Subgroups — C₄₇×#25682 #26065380

Order 12032.

1088 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#540	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#490	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2629	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2034	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2033	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1992	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1957	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1864	C₂	1	2	yes	maximal, complemented
10	C₄₇×#1862	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1750	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₇×#540	—	2	4	no	—
13	C₄₇×#540	—	2	4	no	—
14	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×#123×C₄₇	—	2	2	no	—
18	C₂×#121×C₄₇	—	2	2	no	—
19	C₂×#121×C₄₇	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
21	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
22	C₄₇×#499	—	2	4	no	—
23	C₄₇×#490	—	2	4	no	—
24	C₂×#107×C₄₇	C₂²	1	2	yes	—
25	C₂×#106×C₄₇	C₂²	1	2	yes	—
26	C₂×#102×C₄₇	C₂²	1	2	yes	—
27	C₂×#102×C₄₇	C₂²	1	2	yes	—
28	C₂×#102×C₄₇	C₂²	1	2	yes	—
29	C₂×#102×C₄₇	C₂²	1	2	yes	—
30	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₄₇×#398	—	2	2	no	—
35	C₄₇×#396	—	2	2	no	—
36	C₄₇×#389	C₂²	1	2	yes	—
37	C₄₇×#384	C₂²	1	1	yes	characteristic
38	C₄₇×#380	C₂²	1	2	yes	—
39	C₄₇×#340	C₂²	1	2	yes	—
40	C₄₇×#340	C₂²	1	2	yes	—
41	C₄₇×#336	C₂²	1	1	yes	characteristic
42	C₄₇×#336	C₂²	1	1	yes	characteristic
43	C₂²×D₄×C₄₇	—	2	2	no	—
44	C₂²×D₄×C₄₇	—	2	2	no	—
45	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
46	C₂³×C₄×C₄₇	—	2	2	no	—
47	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
52	#127×C₄₇	—	2	2	no	—
53	#127×C₄₇	D₄	1	4	yes	—
54	#125×C₄₇	—	2	2	no	—
55	#125×C₄₇	—	2	2	no	—
56	#125×C₄₇	—	2	2	no	—
57	#125×C₄₇	D₄	1	4	yes	—
58	#123×C₄₇	—	2	16	no	—
59	#121×C₄₇	—	2	16	no	—
60	#121×C₄₇	—	2	4	no	—
61	#121×C₄₇	—	2	4	no	—
62	C₄×D₄×C₄₇	—	2	4	no	—
63	C₄×D₄×C₄₇	—	2	4	no	—
64	#117×C₄₇	—	2	2	no	—
65	#117×C₄₇	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
74	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	#107×C₄₇	—	2	4	no	—
81	#106×C₄₇	—	2	4	no	—
82	#102×C₄₇	—	2	4	no	—
83	#102×C₄₇	—	2	4	no	—
84	#102×C₄₇	—	2	4	no	—
85	#102×C₄₇	—	2	4	no	—
86	C₂²⋊C₈×C₄₇	—	2	2	no	—
87	C₂²⋊C₈×C₄₇	—	2	2	no	—
88	#97×C₄₇	—	2	2	no	—
89	C₄×C₈×C₄₇	—	2	2	no	—
90	#95×C₄₇	—	2	2	no	—
91	#95×C₄₇	—	2	2	no	—
92	C₂⁴×C₄₇	—	2	2	no	—
93	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂×D₄×C₄₇	—	2	8	no	—
95	C₂×D₄×C₄₇	—	2	8	no	—
96	C₂×D₄×C₄₇	—	2	2	no	—
97	C₂×D₄×C₄₇	—	2	2	no	—
98	C₂×D₄×C₄₇	—	2	2	no	—
99	C₂×D₄×C₄₇	—	2	2	no	—
100	C₂×D₄×C₄₇	—	2	2	no	—
101	C₂×D₄×C₄₇	—	8	2	no	—
102	C₂×D₄×C₄₇	—	8	2	no	—
103	C₂×D₄×C₄₇	—	8	2	no	—
104	C₂×D₄×C₄₇	—	8	2	no	—
105	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	—	2	8	no	—
108	C₂²×C₄×C₄₇	—	2	1	no	—
109	C₂²×C₄×C₄₇	—	2	1	no	—
110	C₂²×C₄×C₄₇	—	2	1	no	—
111	C₂²×C₄×C₄₇	—	2	1	no	—
112	C₂²×C₄×C₄₇	—	2	1	no	—
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	—	8	2	no	—
117	C₂²×C₄×C₄₇	—	8	2	no	—
118	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
122	C₂×C₈×C₄₇	—	2	1	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	1	no	—
128	C₂×C₈×C₄₇	—	2	1	no	—
129	C₂×C₈×C₄₇	—	2	1	no	—
130	C₂×C₈×C₄₇	—	2	1	no	—
131	C₂×C₈×C₄₇	—	2	1	no	—
132	C₂×C₈×C₄₇	#41	1	2	yes	—
133	C₂×C₈×C₄₇	#41	1	2	yes	—
134	C₄⋊C₄×C₄₇	—	2	8	no	—
135	C₄⋊C₄×C₄₇	—	2	4	no	—
136	C₄⋊C₄×C₄₇	—	2	2	no	—
137	C₄⋊C₄×C₄₇	—	2	2	no	—
138	C₄⋊C₄×C₄₇	—	2	2	no	—
139	C₄⋊C₄×C₄₇	—	2	2	no	—
140	C₄⋊C₄×C₄₇	—	2	2	no	—
141	C₄⋊C₄×C₄₇	—	4	4	no	—
142	C₄⋊C₄×C₄₇	—	8	2	no	—
143	C₄⋊C₄×C₄₇	—	8	2	no	—
144	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
145	C₂²⋊C₄×C₄₇	—	2	8	no	—
146	C₂²⋊C₄×C₄₇	—	2	8	no	—
147	C₂²⋊C₄×C₄₇	—	2	4	no	—
148	C₂²⋊C₄×C₄₇	—	8	2	no	—
149	C₄²×C₄₇	—	2	1	no	—
150	C₄²×C₄₇	—	2	1	no	—
151	C₄²×C₄₇	C₂×D₄	1	2	yes	—
152	C₄²×C₄₇	C₂×D₄	1	2	yes	—
153	C₂³×C₄₇	—	2	1	no	—
154	C₂³×C₄₇	—	2	4	no	—
155	C₂³×C₄₇	—	2	1	no	—
156	C₂³×C₄₇	—	2	1	no	—
157	C₂³×C₄₇	—	2	2	no	—
158	C₂³×C₄₇	—	2	2	no	—
159	C₂³×C₄₇	—	4	2	no	—
160	C₂³×C₄₇	—	4	2	no	—
161	C₂³×C₄₇	—	4	2	no	—
162	C₂³×C₄₇	—	4	2	no	—
163	C₂³×C₄₇	—	4	2	no	—
164	C₂³×C₄₇	—	4	2	no	—
165	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
166	D₄×C₄₇	—	2	4	no	—
167	D₄×C₄₇	—	2	4	no	—
168	D₄×C₄₇	—	4	2	no	—
169	D₄×C₄₇	—	4	2	no	—
170	D₄×C₄₇	—	8	8	no	—
171	D₄×C₄₇	—	8	8	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	2	4	no	—
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	2	1	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	4	2	no	—
183	C₂×C₄×C₄₇	—	4	1	no	—
184	C₂×C₄×C₄₇	—	4	1	no	—
185	C₂×C₄×C₄₇	—	4	1	no	—
186	C₂×C₄×C₄₇	—	4	1	no	—
187	C₂×C₄×C₄₇	—	4	2	no	—
188	C₂×C₄×C₄₇	—	4	2	no	—
189	C₂×C₄×C₄₇	—	4	2	no	—
190	C₂×C₄×C₄₇	—	4	2	no	—
191	C₂×C₄×C₄₇	—	4	2	no	—
192	C₂×C₄×C₄₇	—	4	2	no	—
193	C₂×C₄×C₄₇	—	8	8	no	—
194	C₂×C₄×C₄₇	#120	1	4	yes	—
195	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
200	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
201	C₈×C₄₇	—	2	2	no	—
202	C₈×C₄₇	—	2	2	no	—
203	C₈×C₄₇	—	4	1	no	—
204	C₈×C₄₇	—	4	1	no	—
205	#25682	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂²×C₄₇	—	4	1	no	—
207	C₂²×C₄₇	—	4	1	no	—
208	C₂²×C₄₇	—	4	1	no	—
209	C₂²×C₄₇	—	4	4	no	—
210	C₂²×C₄₇	—	4	2	no	—
211	C₂²×C₄₇	—	4	4	no	—
212	C₂²×C₄₇	—	4	2	no	—
213	C₂²×C₄₇	—	4	4	no	—
214	C₂²×C₄₇	—	8	2	no	—
215	C₂²×C₄₇	—	8	2	no	—
216	C₂²×C₄₇	—	8	2	no	—
217	C₂²×C₄₇	—	8	2	no	—
218	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
219	C₂²×C₄₇	#532	1	1	yes	characteristic
220	C₂²×C₄₇	#536	1	1	yes	characteristic
221	C₂²×C₄₇	#576	1	2	yes	—
222	C₂²×C₄₇	#577	1	2	yes	—
223	C₄×C₄₇	—	2	4	no	—
224	C₄×C₄₇	—	4	1	no	—
225	C₄×C₄₇	—	4	2	no	—
226	C₄×C₄₇	—	4	4	no	—
227	C₄×C₄₇	—	8	2	no	—
228	C₄×C₄₇	—	8	2	no	—
229	C₄×C₄₇	#547	1	1	yes	characteristic
230	C₄×C₄₇	#547	1	1	yes	characteristic
231	C₄×C₄₇	#548	1	1	yes	characteristic
232	C₄×C₄₇	#548	1	1	yes	characteristic
233	C₂×#540	C₂×C₄₇	1	1	yes	characteristic
234	C₂×#499	C₂×C₄₇	1	1	yes	characteristic, complemented
235	C₂×#490	C₂×C₄₇	1	1	yes	characteristic, complemented
236	#2629	C₂×C₄₇	1	1	yes	characteristic, complemented
237	#2034	C₂×C₄₇	1	2	yes	complemented
238	#2033	C₂×C₄₇	1	2	yes	complemented
239	#1992	C₂×C₄₇	1	1	yes	characteristic, complemented
240	#1957	C₂×C₄₇	1	1	yes	characteristic, complemented
241	#1864	C₂×C₄₇	1	2	yes	complemented
242	#1862	C₂×C₄₇	1	2	yes	complemented
243	#1750	C₂×C₄₇	1	1	yes	characteristic, complemented
244	C₂×C₄₇	—	8	1	no	—
245	C₂×C₄₇	—	8	4	no	—
246	C₂×C₄₇	#2432	1	1	yes	characteristic
247	C₂×C₄₇	#3012	1	2	yes	—
248	C₂×C₄₇	#3174	1	1	yes	characteristic
249	C₂×C₄₇	#3176	1	1	yes	characteristic
250	C₂×C₄₇	#3241	1	2	yes	—
251	#540	—	2	4	no	—
252	#540	—	2	4	no	—
253	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
254	C₂×#125	C₂²×C₄₇	1	1	yes	characteristic
255	C₂×#125	C₂²×C₄₇	1	1	yes	characteristic
256	C₂×#123	—	2	2	no	—
257	C₂×#121	—	2	2	no	—
258	C₂×#121	C₂²×C₄₇	1	2	yes	—
259	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
260	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
261	#499	—	2	4	no	—
262	#490	—	2	4	no	—
263	C₂×#107	C₂²×C₄₇	1	2	yes	—
264	C₂×#106	C₂²×C₄₇	1	2	yes	—
265	C₂×#102	C₂²×C₄₇	1	2	yes	—
266	C₂×#102	C₂²×C₄₇	1	2	yes	—
267	C₂×#102	C₂²×C₄₇	1	2	yes	—
268	C₂×#102	C₂²×C₄₇	1	2	yes	—
269	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
270	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
271	C₂×#97	C₂²×C₄₇	1	1	yes	characteristic
272	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
273	#398	—	2	2	no	—
274	#396	—	2	2	no	—
275	#389	C₂²×C₄₇	1	2	yes	—
276	#384	C₂²×C₄₇	1	1	yes	characteristic
277	#380	C₂²×C₄₇	1	2	yes	—
278	#340	C₂²×C₄₇	1	2	yes	—
279	#340	C₂²×C₄₇	1	2	yes	—
280	#336	C₂²×C₄₇	1	1	yes	characteristic
281	#336	C₂²×C₄₇	1	1	yes	characteristic
282	C₄₇	#25682	1	1	yes	characteristic, direct product factor, Sylow
283	C₂²×D₄	—	2	2	no	—
284	C₂²×D₄	—	2	2	no	—
285	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
286	C₂³×C₄	—	2	2	no	—
287	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
292	#127	—	2	2	no	—
293	#127	D₄×C₄₇	1	4	yes	—
294	#125	—	2	2	no	—
295	#125	—	2	2	no	—
296	#125	—	2	2	no	—
297	#125	D₄×C₄₇	1	4	yes	—
298	#123	—	2	16	no	—
299	#121	—	2	16	no	—
300	#121	—	2	4	no	—
301	#121	—	2	4	no	—
302	C₄×D₄	—	2	4	no	—
303	C₄×D₄	—	2	4	no	—
304	#117	—	2	2	no	—
305	#117	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
311	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
318	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
320	#107	—	2	4	no	—
321	#106	—	2	4	no	—
322	#102	—	2	4	no	—
323	#102	—	2	4	no	—
324	#102	—	2	4	no	—
325	#102	—	2	4	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	C₂²⋊C₈	—	2	2	no	—
328	#97	—	2	2	no	—
329	C₄×C₈	—	2	2	no	—
330	#95	—	2	2	no	—
331	#95	—	2	2	no	—
332	C₂⁴	—	2	2	no	—
333	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
334	C₂×D₄	—	2	8	no	—
335	C₂×D₄	—	2	8	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	8	2	no	—
342	C₂×D₄	—	8	2	no	—
343	C₂×D₄	—	8	2	no	—
344	C₂×D₄	—	8	2	no	—
345	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	8	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	8	2	no	—
357	C₂²×C₄	—	8	2	no	—
358	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
361	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	#41×C₄₇	1	2	yes	—
373	C₂×C₈	#41×C₄₇	1	2	yes	—
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	4	4	no	—
382	C₄⋊C₄	—	8	2	no	—
383	C₄⋊C₄	—	8	2	no	—
384	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
385	C₂²⋊C₄	—	2	8	no	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	—	2	4	no	—
388	C₂²⋊C₄	—	8	2	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	C₂×D₄×C₄₇	1	2	yes	—
392	C₄²	C₂×D₄×C₄₇	1	2	yes	—
393	C₂³	—	2	1	no	—
394	C₂³	—	2	4	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	1	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
406	D₄	—	2	4	no	—
407	D₄	—	2	4	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	8	8	no	—
411	D₄	—	8	8	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	8	8	no	—
434	C₂×C₄	#120×C₄₇	1	4	yes	—
435	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
436	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
437	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
438	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
439	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
440	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
441	C₈	—	2	2	no	—
442	C₈	—	2	2	no	—
443	C₈	—	4	1	no	—
444	C₈	—	4	1	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	4	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	8	2	no	—
455	C₂²	—	8	2	no	—
456	C₂²	—	8	2	no	—
457	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
458	C₂²	C₄₇×#532	1	1	yes	characteristic
459	C₂²	C₄₇×#536	1	1	yes	characteristic
460	C₂²	C₄₇×#576	1	2	yes	—
461	C₂²	C₄₇×#577	1	2	yes	—
462	C₄	—	2	4	no	—
463	C₄	—	4	1	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	4	no	—
466	C₄	—	8	2	no	—
467	C₄	—	8	2	no	—
468	C₄	C₄₇×#547	1	1	yes	characteristic
469	C₄	C₄₇×#547	1	1	yes	characteristic
470	C₄	C₄₇×#548	1	1	yes	characteristic
471	C₄	C₄₇×#548	1	1	yes	characteristic
472	C₂	—	8	1	no	—
473	C₂	—	8	4	no	—
474	C₂	C₄₇×#2432	1	1	yes	characteristic
475	C₂	C₄₇×#3012	1	2	yes	—
476	C₂	C₄₇×#3174	1	1	yes	characteristic
477	C₂	C₄₇×#3176	1	1	yes	characteristic
478	C₂	C₄₇×#3241	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×C₄₇×#540	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂×#117×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#499	C₂	semidirect
3. C₂×C₄₇×#490	C₂	semidirect
4. C₄₇×#2629	C₂	semidirect
5. C₄₇×#2034	C₂	semidirect
6. C₄₇×#2033	C₂	semidirect
7. C₄₇×#1992	C₂	semidirect
8. C₄₇×#1957	C₂	semidirect
9. C₄₇×#1864	C₂	semidirect
10. C₄₇×#1862	C₂	semidirect
11. C₄₇×#1750	C₂	semidirect
205. #25682	C₄₇	direct (N × H)
234. C₂×#499	C₂×C₄₇	semidirect
235. C₂×#490	C₂×C₄₇	semidirect
236. #2629	C₂×C₄₇	semidirect
237. #2034	C₂×C₄₇	semidirect
238. #2033	C₂×C₄₇	semidirect
239. #1992	C₂×C₄₇	semidirect
240. #1957	C₂×C₄₇	semidirect
241. #1864	C₂×C₄₇	semidirect
242. #1862	C₂×C₄₇	semidirect
243. #1750	C₂×C₄₇	semidirect
282. C₄₇	#25682	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×#540	2
C₂×C₄₇×#499	2
C₂×C₄₇×#490	2
C₄₇×#2629	2
C₄₇×#2034	2
C₄₇×#2033	2
C₄₇×#1992	2
C₄₇×#1957	2
C₄₇×#1864	2
C₄₇×#1862	2
C₄₇×#1750	2
#25682	47

Subgroups — C47×#25682 #26065380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#25682 #26065380