Subgroups — D₄₇×#1849 #26216735

Order 12032.

1006 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#108×D₄₇	C₂	1	4	yes	maximal
2	#423×D₄₇	C₂	1	2	yes	maximal
3	C₂×#97×D₄₇	C₂	1	1	yes	maximal, characteristic
4	#20243563	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243562	C₂	1	2	yes	maximal, complemented
6	#20243561	C₂	1	4	yes	maximal, complemented
7	C₄₇×#1849	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₄₇	C₂²	1	4	yes	—
9	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
10	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
11	C₂×#13093960	C₂²	1	4	yes	—
12	C₂×#13093959	C₂²	1	8	yes	—
13	#108×D₄₇	—	2	16	no	—
14	#15689147	C₂²	1	2	yes	—
15	#15689146	C₂²	1	4	yes	—
16	#15689145	—	2	4	no	—
17	C₄⋊C₈×D₄₇	—	2	4	no	—
18	C₂×#13093935	C₂²	1	1	yes	characteristic
19	C₂×#13093934	C₂²	1	2	yes	—
20	#97×D₄₇	C₄	1	4	yes	—
21	#97×D₄₇	C₄	1	4	yes	—
22	C₂×#108×C₄₇	C₂²	1	4	yes	—
23	C₄₇×#423	C₂²	1	2	yes	—
24	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₄₇	Q₈	1	2	yes	—
26	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
27	C₂×#10625329	C₂³	1	4	yes	—
28	C₂×#10625324	—	2	4	no	—
29	M₁₆×D₄₇	—	2	16	no	—
30	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
31	C₂×C₈×D₄₇	—	2	4	no	—
32	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
33	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
34	C₂×C₈×D₄₇	D₄	1	8	yes	—
35	C₂×C₈×D₄₇	Q₈	1	8	yes	—
36	C₂×C₄×Dic₄₇	Q₈	1	2	yes	—
37	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
38	C₄²×D₄₇	C₂×C₄	1	2	yes	—
39	C₄²×D₄₇	C₂×C₄	1	2	yes	—
40	C₄²×D₄₇	D₄	1	2	yes	—
41	C₄²×D₄₇	D₄	1	2	yes	—
42	#13093960	—	2	8	no	—
43	#13093959	—	2	16	no	—
44	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
45	Dic₄₇⋊C₈	—	2	8	no	—
46	#13093935	C₂×C₄	1	4	yes	—
47	#13093934	C₂×C₄	1	8	yes	—
48	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
49	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
50	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
51	#108×C₄₇	—	2	8	no	—
52	C₄⋊C₈×C₄₇	—	2	4	no	—
53	#97×C₄₇	C₂×C₄	1	4	yes	—
54	C₂³×D₄₇	C₂×Q₈	1	1	yes	characteristic
55	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
56	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
57	C₂²×Dic₄₇	C₂×Q₈	1	2	yes	—
58	C₂²×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
59	C₂×C₄×D₄₇	—	4	4	no	—
60	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
61	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
62	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₄×D₄₇	C₂×D₄	1	4	yes	—
65	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
66	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
67	C₂×C₄×D₄₇	C₂×Q₈	1	4	yes	—
68	M₁₆×C₄₇	—	2	8	no	—
69	C₂×C₈×C₄₇	—	2	4	no	—
70	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
71	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
72	C₂×C₈×C₄₇	C₂×Q₈	1	4	yes	—
73	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
74	C₄²×C₄₇	C₂×D₄	1	2	yes	—
75	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
76	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
77	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
78	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
79	#10625329	—	2	8	no	—
80	C₂×C₄₇⋊C₈	—	2	4	no	—
81	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
82	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
83	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
84	#10625324	—	4	8	no	—
85	C₈×D₄₇	—	4	8	no	—
86	C₈×D₄₇	C₄⋊C₄	1	16	yes	—
87	C₈×D₄₇	C₄⋊C₄	1	16	yes	—
88	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
89	C₂²×D₄₇	—	2	4	no	—
90	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
91	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
92	C₂²×D₄₇	C₄⋊Q₈	1	4	yes	—
93	C₂×C₄×C₄₇	—	4	2	no	—
94	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
95	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
96	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
97	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
98	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
99	C₂×Dic₄₇	—	4	2	no	—
100	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
101	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
102	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
103	C₂×Dic₄₇	C₄⋊Q₈	1	4	yes	—
104	C₄×D₄₇	—	2	8	no	—
105	C₄×D₄₇	—	4	4	no	—
106	C₄×D₄₇	C₂×C₄⋊C₄	1	4	yes	—
107	C₄×D₄₇	C₂×C₄⋊C₄	1	4	yes	—
108	C₄×D₄₇	#127	1	2	yes	—
109	C₄×D₄₇	#127	1	2	yes	—
110	C₄×D₄₇	C₄⋊Q₈	1	2	yes	—
111	C₄×D₄₇	C₄⋊Q₈	1	2	yes	—
112	C₈×C₄₇	—	4	4	no	—
113	C₈×C₄₇	C₂×C₄⋊C₄	1	8	yes	—
114	C₄₇⋊C₈	—	4	4	no	—
115	C₄₇⋊C₈	C₂×C₄⋊C₄	1	8	yes	—
116	C₂×#1849	—	47	1	no	maximal, Sylow
117	C₂²×C₄₇	—	2	2	no	—
118	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
119	C₂²×C₄₇	C₂×C₄⋊Q₈	1	2	yes	—
120	C₂×D₄₇	—	2	2	no	—
121	C₂×D₄₇	—	2	8	no	—
122	C₂×D₄₇	#384	1	2	yes	—
123	C₂×D₄₇	#384	1	2	yes	—
124	C₂×D₄₇	#430	1	4	yes	—
125	C₄×C₄₇	—	2	4	no	—
126	C₄×C₄₇	C₂²×C₄⋊C₄	1	2	yes	—
127	C₄×C₄₇	C₂×#127	1	1	yes	characteristic
128	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
129	Dic₄₇	—	2	4	no	—
130	Dic₄₇	#384	1	2	yes	—
131	Dic₄₇	#384	1	2	yes	—
132	C₂²×#108	—	47	4	no	—
133	C₂×#423	—	47	2	no	—
134	C₂²×#97	—	47	1	no	—
135	#1849	—	47	4	no	—
136	#1849	—	47	2	no	—
137	#1849	—	47	1	no	—
138	#1849	D₄₇	1	1	yes	characteristic, direct product factor
139	C₂×C₄₇	—	2	2	no	—
140	C₂×C₄₇	C₂×#384	1	1	yes	characteristic
141	C₂×C₄₇	C₂×#430	1	2	yes	—
142	D₄₇	—	2	2	no	—
143	D₄₇	#1849	1	4	yes	direct product factor
144	C₂²×M₁₆	—	47	4	no	—
145	C₂³×C₈	—	47	2	no	—
146	C₂²×C₄²	—	47	1	no	—
147	C₂×#108	—	47	8	no	—
148	C₂×#108	—	47	4	no	—
149	C₂×#108	—	94	16	no	—
150	C₂×#108	C₂×D₄₇	1	4	yes	—
151	#423	—	47	4	no	—
152	#423	—	47	2	no	—
153	#423	—	94	4	no	—
154	#423	C₂×D₄₇	1	2	yes	—
155	C₂×C₄⋊C₈	—	94	4	no	—
156	C₂×#97	—	47	2	no	—
157	C₂×#97	—	47	1	no	—
158	C₂×#97	—	47	4	no	—
159	C₂×#97	—	47	4	no	—
160	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
161	C₄₇	C₂×#1849	1	1	yes	characteristic, complemented, Sylow
162	C₂³×C₄	—	47	1	no	—
163	C₂³×C₄	—	47	2	no	—
164	C₂×M₁₆	—	47	4	no	—
165	C₂×M₁₆	—	94	4	no	—
166	C₂×M₁₆	—	94	16	no	—
167	C₂×M₁₆	C₂²×D₄₇	1	4	yes	—
168	C₂²×C₈	—	47	2	no	—
169	C₂²×C₈	—	47	4	no	—
170	C₂²×C₈	—	47	4	no	—
171	C₂²×C₈	—	47	8	no	—
172	C₂²×C₈	—	47	8	no	—
173	C₂²×C₈	—	94	4	no	—
174	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
175	C₂×C₄²	—	47	2	no	—
176	C₂×C₄²	—	47	1	no	—
177	C₂×C₄²	—	47	2	no	—
178	C₂×C₄²	—	47	2	no	—
179	C₂×C₄²	—	47	2	no	—
180	C₂×C₄²	—	47	2	no	—
181	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
182	#108	—	2	8	no	—
183	#108	—	94	16	no	—
184	#108	—	94	8	no	—
185	C₄⋊C₈	—	2	4	no	—
186	C₄⋊C₈	—	94	8	no	—
187	C₄⋊C₈	—	94	4	no	—
188	#97	—	47	8	no	—
189	#97	—	47	4	no	—
190	#97	C₄×D₄₇	1	4	yes	—
191	C₂⁴	—	47	1	no	—
192	C₂²×C₄	—	47	1	no	—
193	C₂²×C₄	—	47	1	no	—
194	C₂²×C₄	—	47	1	no	—
195	C₂²×C₄	—	47	4	no	—
196	C₂²×C₄	—	47	1	no	—
197	C₂²×C₄	—	47	1	no	—
198	C₂²×C₄	—	47	4	no	—
199	C₂²×C₄	—	47	2	no	—
200	C₂²×C₄	—	47	4	no	—
201	C₂²×C₄	—	47	4	no	—
202	C₂²×C₄	—	188	4	no	—
203	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
204	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
205	M₁₆	—	2	8	no	—
206	M₁₆	—	94	8	no	—
207	M₁₆	—	188	8	no	—
208	C₂×C₈	—	2	4	no	—
209	C₂×C₈	—	47	4	no	—
210	C₂×C₈	—	47	4	no	—
211	C₂×C₈	—	47	4	no	—
212	C₂×C₈	—	47	16	no	—
213	C₂×C₈	—	47	16	no	—
214	C₂×C₈	—	94	4	no	—
215	C₂×C₈	—	188	8	no	—
216	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
217	C₂×C₈	D₄×D₄₇	1	4	yes	—
218	C₂×C₈	Q₈×D₄₇	1	4	yes	—
219	C₄²	—	47	4	no	—
220	C₄²	—	47	4	no	—
221	C₄²	—	47	2	no	—
222	C₄²	—	47	2	no	—
223	C₄²	C₂×C₄×D₄₇	1	2	yes	—
224	C₄²	D₄×D₄₇	1	2	yes	—
225	C₂³	—	47	1	no	—
226	C₂³	—	47	1	no	—
227	C₂³	—	47	4	no	—
228	C₂³	—	94	4	no	—
229	C₂³	C₂×Q₈×D₄₇	1	1	yes	characteristic
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	47	1	no	—
232	C₂×C₄	—	47	1	no	—
233	C₂×C₄	—	47	4	no	—
234	C₂×C₄	—	47	4	no	—
235	C₂×C₄	—	47	4	no	—
236	C₂×C₄	—	47	2	no	—
237	C₂×C₄	—	47	2	no	—
238	C₂×C₄	—	47	2	no	—
239	C₂×C₄	—	47	2	no	—
240	C₂×C₄	—	47	4	no	—
241	C₂×C₄	—	94	8	no	—
242	C₂×C₄	—	188	4	no	—
243	C₂×C₄	—	188	2	no	—
244	C₂×C₄	C₄⋊C₄×D₄₇	1	4	yes	—
245	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
246	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
247	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
248	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
249	C₈	—	4	4	no	—
250	C₈	—	47	8	no	—
251	C₈	—	188	4	no	—
252	C₈	C₄⋊C₄×D₄₇	1	8	yes	—
253	C₂²	—	2	2	no	—
254	C₂²	—	47	2	no	—
255	C₂²	—	47	4	no	—
256	C₂²	—	47	2	no	—
257	C₂²	—	94	8	no	—
258	C₂²	—	94	2	no	—
259	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
260	C₂²	C₄⋊Q₈×D₄₇	1	2	yes	—
261	C₄	—	2	4	no	—
262	C₄	—	47	2	no	—
263	C₄	—	47	2	no	—
264	C₄	—	94	4	no	—
265	C₄	C₂×C₄⋊C₄×D₄₇	1	2	yes	—
266	C₄	#127×D₄₇	1	1	yes	characteristic
267	C₄	C₄⋊Q₈×D₄₇	1	1	yes	characteristic
268	C₂	—	2	2	no	—
269	C₂	—	47	4	no	—
270	C₂	—	94	2	no	—
271	C₂	#384×D₄₇	1	1	yes	characteristic
272	C₂	#430×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1849	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂³×D₄₇	C₂×Q₈
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1849	D₄₇
hypocenter	C₄₇	C₂×#1849
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1849

Complements

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

N	H ≅ G/N	type
4. #20243563	C₂	semidirect
5. #20243562	C₂	semidirect
6. #20243561	C₂	semidirect
7. C₄₇×#1849	C₂	semidirect
138. #1849	D₄₇	direct (N × H)
143. D₄₇	#1849	direct (N × H)
161. C₄₇	C₂×#1849	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#108×D₄₇	2
#423×D₄₇	2
C₂×#97×D₄₇	2
#20243563	2
#20243562	2
#20243561	2
C₄₇×#1849	2
C₂×#1849	47

Subgroups — D47×#1849 #26216735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#1849 #26216735