Subgroups — C₄₇×#7915 #26047613

Order 12032.

1026 conjugacy classes of subgroups.

The subgroup lattice has 408 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	1	yes	maximal, characteristic
2	C₂²×C₂²⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₇×#380	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1280	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
6	C₂²×M₁₆×C₄₇	—	2	1	no	—
7	C₂³×C₈×C₄₇	—	2	1	no	—
8	C₂²×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
9	C₂²×C₂²⋊C₄×C₄₇	C₄	1	2	yes	—
10	C₄₇×#407	—	2	2	no	—
11	C₄₇×#407	C₄	1	4	yes	complemented
12	C₂×C₂²⋊C₈×C₄₇	—	2	2	no	—
13	C₂×C₂²⋊C₈×C₄₇	—	2	1	no	—
14	C₂×C₂²⋊C₈×C₄₇	—	2	1	no	—
15	C₂×C₂²⋊C₈×C₄₇	C₄	1	4	yes	complemented
16	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
17	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
18	C₄₇×#380	—	2	1	no	—
19	C₄₇×#380	—	2	1	no	—
20	C₄₇×#380	—	2	1	no	—
21	C₄₇×#380	—	2	1	no	—
22	C₂×#95×C₄₇	C₂²	1	2	yes	—
23	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₄₇	—	4	4	no	—
25	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
27	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
28	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₄₇	D₄	1	2	yes	—
32	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₄₇	Q₈	1	2	yes	—
35	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₄₇	—	2	4	no	—
37	C₂×M₁₆×C₄₇	—	4	4	no	—
38	C₂²×C₈×C₄₇	—	2	4	no	—
39	C₂²×C₈×C₄₇	—	2	2	no	—
40	C₂²×C₈×C₄₇	—	2	2	no	—
41	C₂²×C₈×C₄₇	—	4	4	no	—
42	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
43	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
45	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
46	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
47	C₂×C₂²⋊C₄×C₄₇	—	4	4	no	—
48	C₂²⋊C₈×C₄₇	—	2	4	no	—
49	C₂²⋊C₈×C₄₇	—	2	4	no	—
50	C₂²⋊C₈×C₄₇	—	2	2	no	—
51	C₂²⋊C₈×C₄₇	—	2	2	no	—
52	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
53	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
54	#95×C₄₇	—	2	2	no	—
55	#95×C₄₇	—	2	2	no	—
56	C₂⁴×C₄₇	—	2	2	no	—
57	C₂⁴×C₄₇	—	2	2	no	—
58	C₂⁴×C₄₇	—	2	4	no	—
59	C₂⁴×C₄₇	—	4	2	no	—
60	C₂⁴×C₄₇	C₄²	1	2	yes	—
61	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
62	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
63	C₂⁴×C₄₇	C₄⋊C₄	1	2	yes	—
64	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₇	—	2	4	no	—
66	C₂²×C₄×C₄₇	—	2	4	no	—
67	C₂²×C₄×C₄₇	—	2	4	no	—
68	C₂²×C₄×C₄₇	—	2	4	no	—
69	C₂²×C₄×C₄₇	—	2	8	no	—
70	C₂²×C₄×C₄₇	—	4	4	no	—
71	C₂²×C₄×C₄₇	—	4	4	no	—
72	C₂²×C₄×C₄₇	—	4	4	no	—
73	C₂²×C₄×C₄₇	—	4	4	no	—
74	C₂²×C₄×C₄₇	—	4	2	no	—
75	C₂²×C₄×C₄₇	—	4	2	no	—
76	C₂²×C₄×C₄₇	—	4	2	no	—
77	C₂²×C₄×C₄₇	—	4	4	no	—
78	C₂²×C₄×C₄₇	—	4	4	no	—
79	C₂²×C₄×C₄₇	C₄²	1	2	yes	—
80	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
82	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
83	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
84	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
85	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
87	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
89	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	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	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
97	M₁₆×C₄₇	—	4	8	no	—
98	C₂×C₈×C₄₇	—	2	4	no	—
99	C₂×C₈×C₄₇	—	2	4	no	—
100	C₂×C₈×C₄₇	—	4	4	no	—
101	C₂×C₈×C₄₇	—	4	8	no	—
102	C₂×C₈×C₄₇	—	4	4	no	—
103	C₄⋊C₄×C₄₇	—	4	4	no	—
104	C₄⋊C₄×C₄₇	—	4	4	no	—
105	C₂²⋊C₄×C₄₇	—	4	4	no	—
106	C₂²⋊C₄×C₄₇	—	4	4	no	—
107	C₂³×C₄₇	—	2	2	no	—
108	C₂³×C₄₇	—	2	2	no	—
109	C₂³×C₄₇	—	2	2	no	—
110	C₂³×C₄₇	—	2	1	no	—
111	C₂³×C₄₇	—	2	1	no	—
112	C₂³×C₄₇	—	2	4	no	—
113	C₂³×C₄₇	—	2	4	no	—
114	C₂³×C₄₇	—	2	4	no	—
115	C₂³×C₄₇	—	2	2	no	—
116	C₂³×C₄₇	—	2	2	no	—
117	C₂³×C₄₇	—	2	1	no	—
118	C₂³×C₄₇	—	2	1	no	—
119	C₂³×C₄₇	—	2	4	no	—
120	C₂³×C₄₇	—	4	2	no	—
121	C₂³×C₄₇	—	4	2	no	—
122	C₂³×C₄₇	—	4	8	no	—
123	C₂³×C₄₇	—	4	8	no	—
124	C₂³×C₄₇	#95	1	2	yes	—
125	C₂³×C₄₇	#95	1	2	yes	—
126	C₂³×C₄₇	#100	1	2	yes	—
127	C₂³×C₄₇	#101	1	2	yes	—
128	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
129	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂³×C₄₇	#131	1	4	yes	—
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	2	4	no	—
136	C₂×C₄×C₄₇	—	2	4	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	—	4	2	no	—
142	C₂×C₄×C₄₇	—	4	2	no	—
143	C₂×C₄×C₄₇	—	4	2	no	—
144	C₂×C₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	—	4	1	no	—
146	C₂×C₄×C₄₇	—	4	1	no	—
147	C₂×C₄×C₄₇	—	4	1	no	—
148	C₂×C₄×C₄₇	—	4	1	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	—	8	8	no	—
153	C₂×C₄×C₄₇	#95	1	2	yes	—
154	C₂×C₄×C₄₇	#95	1	2	yes	—
155	C₂×C₄×C₄₇	#99	1	4	yes	—
156	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₈×C₄₇	—	4	4	no	—
161	C₈×C₄₇	—	4	4	no	—
162	#7915	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂²×C₄₇	—	2	4	no	—
164	C₂²×C₄₇	—	2	4	no	—
165	C₂²×C₄₇	—	2	4	no	—
166	C₂²×C₄₇	—	2	4	no	—
167	C₂²×C₄₇	—	2	2	no	—
168	C₂²×C₄₇	—	2	2	no	—
169	C₂²×C₄₇	—	2	1	no	—
170	C₂²×C₄₇	—	2	1	no	—
171	C₂²×C₄₇	—	2	1	no	—
172	C₂²×C₄₇	—	2	1	no	—
173	C₂²×C₄₇	—	2	2	no	—
174	C₂²×C₄₇	—	2	2	no	—
175	C₂²×C₄₇	—	2	2	no	—
176	C₂²×C₄₇	—	4	8	no	—
177	C₂²×C₄₇	—	4	8	no	—
178	C₂²×C₄₇	—	4	2	no	—
179	C₂²×C₄₇	—	4	2	no	—
180	C₂²×C₄₇	#343	1	4	yes	—
181	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
182	C₂²×C₄₇	#405	1	2	yes	—
183	C₂²×C₄₇	#408	1	2	yes	—
184	C₂²×C₄₇	C₂×#99	1	2	yes	—
185	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
186	C₂²×C₄₇	C₂×#101	1	1	yes	characteristic
187	C₂²×C₄₇	#424	1	2	yes	—
188	C₄×C₄₇	—	2	1	no	—
189	C₄×C₄₇	—	2	1	no	—
190	C₄×C₄₇	—	2	2	no	—
191	C₄×C₄₇	—	2	1	no	—
192	C₄×C₄₇	—	2	1	no	—
193	C₄×C₄₇	—	8	4	no	—
194	C₄×C₄₇	#342	1	4	yes	—
195	C₂×#407	C₂×C₄₇	1	1	yes	characteristic
196	C₂²×C₂²⋊C₈	C₂×C₄₇	1	1	yes	characteristic
197	C₂×#380	C₂×C₄₇	1	1	yes	characteristic
198	#1280	C₂×C₄₇	1	4	yes	complemented
199	C₂×C₄₇	—	2	4	no	—
200	C₂×C₄₇	—	2	2	no	—
201	C₂×C₄₇	—	2	2	no	—
202	C₂×C₄₇	—	4	2	no	—
203	C₂×C₄₇	#1471	1	2	yes	—
204	C₂×C₄₇	#1472	1	2	yes	—
205	C₂×C₄₇	#1729	1	1	yes	characteristic
206	C₂×C₄₇	C₂×#342	1	1	yes	characteristic
207	C₂×C₄₇	C₂×#343	1	1	yes	characteristic
208	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
209	C₂²×M₁₆	—	2	1	no	—
210	C₂³×C₈	—	2	1	no	—
211	C₂²×C₄⋊C₄	C₄×C₄₇	1	2	yes	—
212	C₂²×C₂²⋊C₄	C₄×C₄₇	1	2	yes	—
213	#407	—	2	2	no	—
214	#407	C₄×C₄₇	1	4	yes	complemented
215	C₂×C₂²⋊C₈	—	2	1	no	—
216	C₂×C₂²⋊C₈	—	2	2	no	—
217	C₂×C₂²⋊C₈	—	2	1	no	—
218	C₂×C₂²⋊C₈	C₄×C₄₇	1	4	yes	complemented
219	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
220	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
221	#380	—	2	1	no	—
222	#380	—	2	1	no	—
223	#380	—	2	1	no	—
224	#380	—	2	1	no	—
225	C₂×#95	C₂²×C₄₇	1	2	yes	—
226	C₄₇	#7915	1	1	yes	characteristic, direct product factor, Sylow
227	C₂⁵	C₂×C₄×C₄₇	1	1	yes	characteristic
228	C₂³×C₄	—	4	4	no	—
229	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
230	C₂³×C₄	C₂×C₄×C₄₇	1	4	yes	—
231	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
232	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
233	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
234	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
235	C₂³×C₄	D₄×C₄₇	1	2	yes	—
236	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
237	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
238	C₂³×C₄	Q₈×C₄₇	1	2	yes	—
239	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
240	C₂×M₁₆	—	2	4	no	—
241	C₂×M₁₆	—	4	4	no	—
242	C₂²×C₈	—	2	4	no	—
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	2	2	no	—
245	C₂²×C₈	—	4	4	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	4	4	no	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₂²⋊C₄	—	4	4	no	—
252	C₂²⋊C₈	—	2	4	no	—
253	C₂²⋊C₈	—	2	4	no	—
254	C₂²⋊C₈	—	2	2	no	—
255	C₂²⋊C₈	—	2	2	no	—
256	C₂²⋊C₈	C₂×C₄×C₄₇	1	4	yes	—
257	C₂²⋊C₈	C₂×C₄×C₄₇	1	4	yes	—
258	#95	—	2	2	no	—
259	#95	—	2	2	no	—
260	C₂⁴	—	2	4	no	—
261	C₂⁴	—	2	2	no	—
262	C₂⁴	—	2	2	no	—
263	C₂⁴	—	4	2	no	—
264	C₂⁴	C₄²×C₄₇	1	2	yes	—
265	C₂⁴	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
266	C₂⁴	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
267	C₂⁴	C₄⋊C₄×C₄₇	1	2	yes	—
268	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	8	no	—
274	C₂²×C₄	—	4	4	no	—
275	C₂²×C₄	—	4	4	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	—	4	4	no	—
282	C₂²×C₄	—	4	4	no	—
283	C₂²×C₄	C₄²×C₄₇	1	2	yes	—
284	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
285	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
286	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
287	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
288	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
289	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
290	C₂²×C₄	C₄⋊C₄×C₄₇	1	2	yes	—
291	C₂²×C₄	C₄⋊C₄×C₄₇	1	2	yes	—
292	C₂²×C₄	C₄⋊C₄×C₄₇	1	2	yes	—
293	C₂²×C₄	C₄⋊C₄×C₄₇	1	2	yes	—
294	C₂²×C₄	C₄⋊C₄×C₄₇	1	2	yes	—
295	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
296	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
300	C₂²×C₄	C₂×Q₈×C₄₇	1	1	yes	characteristic
301	M₁₆	—	4	8	no	—
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	4	4	no	—
305	C₂×C₈	—	4	8	no	—
306	C₂×C₈	—	4	4	no	—
307	C₄⋊C₄	—	4	4	no	—
308	C₄⋊C₄	—	4	4	no	—
309	C₂²⋊C₄	—	4	4	no	—
310	C₂²⋊C₄	—	4	4	no	—
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	—	2	2	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	4	no	—
317	C₂³	—	2	4	no	—
318	C₂³	—	2	4	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	1	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	2	4	no	—
324	C₂³	—	4	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	8	no	—
327	C₂³	—	4	8	no	—
328	C₂³	#95×C₄₇	1	2	yes	—
329	C₂³	#95×C₄₇	1	2	yes	—
330	C₂³	#100×C₄₇	1	2	yes	—
331	C₂³	#101×C₄₇	1	2	yes	—
332	C₂³	C₂×C₄²×C₄₇	1	1	yes	characteristic
333	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
334	C₂³	C₂×C₄⋊C₄×C₄₇	1	1	yes	characteristic
335	C₂³	#131×C₄₇	1	4	yes	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	8	8	no	—
357	C₂×C₄	#95×C₄₇	1	2	yes	—
358	C₂×C₄	#95×C₄₇	1	2	yes	—
359	C₂×C₄	#99×C₄₇	1	4	yes	—
360	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
361	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
362	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	1	yes	characteristic
364	C₈	—	4	4	no	—
365	C₈	—	4	4	no	—
366	C₂²	—	2	4	no	—
367	C₂²	—	2	4	no	—
368	C₂²	—	2	4	no	—
369	C₂²	—	2	4	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	4	8	no	—
380	C₂²	—	4	8	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	2	no	—
383	C₂²	C₄₇×#343	1	4	yes	—
384	C₂²	C₂×#95×C₄₇	1	1	yes	characteristic
385	C₂²	C₄₇×#405	1	2	yes	—
386	C₂²	C₄₇×#408	1	2	yes	—
387	C₂²	C₂×#99×C₄₇	1	2	yes	—
388	C₂²	C₂×#100×C₄₇	1	1	yes	characteristic
389	C₂²	C₂×#101×C₄₇	1	1	yes	characteristic
390	C₂²	C₄₇×#424	1	2	yes	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	2	no	—
396	C₄	—	8	4	no	—
397	C₄	C₄₇×#342	1	4	yes	—
398	C₂	—	2	4	no	—
399	C₂	—	2	2	no	—
400	C₂	—	2	2	no	—
401	C₂	—	4	2	no	—
402	C₂	C₄₇×#1471	1	2	yes	—
403	C₂	C₄₇×#1472	1	2	yes	—
404	C₂	C₄₇×#1729	1	1	yes	characteristic
405	C₂	C₂×C₄₇×#342	1	1	yes	characteristic
406	C₂	C₂×C₄₇×#343	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂×C₂²⋊C₄
commutator	C₂³	C₂×C₄²×C₄₇
Frattini, cosocle	C₂³×C₄	C₂³×C₄₇
prime radical	C₂⁵×C₄₇	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂⁴×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄₇×#1280	C₂	semidirect
11. C₄₇×#407	C₄	semidirect
15. C₂×C₂²⋊C₈×C₄₇	C₄	semidirect
162. #7915	C₄₇	direct (N × H)
198. #1280	C₂×C₄₇	semidirect
214. #407	C₄×C₄₇	semidirect
218. C₂×C₂²⋊C₈	C₄×C₄₇	semidirect
226. C₄₇	#7915	direct (N × H)

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
C₂²×C₂²⋊C₈×C₄₇	2
C₂×C₄₇×#380	2
C₄₇×#1280	2
#7915	47

Subgroups — C47×#7915 #26047613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#7915 #26047613