Subgroups — C₄₇×#20685 #26060383

Order 12032.

1486 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#117×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#407	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂²⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1818	C₂	1	4	yes	maximal, complemented
5	C₄₇×#1817	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1729	C₂	1	4	yes	maximal, complemented
7	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
9	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
10	C₂×#117×C₄₇	—	2	4	no	—
11	C₂×#117×C₄₇	—	2	4	no	—
12	C₂×#117×C₄₇	C₄	1	2	yes	—
13	C₂×#117×C₄₇	C₄	1	2	yes	—
14	C₂×#117×C₄₇	C₂²	1	2	yes	—
15	C₂×#117×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₄₇	C₄	1	2	yes	—
19	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
20	C₄₇×#407	—	2	4	no	—
21	C₂×C₂²⋊C₈×C₄₇	—	2	4	no	—
22	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
24	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
26	C₄₇×#336	C₂²	1	16	yes	complemented
27	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₄₇	—	2	8	no	—
29	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
30	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₄₇	D₄	1	4	yes	—
35	C₂³×C₄×C₄₇	D₄	1	4	yes	—
36	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
39	C₂×M₁₆×C₄₇	—	2	4	no	—
40	C₂×M₁₆×C₄₇	—	2	8	no	—
41	C₂²×C₈×C₄₇	—	2	4	no	—
42	C₂²×C₈×C₄₇	—	2	8	no	—
43	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
44	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
45	#117×C₄₇	—	2	8	no	—
46	#117×C₄₇	—	2	8	no	—
47	#117×C₄₇	—	2	4	no	—
48	#117×C₄₇	—	2	4	no	—
49	#117×C₄₇	—	2	4	no	—
50	#117×C₄₇	—	2	4	no	—
51	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
52	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
53	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
57	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
58	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
59	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
60	C₂×C₄²×C₄₇	—	2	4	no	—
61	C₂×C₄²×C₄₇	—	2	4	no	—
62	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
63	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
64	C₂²⋊C₈×C₄₇	—	2	4	no	—
65	C₂²⋊C₈×C₄₇	—	2	4	no	—
66	C₂²⋊C₈×C₄₇	—	2	4	no	—
67	C₂²⋊C₈×C₄₇	—	2	4	no	—
68	C₂⁴×C₄₇	—	2	4	no	—
69	C₂⁴×C₄₇	—	2	4	no	—
70	C₂⁴×C₄₇	—	4	2	no	—
71	C₂⁴×C₄₇	C₂²⋊C₄	1	4	yes	—
72	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
73	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
74	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
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	16	no	—
79	C₂²×C₄×C₄₇	—	2	16	no	—
80	C₂²×C₄×C₄₇	—	2	4	no	—
81	C₂²×C₄×C₄₇	—	2	4	no	—
82	C₂²×C₄×C₄₇	—	2	4	no	—
83	C₂²×C₄×C₄₇	—	2	4	no	—
84	C₂²×C₄×C₄₇	—	2	8	no	—
85	C₂²×C₄×C₄₇	—	4	4	no	—
86	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
87	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
88	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
89	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂×D₄	1	2	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	2	yes	—
100	C₂²×C₄×C₄₇	#41	1	8	yes	—
101	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
102	M₁₆×C₄₇	—	4	8	no	—
103	C₂×C₈×C₄₇	—	2	4	no	—
104	C₂×C₈×C₄₇	—	2	4	no	—
105	C₂×C₈×C₄₇	—	2	8	no	—
106	C₂×C₈×C₄₇	—	2	8	no	—
107	C₂×C₈×C₄₇	—	4	8	no	—
108	C₄⋊C₄×C₄₇	—	2	4	no	—
109	C₄⋊C₄×C₄₇	—	2	4	no	—
110	C₄⋊C₄×C₄₇	—	2	4	no	—
111	C₄⋊C₄×C₄₇	—	2	4	no	—
112	C₂²⋊C₄×C₄₇	—	2	8	no	—
113	C₂²⋊C₄×C₄₇	—	2	8	no	—
114	C₄²×C₄₇	—	2	8	no	—
115	C₄²×C₄₇	—	2	4	no	—
116	C₄²×C₄₇	—	2	4	no	—
117	C₂³×C₄₇	—	2	2	no	—
118	C₂³×C₄₇	—	2	2	no	—
119	C₂³×C₄₇	—	2	2	no	—
120	C₂³×C₄₇	—	2	2	no	—
121	C₂³×C₄₇	—	2	2	no	—
122	C₂³×C₄₇	—	2	2	no	—
123	C₂³×C₄₇	—	2	2	no	—
124	C₂³×C₄₇	—	2	8	no	—
125	C₂³×C₄₇	—	2	8	no	—
126	C₂³×C₄₇	—	4	4	no	—
127	C₂³×C₄₇	—	4	16	no	—
128	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
129	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
130	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
131	C₂³×C₄₇	#117	1	4	yes	—
132	C₂³×C₄₇	#131	1	4	yes	—
133	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
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	4	no	—
138	C₂×C₄×C₄₇	—	2	4	no	—
139	C₂×C₄×C₄₇	—	2	4	no	—
140	C₂×C₄×C₄₇	—	2	4	no	—
141	C₂×C₄×C₄₇	—	2	8	no	—
142	C₂×C₄×C₄₇	—	2	8	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	—	2	8	no	—
146	C₂×C₄×C₄₇	—	2	8	no	—
147	C₂×C₄×C₄₇	—	4	8	no	—
148	C₂×C₄×C₄₇	—	4	8	no	—
149	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂×C₄×C₄₇	#117	1	4	yes	—
153	C₂×C₄×C₄₇	#123	1	8	yes	—
154	C₂×C₄×C₄₇	#123	1	8	yes	—
155	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
158	C₈×C₄₇	—	4	4	no	—
159	C₈×C₄₇	—	4	4	no	—
160	#20685	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂²×C₄₇	—	2	2	no	—
162	C₂²×C₄₇	—	2	2	no	—
163	C₂²×C₄₇	—	2	2	no	—
164	C₂²×C₄₇	—	2	8	no	—
165	C₂²×C₄₇	—	2	8	no	—
166	C₂²×C₄₇	—	2	2	no	—
167	C₂²×C₄₇	—	2	2	no	—
168	C₂²×C₄₇	—	2	2	no	—
169	C₂²×C₄₇	—	2	2	no	—
170	C₂²×C₄₇	—	4	16	no	—
171	C₂²×C₄₇	—	4	4	no	—
172	C₂²×C₄₇	#381	1	4	yes	—
173	C₂²×C₄₇	#408	1	4	yes	—
174	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
175	C₂²×C₄₇	C₂×#117	1	2	yes	—
176	C₂²×C₄₇	C₂×#131	1	2	yes	—
177	C₂²×C₄₇	#568	1	2	yes	—
178	C₄×C₄₇	—	2	2	no	—
179	C₄×C₄₇	—	2	2	no	—
180	C₄×C₄₇	—	4	4	no	—
181	C₄×C₄₇	—	4	4	no	—
182	C₄×C₄₇	#381	1	4	yes	—
183	C₄×C₄₇	C₂×#123	1	2	yes	—
184	C₄×C₄₇	C₂×#123	1	2	yes	—
185	C₂²×#117	C₂×C₄₇	1	1	yes	characteristic
186	C₂×#407	C₂×C₄₇	1	1	yes	characteristic
187	C₂²×C₂²⋊C₈	C₂×C₄₇	1	1	yes	characteristic
188	#1818	C₂×C₄₇	1	4	yes	complemented
189	#1817	C₂×C₄₇	1	4	yes	complemented
190	#1729	C₂×C₄₇	1	4	yes	complemented
191	C₂×C₄₇	—	2	4	no	—
192	C₂×C₄₇	—	2	4	no	—
193	C₂×C₄₇	—	4	2	no	—
194	C₂×C₄₇	C₂×#381	1	1	yes	characteristic
195	C₂×C₄₇	C₂×#408	1	1	yes	characteristic
196	C₂×C₄₇	#2879	1	1	yes	characteristic
197	C₂×C₄₇	#2924	1	4	yes	—
198	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
199	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
200	C₂³×C₈	C₂²×C₄₇	1	2	yes	—
201	C₂×#117	—	2	4	no	—
202	C₂×#117	—	2	4	no	—
203	C₂×#117	C₄×C₄₇	1	2	yes	—
204	C₂×#117	C₄×C₄₇	1	2	yes	—
205	C₂×#117	C₂²×C₄₇	1	2	yes	—
206	C₂×#117	C₂²×C₄₇	1	2	yes	—
207	C₂²×C₄⋊C₄	C₄×C₄₇	1	1	yes	characteristic
208	C₂²×C₄⋊C₄	C₄×C₄₇	1	1	yes	characteristic
209	C₂²×C₂²⋊C₄	C₄×C₄₇	1	2	yes	—
210	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
211	#407	—	2	4	no	—
212	C₂×C₂²⋊C₈	—	2	4	no	—
213	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
214	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
215	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
216	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
217	#336	C₂²×C₄₇	1	16	yes	complemented
218	C₄₇	#20685	1	1	yes	characteristic, direct product factor, Sylow
219	C₂⁵	C₂×C₄×C₄₇	1	1	yes	characteristic
220	C₂³×C₄	—	2	8	no	—
221	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
222	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
223	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
224	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
225	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
226	C₂³×C₄	D₄×C₄₇	1	4	yes	—
227	C₂³×C₄	D₄×C₄₇	1	4	yes	—
228	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
229	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
230	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
231	C₂×M₁₆	—	2	4	no	—
232	C₂×M₁₆	—	2	8	no	—
233	C₂²×C₈	—	2	4	no	—
234	C₂²×C₈	—	2	8	no	—
235	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
236	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
237	#117	—	2	8	no	—
238	#117	—	2	8	no	—
239	#117	—	2	4	no	—
240	#117	—	2	4	no	—
241	#117	—	2	4	no	—
242	#117	—	2	4	no	—
243	C₂×C₄⋊C₄	—	2	4	no	—
244	C₂×C₄⋊C₄	—	2	4	no	—
245	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
246	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
247	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
248	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
249	C₂×C₂²⋊C₄	—	2	8	no	—
250	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
251	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
252	C₂×C₄²	—	2	4	no	—
253	C₂×C₄²	—	2	4	no	—
254	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
255	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
256	C₂²⋊C₈	—	2	4	no	—
257	C₂²⋊C₈	—	2	4	no	—
258	C₂²⋊C₈	—	2	4	no	—
259	C₂²⋊C₈	—	2	4	no	—
260	C₂⁴	—	2	4	no	—
261	C₂⁴	—	2	4	no	—
262	C₂⁴	—	4	2	no	—
263	C₂⁴	C₂²⋊C₄×C₄₇	1	4	yes	—
264	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
265	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
266	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	16	no	—
271	C₂²×C₄	—	2	16	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	8	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
279	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
280	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
281	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
282	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
283	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
284	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
285	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
288	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
289	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
290	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
292	C₂²×C₄	#41×C₄₇	1	8	yes	—
293	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
294	M₁₆	—	4	8	no	—
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	2	8	no	—
298	C₂×C₈	—	2	8	no	—
299	C₂×C₈	—	4	8	no	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₂²⋊C₄	—	2	8	no	—
305	C₂²⋊C₄	—	2	8	no	—
306	C₄²	—	2	8	no	—
307	C₄²	—	2	4	no	—
308	C₄²	—	2	4	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	2	2	no	—
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	—	2	2	no	—
314	C₂³	—	2	2	no	—
315	C₂³	—	2	2	no	—
316	C₂³	—	2	8	no	—
317	C₂³	—	2	8	no	—
318	C₂³	—	4	4	no	—
319	C₂³	—	4	16	no	—
320	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
321	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
322	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
323	C₂³	#117×C₄₇	1	4	yes	—
324	C₂³	#131×C₄₇	1	4	yes	—
325	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	8	no	—
339	C₂×C₄	—	4	8	no	—
340	C₂×C₄	—	4	8	no	—
341	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
342	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
343	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
344	C₂×C₄	#117×C₄₇	1	4	yes	—
345	C₂×C₄	#123×C₄₇	1	8	yes	—
346	C₂×C₄	#123×C₄₇	1	8	yes	—
347	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
349	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
350	C₈	—	4	4	no	—
351	C₈	—	4	4	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	8	no	—
357	C₂²	—	2	8	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	4	16	no	—
362	C₂²	—	4	4	no	—
363	C₂²	C₄₇×#381	1	4	yes	—
364	C₂²	C₄₇×#408	1	4	yes	—
365	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
366	C₂²	C₂×#117×C₄₇	1	2	yes	—
367	C₂²	C₂×#131×C₄₇	1	2	yes	—
368	C₂²	C₄₇×#568	1	2	yes	—
369	C₄	—	2	2	no	—
370	C₄	—	2	2	no	—
371	C₄	—	4	4	no	—
372	C₄	—	4	4	no	—
373	C₄	C₄₇×#381	1	4	yes	—
374	C₄	C₂×#123×C₄₇	1	2	yes	—
375	C₄	C₂×#123×C₄₇	1	2	yes	—
376	C₂	—	2	4	no	—
377	C₂	—	2	4	no	—
378	C₂	—	4	2	no	—
379	C₂	C₂×C₄₇×#381	1	1	yes	characteristic
380	C₂	C₂×C₄₇×#408	1	1	yes	characteristic
381	C₂	C₄₇×#2879	1	1	yes	characteristic
382	C₂	C₄₇×#2924	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₄₇×#1818	C₂	semidirect
5. C₄₇×#1817	C₂	semidirect
6. C₄₇×#1729	C₂	semidirect
26. C₄₇×#336	C₂²	semidirect
160. #20685	C₄₇	direct (N × H)
188. #1818	C₂×C₄₇	semidirect
189. #1817	C₂×C₄₇	semidirect
190. #1729	C₂×C₄₇	semidirect
217. #336	C₂²×C₄₇	semidirect
218. C₄₇	#20685	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×#117×C₄₇	2
C₂×C₄₇×#407	2
C₂²×C₂²⋊C₈×C₄₇	2
C₄₇×#1818	2
C₄₇×#1817	2
C₄₇×#1729	2
#20685	47

Subgroups — C47×#20685 #26060383

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#20685 #26060383