Finite Group Databasebeta

← C3×C7×D42 #13061965

Subgroups — C3×C7×D42 #13061965

Order 1344.

856 conjugacy classes of subgroups.

The subgroup lattice has 176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C7×D4C214yesmaximal, complemented
2C3×C7×#127C211yesmaximal, characteristic, complemented
3C3×C7×#121C214yesmaximal, complemented
4C3×C7×#120C214yesmaximal, complemented
5C3×C4×C7×D4C212yesmaximal, complemented
6C7×D42C311yesmaximal, characteristic, direct product factor, Hall
7C24×C3×C7C2214yescomplemented
8C2×C3×C7×D4—216no—
9C2×C3×C7×D4C2212yes—
10C2×C3×C7×D4C2218yescomplemented
11C2×C3×C7×D4C2214yescomplemented
12C2×C3×C7×D4C2212yescomplemented
13C22×C3×C4×C7C2214yescomplemented
14C3×C7×C4⋊C4C2212yescomplemented
15C3×C7×C22⋊C4C2214yescomplemented
16C3×C7×C22⋊C4C2214yescomplemented
17C3×C42×C7C2211yescharacteristic, complemented
18C22×C7×D4C2×C314yescomplemented
19C7×#127C2×C311yescharacteristic, complemented
20C7×#121C2×C314yescomplemented
21C7×#120C2×C314yescomplemented
22C4×C7×D4C2×C312yescomplemented
23C3×D42C711yesmaximal, characteristic, direct product factor, Hall
24C23×C3×C7—216no—
25C23×C3×C7—44no—
26C23×C3×C7C2314yes—
27C23×C3×C7C2314yes—
28C3×C7×D4—216no—
29C3×C7×D4—28no—
30C3×C7×D4—42no—
31C3×C7×D4D418yesdirect product factor
32C2×C3×C4×C7—28no—
33C2×C3×C4×C7C2311yescharacteristic
34C2×C3×C4×C7C2314yes—
35C2×C3×C4×C7C2312yes—
36C24×C7C22×C314yescomplemented
37C2×C7×D4—216no—
38C2×C7×D4C22×C312yes—
39C2×C7×D4C22×C318yescomplemented
40C2×C7×D4C22×C314yescomplemented
41C2×C7×D4C22×C312yescomplemented
42C22×C4×C7C22×C314yescomplemented
43C7×C4⋊C4C22×C312yescomplemented
44C7×C22⋊C4C22×C314yescomplemented
45C7×C22⋊C4C22×C314yescomplemented
46C42×C7C22×C311yescharacteristic, complemented
47C22×C3×D4C2×C714yescomplemented
48C3×#127C2×C711yescharacteristic, complemented
49C3×#121C2×C714yescomplemented
50C3×#120C2×C714yescomplemented
51C3×C4×D4C2×C712yescomplemented
52C22×C3×C7—24no—
53C22×C3×C7—24no—
54C22×C3×C7—28no—
55C22×C3×C7—24no—
56C22×C3×C7—416no—
57C22×C3×C7C2×D418yescomplemented
58C22×C3×C7C2411yescharacteristic
59C3×C4×C7—24no—
60C3×C4×C7—21no—
61C3×C4×C7C2×D414yescomplemented
62D42C3×C711yescharacteristic, direct product factor, Sylow
63C23×C7—216no—
64C23×C7—44no—
65C23×C7C23×C314yes—
66C23×C7C23×C314yes—
67C7×D4—216no—
68C7×D4—28no—
69C7×D4—42no—
70C7×D4C3×D418yesdirect product factor
71C2×C4×C7—28no—
72C2×C4×C7C23×C311yescharacteristic
73C2×C4×C7C23×C314yes—
74C2×C4×C7C23×C312yes—
75C24×C3C22×C714yescomplemented
76C2×C3×D4—216no—
77C2×C3×D4C22×C712yes—
78C2×C3×D4C22×C718yescomplemented
79C2×C3×D4C22×C714yescomplemented
80C2×C3×D4C22×C712yescomplemented
81C22×C3×C4C22×C714yescomplemented
82C3×C4⋊C4C22×C712yescomplemented
83C3×C22⋊C4C22×C714yescomplemented
84C3×C22⋊C4C22×C714yescomplemented
85C3×C42C22×C711yescharacteristic, complemented
86C2×C3×C7—28no—
87C2×C3×C7—44no—
88C2×C3×C7C22×D412yes—
89C2×C3×C7H(5,𝔽2)11yescharacteristic
90C22×D4C2×C3×C714yescomplemented
91#127C2×C3×C711yescharacteristic, complemented
92#121C2×C3×C714yescomplemented
93#120C2×C3×C714yescomplemented
94C4×D4C2×C3×C712yescomplemented
95C22×C7—24no—
96C22×C7—24no—
97C22×C7—28no—
98C22×C7—24no—
99C22×C7—416no—
100C22×C7C2×C3×D418yescomplemented
101C22×C7C24×C311yescharacteristic
102C4×C7—24no—
103C4×C7—21no—
104C4×C7C2×C3×D414yescomplemented
105C23×C3—216no—
106C23×C3—44no—
107C23×C3C23×C714yes—
108C23×C3C23×C714yes—
109C3×D4—216no—
110C3×D4—28no—
111C3×D4—42no—
112C3×D4C7×D418yesdirect product factor
113C2×C3×C4—28no—
114C2×C3×C4C23×C711yescharacteristic
115C2×C3×C4C23×C714yes—
116C2×C3×C4C23×C712yes—
117C3×C7D4211yescharacteristic, direct product factor, Hall
118C24C22×C3×C714yescomplemented
119C2×D4—216no—
120C2×D4C22×C3×C712yes—
121C2×D4C22×C3×C718yescomplemented
122C2×D4C22×C3×C714yescomplemented
123C2×D4C22×C3×C712yescomplemented
124C22×C4C22×C3×C714yescomplemented
125C4⋊C4C22×C3×C712yescomplemented
126C22⋊C4C22×C3×C714yescomplemented
127C22⋊C4C22×C3×C714yescomplemented
128C42C22×C3×C711yescharacteristic, complemented
129C2×C7—28no—
130C2×C7—44no—
131C2×C7C22×C3×D412yes—
132C2×C7C3×H(5,𝔽2)11yescharacteristic
133C22×C3—24no—
134C22×C3—24no—
135C22×C3—28no—
136C22×C3—24no—
137C22×C3—416no—
138C22×C3C2×C7×D418yescomplemented
139C22×C3C24×C711yescharacteristic
140C3×C4—24no—
141C3×C4—21no—
142C3×C4C2×C7×D414yescomplemented
143C23—216no—
144C23—44no—
145C23C23×C3×C714yes—
146C23C23×C3×C714yes—
147D4—216no—
148D4—28no—
149D4—42no—
150D4C3×C7×D418yesdirect product factor
151C2×C4—28no—
152C2×C4C23×C3×C711yescharacteristic
153C2×C4C23×C3×C714yes—
154C2×C4C23×C3×C712yes—
155C7C3×D4211yescharacteristic, direct product factor, Sylow
156C2×C3—28no—
157C2×C3—44no—
158C2×C3C22×C7×D412yes—
159C2×C3C7×H(5,𝔽2)11yescharacteristic
160C22—24no—
161C22—24no—
162C22—28no—
163C22—24no—
164C22—416no—
165C22C2×C3×C7×D418yescomplemented
166C22C24×C3×C711yescharacteristic
167C4—24no—
168C4—21no—
169C4C2×C3×C7×D414yescomplemented
170C3C7×D4211yescharacteristic, direct product factor, Sylow
171C2—28no—
172C2—44no—
173C2C22×C3×C7×D412yes—
174C2C3×C7×H(5,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C3×C7C24
commutator, Frattini, cosocleC22C24×C3×C7
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C3×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×C7×D4C2semidirect
2. C3×C7×#127C2semidirect
3. C3×C7×#121C2semidirect
4. C3×C7×#120C2semidirect
5. C3×C4×C7×D4C2semidirect
6. C7×D42C3direct (N × H)
7. C24×C3×C7C22semidirect
10. C2×C3×C7×D4C22semidirect
11. C2×C3×C7×D4C22semidirect
12. C2×C3×C7×D4C22semidirect
13. C22×C3×C4×C7C22semidirect
14. C3×C7×C4⋊C4C22semidirect
15. C3×C7×C22⋊C4C22semidirect
16. C3×C7×C22⋊C4C22semidirect
17. C3×C42×C7C22semidirect
18. C22×C7×D4C2×C3semidirect
19. C7×#127C2×C3semidirect
20. C7×#121C2×C3semidirect
21. C7×#120C2×C3semidirect
22. C4×C7×D4C2×C3semidirect
23. C3×D42C7direct (N × H)
31. C3×C7×D4D4direct (N × H)
36. C24×C7C22×C3semidirect
39. C2×C7×D4C22×C3semidirect
40. C2×C7×D4C22×C3semidirect
41. C2×C7×D4C22×C3semidirect
42. C22×C4×C7C22×C3semidirect
43. C7×C4⋊C4C22×C3semidirect
44. C7×C22⋊C4C22×C3semidirect
45. C7×C22⋊C4C22×C3semidirect
46. C42×C7C22×C3semidirect
47. C22×C3×D4C2×C7semidirect
48. C3×#127C2×C7semidirect
49. C3×#121C2×C7semidirect
50. C3×#120C2×C7semidirect
51. C3×C4×D4C2×C7semidirect
57. C22×C3×C7C2×D4semidirect
61. C3×C4×C7C2×D4semidirect
62. D42C3×C7direct (N × H)
70. C7×D4C3×D4direct (N × H)
75. C24×C3C22×C7semidirect
78. C2×C3×D4C22×C7semidirect
79. C2×C3×D4C22×C7semidirect
80. C2×C3×D4C22×C7semidirect
81. C22×C3×C4C22×C7semidirect
82. C3×C4⋊C4C22×C7semidirect
83. C3×C22⋊C4C22×C7semidirect
84. C3×C22⋊C4C22×C7semidirect
85. C3×C42C22×C7semidirect
90. C22×D4C2×C3×C7semidirect
91. #127C2×C3×C7semidirect
92. #121C2×C3×C7semidirect
93. #120C2×C3×C7semidirect
94. C4×D4C2×C3×C7semidirect
100. C22×C7C2×C3×D4semidirect
104. C4×C7C2×C3×D4semidirect
112. C3×D4C7×D4direct (N × H)
117. C3×C7D42direct (N × H)
118. C24C22×C3×C7semidirect
121. C2×D4C22×C3×C7semidirect
122. C2×D4C22×C3×C7semidirect
123. C2×D4C22×C3×C7semidirect
124. C22×C4C22×C3×C7semidirect
125. C4⋊C4C22×C3×C7semidirect
126. C22⋊C4C22×C3×C7semidirect
127. C22⋊C4C22×C3×C7semidirect
128. C42C22×C3×C7semidirect
138. C22×C3C2×C7×D4semidirect
142. C3×C4C2×C7×D4semidirect
150. D4C3×C7×D4direct (N × H)
155. C7C3×D42direct (N × H)
165. C22C2×C3×C7×D4semidirect
169. C4C2×C3×C7×D4semidirect
170. C3C7×D42direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C7×D42
C3×C7×#1272
C3×C7×#1212
C3×C7×#1202
C3×C4×C7×D42
C7×D423
C3×D427