Subgroups — C₄₇×#20851 #26060549

Order 12032.

1438 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#430	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₇×#407	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇×#407	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1855	C₂	1	8	yes	maximal, complemented
6	C₄₇×#1738	C₂	1	2	yes	maximal, complemented
7	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₄₇	—	2	2	no	—
9	C₂²×M₁₆×C₄₇	—	2	1	no	—
10	C₂²×M₁₆×C₄₇	—	2	8	no	—
11	C₂²×M₁₆×C₄₇	C₂²	1	4	yes	—
12	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
16	C₂³×C₈×C₄₇	—	2	1	no	—
17	C₄₇×#430	—	2	8	no	—
18	C₂×#108×C₄₇	C₂²	1	8	yes	complemented
19	C₄₇×#407	—	2	1	no	—
20	C₄₇×#407	—	2	1	no	—
21	C₄₇×#407	C₄	1	2	yes	—
22	C₄₇×#407	C₄	1	4	yes	—
23	C₄₇×#407	C₄	1	2	yes	—
24	C₄₇×#407	C₂²	1	4	yes	—
25	C₂×C₂²⋊C₈×C₄₇	—	2	2	no	—
26	C₂×C₂²⋊C₈×C₄₇	C₂²	1	4	yes	—
27	C₄₇×#341	C₂²	1	8	yes	complemented
28	C₂⁵×C₄₇	Q₈	1	1	yes	characteristic
29	C₂³×C₄×C₄₇	—	2	4	no	—
30	C₂³×C₄×C₄₇	—	2	4	no	—
31	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₄₇	D₄	1	2	yes	—
36	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	Q₈	1	1	yes	characteristic
38	C₂³×C₄×C₄₇	Q₈	1	2	yes	—
39	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
40	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
41	C₂×M₁₆×C₄₇	—	2	16	no	—
42	C₂×M₁₆×C₄₇	—	2	8	no	—
43	C₂×M₁₆×C₄₇	—	2	4	no	—
44	C₂×M₁₆×C₄₇	—	2	4	no	—
45	C₂×M₁₆×C₄₇	—	2	2	no	—
46	C₂×M₁₆×C₄₇	—	2	4	no	—
47	C₂×M₁₆×C₄₇	—	2	4	no	—
48	C₂×M₁₆×C₄₇	—	2	16	no	—
49	C₂×M₁₆×C₄₇	—	2	1	no	—
50	C₂×M₁₆×C₄₇	—	2	1	no	—
51	C₂×M₁₆×C₄₇	—	2	4	no	—
52	C₂×M₁₆×C₄₇	—	2	4	no	—
53	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
54	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
55	C₂×M₁₆×C₄₇	D₄	1	8	yes	—
56	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
57	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
58	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
59	C₂²×C₈×C₄₇	—	2	8	no	—
60	C₂²×C₈×C₄₇	—	2	4	no	—
61	C₂²×C₈×C₄₇	—	2	2	no	—
62	C₂²×C₈×C₄₇	—	2	1	no	—
63	C₂²×C₈×C₄₇	—	2	1	no	—
64	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
65	#108×C₄₇	—	2	16	no	—
66	C₂²⋊C₈×C₄₇	—	2	4	no	—
67	C₂²⋊C₈×C₄₇	—	2	4	no	—
68	C₂²⋊C₈×C₄₇	C₂×C₄	1	8	yes	—
69	C₂²⋊C₈×C₄₇	C₂×C₄	1	8	yes	—
70	C₂⁴×C₄₇	—	2	4	no	—
71	C₂⁴×C₄₇	—	4	4	no	—
72	C₂⁴×C₄₇	C₄⋊C₄	1	1	yes	characteristic
73	C₂⁴×C₄₇	C₄⋊C₄	1	2	yes	—
74	C₂⁴×C₄₇	C₄⋊C₄	1	1	yes	characteristic
75	C₂⁴×C₄₇	C₂×Q₈	1	2	yes	—
76	C₂⁴×C₄₇	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	—	2	4	no	—
78	C₂²×C₄×C₄₇	—	2	4	no	—
79	C₂²×C₄×C₄₇	—	2	4	no	—
80	C₂²×C₄×C₄₇	—	2	8	no	—
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	—	2	4	no	—
83	C₂²×C₄×C₄₇	—	2	2	no	—
84	C₂²×C₄×C₄₇	—	2	8	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	4	no	—
90	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
94	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	#41	1	4	yes	—
109	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
110	M₁₆×C₄₇	—	2	16	no	—
111	M₁₆×C₄₇	—	2	8	no	—
112	M₁₆×C₄₇	—	2	8	no	—
113	M₁₆×C₄₇	—	2	8	no	—
114	M₁₆×C₄₇	—	2	4	no	—
115	M₁₆×C₄₇	—	2	4	no	—
116	M₁₆×C₄₇	—	2	4	no	—
117	M₁₆×C₄₇	—	4	2	no	—
118	M₁₆×C₄₇	—	4	2	no	—
119	M₁₆×C₄₇	C₂×D₄	1	8	yes	—
120	C₂×C₈×C₄₇	—	2	16	no	—
121	C₂×C₈×C₄₇	—	2	8	no	—
122	C₂×C₈×C₄₇	—	2	4	no	—
123	C₂×C₈×C₄₇	—	2	4	no	—
124	C₂×C₈×C₄₇	—	2	4	no	—
125	C₂×C₈×C₄₇	—	2	2	no	—
126	C₂×C₈×C₄₇	—	2	2	no	—
127	C₂×C₈×C₄₇	—	4	2	no	—
128	C₂×C₈×C₄₇	—	4	2	no	—
129	C₂×C₈×C₄₇	C₂²×C₄	1	8	yes	—
130	C₂³×C₄₇	—	2	2	no	—
131	C₂³×C₄₇	—	2	4	no	—
132	C₂³×C₄₇	—	2	4	no	—
133	C₂³×C₄₇	—	2	4	no	—
134	C₂³×C₄₇	—	2	2	no	—
135	C₂³×C₄₇	—	2	4	no	—
136	C₂³×C₄₇	—	2	4	no	—
137	C₂³×C₄₇	—	4	2	no	—
138	C₂³×C₄₇	—	4	2	no	—
139	C₂³×C₄₇	—	4	2	no	—
140	C₂³×C₄₇	—	4	2	no	—
141	C₂³×C₄₇	—	4	16	no	—
142	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
143	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
146	C₂³×C₄₇	C₂²⋊Q₈	1	4	yes	—
147	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₄₇	—	2	4	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	4	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	4	no	—
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	4	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
163	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
164	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
167	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
168	C₂×C₄×C₄₇	#120	1	2	yes	—
169	C₂×C₄×C₄₇	#120	1	2	yes	—
170	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
171	C₂×C₄×C₄₇	#123	1	2	yes	—
172	C₂×C₄×C₄₇	#123	1	2	yes	—
173	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
175	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
177	C₈×C₄₇	—	2	8	no	—
178	C₈×C₄₇	—	2	8	no	—
179	C₈×C₄₇	—	4	2	no	—
180	C₈×C₄₇	—	4	2	no	—
181	#20851	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂²×C₄₇	—	2	8	no	—
183	C₂²×C₄₇	—	2	2	no	—
184	C₂²×C₄₇	—	2	2	no	—
185	C₂²×C₄₇	—	2	2	no	—
186	C₂²×C₄₇	—	2	2	no	—
187	C₂²×C₄₇	—	2	2	no	—
188	C₂²×C₄₇	—	2	2	no	—
189	C₂²×C₄₇	—	2	2	no	—
190	C₂²×C₄₇	—	2	2	no	—
191	C₂²×C₄₇	—	4	4	no	—
192	C₂²×C₄₇	—	4	8	no	—
193	C₂²×C₄₇	—	4	8	no	—
194	C₂²×C₄₇	—	4	4	no	—
195	C₂²×C₄₇	#385	1	2	yes	—
196	C₂²×C₄₇	#385	1	2	yes	—
197	C₂²×C₄₇	#430	1	4	yes	complemented
198	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
199	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
200	C₄×C₄₇	—	2	2	no	—
201	C₄×C₄₇	—	2	2	no	—
202	C₄×C₄₇	#385	1	2	yes	—
203	C₄×C₄₇	#385	1	2	yes	—
204	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
205	C₄×C₄₇	C₂×#120	1	1	yes	characteristic
206	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
207	C₂³×M₁₆	C₂×C₄₇	1	1	yes	characteristic
208	C₂×#430	C₂×C₄₇	1	2	yes	complemented
209	C₂×#407	C₂×C₄₇	1	1	yes	characteristic
210	C₂×#407	C₂×C₄₇	1	1	yes	characteristic
211	#1855	C₂×C₄₇	1	8	yes	complemented
212	#1738	C₂×C₄₇	1	2	yes	complemented
213	C₂×C₄₇	—	2	2	no	—
214	C₂×C₄₇	—	2	4	no	—
215	C₂×C₄₇	—	2	2	no	—
216	C₂×C₄₇	—	2	2	no	—
217	C₂×C₄₇	—	4	2	no	—
218	C₂×C₄₇	C₂×#385	1	1	yes	characteristic
219	C₂×C₄₇	C₂×#430	1	2	yes	—
220	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
221	C₂²×M₁₆	—	2	2	no	—
222	C₂²×M₁₆	—	2	1	no	—
223	C₂²×M₁₆	—	2	8	no	—
224	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
225	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
226	C₂²×M₁₆	C₂²×C₄₇	1	4	yes	—
227	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
228	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
229	C₂³×C₈	—	2	1	no	—
230	#430	—	2	8	no	—
231	C₂×#108	C₂²×C₄₇	1	8	yes	complemented
232	#407	—	2	1	no	—
233	#407	—	2	1	no	—
234	#407	C₄×C₄₇	1	2	yes	—
235	#407	C₄×C₄₇	1	4	yes	—
236	#407	C₄×C₄₇	1	2	yes	—
237	#407	C₂²×C₄₇	1	4	yes	—
238	C₂×C₂²⋊C₈	—	2	2	no	—
239	C₂×C₂²⋊C₈	C₂²×C₄₇	1	4	yes	—
240	#341	C₂²×C₄₇	1	8	yes	complemented
241	C₄₇	#20851	1	1	yes	characteristic, direct product factor, Sylow
242	C₂⁵	Q₈×C₄₇	1	1	yes	characteristic
243	C₂³×C₄	—	2	4	no	—
244	C₂³×C₄	—	2	4	no	—
245	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
246	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
247	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
248	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
249	C₂³×C₄	D₄×C₄₇	1	2	yes	—
250	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
251	C₂³×C₄	Q₈×C₄₇	1	1	yes	characteristic
252	C₂³×C₄	Q₈×C₄₇	1	2	yes	—
253	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
254	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
255	C₂×M₁₆	—	2	16	no	—
256	C₂×M₁₆	—	2	8	no	—
257	C₂×M₁₆	—	2	4	no	—
258	C₂×M₁₆	—	2	4	no	—
259	C₂×M₁₆	—	2	2	no	—
260	C₂×M₁₆	—	2	4	no	—
261	C₂×M₁₆	—	2	4	no	—
262	C₂×M₁₆	—	2	16	no	—
263	C₂×M₁₆	—	2	1	no	—
264	C₂×M₁₆	—	2	1	no	—
265	C₂×M₁₆	—	2	4	no	—
266	C₂×M₁₆	—	2	4	no	—
267	C₂×M₁₆	C₂×C₄×C₄₇	1	4	yes	—
268	C₂×M₁₆	C₂×C₄×C₄₇	1	4	yes	—
269	C₂×M₁₆	D₄×C₄₇	1	8	yes	—
270	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
271	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
272	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
273	C₂²×C₈	—	2	8	no	—
274	C₂²×C₈	—	2	4	no	—
275	C₂²×C₈	—	2	2	no	—
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
279	#108	—	2	16	no	—
280	C₂²⋊C₈	—	2	4	no	—
281	C₂²⋊C₈	—	2	4	no	—
282	C₂²⋊C₈	C₂×C₄×C₄₇	1	8	yes	—
283	C₂²⋊C₈	C₂×C₄×C₄₇	1	8	yes	—
284	C₂⁴	—	2	4	no	—
285	C₂⁴	—	4	4	no	—
286	C₂⁴	C₄⋊C₄×C₄₇	1	1	yes	characteristic
287	C₂⁴	C₄⋊C₄×C₄₇	1	2	yes	—
288	C₂⁴	C₄⋊C₄×C₄₇	1	1	yes	characteristic
289	C₂⁴	C₂×Q₈×C₄₇	1	2	yes	—
290	C₂⁴	C₂×Q₈×C₄₇	1	1	yes	characteristic
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	8	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	8	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	C₄⋊C₄×C₄₇	1	1	yes	characteristic
305	C₂²×C₄	C₄⋊C₄×C₄₇	1	2	yes	—
306	C₂²×C₄	C₄⋊C₄×C₄₇	1	1	yes	characteristic
307	C₂²×C₄	C₄⋊C₄×C₄₇	1	2	yes	—
308	C₂²×C₄	C₄⋊C₄×C₄₇	1	2	yes	—
309	C₂²×C₄	C₄⋊C₄×C₄₇	1	2	yes	—
310	C₂²×C₄	C₄⋊C₄×C₄₇	1	2	yes	—
311	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
312	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
313	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
314	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
316	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
320	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
321	C₂²×C₄	C₂×Q₈×C₄₇	1	1	yes	characteristic
322	C₂²×C₄	#41×C₄₇	1	4	yes	—
323	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
324	M₁₆	—	2	16	no	—
325	M₁₆	—	2	8	no	—
326	M₁₆	—	2	8	no	—
327	M₁₆	—	2	8	no	—
328	M₁₆	—	2	4	no	—
329	M₁₆	—	2	4	no	—
330	M₁₆	—	2	4	no	—
331	M₁₆	—	4	2	no	—
332	M₁₆	—	4	2	no	—
333	M₁₆	C₂×D₄×C₄₇	1	8	yes	—
334	C₂×C₈	—	2	16	no	—
335	C₂×C₈	—	2	8	no	—
336	C₂×C₈	—	2	4	no	—
337	C₂×C₈	—	2	4	no	—
338	C₂×C₈	—	2	4	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	4	2	no	—
342	C₂×C₈	—	4	2	no	—
343	C₂×C₈	C₂²×C₄×C₄₇	1	8	yes	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	4	no	—
346	C₂³	—	2	4	no	—
347	C₂³	—	2	4	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	4	no	—
350	C₂³	—	2	4	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	16	no	—
356	C₂³	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
357	C₂³	C₂×C₄⋊C₄×C₄₇	1	1	yes	characteristic
358	C₂³	C₂×C₄⋊C₄×C₄₇	1	1	yes	characteristic
359	C₂³	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
360	C₂³	C₂²⋊Q₈×C₄₇	1	4	yes	—
361	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
377	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
378	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	1	yes	characteristic
379	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	1	yes	characteristic
380	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
381	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
382	C₂×C₄	#120×C₄₇	1	2	yes	—
383	C₂×C₄	#120×C₄₇	1	2	yes	—
384	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
385	C₂×C₄	#123×C₄₇	1	2	yes	—
386	C₂×C₄	#123×C₄₇	1	2	yes	—
387	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
388	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
389	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
390	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
391	C₈	—	2	8	no	—
392	C₈	—	2	8	no	—
393	C₈	—	4	2	no	—
394	C₈	—	4	2	no	—
395	C₂²	—	2	8	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	4	8	no	—
406	C₂²	—	4	8	no	—
407	C₂²	—	4	4	no	—
408	C₂²	C₄₇×#385	1	2	yes	—
409	C₂²	C₄₇×#385	1	2	yes	—
410	C₂²	C₄₇×#430	1	4	yes	complemented
411	C₂²	C₂²×C₄⋊C₄×C₄₇	1	1	yes	characteristic
412	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	2	yes	—
413	C₄	—	2	2	no	—
414	C₄	—	2	2	no	—
415	C₄	C₄₇×#385	1	2	yes	—
416	C₄	C₄₇×#385	1	2	yes	—
417	C₄	C₂×C₄×D₄×C₄₇	1	2	yes	—
418	C₄	C₂×#120×C₄₇	1	1	yes	characteristic
419	C₄	C₂×#123×C₄₇	1	1	yes	characteristic
420	C₂	—	2	2	no	—
421	C₂	—	2	4	no	—
422	C₂	—	2	2	no	—
423	C₂	—	2	2	no	—
424	C₂	—	4	2	no	—
425	C₂	C₂×C₄₇×#385	1	1	yes	characteristic
426	C₂	C₂×C₄₇×#430	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂⁵×C₄₇	Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₇ ◁ C₂⁴×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#430	C₂	semidirect
5. C₄₇×#1855	C₂	semidirect
6. C₄₇×#1738	C₂	semidirect
18. C₂×#108×C₄₇	C₂²	semidirect
27. C₄₇×#341	C₂²	semidirect
181. #20851	C₄₇	direct (N × H)
197. C₂²×C₄₇	#430	semidirect
208. C₂×#430	C₂×C₄₇	semidirect
211. #1855	C₂×C₄₇	semidirect
212. #1738	C₂×C₄₇	semidirect
231. C₂×#108	C₂²×C₄₇	semidirect
240. #341	C₂²×C₄₇	semidirect
241. C₄₇	#20851	direct (N × H)
410. C₂²	C₄₇×#430	semidirect

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₄₇	2
C₂×C₄₇×#430	2
C₂×C₄₇×#407	2
C₄₇×#1855	2
C₄₇×#1738	2
#20851	47

Subgroups — C47×#20851 #26060549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#20851 #26060549