Subgroups — C₄₇×#10738 #26050436

Order 12032.

1374 conjugacy classes of subgroups.

The subgroup lattice has 444 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	C₂×C₄₇×#407	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇×#344	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
6	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
7	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
8	C₂×#117×C₄₇	—	2	1	no	—
9	C₂×#117×C₄₇	—	2	1	no	—
10	C₂×#117×C₄₇	—	2	8	no	—
11	C₂×#117×C₄₇	C₄	1	2	yes	—
12	C₂×#117×C₄₇	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
14	C₂²×C₂²⋊C₄×C₄₇	C₄	1	2	yes	—
15	C₂²×C₄²×C₄₇	—	2	1	no	—
16	C₄₇×#407	—	2	2	no	—
17	C₄₇×#407	—	2	1	no	—
18	C₄₇×#407	—	2	1	no	—
19	C₄₇×#407	—	2	1	no	—
20	C₄₇×#407	—	2	1	no	—
21	C₄₇×#407	C₄	1	4	yes	complemented
22	C₂×C₂²⋊C₈×C₄₇	—	2	2	no	—
23	C₂×C₂²⋊C₈×C₄₇	C₄	1	4	yes	complemented
24	C₄₇×#344	—	2	8	no	—
25	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₄₇	—	2	4	no	—
27	C₂³×C₄×C₄₇	—	2	4	no	—
28	C₂³×C₄×C₄₇	—	2	2	no	—
29	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₄₇	D₄	1	2	yes	—
33	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	Q₈	1	2	yes	—
38	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
39	C₂×M₁₆×C₄₇	—	2	4	no	—
40	C₂×M₁₆×C₄₇	—	2	2	no	—
41	C₂×M₁₆×C₄₇	—	2	2	no	—
42	C₂×M₁₆×C₄₇	—	2	2	no	—
43	C₂×M₁₆×C₄₇	—	2	4	no	—
44	C₂×M₁₆×C₄₇	—	2	4	no	—
45	C₂×M₁₆×C₄₇	—	2	4	no	—
46	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
47	C₂²×C₈×C₄₇	—	2	2	no	—
48	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
49	#117×C₄₇	—	2	8	no	—
50	#117×C₄₇	—	2	8	no	—
51	#117×C₄₇	—	2	4	no	—
52	#117×C₄₇	—	2	8	no	—
53	#117×C₄₇	D₄	1	8	yes	—
54	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
59	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
60	C₂×C₄²×C₄₇	—	2	8	no	—
61	C₂×C₄²×C₄₇	—	2	2	no	—
62	C₂×C₄²×C₄₇	—	2	2	no	—
63	C₂²⋊C₈×C₄₇	—	2	4	no	—
64	C₂²⋊C₈×C₄₇	—	2	4	no	—
65	C₂²⋊C₈×C₄₇	—	2	4	no	—
66	C₂²⋊C₈×C₄₇	—	2	4	no	—
67	C₂⁴×C₄₇	—	2	2	no	—
68	C₂⁴×C₄₇	—	2	2	no	—
69	C₂⁴×C₄₇	—	4	4	no	—
70	C₂⁴×C₄₇	C₄²	1	2	yes	—
71	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
72	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
73	C₂⁴×C₄₇	C₄⋊C₄	1	2	yes	—
74	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	—	2	2	no	—
76	C₂²×C₄×C₄₇	—	2	2	no	—
77	C₂²×C₄×C₄₇	—	2	8	no	—
78	C₂²×C₄×C₄₇	—	2	8	no	—
79	C₂²×C₄×C₄₇	—	2	2	no	—
80	C₂²×C₄×C₄₇	—	2	2	no	—
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	—	2	8	no	—
84	C₂²×C₄×C₄₇	—	2	8	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	8	no	—
90	C₂²×C₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	—	4	8	no	—
92	C₂²×C₄×C₄₇	C₄²	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂²⋊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	C₄⋊C₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	#41	1	4	yes	—
112	M₁₆×C₄₇	—	2	8	no	—
113	M₁₆×C₄₇	—	4	2	no	—
114	M₁₆×C₄₇	—	4	2	no	—
115	M₁₆×C₄₇	—	4	4	no	—
116	M₁₆×C₄₇	—	4	2	no	—
117	M₁₆×C₄₇	—	4	2	no	—
118	C₂×C₈×C₄₇	—	2	4	no	—
119	C₂×C₈×C₄₇	—	2	4	no	—
120	C₂×C₈×C₄₇	—	2	8	no	—
121	C₂×C₈×C₄₇	—	4	4	no	—
122	C₄⋊C₄×C₄₇	—	2	8	no	—
123	C₄⋊C₄×C₄₇	—	2	8	no	—
124	C₂²⋊C₄×C₄₇	—	2	8	no	—
125	C₂²⋊C₄×C₄₇	—	2	4	no	—
126	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
127	C₄²×C₄₇	—	2	8	no	—
128	C₄²×C₄₇	—	2	8	no	—
129	C₂³×C₄₇	—	2	4	no	—
130	C₂³×C₄₇	—	2	1	no	—
131	C₂³×C₄₇	—	2	1	no	—
132	C₂³×C₄₇	—	2	4	no	—
133	C₂³×C₄₇	—	2	4	no	—
134	C₂³×C₄₇	—	2	4	no	—
135	C₂³×C₄₇	—	2	1	no	—
136	C₂³×C₄₇	—	2	4	no	—
137	C₂³×C₄₇	—	2	1	no	—
138	C₂³×C₄₇	—	4	2	no	—
139	C₂³×C₄₇	—	4	2	no	—
140	C₂³×C₄₇	—	4	2	no	—
141	C₂³×C₄₇	—	4	2	no	—
142	C₂³×C₄₇	—	4	8	no	—
143	C₂³×C₄₇	—	4	8	no	—
144	C₂³×C₄₇	#95	1	2	yes	—
145	C₂³×C₄₇	#95	1	2	yes	—
146	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
147	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
149	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂³×C₄₇	#117	1	2	yes	—
151	C₂×C₄×C₄₇	—	2	4	no	—
152	C₂×C₄×C₄₇	—	2	1	no	—
153	C₂×C₄×C₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	2	4	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	4	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	—	2	4	no	—
163	C₂×C₄×C₄₇	—	2	4	no	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	2	8	no	—
166	C₂×C₄×C₄₇	—	4	16	no	—
167	C₂×C₄×C₄₇	—	4	8	no	—
168	C₂×C₄×C₄₇	#95	1	2	yes	—
169	C₂×C₄×C₄₇	#95	1	2	yes	—
170	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
175	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
176	C₂×C₄×C₄₇	#120	1	2	yes	—
177	C₂×C₄×C₄₇	#120	1	2	yes	—
178	C₂×C₄×C₄₇	#121	1	4	yes	—
179	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
180	C₂×C₄×C₄₇	#123	1	2	yes	—
181	C₂×C₄×C₄₇	#123	1	2	yes	—
182	C₈×C₄₇	—	4	4	no	—
183	C₈×C₄₇	—	4	4	no	—
184	#10738	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂²×C₄₇	—	2	4	no	—
186	C₂²×C₄₇	—	2	4	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	—	2	2	no	—
192	C₂²×C₄₇	—	2	2	no	—
193	C₂²×C₄₇	—	2	2	no	—
194	C₂²×C₄₇	—	2	2	no	—
195	C₂²×C₄₇	—	4	2	no	—
196	C₂²×C₄₇	—	4	2	no	—
197	C₂²×C₄₇	—	4	8	no	—
198	C₂²×C₄₇	—	4	8	no	—
199	C₂²×C₄₇	—	4	2	no	—
200	C₂²×C₄₇	—	4	2	no	—
201	C₂²×C₄₇	#344	1	4	yes	complemented
202	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
203	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
204	C₂²×C₄₇	#379	1	1	yes	characteristic
205	C₂²×C₄₇	#380	1	2	yes	—
206	C₂²×C₄₇	#381	1	1	yes	characteristic
207	C₄×C₄₇	—	2	2	no	—
208	C₄×C₄₇	—	2	2	no	—
209	C₄×C₄₇	—	4	8	no	—
210	C₄×C₄₇	#385	1	2	yes	—
211	C₄×C₄₇	#385	1	2	yes	—
212	C₄×C₄₇	#386	1	2	yes	—
213	C₄×C₄₇	#386	1	2	yes	—
214	C₂²×#117	C₂×C₄₇	1	1	yes	characteristic
215	C₂×#407	C₂×C₄₇	1	1	yes	characteristic
216	C₂×#407	C₂×C₄₇	1	1	yes	characteristic
217	C₂×#344	C₂×C₄₇	1	4	yes	complemented
218	C₂×C₄₇	—	2	1	no	—
219	C₂×C₄₇	—	2	4	no	—
220	C₂×C₄₇	—	2	1	no	—
221	C₂×C₄₇	—	2	2	no	—
222	C₂×C₄₇	—	2	2	no	—
223	C₂×C₄₇	—	4	2	no	—
224	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
225	C₂×C₄₇	C₂×#344	1	2	yes	—
226	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
227	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
228	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
229	C₂×#117	—	2	1	no	—
230	C₂×#117	—	2	1	no	—
231	C₂×#117	—	2	8	no	—
232	C₂×#117	C₄×C₄₇	1	2	yes	—
233	C₂×#117	C₂²×C₄₇	1	2	yes	—
234	C₂²×C₄⋊C₄	—	2	1	no	—
235	C₂²×C₂²⋊C₄	C₄×C₄₇	1	2	yes	—
236	C₂²×C₄²	—	2	1	no	—
237	#407	—	2	1	no	—
238	#407	—	2	1	no	—
239	#407	—	2	2	no	—
240	#407	—	2	1	no	—
241	#407	—	2	1	no	—
242	#407	C₄×C₄₇	1	4	yes	complemented
243	C₂×C₂²⋊C₈	—	2	2	no	—
244	C₂×C₂²⋊C₈	C₄×C₄₇	1	4	yes	complemented
245	#344	—	2	8	no	—
246	C₄₇	#10738	1	1	yes	characteristic, direct product factor, Sylow
247	C₂⁵	C₂×C₄×C₄₇	1	1	yes	characteristic
248	C₂³×C₄	—	2	4	no	—
249	C₂³×C₄	—	2	4	no	—
250	C₂³×C₄	—	2	2	no	—
251	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
252	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
253	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
254	C₂³×C₄	D₄×C₄₇	1	2	yes	—
255	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
256	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
257	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
258	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
259	C₂³×C₄	Q₈×C₄₇	1	2	yes	—
260	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
261	C₂×M₁₆	—	2	4	no	—
262	C₂×M₁₆	—	2	2	no	—
263	C₂×M₁₆	—	2	2	no	—
264	C₂×M₁₆	—	2	2	no	—
265	C₂×M₁₆	—	2	4	no	—
266	C₂×M₁₆	—	2	4	no	—
267	C₂×M₁₆	—	2	4	no	—
268	C₂×M₁₆	C₂×C₄×C₄₇	1	4	yes	complemented
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	C₂×C₄×C₄₇	1	4	yes	complemented
271	#117	—	2	8	no	—
272	#117	—	2	8	no	—
273	#117	—	2	4	no	—
274	#117	—	2	8	no	—
275	#117	D₄×C₄₇	1	8	yes	—
276	C₂×C₄⋊C₄	—	2	8	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	8	no	—
281	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
282	C₂×C₄²	—	2	8	no	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	—	2	2	no	—
285	C₂²⋊C₈	—	2	4	no	—
286	C₂²⋊C₈	—	2	4	no	—
287	C₂²⋊C₈	—	2	4	no	—
288	C₂²⋊C₈	—	2	4	no	—
289	C₂⁴	—	2	2	no	—
290	C₂⁴	—	2	2	no	—
291	C₂⁴	—	4	4	no	—
292	C₂⁴	C₄²×C₄₇	1	2	yes	—
293	C₂⁴	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
294	C₂⁴	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
295	C₂⁴	C₄⋊C₄×C₄₇	1	2	yes	—
296	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	8	no	—
300	C₂²×C₄	—	2	8	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	8	no	—
306	C₂²×C₄	—	2	8	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	8	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	4	8	no	—
314	C₂²×C₄	C₄²×C₄₇	1	2	yes	—
315	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
316	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
317	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
318	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
319	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
320	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
321	C₂²×C₄	C₄⋊C₄×C₄₇	1	2	yes	—
322	C₂²×C₄	C₄⋊C₄×C₄₇	1	2	yes	—
323	C₂²×C₄	C₄⋊C₄×C₄₇	1	2	yes	—
324	C₂²×C₄	C₄⋊C₄×C₄₇	1	2	yes	—
325	C₂²×C₄	C₄⋊C₄×C₄₇	1	2	yes	—
326	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
327	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
332	C₂²×C₄	C₂×Q₈×C₄₇	1	1	yes	characteristic
333	C₂²×C₄	#41×C₄₇	1	4	yes	—
334	M₁₆	—	2	8	no	—
335	M₁₆	—	4	2	no	—
336	M₁₆	—	4	2	no	—
337	M₁₆	—	4	4	no	—
338	M₁₆	—	4	2	no	—
339	M₁₆	—	4	2	no	—
340	C₂×C₈	—	2	4	no	—
341	C₂×C₈	—	2	4	no	—
342	C₂×C₈	—	2	8	no	—
343	C₂×C₈	—	4	4	no	—
344	C₄⋊C₄	—	2	8	no	—
345	C₄⋊C₄	—	2	8	no	—
346	C₂²⋊C₄	—	2	8	no	—
347	C₂²⋊C₄	—	2	4	no	—
348	C₂²⋊C₄	C₂²⋊C₄×C₄₇	1	8	yes	—
349	C₄²	—	2	8	no	—
350	C₄²	—	2	8	no	—
351	C₂³	—	2	4	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	4	no	—
355	C₂³	—	2	4	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	8	no	—
365	C₂³	—	4	8	no	—
366	C₂³	#95×C₄₇	1	2	yes	—
367	C₂³	#95×C₄₇	1	2	yes	—
368	C₂³	C₂×C₄²×C₄₇	1	1	yes	characteristic
369	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
370	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
371	C₂³	C₂×C₄⋊C₄×C₄₇	1	1	yes	characteristic
372	C₂³	#117×C₄₇	1	2	yes	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	8	no	—
388	C₂×C₄	—	4	16	no	—
389	C₂×C₄	—	4	8	no	—
390	C₂×C₄	#95×C₄₇	1	2	yes	—
391	C₂×C₄	#95×C₄₇	1	2	yes	—
392	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
393	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
394	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	1	yes	characteristic
395	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	1	yes	characteristic
396	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
397	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
398	C₂×C₄	#120×C₄₇	1	2	yes	—
399	C₂×C₄	#120×C₄₇	1	2	yes	—
400	C₂×C₄	#121×C₄₇	1	4	yes	—
401	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
402	C₂×C₄	#123×C₄₇	1	2	yes	—
403	C₂×C₄	#123×C₄₇	1	2	yes	—
404	C₈	—	4	4	no	—
405	C₈	—	4	4	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	2	4	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	8	no	—
419	C₂²	—	4	8	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	C₄₇×#344	1	4	yes	complemented
423	C₂²	C₂×#95×C₄₇	1	1	yes	characteristic
424	C₂²	C₄×C₂²⋊C₄×C₄₇	1	2	yes	—
425	C₂²	C₄₇×#379	1	1	yes	characteristic
426	C₂²	C₄₇×#380	1	2	yes	—
427	C₂²	C₄₇×#381	1	1	yes	characteristic
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	4	8	no	—
431	C₄	C₄₇×#385	1	2	yes	—
432	C₄	C₄₇×#385	1	2	yes	—
433	C₄	C₄₇×#386	1	2	yes	—
434	C₄	C₄₇×#386	1	2	yes	—
435	C₂	—	2	1	no	—
436	C₂	—	2	4	no	—
437	C₂	—	2	1	no	—
438	C₂	—	2	2	no	—
439	C₂	—	2	2	no	—
440	C₂	—	4	2	no	—
441	C₂	C₄₇×C₂²⋊#95	1	1	yes	characteristic
442	C₂	C₂×C₄₇×#344	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₇	C₂×C₂²⋊C₄
commutator	C₂³	C₂×C₄²×C₄₇
Frattini, cosocle	C₂³×C₄	C₂³×C₄₇
socle	C₂²×C₄₇	C₂×#95
prime radical	C₂⁵×C₄₇	C₂×C₄
LCS	G ▷ C₂³ ▷ 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
4. C₂×C₄₇×#344	C₂	semidirect
21. C₄₇×#407	C₄	semidirect
23. C₂×C₂²⋊C₈×C₄₇	C₄	semidirect
46. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
48. C₂²×C₈×C₄₇	C₂×C₄	semidirect
184. #10738	C₄₇	direct (N × H)
201. C₂²×C₄₇	#344	semidirect
217. C₂×#344	C₂×C₄₇	semidirect
242. #407	C₄×C₄₇	semidirect
244. C₂×C₂²⋊C₈	C₄×C₄₇	semidirect
246. C₄₇	#10738	direct (N × H)
268. C₂×M₁₆	C₂×C₄×C₄₇	semidirect
270. C₂²×C₈	C₂×C₄×C₄₇	semidirect
422. C₂²	C₄₇×#344	semidirect

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
C₂×C₄₇×#344	2
#10738	47

Subgroups — C47×#10738 #26050436

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#10738 #26050436