Subgroups — C₂×#376×D₄₇ #26374446

Order 12032.

5150 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²×D₄₇	C₂	1	3	yes	maximal
2	C₂×#15688969	C₂	1	3	yes	maximal, complemented
3	C₂×#15688968	C₂	1	4	yes	maximal, complemented
4	#376×D₄₇	C₂	1	16	yes	maximal, direct product factor
5	C₂×#95×D₄₇	C₂	1	4	yes	maximal
6	C₂×C₄₇×#376	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×C₄×D₄₇	C₂²	1	6	yes	—
8	C₂³×C₄×D₄₇	C₂²	1	1	yes	characteristic
9	C₂²×C₄×Dic₄₇	C₂²	1	6	yes	—
10	C₂²×C₄×Dic₄₇	C₂²	1	3	yes	—
11	C₂×C₄²×D₄₇	C₄	1	48	yes	complemented
12	C₂×C₄²×D₄₇	C₂²	1	24	yes	—
13	#15688969	C₂²	1	24	yes	complemented
14	#15688968	C₂²	1	32	yes	complemented
15	C₂×C₄₇⋊#95	C₂²	1	12	yes	—
16	#95×D₄₇	C₂²	1	32	yes	—
17	C₂²×C₄²×C₄₇	C₂²	1	3	yes	—
18	C₄₇×#376	C₂²	1	8	yes	complemented
19	C₂×#95×C₄₇	C₂²	1	4	yes	—
20	C₂⁴×D₄₇	C₂³	1	1	yes	characteristic
21	C₂³×Dic₄₇	C₂³	1	6	yes	—
22	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
23	C₂²×C₄×D₄₇	—	2	48	no	—
24	C₂²×C₄×D₄₇	C₂×C₄	1	48	yes	—
25	C₂²×C₄×D₄₇	C₂×C₄	1	24	yes	—
26	C₂²×C₄×D₄₇	C₂³	1	24	yes	—
27	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
28	C₂×C₄×Dic₄₇	C₂×C₄	1	24	yes	complemented
29	C₂×C₄×Dic₄₇	C₂×C₄	1	48	yes	complemented
30	C₂×C₄×Dic₄₇	C₂³	1	24	yes	—
31	C₂×C₄×Dic₄₇	C₂³	1	12	yes	—
32	C₄²×D₄₇	C₂×C₄	1	192	yes	complemented
33	C₄₇⋊#95	C₂³	1	48	yes	—
34	C₂³×C₄×C₄₇	C₂³	1	6	yes	—
35	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
36	C₂×C₄²×C₄₇	C₂×C₄	1	24	yes	complemented
37	C₂×C₄²×C₄₇	C₂³	1	12	yes	—
38	#95×C₄₇	C₂³	1	16	yes	—
39	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
40	C₂³×D₄₇	C₂²×C₄	1	12	yes	—
41	C₂³×D₄₇	#41	1	16	yes	—
42	C₂³×D₄₇	C₂⁴	1	2	yes	—
43	C₂²×C₄×C₄₇	—	2	24	no	—
44	C₂²×C₄×C₄₇	C₂²×C₄	1	24	yes	—
45	C₂²×C₄×C₄₇	C₂²×C₄	1	12	yes	—
46	C₂²×C₄×C₄₇	C₂⁴	1	12	yes	—
47	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
48	C₂²×Dic₄₇	—	2	24	no	—
49	C₂²×Dic₄₇	C₂²×C₄	1	24	yes	—
50	C₂²×Dic₄₇	C₂²×C₄	1	12	yes	—
51	C₂²×Dic₄₇	C₂⁴	1	12	yes	—
52	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
53	C₂×C₄×D₄₇	—	2	192	no	—
54	C₂×C₄×D₄₇	—	2	96	no	—
55	C₂×C₄×D₄₇	C₄²	1	64	yes	—
56	C₂×C₄×D₄₇	C₂²×C₄	1	96	yes	—
57	C₂×C₄×D₄₇	C₂²×C₄	1	48	yes	—
58	C₄²×C₄₇	C₂²×C₄	1	48	yes	complemented
59	C₄×Dic₄₇	C₂²×C₄	1	48	yes	complemented
60	C₄×Dic₄₇	C₂²×C₄	1	96	yes	complemented
61	C₂³×C₄₇	C₂³×C₄	1	6	yes	—
62	C₂³×C₄₇	C₂×#41	1	8	yes	—
63	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
64	C₂²×D₄₇	C₂×C₄²	1	16	yes	—
65	C₂²×D₄₇	#117	1	96	yes	—
66	C₂²×D₄₇	C₂³×C₄	1	12	yes	—
67	C₂²×D₄₇	C₂×#41	1	16	yes	—
68	C₂×C₄×C₄₇	—	2	48	no	—
69	C₂×C₄×C₄₇	—	2	24	no	—
70	C₂×C₄×C₄₇	C₂×C₄²	1	16	yes	—
71	C₂×C₄×C₄₇	C₂³×C₄	1	24	yes	—
72	C₂×C₄×C₄₇	C₂³×C₄	1	12	yes	—
73	C₂×Dic₄₇	—	2	48	no	—
74	C₂×Dic₄₇	—	2	24	no	—
75	C₂×Dic₄₇	C₂×C₄²	1	16	yes	—
76	C₂×Dic₄₇	C₂³×C₄	1	24	yes	—
77	C₂×Dic₄₇	C₂³×C₄	1	12	yes	—
78	C₄×D₄₇	—	2	192	no	—
79	C₄×D₄₇	C₂×C₄²	1	64	yes	—
80	C₂²×#376	—	47	1	no	maximal, Sylow
81	C₂²×C₄₇	C₂²×C₄²	1	4	yes	—
82	C₂²×C₄₇	C₂×#117	1	24	yes	—
83	C₂²×C₄₇	C₂⁴×C₄	1	3	yes	—
84	C₂²×C₄₇	C₂²×#41	1	4	yes	—
85	C₂×D₄₇	#376	1	64	yes	direct product factor
86	C₂×D₄₇	C₂²×C₄²	1	8	yes	—
87	C₂×D₄₇	C₂×#117	1	48	yes	—
88	C₄×C₄₇	—	2	24	no	—
89	C₄×C₄₇	C₂²×C₄²	1	8	yes	—
90	Dic₄₇	—	2	24	no	—
91	Dic₄₇	C₂²×C₄²	1	8	yes	—
92	C₂³×C₄²	—	47	3	no	—
93	C₂×#376	—	47	3	no	—
94	C₂×#376	—	47	16	no	—
95	C₂×#376	—	47	4	no	—
96	C₂×#376	D₄₇	1	1	yes	characteristic, direct product factor
97	C₂²×#95	—	47	4	no	—
98	C₂×C₄₇	C₂×#376	1	8	yes	complemented
99	C₂×C₄₇	C₂³×C₄²	1	1	yes	characteristic
100	C₂×C₄₇	C₂²×#117	1	6	yes	—
101	D₄₇	C₂×#376	1	16	yes	direct product factor
102	C₂⁴×C₄	—	47	1	no	—
103	C₂⁴×C₄	—	47	6	no	—
104	C₂²×C₄²	—	47	6	no	—
105	C₂²×C₄²	—	47	3	no	—
106	C₂²×C₄²	—	47	48	no	—
107	C₂²×C₄²	—	47	24	no	—
108	C₂²×C₄²	C₂×D₄₇	1	3	yes	—
109	#376	—	47	24	no	—
110	#376	—	47	32	no	—
111	#376	C₂×D₄₇	1	8	yes	direct product factor
112	C₂×#95	—	47	12	no	—
113	C₂×#95	—	47	32	no	—
114	C₂×#95	C₂×D₄₇	1	4	yes	—
115	C₄₇	C₂²×#376	1	1	yes	characteristic, complemented, Sylow
116	C₂⁵	—	47	1	no	—
117	C₂³×C₄	—	47	1	no	—
118	C₂³×C₄	—	47	24	no	—
119	C₂³×C₄	—	47	4	no	—
120	C₂³×C₄	—	47	6	no	—
121	C₂³×C₄	—	47	48	no	—
122	C₂³×C₄	—	47	24	no	—
123	C₂³×C₄	—	94	48	no	—
124	C₂³×C₄	C₂²×D₄₇	1	6	yes	—
125	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
126	C₂×C₄²	—	47	48	no	—
127	C₂×C₄²	—	47	24	no	—
128	C₂×C₄²	—	47	24	no	—
129	C₂×C₄²	—	47	12	no	—
130	C₂×C₄²	—	47	192	no	—
131	C₂×C₄²	C₄×D₄₇	1	24	yes	complemented
132	C₂×C₄²	C₂²×D₄₇	1	12	yes	—
133	#95	—	47	48	no	—
134	#95	C₂²×D₄₇	1	16	yes	—
135	C₂⁴	—	47	12	no	—
136	C₂⁴	—	47	16	no	—
137	C₂⁴	—	47	2	no	—
138	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
139	C₂²×C₄	—	2	24	no	—
140	C₂²×C₄	—	47	12	no	—
141	C₂²×C₄	—	47	2	no	—
142	C₂²×C₄	—	47	64	no	—
143	C₂²×C₄	—	47	48	no	—
144	C₂²×C₄	—	47	24	no	—
145	C₂²×C₄	—	47	12	no	—
146	C₂²×C₄	—	47	96	no	—
147	C₂²×C₄	—	94	192	no	—
148	C₂²×C₄	—	94	96	no	—
149	C₂²×C₄	—	94	24	no	—
150	C₂²×C₄	C₂×C₄×D₄₇	1	24	yes	—
151	C₂²×C₄	C₂×C₄×D₄₇	1	12	yes	—
152	C₂²×C₄	C₂³×D₄₇	1	12	yes	—
153	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
154	C₄²	—	47	96	no	—
155	C₄²	—	47	48	no	—
156	C₄²	C₂×C₄×D₄₇	1	48	yes	complemented
157	C₂³	—	47	16	no	—
158	C₂³	—	47	96	no	—
159	C₂³	—	47	12	no	—
160	C₂³	—	47	16	no	—
161	C₂³	C₂²×C₄×D₄₇	1	6	yes	—
162	C₂³	#41×D₄₇	1	8	yes	—
163	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
164	C₂×C₄	—	2	48	no	—
165	C₂×C₄	—	2	24	no	—
166	C₂×C₄	—	47	16	no	—
167	C₂×C₄	—	47	12	no	—
168	C₂×C₄	—	47	64	no	—
169	C₂×C₄	—	47	24	no	—
170	C₂×C₄	—	94	192	no	—
171	C₂×C₄	—	94	48	no	—
172	C₂×C₄	—	94	24	no	—
173	C₂×C₄	C₄²×D₄₇	1	16	yes	—
174	C₂×C₄	C₂²×C₄×D₄₇	1	24	yes	—
175	C₂×C₄	C₂²×C₄×D₄₇	1	12	yes	—
176	C₂²	—	47	8	no	—
177	C₂²	—	47	48	no	—
178	C₂²	—	47	64	no	—
179	C₂²	C₂×C₄²×D₄₇	1	4	yes	—
180	C₂²	#117×D₄₇	1	24	yes	—
181	C₂²	C₂³×C₄×D₄₇	1	3	yes	—
182	C₂²	C₂×#41×D₄₇	1	4	yes	—
183	C₄	—	2	24	no	—
184	C₄	—	47	8	no	—
185	C₄	—	94	24	no	—
186	C₄	C₂×C₄²×D₄₇	1	8	yes	—
187	C₂	—	47	16	no	—
188	C₂	#376×D₄₇	1	8	yes	direct product factor
189	C₂	C₂²×C₄²×D₄₇	1	1	yes	characteristic
190	C₂	C₂×#117×D₄₇	1	6	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₇
commutator	C₂×C₄₇	C₂³×C₄²
Frattini	C₂³	C₂⁴×D₄₇
Fitting	C₂×C₄₇×#376	C₂
socle	C₂⁴×C₄₇	C₂⁴
prime radical	C₂⁴×D₄₇	C₂³
cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×#376	D₄₇
hypocenter	C₄₇	C₂²×#376
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×#376

Complements

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

N	H ≅ G/N	type
2. C₂×#15688969	C₂	semidirect
3. C₂×#15688968	C₂	semidirect
4. #376×D₄₇	C₂	direct (N × H)
6. C₂×C₄₇×#376	C₂	semidirect
11. C₂×C₄²×D₄₇	C₄	semidirect
13. #15688969	C₂²	semidirect
14. #15688968	C₂²	semidirect
18. C₄₇×#376	C₂²	semidirect
28. C₂×C₄×Dic₄₇	C₂×C₄	semidirect
29. C₂×C₄×Dic₄₇	C₂×C₄	semidirect
32. C₄²×D₄₇	C₂×C₄	semidirect
36. C₂×C₄²×C₄₇	C₂×C₄	semidirect
58. C₄²×C₄₇	C₂²×C₄	semidirect
59. C₄×Dic₄₇	C₂²×C₄	semidirect
60. C₄×Dic₄₇	C₂²×C₄	semidirect
85. C₂×D₄₇	#376	direct (N × H)
96. C₂×#376	D₄₇	direct (N × H)
98. C₂×C₄₇	C₂×#376	semidirect
101. D₄₇	C₂×#376	direct (N × H)
111. #376	C₂×D₄₇	direct (N × H)
115. C₄₇	C₂²×#376	semidirect
131. C₂×C₄²	C₄×D₄₇	semidirect
156. C₄²	C₂×C₄×D₄₇	semidirect
188. C₂	#376×D₄₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄²×D₄₇	2
C₂×#15688969	2
C₂×#15688968	2
#376×D₄₇	2
C₂×#95×D₄₇	2
C₂×C₄₇×#376	2
C₂²×#376	47

Subgroups — C2×#376×D47 #26374446

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#376×D₄₇ #26374446