Finite Group Databasebeta

← C22×D3×C7×D4 #13062352

Subgroups — C22×D3×C7×D4 #13062352

Order 1344.

2724 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×D3×C7C212yesmaximal, complemented
2C22×C3×C7×D4C211yesmaximal, characteristic, complemented
3C22×C7×#67C212yesmaximal, complemented
4C2×D3×C7×D4C2124yesmaximal, direct product factor
5C22×C7×D12C211yesmaximal, characteristic, complemented
6C22×C4×D3×C7C211yesmaximal, characteristic, complemented
7C23×C7×D4—31nomaximal, Hall
8C24×C3×C7C2212yescomplemented
9C23×D3×C7—216no—
10C23×D3×C7C2211yescharacteristic
11C23×D3×C7C22124yescomplemented
12C23×D3×C7C2212yescomplemented
13C2×C3×C7×D4C22112yescomplemented
14C22×C3×C4×C7C2211yescharacteristic, complemented
15C2×C7×#67C22124yescomplemented
16C22×C7×Dic3C2211yescharacteristic, complemented
17D3×C7×D4C22164yesdirect product factor
18C2×C7×D12C22112yescomplemented
19C2×C4×D3×C7C22112yescomplemented
20C25×C7—32no—
21C22×C7×D4—32no—
22C22×C7×D4—324no—
23C22×C7×D4—31no—
24C22×C7×D4D311yescharacteristic, direct product factor
25C23×C4×C7—31no—
26C22×D3×D4C711yesmaximal, characteristic, direct product factor, Hall
27C23×C3×C7—28no—
28C23×C3×C7C2311yescharacteristic
29C23×C3×C7C23112yescomplemented
30C22×D3×C7—28no—
31C22×D3×C7—296no—
32C22×D3×C7D418yesdirect product factor
33C22×D3×C7C2316yes—
34C22×D3×C7C23132yescomplemented
35C22×D3×C7C23112yescomplemented
36C3×C7×D4C23116yescomplemented
37C2×C3×C4×C7C2316yescomplemented
38C7×#67C23132yescomplemented
39C2×C7×Dic3C2316yescomplemented
40C7×D12C23116yescomplemented
41C4×D3×C7C23116yescomplemented
42C24×C7—31no—
43C24×C7—32no—
44C24×C7—324no—
45C24×C7—616no—
46C24×C7C2×D312yescomplemented
47C2×C7×D4—324no—
48C2×C7×D4—364no—
49C2×C7×D4—312no—
50C2×C7×D4C2×D3112yesdirect product factor
51C22×C4×C7—31no—
52C22×C4×C7—312no—
53C22×C4×C7C2×D311yescharacteristic, complemented
54C24×D3C2×C712yescomplemented
55C22×C3×D4C2×C711yescharacteristic, complemented
56C22×#67C2×C712yescomplemented
57C2×D3×D4C2×C7124yesdirect product factor
58C22×D12C2×C711yescharacteristic, complemented
59C22×C4×D3C2×C711yescharacteristic, complemented
60C22×C3×C7—224no—
61C22×C3×C7C2×D414yescomplemented
62C22×C3×C7C2413yes—
63C22×C3×C7C2418yescomplemented
64C2×D3×C7—224no—
65C2×D3×C7—264no—
66C2×D3×C7C2×D4124yesdirect product factor
67C2×D3×C7C2414yes—
68C2×D3×C7C2418yescomplemented
69C3×C4×C7C2414yescomplemented
70C7×Dic3C2414yescomplemented
71C23×D4—31noSylow
72C23×C7—28no—
73C23×C7—38no—
74C23×C7—36no—
75C23×C7—312no—
76C23×C7—332no—
77C23×C7—696no—
78C23×C7—68no—
79C23×C7C22×D311yescharacteristic
80C23×C7C22×D3112yescomplemented
81C7×D4—332no—
82C7×D4—316no—
83C7×D4C22×D3116yesdirect product factor
84C2×C4×C7—36no—
85C2×C4×C7—316no—
86C2×C4×C7C22×D316yescomplemented
87C24×C3C22×C712yescomplemented
88C23×D3—216no—
89C23×D3C22×C711yescharacteristic
90C23×D3C22×C7124yescomplemented
91C23×D3C22×C712yescomplemented
92C2×C3×D4C22×C7112yescomplemented
93C22×C3×C4C22×C711yescharacteristic, complemented
94C2×#67C22×C7124yescomplemented
95C22×Dic3C22×C711yescharacteristic, complemented
96D3×D4C22×C7164yesdirect product factor
97C2×D12C22×C7112yescomplemented
98C2×C4×D3C22×C7112yescomplemented
99C2×C3×C7—28no—
100C2×C3×C7C22×D416yescomplemented
101C2×C3×C7C2511yescharacteristic
102D3×C7—28no—
103D3×C7C22×D418yesdirect product factor
104C25—32no—
105C22×D4—32no—
106C22×D4—324no—
107C22×D4—31no—
108C22×D4D3×C711yescharacteristic, direct product factor
109C23×C4—31no—
110C22×C7—224no—
111C22×C7—324no—
112C22×C7—34no—
113C22×C7—38no—
114C22×C7—664no—
115C22×C7—624no—
116C22×C7D3×D414yesdirect product factor
117C22×C7C23×D313yes—
118C22×C7C23×D318yescomplemented
119C4×C7—34no—
120C4×C7C23×D314yescomplemented
121C23×C3—28no—
122C23×C3C23×C711yescharacteristic
123C23×C3C23×C7112yescomplemented
124C22×D3—28no—
125C22×D3—296no—
126C22×D3C7×D418yesdirect product factor
127C22×D3C23×C716yes—
128C22×D3C23×C7132yescomplemented
129C22×D3C23×C7112yescomplemented
130C3×D4C23×C7116yescomplemented
131C2×C3×C4C23×C716yescomplemented
132#67C23×C7132yescomplemented
133C2×Dic3C23×C716yescomplemented
134D12C23×C7116yescomplemented
135C4×D3C23×C7116yescomplemented
136C3×C7C23×D411yescharacteristic, complemented, Hall
137C24—31no—
138C24—32no—
139C24—324no—
140C24—616no—
141C24C2×D3×C712yescomplemented
142C2×D4—324no—
143C2×D4—364no—
144C2×D4—312no—
145C2×D4C2×D3×C7112yesdirect product factor
146C22×C4—31no—
147C22×C4—312no—
148C22×C4C2×D3×C711yescharacteristic, complemented
149C2×C7—28no—
150C2×C7—38no—
151C2×C7—68no—
152C2×C7C2×D3×D416yesdirect product factor
153C2×C7C24×D311yescharacteristic
154C22×C3—224no—
155C22×C3C2×C7×D414yescomplemented
156C22×C3C24×C713yes—
157C22×C3C24×C718yescomplemented
158C2×D3—224no—
159C2×D3—264no—
160C2×D3C2×C7×D4124yesdirect product factor
161C2×D3C24×C714yes—
162C2×D3C24×C718yescomplemented
163C3×C4C24×C714yescomplemented
164Dic3C24×C714yescomplemented
165C23—28no—
166C23—38no—
167C23—36no—
168C23—312no—
169C23—332no—
170C23—696no—
171C23—68no—
172C23C22×D3×C711yescharacteristic
173C23C22×D3×C7112yescomplemented
174D4—332no—
175D4—316no—
176D4C22×D3×C7116yesdirect product factor
177C2×C4—36no—
178C2×C4—316no—
179C2×C4C22×D3×C716yescomplemented
180C7C22×D3×D411yescharacteristic, direct product factor, Sylow
181C2×C3—28no—
182C2×C3C22×C7×D416yescomplemented
183C2×C3C25×C711yescharacteristic
184D3—28no—
185D3C22×C7×D418yesdirect product factor
186C22—224no—
187C22—34no—
188C22—324no—
189C22—38no—
190C22—664no—
191C22—624no—
192C22D3×C7×D414yesdirect product factor
193C22C23×D3×C713yes—
194C22C23×D3×C718yescomplemented
195C4—34no—
196C4C23×D3×C714yescomplemented
197C3C23×C7×D411yescharacteristic, complemented, Sylow
198C2—28no—
199C2—38no—
200C2—68no—
201C2C2×D3×C7×D416yesdirect product factor
202C2C24×D3×C711yescharacteristic
subgroupG/H
centerC23×C7C22×D3
commutator, cosocleC2×C3C25×C7
FrattiniC2C24×D3×C7
FittingC22×C3×C7×D4C2
socleC23×C3×C7C23
hypercenterC22×C7×D4D3
hypocenterC3C23×C7×D4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C7 ◁ C22×C7×D4

Complements

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

NH ≅ G/Ntype
1. C24×D3×C7C2semidirect
2. C22×C3×C7×D4C2semidirect
3. C22×C7×#67C2semidirect
4. C2×D3×C7×D4C2direct (N × H)
5. C22×C7×D12C2semidirect
6. C22×C4×D3×C7C2semidirect
8. C24×C3×C7C22semidirect
11. C23×D3×C7C22semidirect
12. C23×D3×C7C22semidirect
13. C2×C3×C7×D4C22semidirect
14. C22×C3×C4×C7C22semidirect
15. C2×C7×#67C22semidirect
16. C22×C7×Dic3C22semidirect
17. D3×C7×D4C22direct (N × H)
18. C2×C7×D12C22semidirect
19. C2×C4×D3×C7C22semidirect
24. C22×C7×D4D3direct (N × H)
26. C22×D3×D4C7direct (N × H)
29. C23×C3×C7C23semidirect
32. C22×D3×C7D4direct (N × H)
34. C22×D3×C7C23semidirect
35. C22×D3×C7C23semidirect
36. C3×C7×D4C23semidirect
37. C2×C3×C4×C7C23semidirect
38. C7×#67C23semidirect
39. C2×C7×Dic3C23semidirect
40. C7×D12C23semidirect
41. C4×D3×C7C23semidirect
46. C24×C7C2×D3semidirect
50. C2×C7×D4C2×D3direct (N × H)
53. C22×C4×C7C2×D3semidirect
54. C24×D3C2×C7semidirect
55. C22×C3×D4C2×C7semidirect
56. C22×#67C2×C7semidirect
57. C2×D3×D4C2×C7direct (N × H)
58. C22×D12C2×C7semidirect
59. C22×C4×D3C2×C7semidirect
61. C22×C3×C7C2×D4semidirect
63. C22×C3×C7C24semidirect
66. C2×D3×C7C2×D4direct (N × H)
68. C2×D3×C7C24semidirect
69. C3×C4×C7C24semidirect
70. C7×Dic3C24semidirect
80. C23×C7C22×D3semidirect
83. C7×D4C22×D3direct (N × H)
86. C2×C4×C7C22×D3semidirect
87. C24×C3C22×C7semidirect
90. C23×D3C22×C7semidirect
91. C23×D3C22×C7semidirect
92. C2×C3×D4C22×C7semidirect
93. C22×C3×C4C22×C7semidirect
94. C2×#67C22×C7semidirect
95. C22×Dic3C22×C7semidirect
96. D3×D4C22×C7direct (N × H)
97. C2×D12C22×C7semidirect
98. C2×C4×D3C22×C7semidirect
100. C2×C3×C7C22×D4semidirect
103. D3×C7C22×D4direct (N × H)
108. C22×D4D3×C7direct (N × H)
116. C22×C7D3×D4direct (N × H)
118. C22×C7C23×D3semidirect
120. C4×C7C23×D3semidirect
123. C23×C3C23×C7semidirect
126. C22×D3C7×D4direct (N × H)
128. C22×D3C23×C7semidirect
129. C22×D3C23×C7semidirect
130. C3×D4C23×C7semidirect
131. C2×C3×C4C23×C7semidirect
132. #67C23×C7semidirect
133. C2×Dic3C23×C7semidirect
134. D12C23×C7semidirect
135. C4×D3C23×C7semidirect
136. C3×C7C23×D4semidirect
141. C24C2×D3×C7semidirect
145. C2×D4C2×D3×C7direct (N × H)
148. C22×C4C2×D3×C7semidirect
152. C2×C7C2×D3×D4direct (N × H)
155. C22×C3C2×C7×D4semidirect
157. C22×C3C24×C7semidirect
160. C2×D3C2×C7×D4direct (N × H)
162. C2×D3C24×C7semidirect
163. C3×C4C24×C7semidirect
164. Dic3C24×C7semidirect
173. C23C22×D3×C7semidirect
176. D4C22×D3×C7direct (N × H)
179. C2×C4C22×D3×C7semidirect
180. C7C22×D3×D4direct (N × H)
182. C2×C3C22×C7×D4semidirect
185. D3C22×C7×D4direct (N × H)
192. C22D3×C7×D4direct (N × H)
194. C22C23×D3×C7semidirect
196. C4C23×D3×C7semidirect
197. C3C23×C7×D4semidirect
201. C2C2×D3×C7×D4direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D3×C72
C22×C3×C7×D42
C22×C7×#672
C2×D3×C7×D42
C22×C7×D122
C22×C4×D3×C72
C23×C7×D43
C22×D3×D47