Subgroups — D₄₇×#1835 #26216463

Order 12032.

1006 conjugacy classes of subgroups.

The subgroup lattice has 226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#382×D₄₇	C₂	1	2	yes	maximal
3	#20243519	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243518	C₂	1	2	yes	maximal, complemented
5	#20243517	C₂	1	4	yes	maximal, complemented
6	#340×D₄₇	C₂	1	4	yes	maximal
7	C₄₇×#1835	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
9	C₂×C₄⋊C₄×D₄₇	C₂²	1	4	yes	—
10	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
13	C₄×C₈×D₄₇	C₄	1	8	yes	complemented
14	#15688989	C₂²	1	2	yes	—
15	#15688988	C₂²	1	4	yes	—
16	#15688987	—	2	4	no	—
17	#95×D₄₇	—	2	4	no	—
18	#15688886	C₂²	1	4	yes	—
19	#15688885	C₂²	1	8	yes	—
20	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
21	C₄₇×#382	C₂²	1	2	yes	—
22	C₄₇×#340	C₂²	1	4	yes	—
23	C₂²×C₄×D₄₇	—	2	4	no	—
24	C₂²×C₄×D₄₇	D₄	1	2	yes	—
25	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
26	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
27	C₂×C₈×D₄₇	—	2	8	no	—
28	C₂×C₈×D₄₇	C₂×C₄	1	8	yes	—
29	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
30	C₂×Dic₄₇⋊C₄	—	2	4	no	—
31	C₄⋊C₄×D₄₇	—	2	16	no	—
32	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
33	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
34	C₄²×D₄₇	C₂×C₄	1	4	yes	—
35	C₄²×D₄₇	Q₈	1	4	yes	—
36	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
37	C₈×Dic₄₇	C₂×C₄	1	8	yes	complemented
38	C₄₇⋊#95	—	2	4	no	—
39	C₄₇⋊#95	—	2	8	no	—
40	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
41	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
42	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
43	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
44	#95×C₄₇	—	2	4	no	—
45	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₄₇	—	2	4	no	—
47	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
48	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
49	C₂²×Dic₄₇	—	2	4	no	—
50	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
51	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×D₄₇	—	2	8	no	—
53	C₂×C₄×D₄₇	—	4	8	no	—
54	C₂×C₄×D₄₇	—	4	16	no	—
55	C₂×C₄×D₄₇	C₄⋊C₄	1	8	yes	—
56	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
57	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
58	C₂×C₄×D₄₇	#41	1	8	yes	—
59	C₂×C₈×C₄₇	—	2	4	no	—
60	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
61	C₄⋊C₄×C₄₇	—	2	8	no	—
62	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
63	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
64	C₄⋊Dic₄₇	—	2	8	no	—
65	Dic₄₇⋊C₄	—	4	8	no	—
66	C₄×Dic₄₇	C₄⋊C₄	1	8	yes	—
67	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
68	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
69	C₂×C₄₇⋊C₈	—	2	4	no	—
70	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
71	C₈×D₄₇	—	2	16	no	—
72	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
73	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
74	C₂²×D₄₇	#124	1	4	yes	—
75	C₂²×D₄₇	#135	1	8	yes	—
76	C₂×C₄×C₄₇	—	2	4	no	—
77	C₂×C₄×C₄₇	—	4	4	no	—
78	C₂×C₄×C₄₇	—	4	8	no	—
79	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
80	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
81	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
82	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
83	C₂×Dic₄₇	—	2	4	no	—
84	C₂×Dic₄₇	—	4	4	no	—
85	C₂×Dic₄₇	—	4	8	no	—
86	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
87	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
88	C₂×Dic₄₇	#124	1	4	yes	—
89	C₄×D₄₇	—	2	16	no	—
90	C₄×D₄₇	—	8	16	no	—
91	C₄×D₄₇	#117	1	8	yes	—
92	C₄×D₄₇	#125	1	8	yes	—
93	C₈×C₄₇	—	2	4	no	—
94	C₄₇⋊C₈	—	2	4	no	—
95	C₂×#1835	—	47	1	no	maximal, Sylow
96	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
97	C₂²×C₄₇	C₂×#124	1	2	yes	—
98	C₂²×C₄₇	C₂×#135	1	4	yes	—
99	C₂×D₄₇	#382	1	4	yes	—
100	C₂×D₄₇	#427	1	8	yes	—
101	C₂×D₄₇	#488	1	16	yes	—
102	C₄×C₄₇	—	2	4	no	—
103	C₄×C₄₇	—	8	4	no	—
104	C₄×C₄₇	C₂×#117	1	2	yes	—
105	C₄×C₄₇	C₂×#125	1	2	yes	—
106	Dic₄₇	—	2	4	no	—
107	Dic₄₇	—	8	4	no	—
108	Dic₄₇	#382	1	4	yes	—
109	C₂²×C₄×C₈	—	47	1	no	—
110	C₂×#382	—	47	2	no	—
111	#1835	—	47	1	no	—
112	#1835	—	47	2	no	—
113	#1835	—	47	4	no	—
114	#1835	D₄₇	1	1	yes	characteristic, direct product factor
115	C₂×#340	—	47	4	no	—
116	C₂×C₄₇	C₂×#382	1	1	yes	characteristic
117	C₂×C₄₇	C₂×#427	1	2	yes	—
118	C₂×C₄₇	C₂×#488	1	4	yes	—
119	D₄₇	#1835	1	8	yes	direct product factor
120	C₂³×C₈	—	47	2	no	—
121	C₂²×C₄⋊C₄	—	47	4	no	—
122	C₂²×C₄²	—	47	1	no	—
123	C₂×C₄×C₈	—	47	2	no	—
124	C₂×C₄×C₈	—	47	1	no	—
125	C₂×C₄×C₈	—	47	8	no	—
126	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
127	#382	—	47	4	no	—
128	#382	—	47	2	no	—
129	#382	—	94	4	no	—
130	#382	C₂×D₄₇	1	2	yes	—
131	C₂×#95	—	94	4	no	—
132	#340	—	47	4	no	—
133	#340	—	47	8	no	—
134	#340	C₂×D₄₇	1	4	yes	—
135	C₄₇	C₂×#1835	1	1	yes	characteristic, complemented, Sylow
136	C₂³×C₄	—	47	1	no	—
137	C₂³×C₄	—	47	2	no	—
138	C₂³×C₄	—	94	4	no	—
139	C₂²×C₈	—	47	2	no	—
140	C₂²×C₈	—	47	8	no	—
141	C₂²×C₈	—	94	8	no	—
142	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
143	C₂×C₄⋊C₄	—	47	4	no	—
144	C₂×C₄⋊C₄	—	94	16	no	—
145	C₂×C₄⋊C₄	—	94	4	no	—
146	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
147	C₂×C₄²	—	47	2	no	—
148	C₂×C₄²	—	47	1	no	—
149	C₂×C₄²	—	47	4	no	—
150	C₂×C₄²	—	47	4	no	—
151	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
152	C₄×C₈	—	47	8	no	—
153	C₄×C₈	—	47	4	no	—
154	C₄×C₈	C₄×D₄₇	1	4	yes	complemented
155	#95	—	2	4	no	—
156	#95	—	94	8	no	—
157	#95	—	94	4	no	—
158	C₂⁴	—	47	1	no	—
159	C₂²×C₄	—	2	4	no	—
160	C₂²×C₄	—	47	1	no	—
161	C₂²×C₄	—	47	2	no	—
162	C₂²×C₄	—	47	2	no	—
163	C₂²×C₄	—	47	8	no	—
164	C₂²×C₄	—	47	2	no	—
165	C₂²×C₄	—	47	8	no	—
166	C₂²×C₄	—	94	8	no	—
167	C₂²×C₄	—	94	4	no	—
168	C₂²×C₄	—	188	8	no	—
169	C₂²×C₄	—	188	16	no	—
170	C₂²×C₄	D₄×D₄₇	1	2	yes	—
171	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
172	C₂×C₈	—	2	4	no	—
173	C₂×C₈	—	47	4	no	—
174	C₂×C₈	—	94	16	no	—
175	C₂×C₈	—	94	4	no	—
176	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
177	C₄⋊C₄	—	2	8	no	—
178	C₄⋊C₄	—	94	8	no	—
179	C₄⋊C₄	—	188	8	no	—
180	C₄²	—	47	8	no	—
181	C₄²	—	47	2	no	—
182	C₄²	—	47	2	no	—
183	C₄²	C₂×C₄×D₄₇	1	2	yes	—
184	C₄²	Q₈×D₄₇	1	2	yes	—
185	C₂³	—	47	2	no	—
186	C₂³	—	47	4	no	—
187	C₂³	—	47	8	no	—
188	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
189	C₂×C₄	—	2	4	no	—
190	C₂×C₄	—	4	4	no	—
191	C₂×C₄	—	4	8	no	—
192	C₂×C₄	—	47	2	no	—
193	C₂×C₄	—	47	4	no	—
194	C₂×C₄	—	47	8	no	—
195	C₂×C₄	—	47	8	no	—
196	C₂×C₄	—	47	4	no	—
197	C₂×C₄	—	94	16	no	—
198	C₂×C₄	—	94	4	no	—
199	C₂×C₄	—	376	16	no	—
200	C₂×C₄	—	188	4	no	—
201	C₂×C₄	—	188	8	no	—
202	C₂×C₄	C₄⋊C₄×D₄₇	1	4	yes	—
203	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
204	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
205	C₂×C₄	#41×D₄₇	1	4	yes	—
206	C₈	—	2	4	no	—
207	C₈	—	94	4	no	—
208	C₂²	—	47	16	no	—
209	C₂²	—	47	4	no	—
210	C₂²	—	47	8	no	—
211	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
212	C₂²	#124×D₄₇	1	2	yes	—
213	C₂²	#135×D₄₇	1	4	yes	—
214	C₄	—	2	4	no	—
215	C₄	—	8	4	no	—
216	C₄	—	47	4	no	—
217	C₄	—	94	4	no	—
218	C₄	—	376	4	no	—
219	C₄	#117×D₄₇	1	2	yes	—
220	C₄	#125×D₄₇	1	2	yes	—
221	C₂	—	47	8	no	—
222	C₂	#382×D₄₇	1	1	yes	characteristic
223	C₂	#427×D₄₇	1	2	yes	—
224	C₂	#488×D₄₇	1	4	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1835	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂³×D₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1835	D₄₇
hypocenter	C₄₇	C₂×#1835
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1835

Complements

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

N	H ≅ G/N	type
3. #20243519	C₂	semidirect
4. #20243518	C₂	semidirect
5. #20243517	C₂	semidirect
7. C₄₇×#1835	C₂	semidirect
13. C₄×C₈×D₄₇	C₄	semidirect
36. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
37. C₈×Dic₄₇	C₂×C₄	semidirect
43. C₄×C₈×C₄₇	C₂×C₄	semidirect
114. #1835	D₄₇	direct (N × H)
119. D₄₇	#1835	direct (N × H)
135. C₄₇	C₂×#1835	semidirect
154. C₄×C₈	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×C₄×C₈×D₄₇	2
#382×D₄₇	2
#20243519	2
#20243518	2
#20243517	2
#340×D₄₇	2
C₄₇×#1835	2
C₂×#1835	47

Subgroups — D47×#1835 #26216463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#1835 #26216463