Subgroups — C₄₇×#17877 #26057575

Order 12032.

726 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#2975	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#2972	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1586	C₂	1	4	yes	maximal, complemented
5	C₄₇×#1581	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1564	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1478	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1478	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1452	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×C₄₇	C₄	1	1	yes	characteristic
11	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₄×D₈×C₄₇	C₄	1	2	yes	—
14	C₄×D₈×C₄₇	C₄	1	2	yes	—
15	C₄×D₈×C₄₇	C₂²	1	2	yes	—
16	C₄×D₈×C₄₇	C₂²	1	2	yes	—
17	C₄₇×#436	—	2	2	no	—
18	C₄₇×#436	C₂²	1	4	yes	complemented
19	C₈×D₄×C₄₇	—	2	2	no	—
20	C₈×D₄×C₄₇	C₂²	1	4	yes	complemented
21	C₄₇×#431	C₂²	1	1	yes	characteristic
22	C₄₇×#431	C₂²	1	1	yes	characteristic
23	C₄₇×#431	C₂²	1	1	yes	characteristic
24	C₄₇×#431	C₂²	1	1	yes	characteristic
25	C₂×#107×C₄₇	C₄	1	1	yes	characteristic
26	C₂×#102×C₄₇	C₄	1	1	yes	characteristic
27	C₂×#102×C₄₇	C₄	1	1	yes	characteristic
28	C₄₇×#407	—	2	2	no	—
29	C₂×C₂²⋊C₈×C₄₇	—	2	2	no	—
30	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#335	C₂²	1	2	yes	complemented
32	C₄₇×#334	C₂²	1	2	yes	complemented
33	C₄₇×D₄⋊C₈	C₂²	1	4	yes	complemented
34	C₄₇×D₄⋊C₈	C₂²	1	4	yes	complemented
35	C₄₇×#322	C₂²	1	2	yes	complemented
36	C₄₇×#322	C₂²	1	2	yes	complemented
37	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
38	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	—	2	1	no	—
40	C₂³×C₄×C₄₇	—	2	1	no	—
41	C₂×D₈×C₄₇	—	2	4	no	—
42	C₂×D₈×C₄₇	C₂×C₄	1	2	yes	—
43	C₂×D₈×C₄₇	C₂×C₄	1	2	yes	—
44	C₂×M₁₆×C₄₇	—	2	4	no	—
45	C₂²×C₈×C₄₇	—	2	4	no	—
46	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
48	C₄×D₄×C₄₇	—	2	1	no	—
49	C₄×D₄×C₄₇	—	2	1	no	—
50	C₄×D₄×C₄₇	—	2	1	no	—
51	C₄×D₄×C₄₇	—	2	1	no	—
52	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
53	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
54	C₄×D₄×C₄₇	C₂³	1	2	yes	—
55	C₄×D₄×C₄₇	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
60	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
61	#107×C₄₇	C₂×C₄	1	2	yes	—
62	#107×C₄₇	C₂×C₄	1	2	yes	—
63	C₄⋊C₈×C₄₇	—	2	1	no	—
64	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
65	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
66	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
67	#102×C₄₇	C₂×C₄	1	2	yes	—
68	#102×C₄₇	C₂×C₄	1	2	yes	—
69	#102×C₄₇	C₂×C₄	1	2	yes	—
70	#102×C₄₇	C₂×C₄	1	2	yes	—
71	C₂²⋊C₈×C₄₇	—	2	1	no	—
72	C₂²⋊C₈×C₄₇	—	2	1	no	—
73	C₂²⋊C₈×C₄₇	—	2	1	no	—
74	C₂²⋊C₈×C₄₇	—	2	4	no	—
75	C₂²⋊C₈×C₄₇	—	2	4	no	—
76	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
77	C₄×C₈×C₄₇	—	2	1	no	—
78	C₄×C₈×C₄₇	—	2	1	no	—
79	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₄₇	C₂³	1	2	yes	—
82	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
83	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₄×C₈×C₄₇	C₂³	1	2	yes	—
85	C₂⁴×C₄₇	—	2	1	no	—
86	C₂⁴×C₄₇	—	2	1	no	—
87	C₂×D₄×C₄₇	—	2	1	no	—
88	C₂×D₄×C₄₇	—	2	1	no	—
89	C₂×D₄×C₄₇	—	2	2	no	—
90	C₂×D₄×C₄₇	—	2	2	no	—
91	C₂×D₄×C₄₇	—	2	2	no	—
92	C₂×D₄×C₄₇	M₁₆	1	4	yes	complemented
93	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
94	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	—	2	1	no	—
96	C₂²×C₄×C₄₇	—	2	1	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	8	2	no	—
102	C₂²×C₄×C₄₇	—	8	2	no	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
106	D₈×C₄₇	—	2	4	no	—
107	D₈×C₄₇	—	2	4	no	—
108	M₁₆×C₄₇	—	8	4	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₂×C₈×C₄₇	—	8	4	no	—
115	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
120	C₄⋊C₄×C₄₇	—	2	1	no	—
121	C₄⋊C₄×C₄₇	—	2	1	no	—
122	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
123	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
124	C₂²⋊C₄×C₄₇	—	2	2	no	—
125	C₂²⋊C₄×C₄₇	—	2	2	no	—
126	C₂²⋊C₄×C₄₇	—	2	2	no	—
127	C₂²⋊C₄×C₄₇	—	2	2	no	—
128	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₄₇	#41	1	1	yes	characteristic
131	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
132	C₂³×C₄₇	—	2	2	no	—
133	C₂³×C₄₇	—	2	4	no	—
134	C₂³×C₄₇	—	2	2	no	—
135	C₂³×C₄₇	—	4	2	no	—
136	C₂³×C₄₇	—	8	1	no	—
137	C₂³×C₄₇	—	8	1	no	—
138	C₂³×C₄₇	—	8	1	no	—
139	C₂³×C₄₇	—	8	1	no	—
140	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
141	D₄×C₄₇	—	2	2	no	—
142	D₄×C₄₇	—	2	2	no	—
143	D₄×C₄₇	—	2	2	no	—
144	D₄×C₄₇	—	2	4	no	—
145	D₄×C₄₇	—	4	2	no	—
146	D₄×C₄₇	C₂×M₁₆	1	4	yes	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	4	1	no	—
151	C₂×C₄×C₄₇	—	4	4	no	—
152	C₂×C₄×C₄₇	—	4	4	no	—
153	C₂×C₄×C₄₇	—	8	2	no	—
154	C₂×C₄×C₄₇	—	8	2	no	—
155	C₂×C₄×C₄₇	—	8	1	no	—
156	C₂×C₄×C₄₇	—	8	1	no	—
157	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
161	C₂×C₄×C₄₇	#131	1	2	yes	—
162	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
165	C₈×C₄₇	—	2	1	no	—
166	C₈×C₄₇	—	2	1	no	—
167	C₈×C₄₇	—	2	1	no	—
168	C₈×C₄₇	—	2	1	no	—
169	C₈×C₄₇	—	2	4	no	—
170	C₈×C₄₇	—	4	2	no	—
171	C₈×C₄₇	—	4	2	no	—
172	C₈×C₄₇	—	4	2	no	—
173	#17877	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂²×C₄₇	—	2	1	no	—
175	C₂²×C₄₇	—	2	1	no	—
176	C₂²×C₄₇	—	2	4	no	—
177	C₂²×C₄₇	—	4	2	no	—
178	C₂²×C₄₇	—	4	2	no	—
179	C₂²×C₄₇	—	4	2	no	—
180	C₂²×C₄₇	—	4	2	no	—
181	C₂²×C₄₇	—	4	2	no	—
182	C₂²×C₄₇	—	8	4	no	—
183	C₂²×C₄₇	—	8	4	no	—
184	C₂²×C₄₇	#435	1	2	yes	—
185	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
186	C₄×C₄₇	—	2	1	no	—
187	C₄×C₄₇	—	2	1	no	—
188	C₄×C₄₇	—	2	1	no	—
189	C₄×C₄₇	—	4	2	no	—
190	C₄×C₄₇	—	4	2	no	—
191	C₄×C₄₇	#435	1	2	yes	—
192	C₄×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
193	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
194	C₄×C₄₇	#576	1	2	yes	—
195	#2975	C₂×C₄₇	1	1	yes	characteristic, complemented
196	#2972	C₂×C₄₇	1	1	yes	characteristic, complemented
197	C₂×C₄×D₈	C₂×C₄₇	1	1	yes	characteristic
198	#1586	C₂×C₄₇	1	4	yes	complemented
199	#1581	C₂×C₄₇	1	4	yes	complemented
200	#1564	C₂×C₄₇	1	1	yes	characteristic, complemented
201	#1478	C₂×C₄₇	1	1	yes	characteristic, complemented
202	#1478	C₂×C₄₇	1	1	yes	characteristic, complemented
203	#1452	C₂×C₄₇	1	1	yes	characteristic, complemented
204	C₂×C₄₇	—	2	2	no	—
205	C₂×C₄₇	—	4	4	no	—
206	C₂×C₄₇	—	8	2	no	—
207	C₂×C₄₇	C₂×#435	1	1	yes	characteristic
208	C₂×C₄₇	#2948	1	1	yes	characteristic
209	C₂×C₄₇	#2957	1	1	yes	characteristic
210	C₂²×D₈	C₄×C₄₇	1	1	yes	characteristic
211	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
212	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
213	C₄×D₈	C₄×C₄₇	1	2	yes	—
214	C₄×D₈	C₄×C₄₇	1	2	yes	—
215	C₄×D₈	C₂²×C₄₇	1	2	yes	—
216	C₄×D₈	C₂²×C₄₇	1	2	yes	—
217	#436	—	2	2	no	—
218	#436	C₂²×C₄₇	1	4	yes	complemented
219	C₈×D₄	—	2	2	no	—
220	C₈×D₄	C₂²×C₄₇	1	4	yes	complemented
221	#431	C₂²×C₄₇	1	1	yes	characteristic
222	#431	C₂²×C₄₇	1	1	yes	characteristic
223	#431	C₂²×C₄₇	1	1	yes	characteristic
224	#431	C₂²×C₄₇	1	1	yes	characteristic
225	C₂×#107	C₄×C₄₇	1	1	yes	characteristic
226	C₂×#102	C₄×C₄₇	1	1	yes	characteristic
227	C₂×#102	C₄×C₄₇	1	1	yes	characteristic
228	#407	—	2	2	no	—
229	C₂×C₂²⋊C₈	—	2	2	no	—
230	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
231	#335	C₂²×C₄₇	1	2	yes	complemented
232	#334	C₂²×C₄₇	1	2	yes	complemented
233	D₄⋊C₈	C₂²×C₄₇	1	4	yes	complemented
234	D₄⋊C₈	C₂²×C₄₇	1	4	yes	complemented
235	#322	C₂²×C₄₇	1	2	yes	complemented
236	#322	C₂²×C₄₇	1	2	yes	complemented
237	C₄₇	#17877	1	1	yes	characteristic, direct product factor, Sylow
238	C₂²×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
239	C₂²×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
240	C₂³×C₄	—	2	1	no	—
241	C₂³×C₄	—	2	1	no	—
242	C₂×D₈	—	2	4	no	—
243	C₂×D₈	C₂×C₄×C₄₇	1	2	yes	—
244	C₂×D₈	C₂×C₄×C₄₇	1	2	yes	—
245	C₂×M₁₆	—	2	4	no	—
246	C₂²×C₈	—	2	4	no	—
247	C₂²×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
248	C₂²×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	C₂×C₄×C₄₇	1	2	yes	—
254	C₄×D₄	C₂×C₄×C₄₇	1	2	yes	—
255	C₄×D₄	C₂³×C₄₇	1	2	yes	—
256	C₄×D₄	C₂³×C₄₇	1	2	yes	—
257	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	—	2	1	no	—
260	C₂×C₂²⋊C₄	—	2	1	no	—
261	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
262	#107	C₂×C₄×C₄₇	1	2	yes	—
263	#107	C₂×C₄×C₄₇	1	2	yes	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	D₄×C₄₇	1	2	yes	—
266	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
267	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
268	#102	C₂×C₄×C₄₇	1	2	yes	—
269	#102	C₂×C₄×C₄₇	1	2	yes	—
270	#102	C₂×C₄×C₄₇	1	2	yes	—
271	#102	C₂×C₄×C₄₇	1	2	yes	—
272	C₂²⋊C₈	—	2	1	no	—
273	C₂²⋊C₈	—	2	1	no	—
274	C₂²⋊C₈	—	2	1	no	—
275	C₂²⋊C₈	—	2	4	no	—
276	C₂²⋊C₈	—	2	4	no	—
277	C₂²⋊C₈	D₄×C₄₇	1	2	yes	—
278	C₄×C₈	—	2	1	no	—
279	C₄×C₈	—	2	1	no	—
280	C₄×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
281	C₄×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
282	C₄×C₈	C₂³×C₄₇	1	2	yes	—
283	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
285	C₄×C₈	C₂³×C₄₇	1	2	yes	—
286	C₂⁴	—	2	1	no	—
287	C₂⁴	—	2	1	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	M₁₆×C₄₇	1	4	yes	complemented
294	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
295	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	8	2	no	—
303	C₂²×C₄	—	8	2	no	—
304	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
306	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
307	D₈	—	2	4	no	—
308	D₈	—	2	4	no	—
309	M₁₆	—	8	4	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	8	4	no	—
316	C₂×C₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
317	C₂×C₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
318	C₂×C₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
319	C₂×C₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
320	C₂×C₈	C₂×D₄×C₄₇	1	4	yes	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
324	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
325	C₂²⋊C₄	—	2	2	no	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
330	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
331	C₄²	#41×C₄₇	1	1	yes	characteristic
332	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
333	C₂³	—	2	2	no	—
334	C₂³	—	2	4	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	8	1	no	—
338	C₂³	—	8	1	no	—
339	C₂³	—	8	1	no	—
340	C₂³	—	8	1	no	—
341	C₂³	C₄×D₄×C₄₇	1	1	yes	characteristic
342	D₄	—	2	2	no	—
343	D₄	—	2	2	no	—
344	D₄	—	2	2	no	—
345	D₄	—	2	4	no	—
346	D₄	—	4	2	no	—
347	D₄	C₂×M₁₆×C₄₇	1	4	yes	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	8	2	no	—
355	C₂×C₄	—	8	2	no	—
356	C₂×C₄	—	8	1	no	—
357	C₂×C₄	—	8	1	no	—
358	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
359	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
360	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
361	C₂×C₄	C₂×M₁₆×C₄₇	1	2	yes	—
362	C₂×C₄	#131×C₄₇	1	2	yes	—
363	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
364	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
365	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
366	C₈	—	2	1	no	—
367	C₈	—	2	1	no	—
368	C₈	—	2	1	no	—
369	C₈	—	2	1	no	—
370	C₈	—	2	4	no	—
371	C₈	—	4	2	no	—
372	C₈	—	4	2	no	—
373	C₈	—	4	2	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	4	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	8	4	no	—
383	C₂²	—	8	4	no	—
384	C₂²	C₄₇×#435	1	2	yes	—
385	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	4	2	no	—
390	C₄	—	4	2	no	—
391	C₄	C₄₇×#435	1	2	yes	—
392	C₄	C₂²×M₁₆×C₄₇	1	1	yes	characteristic
393	C₄	C₂×#131×C₄₇	1	1	yes	characteristic
394	C₄	C₄₇×#576	1	2	yes	—
395	C₂	—	2	2	no	—
396	C₂	—	4	4	no	—
397	C₂	—	8	2	no	—
398	C₂	C₂×C₄₇×#435	1	1	yes	characteristic
399	C₂	C₄₇×#2948	1	1	yes	characteristic
400	C₂	C₄₇×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₄²	C₂⁴×C₄₇
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂²×D₈×C₄₇	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₇ ◁ C₄₇×#431 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₇×#2975	C₂	semidirect
2. C₄₇×#2972	C₂	semidirect
4. C₄₇×#1586	C₂	semidirect
5. C₄₇×#1581	C₂	semidirect
6. C₄₇×#1564	C₂	semidirect
7. C₄₇×#1478	C₂	semidirect
8. C₄₇×#1478	C₂	semidirect
9. C₄₇×#1452	C₂	semidirect
18. C₄₇×#436	C₂²	semidirect
20. C₈×D₄×C₄₇	C₂²	semidirect
31. C₄₇×#335	C₂²	semidirect
32. C₄₇×#334	C₂²	semidirect
33. C₄₇×D₄⋊C₈	C₂²	semidirect
34. C₄₇×D₄⋊C₈	C₂²	semidirect
35. C₄₇×#322	C₂²	semidirect
36. C₄₇×#322	C₂²	semidirect
92. C₂×D₄×C₄₇	M₁₆	semidirect
173. #17877	C₄₇	direct (N × H)
195. #2975	C₂×C₄₇	semidirect
196. #2972	C₂×C₄₇	semidirect
198. #1586	C₂×C₄₇	semidirect
199. #1581	C₂×C₄₇	semidirect
200. #1564	C₂×C₄₇	semidirect
201. #1478	C₂×C₄₇	semidirect
202. #1478	C₂×C₄₇	semidirect
203. #1452	C₂×C₄₇	semidirect
218. #436	C₂²×C₄₇	semidirect
220. C₈×D₄	C₂²×C₄₇	semidirect
231. #335	C₂²×C₄₇	semidirect
232. #334	C₂²×C₄₇	semidirect
233. D₄⋊C₈	C₂²×C₄₇	semidirect
234. D₄⋊C₈	C₂²×C₄₇	semidirect
235. #322	C₂²×C₄₇	semidirect
236. #322	C₂²×C₄₇	semidirect
237. C₄₇	#17877	direct (N × H)
293. C₂×D₄	M₁₆×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#2975	2
C₄₇×#2972	2
C₂×C₄×D₈×C₄₇	2
C₄₇×#1586	2
C₄₇×#1581	2
C₄₇×#1564	2
C₄₇×#1478	2
C₄₇×#1452	2
#17877	47

Subgroups — C47×#17877 #26057575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#17877 #26057575