Subgroups — D₄₇×#1384 #26131185

Order 12032.

586 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#427×D₄₇	C₂	1	2	yes	maximal
3	#20241490	C₂	1	1	yes	maximal, characteristic, complemented
4	#20241489	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1384	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
7	#117×D₄₇	—	2	2	no	—
8	C₂×#13093964	C₂²	1	1	yes	characteristic
9	C₂×#13093963	C₄	1	2	yes	complemented
10	M₃₂×D₄₇	—	2	2	no	—
11	M₃₂×D₄₇	—	2	2	no	—
12	C₂×C₁₆×D₄₇	C₄	1	2	yes	complemented
13	#15689161	C₂²	1	2	yes	—
14	#15689160	—	2	2	no	—
15	#15689159	—	2	2	no	—
16	#15689158	C₄	1	4	yes	complemented
17	#107×D₄₇	—	2	2	no	—
18	#106×D₄₇	C₄	1	4	yes	complemented
19	C₂×M₃₂×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#427	C₂²	1	2	yes	—
21	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
22	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
23	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×D₄₇	C₂×C₄	1	2	yes	—
26	C₂×C₈×D₄₇	C₂×C₄	1	2	yes	—
27	C₂×C₈×D₄₇	D₄	1	2	yes	—
28	C₂×C₈×D₄₇	D₄	1	2	yes	—
29	C₂×C₈×D₄₇	Q₈	1	1	yes	characteristic
30	C₂×C₈×D₄₇	Q₈	1	1	yes	characteristic
31	#13093983	—	2	2	no	—
32	#13093982	—	2	4	no	—
33	#13093981	—	4	2	no	—
34	#13093980	—	4	2	no	—
35	C₄⋊C₄×D₄₇	—	2	4	no	—
36	C₂²⋊C₄×D₄₇	—	4	2	no	—
37	C₄²×D₄₇	—	4	2	no	—
38	#13093964	—	2	2	no	—
39	#13093963	—	2	4	no	—
40	C₂×C₄₇⋊C₁₆	C₂×C₄	1	2	yes	complemented
41	C₁₆×D₄₇	—	2	2	no	—
42	C₁₆×D₄₇	—	2	2	no	—
43	#13093958	—	2	2	no	—
44	#13093957	—	2	4	no	—
45	#13093956	C₂×C₄	1	4	yes	complemented
46	#13093955	—	2	4	no	—
47	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
48	#117×C₄₇	—	2	2	no	—
49	M₃₂×C₄₇	—	2	2	no	—
50	C₂×C₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
51	#107×C₄₇	—	2	2	no	—
52	#106×C₄₇	C₂×C₄	1	4	yes	complemented
53	C₂³×D₄₇	D₈	1	1	yes	characteristic
54	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
55	C₂²×Dic₄₇	D₈	1	1	yes	characteristic
56	C₂×C₄×D₄₇	—	4	4	no	—
57	C₂×C₄×D₄₇	C₂²⋊C₄	1	2	yes	—
58	C₂×C₄×D₄₇	C₂²⋊C₄	1	2	yes	—
59	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
60	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
61	C₂×C₄×D₄₇	SD₁₆	1	2	yes	—
62	C₂×C₄×D₄₇	SD₁₆	1	2	yes	—
63	C₂×C₄×D₄₇	Q₁₆	1	1	yes	characteristic
64	C₂×C₄×D₄₇	Q₁₆	1	1	yes	characteristic
65	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
67	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
68	C₂×C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
69	C₄⋊C₄×C₄₇	—	2	4	no	—
70	C₂²⋊C₄×C₄₇	—	4	2	no	—
71	C₄²×C₄₇	—	4	2	no	—
72	C₂²⋊Dic₄₇	—	4	2	no	—
73	(C₂×D₄₇)⋊C₄	—	4	4	no	—
74	C₄⋊Dic₄₇	—	2	4	no	—
75	Dic₄₇⋊C₄	—	4	4	no	—
76	C₄×Dic₄₇	—	4	2	no	—
77	C₄×Dic₄₇	—	4	4	no	—
78	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
79	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
80	C₂×C₄₇⋊C₈	C₄⋊C₄	1	1	yes	characteristic
81	C₂×C₄₇⋊C₈	C₄⋊C₄	1	1	yes	characteristic
82	C₈×D₄₇	C₄²	1	1	yes	characteristic
83	C₈×D₄₇	C₄²	1	1	yes	characteristic
84	C₈×D₄₇	C₄²	1	2	yes	—
85	C₈×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
86	C₈×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
87	C₈×D₄₇	C₂²⋊C₄	1	2	yes	—
88	C₈×D₄₇	C₄⋊C₄	1	2	yes	—
89	C₈×D₄₇	C₄⋊C₄	1	2	yes	—
90	C₈×D₄₇	C₄⋊C₄	1	2	yes	—
91	C₈×D₄₇	C₄⋊C₄	1	2	yes	—
92	C₁₆×C₄₇	—	2	2	no	—
93	C₄₇⋊C₁₆	—	2	2	no	—
94	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
95	C₂²×D₄₇	—	4	2	no	—
96	C₂²×D₄₇	#102	1	2	yes	—
97	C₂²×D₄₇	#102	1	2	yes	—
98	C₂²×D₄₇	#107	1	1	yes	characteristic
99	C₂²×D₄₇	#107	1	1	yes	characteristic
100	C₂×C₄×C₄₇	—	4	4	no	—
101	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
102	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
104	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
105	C₂×Dic₄₇	—	4	4	no	—
106	C₂×Dic₄₇	#102	1	2	yes	—
107	C₂×Dic₄₇	#102	1	2	yes	—
108	C₂×Dic₄₇	#107	1	1	yes	characteristic
109	C₂×Dic₄₇	#107	1	1	yes	characteristic
110	C₄×D₄₇	—	8	8	no	—
111	C₄×D₄₇	#95	1	1	yes	characteristic
112	C₄×D₄₇	#95	1	2	yes	—
113	C₄×D₄₇	#95	1	1	yes	characteristic
114	C₄×D₄₇	#103	1	2	yes	—
115	C₄×D₄₇	#103	1	2	yes	—
116	C₄×D₄₇	#103	1	2	yes	—
117	C₄×D₄₇	#103	1	2	yes	—
118	C₄×D₄₇	#106	1	2	yes	—
119	C₄×D₄₇	#106	1	1	yes	characteristic
120	C₄×D₄₇	#106	1	1	yes	characteristic
121	C₈×C₄₇	C₂×C₄²	1	1	yes	characteristic
122	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
123	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
124	C₄₇⋊C₈	#95	1	1	yes	characteristic
125	C₄₇⋊C₈	#95	1	1	yes	characteristic
126	C₄₇⋊C₈	#95	1	2	yes	—
127	C₂×#1384	—	47	1	no	maximal, Sylow
128	C₂²×C₄₇	—	4	1	no	—
129	C₂²×C₄₇	C₂×#102	1	2	yes	—
130	C₂²×C₄₇	C₂×#107	1	1	yes	characteristic
131	C₂×D₄₇	—	2	4	no	—
132	C₂×D₄₇	—	2	2	no	—
133	C₂×D₄₇	—	4	2	no	—
134	C₂×D₄₇	—	4	1	no	—
135	C₂×D₄₇	#340	1	2	yes	—
136	C₂×D₄₇	#340	1	1	yes	characteristic
137	C₂×D₄₇	#340	1	1	yes	characteristic
138	C₄×C₄₇	—	8	4	no	—
139	C₄×C₄₇	C₂×#95	1	1	yes	characteristic
140	C₄×C₄₇	C₂×#103	1	2	yes	—
141	C₄×C₄₇	C₂×#106	1	1	yes	characteristic
142	Dic₄₇	—	8	4	no	—
143	Dic₄₇	#340	1	1	yes	characteristic
144	Dic₄₇	#340	1	2	yes	—
145	Dic₄₇	#340	1	1	yes	characteristic
146	C₂²×M₃₂	—	47	1	no	—
147	C₂×#427	—	47	2	no	—
148	#1384	—	47	1	no	—
149	#1384	—	47	2	no	—
150	#1384	D₄₇	1	1	yes	characteristic, direct product factor
151	C₂×C₄₇	—	2	2	no	—
152	C₂×C₄₇	—	2	1	no	—
153	C₂×C₄₇	C₂×#340	1	1	yes	characteristic
154	D₄₇	—	2	2	no	—
155	D₄₇	—	2	1	no	—
156	D₄₇	#1384	1	2	yes	direct product factor
157	C₂³×C₈	—	47	1	no	—
158	C₂×#117	—	94	2	no	—
159	C₂×M₃₂	—	47	1	no	—
160	C₂×M₃₂	—	47	2	no	—
161	C₂×M₃₂	—	94	2	no	—
162	C₂×M₃₂	—	94	2	no	—
163	C₂×M₃₂	C₂×D₄₇	1	1	yes	characteristic
164	C₂²×C₁₆	—	47	2	no	—
165	#427	—	47	2	no	—
166	#427	—	47	4	no	—
167	#427	—	94	2	no	—
168	#427	—	94	2	no	—
169	#427	C₂×D₄₇	1	2	yes	—
170	C₂×#107	—	94	2	no	—
171	C₂×#106	—	47	4	no	—
172	C₄₇	C₂×#1384	1	1	yes	characteristic, complemented, Sylow
173	C₂³×C₄	—	47	1	no	—
174	C₂²×C₈	—	47	1	no	—
175	C₂²×C₈	—	47	2	no	—
176	C₂²×C₈	—	47	2	no	—
177	C₂²×C₈	—	47	1	no	—
178	C₂²×C₈	—	47	1	no	—
179	C₂²×C₈	—	47	2	no	—
180	C₂²×C₈	—	47	2	no	—
181	C₂²×C₈	—	47	1	no	—
182	C₂²×C₈	—	47	1	no	—
183	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
184	#117	—	2	2	no	—
185	#117	—	94	4	no	—
186	#117	—	94	2	no	—
187	#117	—	188	2	no	—
188	#117	—	188	2	no	—
189	C₂×C₄⋊C₄	—	94	4	no	—
190	C₂×C₂²⋊C₄	—	188	2	no	—
191	C₂×C₄²	—	188	2	no	—
192	M₃₂	—	2	2	no	—
193	M₃₂	—	94	4	no	—
194	M₃₂	—	94	2	no	—
195	C₂×C₁₆	—	47	2	no	—
196	C₂×C₁₆	—	94	2	no	—
197	C₂×C₁₆	—	94	2	no	—
198	C₂×C₁₆	C₄×D₄₇	1	2	yes	complemented
199	#107	—	2	2	no	—
200	#107	—	94	4	no	—
201	#107	—	94	2	no	—
202	#106	—	47	4	no	—
203	#106	—	94	4	no	—
204	#106	C₄×D₄₇	1	4	yes	complemented
205	C₂⁴	—	47	1	no	—
206	C₂²×C₄	—	47	1	no	—
207	C₂²×C₄	—	47	2	no	—
208	C₂²×C₄	—	47	2	no	—
209	C₂²×C₄	—	47	1	no	—
210	C₂²×C₄	—	47	1	no	—
211	C₂²×C₄	—	47	2	no	—
212	C₂²×C₄	—	47	2	no	—
213	C₂²×C₄	—	47	1	no	—
214	C₂²×C₄	—	47	1	no	—
215	C₂²×C₄	—	188	4	no	—
216	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
217	C₂×C₈	—	47	2	no	—
218	C₂×C₈	—	47	2	no	—
219	C₂×C₈	—	47	1	no	—
220	C₂×C₈	—	47	1	no	—
221	C₂×C₈	—	47	1	no	—
222	C₂×C₈	—	47	2	no	—
223	C₂×C₈	—	47	1	no	—
224	C₂×C₈	—	47	1	no	—
225	C₂×C₈	—	47	1	no	—
226	C₂×C₈	—	47	2	no	—
227	C₂×C₈	—	47	2	no	—
228	C₂×C₈	—	47	2	no	—
229	C₂×C₈	—	47	2	no	—
230	C₂×C₈	—	47	2	no	—
231	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
232	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
233	C₂×C₈	D₄×D₄₇	1	2	yes	—
234	C₂×C₈	Q₈×D₄₇	1	1	yes	characteristic
235	C₄⋊C₄	—	2	4	no	—
236	C₄⋊C₄	—	94	4	no	—
237	C₄⋊C₄	—	188	4	no	—
238	C₂²⋊C₄	—	4	2	no	—
239	C₂²⋊C₄	—	188	4	no	—
240	C₂²⋊C₄	—	188	2	no	—
241	C₄²	—	4	2	no	—
242	C₄²	—	188	4	no	—
243	C₄²	—	188	2	no	—
244	C₁₆	—	2	2	no	—
245	C₁₆	—	94	2	no	—
246	C₂³	—	47	2	no	—
247	C₂³	—	47	1	no	—
248	C₂³	—	47	2	no	—
249	C₂³	—	47	1	no	—
250	C₂³	—	188	2	no	—
251	C₂³	D₈×D₄₇	1	1	yes	characteristic
252	C₂×C₄	—	4	4	no	—
253	C₂×C₄	—	47	2	no	—
254	C₂×C₄	—	47	2	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	—	47	2	no	—
260	C₂×C₄	—	47	2	no	—
261	C₂×C₄	—	47	2	no	—
262	C₂×C₄	—	47	2	no	—
263	C₂×C₄	—	47	2	no	—
264	C₂×C₄	—	47	1	no	—
265	C₂×C₄	—	47	2	no	—
266	C₂×C₄	—	47	1	no	—
267	C₂×C₄	—	376	8	no	—
268	C₂×C₄	—	188	4	no	—
269	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
270	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
271	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
272	C₂×C₄	Q₁₆×D₄₇	1	1	yes	characteristic
273	C₈	—	47	1	no	—
274	C₈	—	47	2	no	—
275	C₈	—	47	1	no	—
276	C₈	C₄²×D₄₇	1	1	yes	characteristic
277	C₈	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
278	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
279	C₂²	—	4	1	no	—
280	C₂²	—	47	1	no	—
281	C₂²	—	47	2	no	—
282	C₂²	—	47	1	no	—
283	C₂²	—	94	4	no	—
284	C₂²	—	94	2	no	—
285	C₂²	—	188	2	no	—
286	C₂²	—	188	1	no	—
287	C₂²	#102×D₄₇	1	2	yes	—
288	C₂²	#107×D₄₇	1	1	yes	characteristic
289	C₄	—	8	4	no	—
290	C₄	—	47	1	no	—
291	C₄	—	47	2	no	—
292	C₄	—	47	1	no	—
293	C₄	—	376	4	no	—
294	C₄	#95×D₄₇	1	1	yes	characteristic
295	C₄	#103×D₄₇	1	2	yes	—
296	C₄	#106×D₄₇	1	1	yes	characteristic
297	C₂	—	2	2	no	—
298	C₂	—	2	1	no	—
299	C₂	—	47	2	no	—
300	C₂	—	94	2	no	—
301	C₂	—	94	1	no	—
302	C₂	#340×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#106×D₄₇
commutator	C₈×C₄₇	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₄₇×#1384	C₂
socle	C₂×C₄₇	C₂×#340
prime radical	C₂³×D₄₇	D₈
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	#1384	D₄₇
hypocenter	C₄₇	C₂×#1384
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1384

Complements

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

N	H ≅ G/N	type
3. #20241490	C₂	semidirect
4. #20241489	C₂	semidirect
5. C₄₇×#1384	C₂	semidirect
9. C₂×#13093963	C₄	semidirect
12. C₂×C₁₆×D₄₇	C₄	semidirect
16. #15689158	C₄	semidirect
18. #106×D₄₇	C₄	semidirect
40. C₂×C₄₇⋊C₁₆	C₂×C₄	semidirect
45. #13093956	C₂×C₄	semidirect
50. C₂×C₁₆×C₄₇	C₂×C₄	semidirect
52. #106×C₄₇	C₂×C₄	semidirect
150. #1384	D₄₇	direct (N × H)
156. D₄₇	#1384	direct (N × H)
172. C₄₇	C₂×#1384	semidirect
198. C₂×C₁₆	C₄×D₄₇	semidirect
204. #106	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₃₂×D₄₇	2
#427×D₄₇	2
#20241490	2
#20241489	2
C₄₇×#1384	2
C₂×#1384	47

Subgroups — D47×#1384 #26131185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#1384 #26131185