Subgroups — C₄₇×#8016 #26047714

Order 12032.

1026 conjugacy classes of subgroups.

The subgroup lattice has 414 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	C₄₇×#2280	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₇×#380	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1294	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
6	C₂²×M₁₆×C₄₇	—	2	1	no	—
7	C₂×#117×C₄₇	C₄	1	2	yes	complemented
8	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
9	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
10	C₄₇×#407	—	2	2	no	—
11	C₄₇×#407	C₄	1	4	yes	complemented
12	C₂×C₂²⋊C₈×C₄₇	—	2	1	no	—
13	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
14	C₄₇×#381	—	2	1	no	—
15	C₄₇×#380	—	2	2	no	—
16	C₄₇×#380	C₄	1	4	yes	complemented
17	C₄₇×#380	C₄	1	2	yes	complemented
18	C₄₇×#380	C₂²	1	2	yes	—
19	C₄₇×#379	—	2	1	no	—
20	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
21	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
22	C₂×#95×C₄₇	C₂²	1	2	yes	—
23	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₄₇	—	2	2	no	—
25	C₂³×C₄×C₄₇	—	4	4	no	—
26	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
28	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₄₇	D₄	1	2	yes	—
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	2	no	—
39	#117×C₄₇	—	4	4	no	—
40	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
41	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
42	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
43	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
44	C₂×C₂²⋊C₄×C₄₇	—	2	2	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	C₂×C₄²×C₄₇	—	2	2	no	—
49	C₂²⋊C₈×C₄₇	—	2	4	no	—
50	C₂²⋊C₈×C₄₇	—	2	2	no	—
51	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
52	#95×C₄₇	—	2	2	no	—
53	#95×C₄₇	—	2	2	no	—
54	#95×C₄₇	—	2	2	no	—
55	#95×C₄₇	C₂×C₄	1	4	yes	—
56	C₂⁴×C₄₇	—	2	2	no	—
57	C₂⁴×C₄₇	—	2	2	no	—
58	C₂⁴×C₄₇	—	4	2	no	—
59	C₂⁴×C₄₇	—	4	2	no	—
60	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
61	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
62	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
63	C₂⁴×C₄₇	C₄⋊C₄	1	2	yes	—
64	C₂⁴×C₄₇	C₂×D₄	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	4	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	—	4	4	no	—
80	C₂²×C₄×C₄₇	C₄²	1	2	yes	—
81	C₂²×C₄×C₄₇	C₄²	1	2	yes	—
82	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
83	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
85	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
86	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
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	C₄⋊C₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
98	M₁₆×C₄₇	—	4	8	no	—
99	C₂×C₈×C₄₇	—	2	4	no	—
100	C₂×C₈×C₄₇	—	4	4	no	—
101	C₄⋊C₄×C₄₇	—	4	8	no	—
102	C₄⋊C₄×C₄₇	—	4	4	no	—
103	C₂²⋊C₄×C₄₇	—	4	4	no	—
104	C₂²⋊C₄×C₄₇	—	4	8	no	—
105	C₂²⋊C₄×C₄₇	—	4	4	no	—
106	C₂²⋊C₄×C₄₇	—	4	2	no	—
107	C₂²⋊C₄×C₄₇	—	4	2	no	—
108	C₄²×C₄₇	—	4	4	no	—
109	C₂³×C₄₇	—	2	2	no	—
110	C₂³×C₄₇	—	2	2	no	—
111	C₂³×C₄₇	—	2	2	no	—
112	C₂³×C₄₇	—	2	2	no	—
113	C₂³×C₄₇	—	2	2	no	—
114	C₂³×C₄₇	—	2	2	no	—
115	C₂³×C₄₇	—	2	2	no	—
116	C₂³×C₄₇	—	2	2	no	—
117	C₂³×C₄₇	—	2	2	no	—
118	C₂³×C₄₇	—	2	2	no	—
119	C₂³×C₄₇	—	2	4	no	—
120	C₂³×C₄₇	—	4	2	no	—
121	C₂³×C₄₇	—	4	2	no	—
122	C₂³×C₄₇	—	4	2	no	—
123	C₂³×C₄₇	—	4	2	no	—
124	C₂³×C₄₇	—	4	8	no	—
125	C₂³×C₄₇	—	4	8	no	—
126	C₂³×C₄₇	#95	1	2	yes	—
127	C₂³×C₄₇	#95	1	2	yes	—
128	C₂³×C₄₇	C₂×C₂²⋊C₄	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	AGL(1,ℤ/8)	1	2	yes	—
132	C₂³×C₄₇	#137	1	2	yes	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	2	2	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	—	2	4	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	2	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	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	4	no	—
154	C₂×C₄×C₄₇	—	4	4	no	—
155	C₂×C₄×C₄₇	—	4	4	no	—
156	C₂×C₄×C₄₇	—	8	8	no	—
157	C₂×C₄×C₄₇	#95	1	2	yes	—
158	C₂×C₄×C₄₇	#95	1	2	yes	—
159	C₂×C₄×C₄₇	#99	1	4	yes	—
160	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₈×C₄₇	—	4	4	no	—
165	#8016	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂²×C₄₇	—	2	1	no	—
167	C₂²×C₄₇	—	2	1	no	—
168	C₂²×C₄₇	—	2	1	no	—
169	C₂²×C₄₇	—	2	1	no	—
170	C₂²×C₄₇	—	2	4	no	—
171	C₂²×C₄₇	—	2	4	no	—
172	C₂²×C₄₇	—	2	2	no	—
173	C₂²×C₄₇	—	2	2	no	—
174	C₂²×C₄₇	—	2	2	no	—
175	C₂²×C₄₇	—	2	2	no	—
176	C₂²×C₄₇	—	2	2	no	—
177	C₂²×C₄₇	—	2	2	no	—
178	C₂²×C₄₇	—	4	4	no	—
179	C₂²×C₄₇	—	4	4	no	—
180	C₂²×C₄₇	—	4	8	no	—
181	C₂²×C₄₇	—	4	4	no	—
182	C₂²×C₄₇	—	4	4	no	—
183	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
184	C₂²×C₄₇	C₂×#99	1	2	yes	—
185	C₂²×C₄₇	#417	1	2	yes	—
186	C₂²×C₄₇	#418	1	1	yes	characteristic
187	C₂²×C₄₇	#419	1	1	yes	characteristic
188	C₂²×C₄₇	#421	1	2	yes	—
189	C₂²×C₄₇	#428	1	2	yes	—
190	C₄×C₄₇	—	2	1	no	—
191	C₄×C₄₇	—	2	2	no	—
192	C₄×C₄₇	—	2	1	no	—
193	C₄×C₄₇	—	2	1	no	—
194	C₄×C₄₇	—	2	1	no	—
195	C₄×C₄₇	—	8	4	no	—
196	C₄×C₄₇	—	8	4	no	—
197	C₄×C₄₇	#342	1	4	yes	—
198	C₂×#407	C₂×C₄₇	1	1	yes	characteristic
199	#2280	C₂×C₄₇	1	1	yes	characteristic
200	C₂×#380	C₂×C₄₇	1	1	yes	characteristic
201	#1294	C₂×C₄₇	1	4	yes	complemented
202	C₂×C₄₇	—	2	1	no	—
203	C₂×C₄₇	—	2	1	no	—
204	C₂×C₄₇	—	2	2	no	—
205	C₂×C₄₇	—	4	2	no	—
206	C₂×C₄₇	—	4	2	no	—
207	C₂×C₄₇	#1513	1	4	yes	—
208	C₂×C₄₇	#1733	1	1	yes	characteristic
209	C₂×C₄₇	#1736	1	1	yes	characteristic
210	C₂×C₄₇	C₂×#342	1	1	yes	characteristic
211	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
212	C₂²×M₁₆	—	2	1	no	—
213	C₂×#117	C₄×C₄₇	1	2	yes	complemented
214	C₂²×C₄⋊C₄	—	2	1	no	—
215	C₂²×C₂²⋊C₄	—	2	1	no	—
216	#407	—	2	2	no	—
217	#407	C₄×C₄₇	1	4	yes	complemented
218	C₂×C₂²⋊C₈	—	2	1	no	—
219	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
220	#381	—	2	1	no	—
221	#380	—	2	2	no	—
222	#380	C₄×C₄₇	1	2	yes	complemented
223	#380	C₄×C₄₇	1	4	yes	complemented
224	#380	C₂²×C₄₇	1	2	yes	—
225	#379	—	2	1	no	—
226	C₄×C₂²⋊C₄	—	2	1	no	—
227	C₄×C₂²⋊C₄	—	2	1	no	—
228	C₂×#95	C₂²×C₄₇	1	2	yes	—
229	C₄₇	#8016	1	1	yes	characteristic, direct product factor, Sylow
230	C₂⁵	D₄×C₄₇	1	1	yes	characteristic
231	C₂³×C₄	—	2	2	no	—
232	C₂³×C₄	—	4	4	no	—
233	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
234	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
235	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
236	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
237	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
238	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
239	C₂³×C₄	D₄×C₄₇	1	2	yes	—
240	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
241	C₂³×C₄	Q₈×C₄₇	1	2	yes	—
242	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
243	C₂×M₁₆	—	2	4	no	—
244	C₂×M₁₆	—	4	4	no	—
245	C₂²×C₈	—	2	2	no	—
246	#117	—	4	4	no	—
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	4	4	no	—
249	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
250	C₂×C₂²⋊C₄	—	2	4	no	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₂²⋊C₄	—	4	4	no	—
255	C₂×C₄²	—	2	2	no	—
256	C₂²⋊C₈	—	2	4	no	—
257	C₂²⋊C₈	—	2	2	no	—
258	C₂²⋊C₈	C₂×C₄×C₄₇	1	4	yes	—
259	#95	—	2	2	no	—
260	#95	—	2	2	no	—
261	#95	—	2	2	no	—
262	#95	C₂×C₄×C₄₇	1	4	yes	—
263	C₂⁴	—	2	2	no	—
264	C₂⁴	—	2	2	no	—
265	C₂⁴	—	4	2	no	—
266	C₂⁴	—	4	2	no	—
267	C₂⁴	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
268	C₂⁴	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
269	C₂⁴	C₂²⋊C₄×C₄₇	1	2	yes	—
270	C₂⁴	C₄⋊C₄×C₄₇	1	2	yes	—
271	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
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	4	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	—	4	4	no	—
279	C₂²×C₄	—	4	4	no	—
280	C₂²×C₄	—	4	4	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	4	no	—
285	C₂²×C₄	—	4	4	no	—
286	C₂²×C₄	—	4	4	no	—
287	C₂²×C₄	C₄²×C₄₇	1	2	yes	—
288	C₂²×C₄	C₄²×C₄₇	1	2	yes	—
289	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
290	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
291	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
292	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
293	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
294	C₂²×C₄	C₄⋊C₄×C₄₇	1	2	yes	—
295	C₂²×C₄	C₄⋊C₄×C₄₇	1	2	yes	—
296	C₂²×C₄	C₄⋊C₄×C₄₇	1	2	yes	—
297	C₂²×C₄	C₄⋊C₄×C₄₇	1	2	yes	—
298	C₂²×C₄	C₄⋊C₄×C₄₇	1	2	yes	—
299	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
300	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
301	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
304	C₂²×C₄	C₂×Q₈×C₄₇	1	1	yes	characteristic
305	M₁₆	—	4	8	no	—
306	C₂×C₈	—	2	4	no	—
307	C₂×C₈	—	4	4	no	—
308	C₄⋊C₄	—	4	4	no	—
309	C₄⋊C₄	—	4	8	no	—
310	C₂²⋊C₄	—	4	4	no	—
311	C₂²⋊C₄	—	4	8	no	—
312	C₂²⋊C₄	—	4	4	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₄²	—	4	4	no	—
316	C₂³	—	2	2	no	—
317	C₂³	—	2	2	no	—
318	C₂³	—	2	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	2	2	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	2	no	—
326	C₂³	—	2	4	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	8	no	—
332	C₂³	—	4	8	no	—
333	C₂³	#95×C₄₇	1	2	yes	—
334	C₂³	#95×C₄₇	1	2	yes	—
335	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
336	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
337	C₂³	C₂×C₄⋊C₄×C₄₇	1	1	yes	characteristic
338	C₂³	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
339	C₂³	#137×C₄₇	1	2	yes	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	8	8	no	—
364	C₂×C₄	#95×C₄₇	1	2	yes	—
365	C₂×C₄	#95×C₄₇	1	2	yes	—
366	C₂×C₄	#99×C₄₇	1	4	yes	—
367	C₂×C₄	C₂×C₄²×C₄₇	1	1	yes	characteristic
368	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
369	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	1	yes	characteristic
370	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	1	yes	characteristic
371	C₈	—	4	4	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	4	no	—
386	C₂²	—	4	8	no	—
387	C₂²	—	4	4	no	—
388	C₂²	—	4	4	no	—
389	C₂²	C₂×#95×C₄₇	1	1	yes	characteristic
390	C₂²	C₂×#99×C₄₇	1	2	yes	—
391	C₂²	C₄₇×#417	1	2	yes	—
392	C₂²	C₄₇×#418	1	1	yes	characteristic
393	C₂²	C₄₇×#419	1	1	yes	characteristic
394	C₂²	C₄₇×#421	1	2	yes	—
395	C₂²	C₄₇×#428	1	2	yes	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	2	no	—
401	C₄	—	8	4	no	—
402	C₄	—	8	4	no	—
403	C₄	C₄₇×#342	1	4	yes	—
404	C₂	—	2	1	no	—
405	C₂	—	2	1	no	—
406	C₂	—	2	2	no	—
407	C₂	—	4	2	no	—
408	C₂	—	4	2	no	—
409	C₂	C₄₇×#1513	1	4	yes	—
410	C₂	C₄₇×#1733	1	1	yes	characteristic
411	C₂	C₄₇×#1736	1	1	yes	characteristic
412	C₂	C₂×C₄₇×#342	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₄₇
Frattini, cosocle	C₂³×C₄	C₂³×C₄₇
prime radical	C₂⁵×C₄₇	D₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ 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×#1294	C₂	semidirect
7. C₂×#117×C₄₇	C₄	semidirect
11. C₄₇×#407	C₄	semidirect
16. C₄₇×#380	C₄	semidirect
17. C₄₇×#380	C₄	semidirect
165. #8016	C₄₇	direct (N × H)
201. #1294	C₂×C₄₇	semidirect
213. C₂×#117	C₄×C₄₇	semidirect
217. #407	C₄×C₄₇	semidirect
222. #380	C₄×C₄₇	semidirect
223. #380	C₄×C₄₇	semidirect
229. C₄₇	#8016	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
C₄₇×#2280	2
C₂×C₄₇×#380	2
C₄₇×#1294	2
#8016	47

Subgroups — C47×#8016 #26047714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#8016 #26047714