Subgroups — #444×D₄₇ #20252280

Order 6016.

464 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#135×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#131×D₄₇	C₂	1	2	yes	maximal, complemented
3	#15689246	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689245	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689244	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689243	C₂	1	2	yes	maximal, complemented
7	#15689242	C₂	1	2	yes	maximal, complemented
8	#108×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#104×D₄₇	C₂	1	2	yes	maximal, complemented
10	#97×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#444	C₂	1	1	yes	maximal, characteristic, complemented
12	#41×D₄₇	C₂²	1	2	yes	—
13	#13094047	C₄	1	1	yes	characteristic, complemented
14	#13094046	C₂²	1	1	yes	characteristic
15	#13094045	C₄	1	2	yes	complemented
16	#13094044	C₂²	1	2	yes	—
17	#13094043	C₄	1	1	yes	characteristic, complemented
18	Q₁₆×D₄₇	C₄	1	1	yes	characteristic, complemented
19	SD₁₆×D₄₇	C₄	1	2	yes	complemented
20	D₈×D₄₇	C₄	1	1	yes	characteristic, complemented
21	#13094032	—	2	2	no	—
22	#13094032	C₂²	1	2	yes	complemented
23	#13094031	C₂²	1	2	yes	complemented
24	#13094030	—	2	2	no	—
25	#13094030	C₂²	1	2	yes	complemented
26	M₁₆×D₄₇	—	2	2	no	—
27	M₁₆×D₄₇	C₂²	1	2	yes	—
28	C₂×C₈×D₄₇	—	2	2	no	—
29	C₂×C₈×D₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₈×D₄₇	C₂²	1	1	yes	characteristic
31	C₄²×D₄₇	C₂²	1	1	yes	characteristic
32	#13093960	C₂²	1	1	yes	characteristic, complemented
33	#13093959	C₂²	1	2	yes	complemented
34	#13093952	C₂²	1	2	yes	complemented
35	#13093951	C₂²	1	2	yes	complemented
36	#13093950	C₂²	1	2	yes	complemented
37	#13093935	C₂²	1	1	yes	characteristic, complemented
38	#13093934	C₂²	1	1	yes	characteristic, complemented
39	#13093934	C₂²	1	1	yes	characteristic, complemented
40	#135×C₄₇	C₂²	1	1	yes	characteristic
41	#131×C₄₇	C₂²	1	2	yes	complemented
42	#108×C₄₇	C₂²	1	1	yes	characteristic, complemented
43	#104×C₄₇	C₂²	1	2	yes	complemented
44	#97×C₄₇	C₂²	1	1	yes	characteristic, complemented
45	#41×C₄₇	C₂³	1	2	yes	—
46	#10625354	C₂×C₄	1	2	yes	—
47	Q₈×D₄₇	C₂×C₄	1	2	yes	—
48	#10625352	—	2	2	no	—
49	#10625352	C₂×C₄	1	2	yes	—
50	D₄×D₄₇	—	2	2	no	—
51	D₄×D₄₇	C₂×C₄	1	2	yes	—
52	#10625350	—	2	2	no	—
53	#10625350	C₂³	1	2	yes	—
54	C₂×C₄×D₄₇	—	2	2	no	—
55	C₂×C₄×D₄₇	—	2	1	no	—
56	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
57	Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
58	SD₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
59	D₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
60	M₁₆×C₄₇	—	2	2	no	—
61	M₁₆×C₄₇	C₂³	1	2	yes	—
62	C₂×C₈×C₄₇	—	2	2	no	—
63	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
64	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
65	C₄²×C₄₇	C₂³	1	1	yes	characteristic
66	#10625337	C₂×C₄	1	2	yes	complemented
67	#10625336	C₂×C₄	1	2	yes	complemented
68	#10625335	C₂×C₄	1	2	yes	complemented
69	#10625334	C₂×C₄	1	2	yes	complemented
70	C₄×Dic₄₇	—	2	1	no	—
71	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
72	#10625329	—	2	2	no	—
73	#10625329	C₂³	1	2	yes	—
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	Dic₁₈₈	C₂×C₄	1	1	yes	characteristic, complemented
78	D₃₇₆	C₂×C₄	1	1	yes	characteristic, complemented
79	#10625325	C₂×C₄	1	2	yes	complemented
80	#10625324	—	2	2	no	—
81	#10625324	—	2	2	no	—
82	#10625324	—	2	2	no	—
83	C₈×D₄₇	—	2	2	no	—
84	C₈×D₄₇	—	2	2	no	—
85	C₈×D₄₇	—	2	2	no	—
86	C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
87	C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
88	C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
89	C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
90	C₈×D₄₇	D₄	1	2	yes	—
91	C₈×D₄₇	D₄	1	2	yes	—
92	C₂²×D₄₇	—	2	2	no	—
93	C₂²×D₄₇	#41	1	1	yes	characteristic
94	Q₈×C₄₇	C₂²×C₄	1	2	yes	—
95	D₄×C₄₇	—	2	2	no	—
96	D₄×C₄₇	C₂²×C₄	1	2	yes	—
97	C₂×C₄×C₄₇	—	2	2	no	—
98	C₂×C₄×C₄₇	—	2	1	no	—
99	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
100	C₂²⋊D₄₇	—	2	2	no	—
101	C₂²⋊D₄₇	—	2	2	no	—
102	C₂²⋊D₄₇	—	2	2	no	—
103	C₂×Dic₄₇	—	2	2	no	—
104	C₂×Dic₄₇	—	2	1	no	—
105	C₂×Dic₄₇	#41	1	1	yes	characteristic
106	D₁₈₈	—	2	2	no	—
107	D₁₈₈	C₂²×C₄	1	2	yes	—
108	C₄×D₄₇	—	2	2	no	—
109	C₄×D₄₇	—	2	2	no	—
110	C₄×D₄₇	—	2	2	no	—
111	C₄×D₄₇	—	4	2	no	—
112	C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
115	C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
116	Dic₉₄	—	2	2	no	—
117	Dic₉₄	C₂²×C₄	1	2	yes	—
118	C₈×C₄₇	—	2	2	no	—
119	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
120	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₈×C₄₇	C₂×D₄	1	2	yes	—
122	C₄₇⋊C₈	—	2	2	no	—
123	C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
124	C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
125	C₄₇⋊C₈	C₂×D₄	1	2	yes	—
126	C₂²×C₄₇	—	2	2	no	—
127	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
128	C₂×D₄₇	—	2	2	no	—
129	C₂×D₄₇	—	2	2	no	—
130	C₂×D₄₇	—	4	4	no	—
131	C₂×D₄₇	C₄×D₄	1	1	yes	characteristic
132	C₂×D₄₇	C₄×D₄	1	1	yes	characteristic
133	C₄×C₄₇	—	2	2	no	—
134	C₄×C₄₇	—	4	1	no	—
135	C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
136	C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
137	Dic₄₇	—	2	2	no	—
138	Dic₄₇	—	4	1	no	—
139	Dic₄₇	C₄×D₄	1	1	yes	characteristic
140	Dic₄₇	C₄×D₄	1	1	yes	characteristic
141	C₂×#444	—	47	1	no	maximal, Sylow
142	C₂×C₄₇	—	2	1	no	—
143	C₂×C₄₇	—	4	2	no	—
144	C₂×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
145	D₄₇	—	2	1	no	—
146	D₄₇	—	4	2	no	—
147	D₄₇	#444	1	2	yes	direct product factor
148	C₂×#135	—	47	1	no	—
149	C₂×#131	—	47	2	no	—
150	#444	—	47	1	no	—
151	#444	—	47	2	no	—
152	#444	—	47	1	no	—
153	#444	—	47	2	no	—
154	#444	—	47	1	no	—
155	#444	D₄₇	1	1	yes	characteristic, direct product factor
156	C₂×#108	—	47	1	no	—
157	C₂×#104	—	47	2	no	—
158	C₂×#97	—	47	1	no	—
159	C₄₇	C₂×#444	1	1	yes	characteristic, complemented, Sylow
160	C₂×#41	—	47	2	no	—
161	#135	—	47	2	no	—
162	#135	—	47	1	no	—
163	#135	—	47	2	no	—
164	#135	—	47	1	no	—
165	#135	—	47	1	no	—
166	#135	C₂×D₄₇	1	1	yes	characteristic
167	C₂×Q₁₆	—	47	1	no	—
168	C₂×SD₁₆	—	47	2	no	—
169	C₂×D₈	—	47	1	no	—
170	#131	—	47	2	no	—
171	#131	—	47	2	no	—
172	#131	—	47	2	no	—
173	#131	—	94	2	no	—
174	#131	—	94	2	no	—
175	#131	C₂×D₄₇	1	2	yes	complemented
176	C₂×M₁₆	—	47	2	no	—
177	C₂×M₁₆	—	94	2	no	—
178	C₂²×C₈	—	47	1	no	—
179	C₂²×C₈	—	47	1	no	—
180	C₂²×C₈	—	94	2	no	—
181	C₂×C₄²	—	47	1	no	—
182	#108	—	47	2	no	—
183	#108	—	47	1	no	—
184	#108	C₂×D₄₇	1	1	yes	characteristic, complemented
185	#104	—	47	2	no	—
186	#104	—	47	2	no	—
187	#104	—	47	2	no	—
188	#104	C₂×D₄₇	1	2	yes	complemented
189	#97	—	47	1	no	—
190	#97	—	47	1	no	—
191	#97	—	47	1	no	—
192	#97	C₂×D₄₇	1	1	yes	characteristic, complemented
193	#41	—	47	2	no	—
194	#41	—	47	2	no	—
195	#41	—	47	2	no	—
196	#41	—	94	2	no	—
197	#41	—	94	2	no	—
198	#41	C₂²×D₄₇	1	2	yes	—
199	C₂×Q₈	—	47	2	no	—
200	C₂×D₄	—	47	2	no	—
201	C₂×D₄	—	94	2	no	—
202	C₂²×C₄	—	47	1	no	—
203	C₂²×C₄	—	94	2	no	—
204	C₂²×C₄	—	94	1	no	—
205	Q₁₆	—	47	2	no	—
206	Q₁₆	—	47	1	no	—
207	Q₁₆	C₄×D₄₇	1	1	yes	characteristic, complemented
208	SD₁₆	—	47	2	no	—
209	SD₁₆	—	47	2	no	—
210	SD₁₆	—	47	2	no	—
211	SD₁₆	C₄×D₄₇	1	2	yes	complemented
212	D₈	—	47	2	no	—
213	D₈	—	47	1	no	—
214	D₈	C₄×D₄₇	1	1	yes	characteristic, complemented
215	M₁₆	—	2	2	no	—
216	M₁₆	—	47	2	no	—
217	M₁₆	—	94	2	no	—
218	M₁₆	—	94	2	no	—
219	M₁₆	—	94	2	no	—
220	M₁₆	—	94	2	no	—
221	M₁₆	C₂²×D₄₇	1	2	yes	—
222	C₂×C₈	—	2	2	no	—
223	C₂×C₈	—	47	1	no	—
224	C₂×C₈	—	47	1	no	—
225	C₂×C₈	—	47	1	no	—
226	C₂×C₈	—	47	1	no	—
227	C₂×C₈	—	47	1	no	—
228	C₂×C₈	—	47	1	no	—
229	C₂×C₈	—	47	2	no	—
230	C₂×C₈	—	47	2	no	—
231	C₂×C₈	—	94	2	no	—
232	C₂×C₈	—	94	2	no	—
233	C₂×C₈	—	94	2	no	—
234	C₂×C₈	—	94	2	no	—
235	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
236	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
237	C₄²	—	47	1	no	—
238	C₄²	—	94	1	no	—
239	C₄²	C₂²×D₄₇	1	1	yes	characteristic
240	C₂³	—	47	1	no	—
241	C₂³	—	94	2	no	—
242	Q₈	—	47	2	no	—
243	Q₈	—	94	2	no	—
244	Q₈	C₂×C₄×D₄₇	1	2	yes	—
245	D₄	—	2	2	no	—
246	D₄	—	47	2	no	—
247	D₄	—	94	2	no	—
248	D₄	—	94	2	no	—
249	D₄	—	94	2	no	—
250	D₄	—	94	2	no	—
251	D₄	C₂×C₄×D₄₇	1	2	yes	—
252	C₂×C₄	—	2	2	no	—
253	C₂×C₄	—	2	1	no	—
254	C₂×C₄	—	47	1	no	—
255	C₂×C₄	—	47	1	no	—
256	C₂×C₄	—	47	1	no	—
257	C₂×C₄	—	47	1	no	—
258	C₂×C₄	—	47	1	no	—
259	C₂×C₄	—	94	2	no	—
260	C₂×C₄	—	94	2	no	—
261	C₂×C₄	—	94	2	no	—
262	C₂×C₄	—	94	2	no	—
263	C₂×C₄	—	94	1	no	—
264	C₂×C₄	—	188	2	no	—
265	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
266	C₈	—	2	2	no	—
267	C₈	—	47	1	no	—
268	C₈	—	47	1	no	—
269	C₈	—	47	2	no	—
270	C₈	—	94	2	no	—
271	C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
272	C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
273	C₈	D₄×D₄₇	1	2	yes	—
274	C₂²	—	2	2	no	—
275	C₂²	—	47	1	no	—
276	C₂²	—	47	1	no	—
277	C₂²	—	94	2	no	—
278	C₂²	—	94	2	no	—
279	C₂²	—	188	4	no	—
280	C₂²	#41×D₄₇	1	1	yes	characteristic
281	C₄	—	2	2	no	—
282	C₄	—	4	1	no	—
283	C₄	—	47	1	no	—
284	C₄	—	47	1	no	—
285	C₄	—	94	2	no	—
286	C₄	—	188	1	no	—
287	C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
288	C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
289	C₂	—	2	1	no	—
290	C₂	—	4	2	no	—
291	C₂	—	47	2	no	—
292	C₂	—	94	1	no	—
293	C₂	—	188	2	no	—
294	C₂	C₄×D₄×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₄₇×#444	C₂
socle	C₂×C₄₇	C₂×C₄×D₄
hypercenter	#444	D₄₇
hypocenter	C₄₇	C₂×#444
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #444

Complements

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

N	H ≅ G/N	type
2. #131×D₄₇	C₂	semidirect
3. #15689246	C₂	semidirect
4. #15689245	C₂	semidirect
5. #15689244	C₂	semidirect
6. #15689243	C₂	semidirect
7. #15689242	C₂	semidirect
8. #108×D₄₇	C₂	semidirect
9. #104×D₄₇	C₂	semidirect
10. #97×D₄₇	C₂	semidirect
11. C₄₇×#444	C₂	semidirect
13. #13094047	C₄	semidirect
15. #13094045	C₄	semidirect
17. #13094043	C₄	semidirect
18. Q₁₆×D₄₇	C₄	semidirect
19. SD₁₆×D₄₇	C₄	semidirect
20. D₈×D₄₇	C₄	semidirect
22. #13094032	C₂²	semidirect
23. #13094031	C₂²	semidirect
25. #13094030	C₂²	semidirect
32. #13093960	C₂²	semidirect
33. #13093959	C₂²	semidirect
34. #13093952	C₂²	semidirect
35. #13093951	C₂²	semidirect
36. #13093950	C₂²	semidirect
37. #13093935	C₂²	semidirect
38. #13093934	C₂²	semidirect
39. #13093934	C₂²	semidirect
41. #131×C₄₇	C₂²	semidirect
42. #108×C₄₇	C₂²	semidirect
43. #104×C₄₇	C₂²	semidirect
44. #97×C₄₇	C₂²	semidirect
57. Q₁₆×C₄₇	C₂×C₄	semidirect
58. SD₁₆×C₄₇	C₂×C₄	semidirect
59. D₈×C₄₇	C₂×C₄	semidirect
66. #10625337	C₂×C₄	semidirect
67. #10625336	C₂×C₄	semidirect
68. #10625335	C₂×C₄	semidirect
69. #10625334	C₂×C₄	semidirect
77. Dic₁₈₈	C₂×C₄	semidirect
78. D₃₇₆	C₂×C₄	semidirect
79. #10625325	C₂×C₄	semidirect
147. D₄₇	#444	direct (N × H)
155. #444	D₄₇	direct (N × H)
159. C₄₇	C₂×#444	semidirect
175. #131	C₂×D₄₇	semidirect
184. #108	C₂×D₄₇	semidirect
188. #104	C₂×D₄₇	semidirect
192. #97	C₂×D₄₇	semidirect
207. Q₁₆	C₄×D₄₇	semidirect
211. SD₁₆	C₄×D₄₇	semidirect
214. D₈	C₄×D₄₇	semidirect

Subgroups — #444×D47 #20252280

Conjugacy classes of subgroups

Complements

Subgroups — #444×D₄₇ #20252280