Subgroups — #466×D₄₇ #20252952

Order 6016.

616 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#121×D₄₇	C₂	1	2	yes	maximal, complemented
4	#15689360	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689359	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689358	C₂	1	2	yes	maximal, complemented
7	#15689357	C₂	1	2	yes	maximal, complemented
8	#15689356	C₂	1	1	yes	maximal, characteristic, complemented
9	#107×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#102×D₄₇	C₂	1	2	yes	maximal, complemented
11	C₄₇×#466	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₄×D₄₇	—	2	2	no	—
13	C₂×D₄×D₄₇	C₂²	1	2	yes	—
14	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
15	C₂×D₃₇₆	C₂²	1	1	yes	characteristic, complemented
16	C₂×#10625334	C₂²	1	2	yes	complemented
17	D₈×D₄₇	—	2	4	no	—
18	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₈×D₄₇	—	2	4	no	—
20	C₂×C₈×D₄₇	C₂²	1	1	yes	characteristic
21	C₂×C₈×D₄₇	C₂²	1	1	yes	characteristic
22	C₂×C₈×D₄₇	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₈×D₄₇	C₂²	1	1	yes	characteristic, complemented
24	#13093999	C₂²	1	2	yes	complemented
25	#13093998	C₂²	1	2	yes	complemented
26	#13093997	—	2	2	no	—
27	#13093996	—	2	2	no	—
28	#13093995	C₂²	1	2	yes	complemented
29	C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
30	C₂²⋊C₄×D₄₇	—	2	2	no	—
31	#13093958	C₂²	1	1	yes	characteristic, complemented
32	#13093957	C₂²	1	2	yes	complemented
33	#13093946	C₂²	1	2	yes	complemented
34	#13093945	C₂²	1	2	yes	complemented
35	#13093944	C₂²	1	2	yes	complemented
36	C₂×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
38	#121×C₄₇	C₂²	1	2	yes	complemented
39	#107×C₄₇	C₂²	1	1	yes	characteristic, complemented
40	#102×C₄₇	C₂²	1	2	yes	complemented
41	C₂³×D₄₇	—	2	2	no	—
42	C₂³×D₄₇	D₄	1	1	yes	characteristic
43	C₂×D₄×C₄₇	—	2	2	no	—
44	C₂×D₄×C₄₇	C₂³	1	2	yes	—
45	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
46	C₂×C₂²⋊D₄₇	—	2	2	no	—
47	C₂×C₂²⋊D₄₇	—	2	2	no	—
48	C₂×C₂²⋊D₄₇	—	2	2	no	—
49	C₂²×Dic₄₇	D₄	1	1	yes	characteristic
50	D₄×D₄₇	—	2	4	no	—
51	D₄×D₄₇	—	2	4	no	—
52	D₄×D₄₇	—	4	8	no	—
53	C₂×D₁₈₈	—	2	2	no	—
54	C₂×D₁₈₈	C₂³	1	2	yes	—
55	C₂×C₄×D₄₇	—	2	2	no	—
56	C₂×C₄×D₄₇	—	2	2	no	—
57	C₂×C₄×D₄₇	—	2	2	no	—
58	C₂×C₄×D₄₇	D₄	1	1	yes	characteristic
59	C₂×C₄×D₄₇	D₄	1	1	yes	characteristic
60	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
61	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
62	D₈×C₄₇	—	2	2	no	—
63	C₂×C₈×C₄₇	—	2	2	no	—
64	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
65	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
66	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
67	C₂²⋊C₄×C₄₇	—	2	2	no	—
68	C₂²⋊Dic₄₇	—	2	2	no	—
69	#10625334	—	2	4	no	—
70	(C₂×D₄₇)⋊C₄	—	2	2	no	—
71	(C₂×D₄₇)⋊C₄	—	2	2	no	—
72	C₄⋊Dic₄₇	C₂³	1	2	yes	—
73	Dic₄₇⋊C₄	—	2	2	no	—
74	C₂×C₄₇⋊C₈	—	2	2	no	—
75	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
76	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
77	D₃₇₆	—	2	2	no	—
78	C₈×D₄₇	—	2	2	no	—
79	C₈×D₄₇	—	2	2	no	—
80	C₈×D₄₇	—	2	2	no	—
81	C₈×D₄₇	D₄	1	4	yes	complemented
82	C₂³×C₄₇	—	2	2	no	—
83	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×D₄₇	—	2	2	no	—
85	C₂²×D₄₇	—	2	2	no	—
86	C₂²×D₄₇	—	2	2	no	—
87	C₂²×D₄₇	—	4	4	no	—
88	C₂²×D₄₇	—	4	4	no	—
89	C₂²×D₄₇	—	4	4	no	—
90	C₂²×D₄₇	D₈	1	4	yes	complemented
91	C₂²×D₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×D₄₇	C₂×D₄	1	1	yes	characteristic
93	D₄×C₄₇	—	2	2	no	—
94	D₄×C₄₇	—	2	2	no	—
95	D₄×C₄₇	—	4	4	no	—
96	C₂×C₄×C₄₇	—	2	1	no	—
97	C₂×C₄×C₄₇	—	2	1	no	—
98	C₂×C₄×C₄₇	—	2	2	no	—
99	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
101	C₂²⋊D₄₇	—	4	4	no	—
102	C₂²⋊D₄₇	—	4	4	no	—
103	C₂²⋊D₄₇	—	4	4	no	—
104	C₂×Dic₄₇	—	2	2	no	—
105	C₂×Dic₄₇	—	2	2	no	—
106	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
108	D₁₈₈	—	2	2	no	—
109	D₁₈₈	—	2	2	no	—
110	D₁₈₈	—	4	4	no	—
111	C₄×D₄₇	—	2	2	no	—
112	C₄×D₄₇	—	2	1	no	—
113	C₄×D₄₇	—	2	1	no	—
114	C₄×D₄₇	—	2	2	no	—
115	C₄×D₄₇	—	4	4	no	—
116	C₄×D₄₇	C₂×D₄	1	2	yes	—
117	C₄×D₄₇	#41	1	2	yes	—
118	C₈×C₄₇	—	2	1	no	—
119	C₈×C₄₇	C₂×D₄	1	2	yes	complemented
120	C₄₇⋊C₈	—	2	1	no	—
121	C₄₇⋊C₈	C₂×D₄	1	2	yes	complemented
122	C₂²×C₄₇	—	2	1	no	—
123	C₂²×C₄₇	—	2	1	no	—
124	C₂²×C₄₇	—	4	2	no	—
125	C₂²×C₄₇	—	4	2	no	—
126	C₂²×C₄₇	—	4	2	no	—
127	C₂²×C₄₇	C₂×D₈	1	2	yes	complemented
128	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
129	C₂×D₄₇	—	2	1	no	—
130	C₂×D₄₇	—	2	1	no	—
131	C₂×D₄₇	—	2	8	no	—
132	C₂×D₄₇	—	4	2	no	—
133	C₂×D₄₇	—	4	2	no	—
134	C₂×D₄₇	—	4	2	no	—
135	C₂×D₄₇	—	8	8	no	—
136	C₂×D₄₇	#121	1	2	yes	—
137	C₂×D₄₇	C₂×D₈	1	2	yes	—
138	C₂×D₄₇	C₂×D₈	1	2	yes	complemented
139	C₂×D₄₇	#135	1	2	yes	—
140	C₄×C₄₇	—	2	1	no	—
141	C₄×C₄₇	—	4	2	no	—
142	C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
143	C₄×C₄₇	C₂×#41	1	1	yes	characteristic
144	Dic₄₇	—	2	1	no	—
145	Dic₄₇	—	4	2	no	—
146	Dic₄₇	#121	1	2	yes	—
147	C₂×#466	—	47	1	no	maximal, Sylow
148	C₂×C₄₇	—	2	2	no	—
149	C₂×C₄₇	—	8	2	no	—
150	C₂×C₄₇	C₂×#121	1	1	yes	characteristic
151	C₂×C₄₇	C₂²×D₈	1	1	yes	characteristic
152	C₂×C₄₇	C₂×#135	1	1	yes	characteristic
153	D₄₇	—	2	2	no	—
154	D₄₇	—	8	2	no	—
155	D₄₇	#466	1	4	yes	direct product factor
156	C₂²×D₈	—	47	1	no	—
157	C₂³×C₈	—	47	1	no	—
158	C₂×#121	—	47	2	no	—
159	#466	—	47	1	no	—
160	#466	—	47	1	no	—
161	#466	—	47	2	no	—
162	#466	—	47	1	no	—
163	#466	—	47	2	no	—
164	#466	D₄₇	1	1	yes	characteristic, direct product factor
165	C₂×#107	—	47	1	no	—
166	C₂×#102	—	47	2	no	—
167	C₄₇	C₂×#466	1	1	yes	characteristic, complemented, Sylow
168	C₂²×D₄	—	47	2	no	—
169	C₂²×D₄	—	94	2	no	—
170	C₂³×C₄	—	47	1	no	—
171	C₂×D₈	—	47	2	no	—
172	C₂×D₈	—	47	1	no	—
173	C₂×D₈	—	94	4	no	—
174	C₂×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
175	C₂²×C₈	—	47	1	no	—
176	C₂²×C₈	—	47	1	no	—
177	C₂²×C₈	—	47	1	no	—
178	C₂²×C₈	—	47	1	no	—
179	C₂²×C₈	—	47	1	no	—
180	C₂²×C₈	—	94	4	no	—
181	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
182	#121	—	47	2	no	—
183	#121	—	47	2	no	—
184	#121	—	47	2	no	—
185	#121	—	94	2	no	—
186	#121	—	94	2	no	—
187	#121	C₂×D₄₇	1	2	yes	complemented
188	C₂×C₄⋊C₄	—	47	2	no	—
189	C₂×C₂²⋊C₄	—	94	2	no	—
190	#107	—	47	1	no	—
191	#107	—	47	2	no	—
192	#107	C₂×D₄₇	1	1	yes	characteristic, complemented
193	#102	—	47	2	no	—
194	#102	—	47	2	no	—
195	#102	—	47	2	no	—
196	#102	C₂×D₄₇	1	2	yes	complemented
197	C₂⁴	—	47	1	no	—
198	C₂⁴	—	94	2	no	—
199	C₂×D₄	—	2	2	no	—
200	C₂×D₄	—	47	2	no	—
201	C₂×D₄	—	94	2	no	—
202	C₂×D₄	—	94	4	no	—
203	C₂×D₄	—	94	4	no	—
204	C₂×D₄	—	94	2	no	—
205	C₂×D₄	—	94	2	no	—
206	C₂×D₄	—	94	2	no	—
207	C₂×D₄	—	188	8	no	—
208	C₂×D₄	C₂²×D₄₇	1	2	yes	—
209	C₂²×C₄	—	47	1	no	—
210	C₂²×C₄	—	47	1	no	—
211	C₂²×C₄	—	47	1	no	—
212	C₂²×C₄	—	47	1	no	—
213	C₂²×C₄	—	47	1	no	—
214	C₂²×C₄	—	94	2	no	—
215	C₂²×C₄	—	94	2	no	—
216	C₂²×C₄	—	94	2	no	—
217	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
218	D₈	—	2	2	no	—
219	D₈	—	94	4	no	—
220	D₈	—	94	2	no	—
221	C₂×C₈	—	2	2	no	—
222	C₂×C₈	—	47	1	no	—
223	C₂×C₈	—	47	4	no	—
224	C₂×C₈	—	47	1	no	—
225	C₂×C₈	—	94	2	no	—
226	C₂×C₈	—	94	2	no	—
227	C₂×C₈	—	94	2	no	—
228	C₂×C₈	—	94	2	no	—
229	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
230	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
231	C₄⋊C₄	—	47	2	no	—
232	C₄⋊C₄	—	94	2	no	—
233	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
234	C₂²⋊C₄	—	2	2	no	—
235	C₂²⋊C₄	—	94	2	no	—
236	C₂²⋊C₄	—	94	2	no	—
237	C₂²⋊C₄	—	94	2	no	—
238	C₂³	—	2	2	no	—
239	C₂³	—	47	1	no	—
240	C₂³	—	47	4	no	—
241	C₂³	—	47	1	no	—
242	C₂³	—	94	2	no	—
243	C₂³	—	94	2	no	—
244	C₂³	—	94	2	no	—
245	C₂³	—	188	4	no	—
246	C₂³	—	188	4	no	—
247	C₂³	—	188	4	no	—
248	C₂³	D₄×D₄₇	1	1	yes	characteristic
249	D₄	—	2	2	no	—
250	D₄	—	2	2	no	—
251	D₄	—	4	4	no	—
252	D₄	—	94	2	no	—
253	D₄	—	94	2	no	—
254	D₄	—	188	4	no	—
255	D₄	—	188	4	no	—
256	D₄	—	188	4	no	—
257	D₄	—	188	4	no	—
258	C₂×C₄	—	2	1	no	—
259	C₂×C₄	—	2	1	no	—
260	C₂×C₄	—	2	2	no	—
261	C₂×C₄	—	47	1	no	—
262	C₂×C₄	—	47	2	no	—
263	C₂×C₄	—	47	2	no	—
264	C₂×C₄	—	47	1	no	—
265	C₂×C₄	—	94	2	no	—
266	C₂×C₄	—	94	2	no	—
267	C₂×C₄	—	94	2	no	—
268	C₂×C₄	—	94	1	no	—
269	C₂×C₄	—	94	1	no	—
270	C₂×C₄	—	94	2	no	—
271	C₂×C₄	—	188	4	no	—
272	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
273	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
274	C₈	—	2	1	no	—
275	C₈	—	47	2	no	—
276	C₈	—	94	1	no	—
277	C₈	D₄×D₄₇	1	2	yes	complemented
278	C₂²	—	2	1	no	—
279	C₂²	—	2	1	no	—
280	C₂²	—	4	2	no	—
281	C₂²	—	4	2	no	—
282	C₂²	—	4	2	no	—
283	C₂²	—	47	2	no	—
284	C₂²	—	47	2	no	—
285	C₂²	—	47	2	no	—
286	C₂²	—	47	2	no	—
287	C₂²	—	94	8	no	—
288	C₂²	—	94	1	no	—
289	C₂²	—	94	1	no	—
290	C₂²	—	376	8	no	—
291	C₂²	—	188	2	no	—
292	C₂²	—	188	2	no	—
293	C₂²	—	188	2	no	—
294	C₂²	D₈×D₄₇	1	2	yes	complemented
295	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
296	C₄	—	2	1	no	—
297	C₄	—	4	2	no	—
298	C₄	—	47	2	no	—
299	C₄	—	94	1	no	—
300	C₄	—	188	2	no	—
301	C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
302	C₄	#41×D₄₇	1	1	yes	characteristic
303	C₂	—	2	2	no	—
304	C₂	—	8	2	no	—
305	C₂	—	47	4	no	—
306	C₂	—	94	2	no	—
307	C₂	—	376	2	no	—
308	C₂	#121×D₄₇	1	1	yes	characteristic
309	C₂	C₂×D₈×D₄₇	1	1	yes	characteristic
310	C₂	#135×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₄₇×#466	C₂
socle	C₂²×C₄₇	C₂²×D₄
hypercenter	#466	D₄₇
hypocenter	C₄₇	C₂×#466
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #466

Complements

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

N	H ≅ G/N	type
1. C₂×D₈×D₄₇	C₂	semidirect
2. C₂²×C₈×D₄₇	C₂	semidirect
3. #121×D₄₇	C₂	semidirect
4. #15689360	C₂	semidirect
5. #15689359	C₂	semidirect
6. #15689358	C₂	semidirect
7. #15689357	C₂	semidirect
8. #15689356	C₂	semidirect
9. #107×D₄₇	C₂	semidirect
10. #102×D₄₇	C₂	semidirect
11. C₄₇×#466	C₂	semidirect
15. C₂×D₃₇₆	C₂²	semidirect
16. C₂×#10625334	C₂²	semidirect
18. C₂²×C₄₇⋊C₈	C₂²	semidirect
22. C₂×C₈×D₄₇	C₂²	semidirect
23. C₂×C₈×D₄₇	C₂²	semidirect
24. #13093999	C₂²	semidirect
25. #13093998	C₂²	semidirect
28. #13093995	C₂²	semidirect
31. #13093958	C₂²	semidirect
32. #13093957	C₂²	semidirect
33. #13093946	C₂²	semidirect
34. #13093945	C₂²	semidirect
35. #13093944	C₂²	semidirect
36. C₂×D₈×C₄₇	C₂²	semidirect
37. C₂²×C₈×C₄₇	C₂²	semidirect
38. #121×C₄₇	C₂²	semidirect
39. #107×C₄₇	C₂²	semidirect
40. #102×C₄₇	C₂²	semidirect
81. C₈×D₄₇	D₄	semidirect
90. C₂²×D₄₇	D₈	semidirect
119. C₈×C₄₇	C₂×D₄	semidirect
121. C₄₇⋊C₈	C₂×D₄	semidirect
127. C₂²×C₄₇	C₂×D₈	semidirect
138. C₂×D₄₇	C₂×D₈	semidirect
155. D₄₇	#466	direct (N × H)
164. #466	D₄₇	direct (N × H)
167. C₄₇	C₂×#466	semidirect
174. C₂×D₈	C₂×D₄₇	semidirect
181. C₂²×C₈	C₂×D₄₇	semidirect
187. #121	C₂×D₄₇	semidirect
192. #107	C₂×D₄₇	semidirect
196. #102	C₂×D₄₇	semidirect
277. C₈	D₄×D₄₇	semidirect
294. C₂²	D₈×D₄₇	semidirect

Subgroups — #466×D47 #20252952

Conjugacy classes of subgroups

Complements

Subgroups — #466×D₄₇ #20252952