
220	#421	C₄×C₄₇	1	8	yes	complemented
221	C₂×#104	—	2	4	no	—
222	#391	C₄×C₄₇	1	2	yes	complemented
223	#390	C₄×C₄₇	1	2	yes	complemented
224	#386	—	2	2	no	—
225	#380	—	2	2	no	—
226	C₄×C₄⋊C₄	—	2	4	no	—
227	C₄×C₂²⋊C₄	—	2	2	no	—
228	#343	—	2	2	no	—
229	H(3,ℤ/4)	—	2	4	no	—
230	C₄₇	#10949	1	1	yes	characteristic, direct product factor, Sylow
231	C₂×#41	—	2	2	no	—
232	C₂×#41	—	2	2	no	—
233	C₂×#41	—	2	2	no	—
234	C₂×#41	—	2	2	no	—
235	C₂×#41	—	2	2	no	—
236	C₂×#41	C₂×C₄×C₄₇	1	4	yes	—
237	C₂²×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
240	C₂³×C₄	—	2	1	no	—
241	C₂³×C₄	D₄×C₄₇	1	2	yes	—
242	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
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	—	2	2	no	—
248	C₂×M₁₆	C₂×C₄×C₄₇	1	4	yes	—
249	C₂²×C₈	—	2	2	no	—
250	#117	—	2	2	no	—
251	#117	—	2	2	no	—
252	#117	—	2	2	no	—
253	#117	—	2	2	no	—
254	#117	C₂×C₄×C₄₇	1	4	yes	—
255	#117	D₄×C₄₇	1	4	yes	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
261	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	4	no	—
265	C₂×C₄²	—	2	4	no	—
266	C₂×C₄²	C₂×C₄×C₄₇	1	2	yes	—
267	C₂×C₄²	D₄×C₄₇	1	4	yes	—
268	#104	—	2	16	no	—
269	#95	—	2	4	no	—
270	#95	—	2	4	no	—
271	C₂⁴	—	2	1	no	—
272	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
273	#41	—	2	4	no	—
274	#41	—	2	4	no	—
275	#41	—	2	4	no	—
276	#41	—	2	4	no	—
277	#41	—	4	2	no	—
278	#41	—	4	2	no	—
279	#41	—	4	2	no	—
280	#41	—	4	2	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	C₄²×C₄₇	1	2	yes	complemented
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	C₄²×C₄₇	1	2	yes	complemented
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	8	2	no	—
303	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
304	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
305	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
309	C₂²×C₄	#41×C₄₇	1	2	yes	—
310	C₂²×C₄	#41×C₄₇	1	2	yes	—
311	C₂²×C₄	#41×C₄₇	1	2	yes	—
312	M₁₆	—	2	4	no	—
313	M₁₆	—	2	4	no	—
314	M₁₆	—	4	2	no	—
315	M₁₆	—	4	2	no	—
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	4	2	no	—
318	C₂×C₈	—	4	2	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	—	2	4	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	8	4	no	—
329	C₄²	—	2	4	no	—
330	C₄²	—	2	4	no	—
331	C₄²	—	8	4	no	—
332	C₄²	C₂²⋊C₄×C₄₇	1	8	yes	complemented
333	C₂³	—	2	2	no	—
334	C₂³	—	4	1	no	—
335	C₂³	—	4	1	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	1	no	—
339	C₂³	—	4	1	no	—
340	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
341	C₂³	C₄×D₄×C₄₇	1	2	yes	—
342	C₂³	#120×C₄₇	1	1	yes	characteristic
343	C₂³	#121×C₄₇	1	2	yes	—
344	C₂³	#123×C₄₇	1	1	yes	characteristic
345	Q₈	—	2	4	no	—
346	Q₈	—	4	2	no	—
347	D₄	—	2	4	no	—
348	D₄	—	4	4	no	—
349	D₄	—	4	4	no	—
350	D₄	—	4	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	8	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	8	2	no	—
366	C₂×C₄	C₂×C₄²×C₄₇	1	1	yes	characteristic
367	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
368	C₂×C₄	#117×C₄₇	1	2	yes	—
369	C₂×C₄	#117×C₄₇	1	1	yes	characteristic
370	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
371	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
372	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
373	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
374	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
375	C₂×C₄	#121×C₄₇	1	2	yes	—
376	C₂×C₄	#121×C₄₇	1	2	yes	—
377	C₂×C₄	#123×C₄₇	1	2	yes	—
378	C₂×C₄	#124×C₄₇	1	1	yes	characteristic
379	C₂×C₄	#124×C₄₇	1	2	yes	—
380	C₂×C₄	#126×C₄₇	1	2	yes	—
381	C₂×C₄	#127×C₄₇	1	1	yes	characteristic
382	C₈	—	4	4	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	4	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	1	no	—
395	C₂²	—	8	1	no	—
396	C₂²	C₄×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
397	C₂²	C₄₇×#386	1	2	yes	—
398	C₂²	C₄₇×#386	1	1	yes	characteristic
399	C₂²	C₄₇×#388	1	2	yes	—
400	C₂²	C₄₇×#390	1	1	yes	characteristic
401	C₄	—	4	8	no	—
402	C₄	—	4	4	no	—
403	C₄	—	4	2	no	—
404	C₄	—	8	2	no	—
405	C₄	C₄×C₂²⋊C₄×C₄₇	1	2	yes	—
406	C₄	C₄₇×#388	1	2	yes	—
407	C₄	C₄₇×#388	1	2	yes	—
408	C₄	C₄₇×#390	1	2	yes	—
409	C₂	—	2	2	no	—
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	2	2	no	—
413	C₂	—	8	2	no	—
414	C₂	C₄₇×#1437	1	1	yes	characteristic
415	C₂	C₄₇×#1911	1	1	yes	characteristic
416	C₂	C₄₇×#1912	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	#386
commutator	C₂×C₄	C₂×C₄²×C₄₇
Frattini, cosocle	C₂³×C₄	C₂³×C₄₇
prime radical	C₂²×#41×C₄₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂³×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₇×#2274	C₂	semidirect
4. C₂×C₄₇×#343	C₂	semidirect
5. C₂×C₄₇×H(3,ℤ/4)	C₂	semidirect
12. C₄₇×#421	C₄	semidirect
14. C₄₇×#391	C₄	semidirect
15. C₄₇×#390	C₄	semidirect
75. C₂×Q₈×C₄₇	C₄²	semidirect
83. C₂×D₄×C₄₇	C₄²	semidirect
123. C₄²×C₄₇	C₂²⋊C₄	semidirect
174. #10949	C₄₇	direct (N × H)
203. #2274	C₂×C₄₇	semidirect
204. C₂×#343	C₂×C₄₇	semidirect
205. C₂×H(3,ℤ/4)	C₂×C₄₇	semidirect
220. #421	C₄×C₄₇	semidirect
222. #391	C₄×C₄₇	semidirect
223. #390	C₄×C₄₇	semidirect
230. C₄₇	#10949	direct (N × H)
284. C₂×Q₈	C₄²×C₄₇	semidirect
292. C₂×D₄	C₄²×C₄₇	semidirect
332. C₄²	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×#421	2
C₄₇×#2311	2
C₄₇×#2274	2
C₂×C₄₇×#343	2
C₂×C₄₇×H(3,ℤ/4)	2
#10949	47

Subgroups — C47×#10949 #26050647

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#10949 #26050647