Subgroups — #473×D₄₇ #20253097

Order 6016.

448 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#137×D₄₇	C₂	1	2	yes	maximal
2	C₂×Q₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#131×D₄₇	C₂	1	1	yes	maximal, characteristic
4	#15689399	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689398	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689397	C₂	1	2	yes	maximal, complemented
7	#15689396	C₂	1	2	yes	maximal, complemented
8	#15689395	C₂	1	1	yes	maximal, characteristic, complemented
9	#108×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#101×D₄₇	C₂	1	2	yes	maximal, complemented
11	C₄₇×#473	C₂	1	1	yes	maximal, characteristic, complemented
12	#41×D₄₇	C₂²	1	1	yes	characteristic
13	C₂×Q₈×D₄₇	C₂²	1	2	yes	—
14	#13094057	C₂²	1	2	yes	—
15	#13094056	—	2	2	no	—
16	#13094055	C₂²	1	2	yes	—
17	#13094054	C₂²	1	2	yes	—
18	#13094053	—	2	2	no	—
19	C₂×Dic₁₈₈	C₂²	1	1	yes	characteristic, complemented
20	C₂×#10625337	C₂²	1	2	yes	complemented
21	Q₁₆×D₄₇	—	2	2	no	—
22	Q₁₆×D₄₇	—	2	1	no	—
23	Q₁₆×D₄₇	—	2	1	no	—
24	Q₁₆×D₄₇	—	2	1	no	—
25	Q₁₆×D₄₇	—	2	1	no	—
26	SD₁₆×D₄₇	—	2	2	no	—
27	#13094032	—	2	1	no	—
28	#13094032	C₂²	1	1	yes	characteristic
29	#13094031	C₂²	1	1	yes	characteristic
30	#13094030	—	2	1	no	—
31	#13094030	C₂²	1	1	yes	characteristic
32	M₁₆×D₄₇	—	2	1	no	—
33	M₁₆×D₄₇	C₂²	1	1	yes	characteristic
34	M₁₆×D₄₇	C₂²	1	2	yes	—
35	C₂×C₈×D₄₇	—	2	1	no	—
36	C₂×C₈×D₄₇	C₂²	1	1	yes	characteristic
37	#13093960	C₂²	1	1	yes	characteristic, complemented
38	#13093959	C₂²	1	2	yes	complemented
39	#13093943	C₂²	1	2	yes	complemented
40	#13093942	C₂²	1	2	yes	complemented
41	#13093942	C₂²	1	2	yes	complemented
42	#137×C₄₇	C₂²	1	2	yes	—
43	C₂×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
44	#131×C₄₇	C₂²	1	1	yes	characteristic
45	#108×C₄₇	C₂²	1	1	yes	characteristic, complemented
46	#101×C₄₇	C₂²	1	2	yes	complemented
47	#41×C₄₇	C₂³	1	1	yes	characteristic
48	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
49	#10625354	D₄	1	1	yes	characteristic
50	Q₈×D₄₇	—	2	2	no	—
51	Q₈×D₄₇	—	2	2	no	—
52	Q₈×D₄₇	—	2	2	no	—
53	Q₈×D₄₇	—	2	2	no	—
54	Q₈×D₄₇	D₄	1	1	yes	characteristic
55	#10625352	—	2	1	no	—
56	#10625352	D₄	1	1	yes	characteristic
57	D₄×D₄₇	—	2	1	no	—
58	D₄×D₄₇	D₄	1	1	yes	characteristic
59	#10625350	—	2	1	no	—
60	#10625350	C₂³	1	1	yes	characteristic
61	C₂×C₄×D₄₇	—	2	1	no	—
62	C₂×C₄×D₄₇	—	2	2	no	—
63	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
64	C₂×Dic₉₄	—	2	2	no	—
65	C₂×Dic₉₄	C₂³	1	2	yes	—
66	Q₁₆×C₄₇	—	2	2	no	—
67	Q₁₆×C₄₇	—	2	1	no	—
68	Q₁₆×C₄₇	—	2	1	no	—
69	SD₁₆×C₄₇	—	2	2	no	—
70	M₁₆×C₄₇	—	2	1	no	—
71	M₁₆×C₄₇	C₂³	1	2	yes	—
72	M₁₆×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×C₈×C₄₇	—	2	1	no	—
74	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
75	#10625337	—	2	2	no	—
76	#10625337	—	2	2	no	—
77	#10625337	—	2	2	no	—
78	#10625337	—	2	2	no	—
79	#10625336	—	2	2	no	—
80	#10625335	—	2	2	no	—
81	#10625329	—	2	1	no	—
82	#10625329	C₂³	1	1	yes	characteristic
83	#10625329	C₂³	1	2	yes	—
84	C₂×C₄₇⋊C₈	—	2	1	no	—
85	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
86	Dic₁₈₈	—	2	2	no	—
87	Dic₁₈₈	—	2	1	no	—
88	Dic₁₈₈	—	2	1	no	—
89	#10625325	—	2	2	no	—
90	#10625324	—	2	1	no	—
91	#10625324	—	2	2	no	—
92	#10625324	—	2	1	no	—
93	#10625324	—	2	1	no	—
94	C₈×D₄₇	—	2	1	no	—
95	C₈×D₄₇	—	2	2	no	—
96	C₈×D₄₇	—	2	1	no	—
97	C₈×D₄₇	—	2	1	no	—
98	C₈×D₄₇	D₄	1	1	yes	characteristic
99	C₈×D₄₇	D₄	1	1	yes	characteristic
100	C₈×D₄₇	D₄	1	1	yes	characteristic
101	C₈×D₄₇	D₄	1	1	yes	characteristic
102	C₂²×D₄₇	—	2	1	no	—
103	C₂²×D₄₇	#41	1	1	yes	characteristic
104	Q₈×C₄₇	—	2	2	no	—
105	Q₈×C₄₇	—	2	2	no	—
106	Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
107	D₄×C₄₇	—	2	1	no	—
108	D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂×C₄×C₄₇	—	2	1	no	—
110	C₂×C₄×C₄₇	—	2	2	no	—
111	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
112	C₂²⋊D₄₇	—	2	1	no	—
113	C₂²⋊D₄₇	—	2	1	no	—
114	C₂²⋊D₄₇	—	2	1	no	—
115	C₂×Dic₄₇	—	2	1	no	—
116	C₂×Dic₄₇	—	2	2	no	—
117	C₂×Dic₄₇	#41	1	1	yes	characteristic
118	D₁₈₈	—	2	1	no	—
119	D₁₈₈	C₂×D₄	1	1	yes	characteristic
120	C₄×D₄₇	—	2	1	no	—
121	C₄×D₄₇	—	2	1	no	—
122	C₄×D₄₇	—	2	1	no	—
123	C₄×D₄₇	—	4	2	no	—
124	C₄×D₄₇	—	4	2	no	—
125	C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
126	C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
127	C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
128	C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
129	Dic₉₄	—	2	1	no	—
130	Dic₉₄	—	2	2	no	—
131	Dic₉₄	—	2	2	no	—
132	Dic₉₄	—	4	2	no	—
133	Dic₉₄	—	4	2	no	—
134	Dic₉₄	C₂×D₄	1	1	yes	characteristic
135	C₈×C₄₇	—	2	1	no	—
136	C₈×C₄₇	—	2	2	no	—
137	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
138	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
139	C₄₇⋊C₈	—	2	1	no	—
140	C₄₇⋊C₈	—	2	2	no	—
141	C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
142	C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄₇	—	2	1	no	—
144	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
145	C₂×D₄₇	—	2	2	no	—
146	C₂×D₄₇	—	2	1	no	—
147	C₂×D₄₇	—	4	2	no	—
148	C₂×D₄₇	#121	1	1	yes	characteristic
149	C₂×D₄₇	#121	1	1	yes	characteristic
150	C₄×C₄₇	—	2	1	no	—
151	C₄×C₄₇	—	4	2	no	—
152	C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
153	C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
154	Dic₄₇	—	2	1	no	—
155	Dic₄₇	—	4	2	no	—
156	Dic₄₇	#121	1	1	yes	characteristic
157	Dic₄₇	#121	1	1	yes	characteristic
158	C₂×#473	—	47	1	no	maximal, Sylow
159	C₂×C₄₇	—	2	1	no	—
160	C₂×C₄₇	—	4	1	no	—
161	C₂×C₄₇	C₂×#121	1	1	yes	characteristic
162	D₄₇	—	2	1	no	—
163	D₄₇	—	4	1	no	—
164	D₄₇	#473	1	2	yes	direct product factor
165	C₂×#137	—	47	2	no	—
166	C₂²×Q₁₆	—	47	1	no	—
167	C₂×#131	—	47	1	no	—
168	#473	—	47	2	no	—
169	#473	—	47	1	no	—
170	#473	—	47	1	no	—
171	#473	—	47	1	no	—
172	#473	—	47	2	no	—
173	#473	D₄₇	1	1	yes	characteristic, direct product factor
174	C₂×#108	—	47	1	no	—
175	C₂×#101	—	47	2	no	—
176	C₄₇	C₂×#473	1	1	yes	characteristic, complemented, Sylow
177	C₂×#41	—	47	1	no	—
178	C₂²×Q₈	—	47	2	no	—
179	#137	—	47	2	no	—
180	#137	—	47	2	no	—
181	#137	—	47	2	no	—
182	#137	—	94	2	no	—
183	#137	—	94	2	no	—
184	#137	C₂×D₄₇	1	2	yes	—
185	C₂×Q₁₆	—	47	2	no	—
186	C₂×Q₁₆	—	47	1	no	—
187	C₂×Q₁₆	—	94	1	no	—
188	C₂×Q₁₆	—	94	1	no	—
189	C₂×Q₁₆	—	94	1	no	—
190	C₂×Q₁₆	—	94	1	no	—
191	C₂×Q₁₆	—	94	2	no	—
192	C₂×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
193	C₂×SD₁₆	—	94	2	no	—
194	#131	—	47	1	no	—
195	#131	—	47	1	no	—
196	#131	—	47	1	no	—
197	#131	—	94	1	no	—
198	#131	—	94	1	no	—
199	#131	C₂×D₄₇	1	1	yes	characteristic
200	C₂×M₁₆	—	47	1	no	—
201	C₂×M₁₆	—	47	2	no	—
202	C₂×M₁₆	—	94	1	no	—
203	C₂²×C₈	—	47	1	no	—
204	C₂²×C₈	—	94	1	no	—
205	#108	—	47	2	no	—
206	#108	—	47	1	no	—
207	#108	C₂×D₄₇	1	1	yes	characteristic, complemented
208	#101	—	47	2	no	—
209	#101	—	47	2	no	—
210	#101	—	47	2	no	—
211	#101	C₂×D₄₇	1	2	yes	complemented
212	#41	—	47	1	no	—
213	#41	—	47	1	no	—
214	#41	—	47	1	no	—
215	#41	—	94	1	no	—
216	#41	—	94	1	no	—
217	#41	C₂²×D₄₇	1	1	yes	characteristic
218	C₂×Q₈	—	47	1	no	—
219	C₂×Q₈	—	47	2	no	—
220	C₂×Q₈	—	94	2	no	—
221	C₂×Q₈	—	94	2	no	—
222	C₂×Q₈	—	94	2	no	—
223	C₂×Q₈	—	94	2	no	—
224	C₂×Q₈	—	94	2	no	—
225	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
226	C₂×D₄	—	47	1	no	—
227	C₂×D₄	—	94	1	no	—
228	C₂²×C₄	—	47	1	no	—
229	C₂²×C₄	—	94	1	no	—
230	C₂²×C₄	—	94	2	no	—
231	Q₁₆	—	2	2	no	—
232	Q₁₆	—	2	1	no	—
233	Q₁₆	—	2	1	no	—
234	Q₁₆	—	94	2	no	—
235	Q₁₆	—	94	2	no	—
236	Q₁₆	—	94	2	no	—
237	Q₁₆	—	94	2	no	—
238	Q₁₆	—	94	2	no	—
239	Q₁₆	—	94	1	no	—
240	Q₁₆	—	94	1	no	—
241	SD₁₆	—	2	2	no	—
242	SD₁₆	—	94	2	no	—
243	SD₁₆	—	94	2	no	—
244	SD₁₆	—	94	2	no	—
245	M₁₆	—	2	1	no	—
246	M₁₆	—	47	1	no	—
247	M₁₆	—	47	2	no	—
248	M₁₆	—	94	1	no	—
249	M₁₆	—	94	1	no	—
250	M₁₆	—	94	2	no	—
251	M₁₆	—	94	1	no	—
252	M₁₆	—	94	1	no	—
253	M₁₆	C₂²×D₄₇	1	1	yes	characteristic
254	M₁₆	C₂²×D₄₇	1	2	yes	—
255	C₂×C₈	—	2	1	no	—
256	C₂×C₈	—	47	1	no	—
257	C₂×C₈	—	47	1	no	—
258	C₂×C₈	—	47	1	no	—
259	C₂×C₈	—	47	1	no	—
260	C₂×C₈	—	47	1	no	—
261	C₂×C₈	—	94	1	no	—
262	C₂×C₈	—	94	1	no	—
263	C₂×C₈	—	94	2	no	—
264	C₂×C₈	—	94	1	no	—
265	C₂×C₈	—	94	1	no	—
266	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
267	C₂³	—	47	1	no	—
268	C₂³	—	94	1	no	—
269	Q₈	—	2	2	no	—
270	Q₈	—	2	2	no	—
271	Q₈	—	47	1	no	—
272	Q₈	—	94	1	no	—
273	Q₈	—	94	2	no	—
274	Q₈	—	94	2	no	—
275	Q₈	—	188	2	no	—
276	Q₈	—	188	2	no	—
277	Q₈	D₄×D₄₇	1	1	yes	characteristic
278	D₄	—	2	1	no	—
279	D₄	—	47	1	no	—
280	D₄	—	94	1	no	—
281	D₄	—	94	1	no	—
282	D₄	—	94	1	no	—
283	D₄	—	94	1	no	—
284	D₄	D₄×D₄₇	1	1	yes	characteristic
285	C₂×C₄	—	2	1	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	47	1	no	—
288	C₂×C₄	—	47	1	no	—
289	C₂×C₄	—	47	1	no	—
290	C₂×C₄	—	47	1	no	—
291	C₂×C₄	—	47	1	no	—
292	C₂×C₄	—	94	1	no	—
293	C₂×C₄	—	94	1	no	—
294	C₂×C₄	—	94	1	no	—
295	C₂×C₄	—	94	1	no	—
296	C₂×C₄	—	94	2	no	—
297	C₂×C₄	—	188	2	no	—
298	C₂×C₄	—	188	2	no	—
299	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
300	C₈	—	2	1	no	—
301	C₈	—	2	2	no	—
302	C₈	—	47	1	no	—
303	C₈	—	47	1	no	—
304	C₈	—	94	1	no	—
305	C₈	—	94	2	no	—
306	C₈	D₄×D₄₇	1	1	yes	characteristic
307	C₈	D₄×D₄₇	1	1	yes	characteristic
308	C₂²	—	2	1	no	—
309	C₂²	—	47	1	no	—
310	C₂²	—	47	1	no	—
311	C₂²	—	94	2	no	—
312	C₂²	—	94	1	no	—
313	C₂²	—	188	2	no	—
314	C₂²	#41×D₄₇	1	1	yes	characteristic
315	C₄	—	2	1	no	—
316	C₄	—	4	2	no	—
317	C₄	—	47	1	no	—
318	C₄	—	47	1	no	—
319	C₄	—	94	1	no	—
320	C₄	—	188	2	no	—
321	C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
322	C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
323	C₂	—	2	1	no	—
324	C₂	—	4	1	no	—
325	C₂	—	47	2	no	—
326	C₂	—	94	1	no	—
327	C₂	—	188	1	no	—
328	C₂	#121×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#121×D₄₇
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₄₇×#473	C₂
socle	C₂×C₄₇	C₂×#121
hypercenter	#473	D₄₇
hypocenter	C₄₇	C₂×#473
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #473

Complements

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

N	H ≅ G/N	type
2. C₂×Q₁₆×D₄₇	C₂	semidirect
4. #15689399	C₂	semidirect
5. #15689398	C₂	semidirect
6. #15689397	C₂	semidirect
7. #15689396	C₂	semidirect
8. #15689395	C₂	semidirect
9. #108×D₄₇	C₂	semidirect
10. #101×D₄₇	C₂	semidirect
11. C₄₇×#473	C₂	semidirect
19. C₂×Dic₁₈₈	C₂²	semidirect
20. C₂×#10625337	C₂²	semidirect
37. #13093960	C₂²	semidirect
38. #13093959	C₂²	semidirect
39. #13093943	C₂²	semidirect
40. #13093942	C₂²	semidirect
41. #13093942	C₂²	semidirect
43. C₂×Q₁₆×C₄₇	C₂²	semidirect
45. #108×C₄₇	C₂²	semidirect
46. #101×C₄₇	C₂²	semidirect
164. D₄₇	#473	direct (N × H)
173. #473	D₄₇	direct (N × H)
176. C₄₇	C₂×#473	semidirect
192. C₂×Q₁₆	C₂×D₄₇	semidirect
207. #108	C₂×D₄₇	semidirect
211. #101	C₂×D₄₇	semidirect

Subgroups — #473×D47 #20253097

Conjugacy classes of subgroups

Complements

Subgroups — #473×D₄₇ #20253097