Subgroups — C₄₇×#21050 #26060748

Order 12032.

1226 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#424	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₇×#407	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂²⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2280	C₂	1	1	yes	maximal, characteristic
6	C₄₇×#1924	C₂	1	4	yes	maximal, complemented
7	C₄₇×#1923	C₂	1	4	yes	maximal, complemented
8	C₄₇×#1729	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1729	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×#424	—	2	4	no	—
18	C₂×C₄⋊C₈×C₄₇	C₂²	1	4	yes	complemented
19	C₄₇×#407	—	2	4	no	—
20	C₂×C₂²⋊C₈×C₄₇	—	2	4	no	—
21	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
22	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₄₇	C₂²	1	4	yes	—
24	C₄₇×#405	—	2	4	no	—
25	C₂×#97×C₄₇	C₂²	1	2	yes	complemented
26	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	complemented
27	C₄₇×#381	C₄	1	2	yes	—
28	C₄₇×#380	C₄	1	2	yes	—
29	C₄₇×#380	C₄	1	2	yes	—
30	C₄₇×#379	C₄	1	2	yes	—
31	C₄×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	—
32	C₄₇×#336	C₂²	1	2	yes	complemented
33	C₄₇×#336	C₂²	1	4	yes	complemented
34	C₄₇×#336	C₂²	1	2	yes	complemented
35	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₇	—	2	2	no	—
37	C₂³×C₄×C₄₇	—	2	2	no	—
38	C₂³×C₄×C₄₇	—	2	2	no	—
39	C₂³×C₄×C₄₇	—	2	2	no	—
40	C₂³×C₄×C₄₇	—	2	2	no	—
41	C₂³×C₄×C₄₇	—	2	2	no	—
42	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
43	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
45	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₄₇	—	2	2	no	—
47	C₂×M₁₆×C₄₇	—	2	2	no	—
48	C₂×M₁₆×C₄₇	—	2	2	no	—
49	C₂×M₁₆×C₄₇	—	2	2	no	—
50	C₂×M₁₆×C₄₇	—	2	2	no	—
51	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
52	C₂²×C₈×C₄₇	—	2	2	no	—
53	C₂²×C₈×C₄₇	—	2	2	no	—
54	C₂²×C₈×C₄₇	—	2	2	no	—
55	C₂²×C₈×C₄₇	—	2	2	no	—
56	C₂²×C₈×C₄₇	—	2	2	no	—
57	C₂²×C₈×C₄₇	D₄	1	4	yes	—
58	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
59	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
60	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
63	#117×C₄₇	—	2	2	no	—
64	#117×C₄₇	—	2	2	no	—
65	#117×C₄₇	—	2	2	no	—
66	#117×C₄₇	—	2	2	no	—
67	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
70	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
71	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
72	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
73	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
74	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
75	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
76	C₄⋊C₈×C₄₇	—	2	8	no	—
77	C₂²⋊C₈×C₄₇	—	2	4	no	—
78	C₂²⋊C₈×C₄₇	—	2	4	no	—
79	C₂²⋊C₈×C₄₇	—	2	8	no	—
80	#97×C₄₇	—	2	4	no	—
81	C₄×C₈×C₄₇	—	2	4	no	—
82	#95×C₄₇	C₂×C₄	1	4	yes	—
83	#95×C₄₇	C₂×C₄	1	4	yes	—
84	C₂⁴×C₄₇	—	2	2	no	—
85	C₂⁴×C₄₇	—	2	4	no	—
86	C₂⁴×C₄₇	—	2	2	no	—
87	C₂⁴×C₄₇	—	2	2	no	—
88	C₂⁴×C₄₇	—	4	2	no	—
89	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
90	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	4	no	—
95	C₂²×C₄×C₄₇	—	2	4	no	—
96	C₂²×C₄×C₄₇	—	2	4	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	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	—	4	4	no	—
104	C₂²×C₄×C₄₇	—	4	4	no	—
105	C₂²×C₄×C₄₇	—	4	4	no	—
106	C₂²×C₄×C₄₇	—	4	4	no	—
107	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
109	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₇	#41	1	2	yes	—
115	C₂²×C₄×C₄₇	#41	1	2	yes	—
116	C₂²×C₄×C₄₇	#41	1	2	yes	—
117	C₂²×C₄×C₄₇	#41	1	2	yes	—
118	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
119	M₁₆×C₄₇	—	2	8	no	—
120	M₁₆×C₄₇	—	4	4	no	—
121	C₂×C₈×C₄₇	—	2	8	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	2	1	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	—	2	1	no	—
126	C₂×C₈×C₄₇	—	2	1	no	—
127	C₂×C₈×C₄₇	—	2	2	no	—
128	C₂×C₈×C₄₇	—	2	2	no	—
129	C₂×C₈×C₄₇	—	2	2	no	—
130	C₂×C₈×C₄₇	—	2	2	no	—
131	C₂×C₈×C₄₇	—	2	2	no	—
132	C₂×C₈×C₄₇	—	2	2	no	—
133	C₂×C₈×C₄₇	—	2	2	no	—
134	C₂×C₈×C₄₇	—	4	4	no	—
135	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
136	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
138	C₄⋊C₄×C₄₇	—	2	2	no	—
139	C₄⋊C₄×C₄₇	—	2	2	no	—
140	C₄⋊C₄×C₄₇	—	2	4	no	—
141	C₂²⋊C₄×C₄₇	—	2	4	no	—
142	C₂²⋊C₄×C₄₇	—	2	4	no	—
143	C₂²⋊C₄×C₄₇	—	2	8	no	—
144	C₂²⋊C₄×C₄₇	—	4	4	no	—
145	C₄²×C₄₇	—	2	2	no	—
146	C₄²×C₄₇	—	2	2	no	—
147	C₄²×C₄₇	—	2	2	no	—
148	C₄²×C₄₇	—	2	2	no	—
149	C₂³×C₄₇	—	2	2	no	—
150	C₂³×C₄₇	—	2	2	no	—
151	C₂³×C₄₇	—	2	8	no	—
152	C₂³×C₄₇	—	2	2	no	—
153	C₂³×C₄₇	—	2	2	no	—
154	C₂³×C₄₇	—	2	2	no	—
155	C₂³×C₄₇	—	2	2	no	—
156	C₂³×C₄₇	—	2	2	no	—
157	C₂³×C₄₇	—	2	2	no	—
158	C₂³×C₄₇	—	4	8	no	—
159	C₂³×C₄₇	—	4	8	no	—
160	C₂³×C₄₇	—	4	4	no	—
161	C₂³×C₄₇	—	4	4	no	—
162	C₂³×C₄₇	#117	1	2	yes	—
163	C₂³×C₄₇	C₄×D₄	1	2	yes	—
164	C₂³×C₄₇	C₄×D₄	1	2	yes	—
165	C₂³×C₄₇	#131	1	4	yes	—
166	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	4	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	4	no	—
174	C₂×C₄×C₄₇	—	2	4	no	—
175	C₂×C₄×C₄₇	—	2	4	no	—
176	C₂×C₄×C₄₇	—	2	4	no	—
177	C₂×C₄×C₄₇	—	4	4	no	—
178	C₂×C₄×C₄₇	—	4	2	no	—
179	C₂×C₄×C₄₇	—	4	2	no	—
180	C₂×C₄×C₄₇	—	4	2	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	4	8	no	—
183	C₂×C₄×C₄₇	#117	1	2	yes	—
184	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
185	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₄₇	#121	1	4	yes	—
187	C₂×C₄×C₄₇	#123	1	4	yes	—
188	C₂×C₄×C₄₇	#124	1	4	yes	—
189	C₂×C₄×C₄₇	#126	1	4	yes	—
190	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
196	C₈×C₄₇	—	2	4	no	—
197	C₈×C₄₇	—	2	2	no	—
198	C₈×C₄₇	—	2	2	no	—
199	C₈×C₄₇	—	4	2	no	—
200	C₈×C₄₇	—	4	2	no	—
201	#21050	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂²×C₄₇	—	2	4	no	—
203	C₂²×C₄₇	—	2	2	no	—
204	C₂²×C₄₇	—	2	2	no	—
205	C₂²×C₄₇	—	2	4	no	—
206	C₂²×C₄₇	—	2	4	no	—
207	C₂²×C₄₇	—	2	4	no	—
208	C₂²×C₄₇	—	2	4	no	—
209	C₂²×C₄₇	—	4	16	no	—
210	C₂²×C₄₇	—	4	2	no	—
211	C₂²×C₄₇	—	4	2	no	—
212	C₂²×C₄₇	—	4	2	no	—
213	C₂²×C₄₇	—	4	2	no	—
214	C₂²×C₄₇	#388	1	4	yes	—
215	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
216	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
217	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
218	C₂²×C₄₇	C₂×#131	1	2	yes	—
219	C₂²×C₄₇	#568	1	2	yes	—
220	C₄×C₄₇	—	4	2	no	—
221	C₄×C₄₇	—	4	2	no	—
222	C₄×C₄₇	—	4	4	no	—
223	C₄×C₄₇	—	4	2	no	—
224	C₄×C₄₇	#388	1	4	yes	—
225	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
226	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
227	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
228	C₄×C₄₇	C₂×#126	1	1	yes	characteristic
229	C₂×#424	C₂×C₄₇	1	1	yes	characteristic, complemented
230	C₂×#407	C₂×C₄₇	1	1	yes	characteristic
231	C₂²×C₂²⋊C₈	C₂×C₄₇	1	1	yes	characteristic
232	C₂×#405	C₂×C₄₇	1	1	yes	characteristic, complemented
233	#2280	C₂×C₄₇	1	1	yes	characteristic
234	#1924	C₂×C₄₇	1	4	yes	complemented
235	#1923	C₂×C₄₇	1	4	yes	complemented
236	#1729	C₂×C₄₇	1	1	yes	characteristic, complemented
237	#1729	C₂×C₄₇	1	1	yes	characteristic, complemented
238	C₂×C₄₇	—	2	4	no	—
239	C₂×C₄₇	—	4	4	no	—
240	C₂×C₄₇	C₂×#388	1	1	yes	characteristic
241	C₂×C₄₇	#2924	1	2	yes	—
242	C₂×C₄₇	#2929	1	1	yes	characteristic
243	C₂×C₄₇	#2930	1	1	yes	characteristic
244	C₂×C₄₇	#2933	1	2	yes	—
245	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
246	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
247	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
248	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
249	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
250	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
251	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
252	#424	—	2	4	no	—
253	C₂×C₄⋊C₈	C₂²×C₄₇	1	4	yes	complemented
254	#407	—	2	4	no	—
255	C₂×C₂²⋊C₈	—	2	4	no	—
256	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
257	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
258	C₂×C₂²⋊C₈	C₂²×C₄₇	1	4	yes	—
259	#405	—	2	4	no	—
260	C₂×#97	C₂²×C₄₇	1	2	yes	complemented
261	C₂×C₄×C₈	C₂²×C₄₇	1	2	yes	complemented
262	#381	C₄×C₄₇	1	2	yes	—
263	#380	C₄×C₄₇	1	2	yes	—
264	#380	C₄×C₄₇	1	2	yes	—
265	#379	C₄×C₄₇	1	2	yes	—
266	C₄×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	—
267	#336	C₂²×C₄₇	1	2	yes	complemented
268	#336	C₂²×C₄₇	1	4	yes	complemented
269	#336	C₂²×C₄₇	1	2	yes	complemented
270	C₄₇	#21050	1	1	yes	characteristic, direct product factor, Sylow
271	C₂⁵	C₂×C₄×C₄₇	1	1	yes	characteristic
272	C₂³×C₄	—	2	2	no	—
273	C₂³×C₄	—	2	2	no	—
274	C₂³×C₄	—	2	2	no	—
275	C₂³×C₄	—	2	2	no	—
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	—	2	2	no	—
278	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
279	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
280	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
281	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	—	2	2	no	—
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	—	2	2	no	—
286	C₂×M₁₆	—	2	2	no	—
287	C₂×M₁₆	D₄×C₄₇	1	4	yes	—
288	C₂²×C₈	—	2	2	no	—
289	C₂²×C₈	—	2	2	no	—
290	C₂²×C₈	—	2	2	no	—
291	C₂²×C₈	—	2	2	no	—
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	D₄×C₄₇	1	4	yes	—
294	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
295	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
296	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
298	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
299	#117	—	2	2	no	—
300	#117	—	2	2	no	—
301	#117	—	2	2	no	—
302	#117	—	2	2	no	—
303	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
306	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
307	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
308	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
309	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
310	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
311	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
312	C₄⋊C₈	—	2	8	no	—
313	C₂²⋊C₈	—	2	4	no	—
314	C₂²⋊C₈	—	2	4	no	—
315	C₂²⋊C₈	—	2	8	no	—
316	#97	—	2	4	no	—
317	C₄×C₈	—	2	4	no	—
318	#95	C₂×C₄×C₄₇	1	4	yes	—
319	#95	C₂×C₄×C₄₇	1	4	yes	—
320	C₂⁴	—	2	2	no	—
321	C₂⁴	—	2	4	no	—
322	C₂⁴	—	2	2	no	—
323	C₂⁴	—	2	2	no	—
324	C₂⁴	—	4	2	no	—
325	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
326	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	4	4	no	—
340	C₂²×C₄	—	4	4	no	—
341	C₂²×C₄	—	4	4	no	—
342	C₂²×C₄	—	4	4	no	—
343	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
344	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
345	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
346	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
347	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
350	C₂²×C₄	#41×C₄₇	1	2	yes	—
351	C₂²×C₄	#41×C₄₇	1	2	yes	—
352	C₂²×C₄	#41×C₄₇	1	2	yes	—
353	C₂²×C₄	#41×C₄₇	1	2	yes	—
354	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
355	M₁₆	—	2	8	no	—
356	M₁₆	—	4	4	no	—
357	C₂×C₈	—	2	8	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	4	4	no	—
371	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
372	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
373	C₂×C₈	C₂×D₄×C₄₇	1	4	yes	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₂²⋊C₄	—	2	4	no	—
378	C₂²⋊C₄	—	2	4	no	—
379	C₂²⋊C₄	—	2	8	no	—
380	C₂²⋊C₄	—	4	4	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	8	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	4	8	no	—
395	C₂³	—	4	8	no	—
396	C₂³	—	4	4	no	—
397	C₂³	—	4	4	no	—
398	C₂³	#117×C₄₇	1	2	yes	—
399	C₂³	C₄×D₄×C₄₇	1	2	yes	—
400	C₂³	C₄×D₄×C₄₇	1	2	yes	—
401	C₂³	#131×C₄₇	1	4	yes	—
402	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	8	no	—
419	C₂×C₄	#117×C₄₇	1	2	yes	—
420	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
421	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
422	C₂×C₄	#121×C₄₇	1	4	yes	—
423	C₂×C₄	#123×C₄₇	1	4	yes	—
424	C₂×C₄	#124×C₄₇	1	4	yes	—
425	C₂×C₄	#126×C₄₇	1	4	yes	—
426	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
427	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
428	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
429	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
430	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
431	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
432	C₈	—	2	4	no	—
433	C₈	—	2	2	no	—
434	C₈	—	2	2	no	—
435	C₈	—	4	2	no	—
436	C₈	—	4	2	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	4	16	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	C₄₇×#388	1	4	yes	—
450	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
451	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
452	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
453	C₂²	C₂×#131×C₄₇	1	2	yes	—
454	C₂²	C₄₇×#568	1	2	yes	—
455	C₄	—	4	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	4	no	—
459	C₄	C₄₇×#388	1	4	yes	—
460	C₄	C₂×#121×C₄₇	1	1	yes	characteristic
461	C₄	C₂×#123×C₄₇	1	1	yes	characteristic
462	C₄	C₂×#124×C₄₇	1	1	yes	characteristic
463	C₄	C₂×#126×C₄₇	1	1	yes	characteristic
464	C₂	—	2	4	no	—
465	C₂	—	4	4	no	—
466	C₂	C₂×C₄₇×#388	1	1	yes	characteristic
467	C₂	C₄₇×#2924	1	2	yes	—
468	C₂	C₄₇×#2929	1	1	yes	characteristic
469	C₂	C₄₇×#2930	1	1	yes	characteristic
470	C₂	C₄₇×#2933	1	2	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
1. C₂×C₄₇×#424	C₂	semidirect
4. C₂×C₄₇×#405	C₂	semidirect
6. C₄₇×#1924	C₂	semidirect
7. C₄₇×#1923	C₂	semidirect
8. C₄₇×#1729	C₂	semidirect
9. C₄₇×#1729	C₂	semidirect
18. C₂×C₄⋊C₈×C₄₇	C₂²	semidirect
25. C₂×#97×C₄₇	C₂²	semidirect
26. C₂×C₄×C₈×C₄₇	C₂²	semidirect
32. C₄₇×#336	C₂²	semidirect
33. C₄₇×#336	C₂²	semidirect
34. C₄₇×#336	C₂²	semidirect
201. #21050	C₄₇	direct (N × H)
229. C₂×#424	C₂×C₄₇	semidirect
232. C₂×#405	C₂×C₄₇	semidirect
234. #1924	C₂×C₄₇	semidirect
235. #1923	C₂×C₄₇	semidirect
236. #1729	C₂×C₄₇	semidirect
237. #1729	C₂×C₄₇	semidirect
253. C₂×C₄⋊C₈	C₂²×C₄₇	semidirect
260. C₂×#97	C₂²×C₄₇	semidirect
261. C₂×C₄×C₈	C₂²×C₄₇	semidirect
267. #336	C₂²×C₄₇	semidirect
268. #336	C₂²×C₄₇	semidirect
269. #336	C₂²×C₄₇	semidirect
270. C₄₇	#21050	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×#424	2
C₂×C₄₇×#407	2
C₂²×C₂²⋊C₈×C₄₇	2
C₂×C₄₇×#405	2
C₄₇×#2280	2
C₄₇×#1924	2
C₄₇×#1923	2
C₄₇×#1729	2
#21050	47

Subgroups — C47×#21050 #26060748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#21050 #26060748