Finite Group Databasebeta

← C7×D42 #90566

Subgroups — C7×D42 #90566

Order 448.

428 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×D4C214yesmaximal, complemented
2C7×#127C211yesmaximal, characteristic, complemented
3C7×#121C214yesmaximal, complemented
4C7×#120C214yesmaximal, complemented
5C4×C7×D4C212yesmaximal, complemented
6C24×C7C2214yescomplemented
7C2×C7×D4—216no—
8C2×C7×D4C2212yes—
9C2×C7×D4C2218yescomplemented
10C2×C7×D4C2214yescomplemented
11C2×C7×D4C2212yescomplemented
12C22×C4×C7C2214yescomplemented
13C7×C4⋊C4C2212yescomplemented
14C7×C22⋊C4C2214yescomplemented
15C7×C22⋊C4C2214yescomplemented
16C42×C7C2211yescharacteristic, complemented
17D42C711yesmaximal, characteristic, direct product factor, Sylow
18C23×C7—216no—
19C23×C7—44no—
20C23×C7C2314yes—
21C23×C7C2314yes—
22C7×D4—216no—
23C7×D4—28no—
24C7×D4—42no—
25C7×D4D418yesdirect product factor
26C2×C4×C7—28no—
27C2×C4×C7C2311yescharacteristic
28C2×C4×C7C2314yes—
29C2×C4×C7C2312yes—
30C22×D4C2×C714yescomplemented
31#127C2×C711yescharacteristic, complemented
32#121C2×C714yescomplemented
33#120C2×C714yescomplemented
34C4×D4C2×C712yescomplemented
35C22×C7—24no—
36C22×C7—24no—
37C22×C7—28no—
38C22×C7—24no—
39C22×C7—416no—
40C22×C7C2×D418yescomplemented
41C22×C7C2411yescharacteristic
42C4×C7—24no—
43C4×C7—21no—
44C4×C7C2×D414yescomplemented
45C24C22×C714yescomplemented
46C2×D4—216no—
47C2×D4C22×C712yes—
48C2×D4C22×C718yescomplemented
49C2×D4C22×C714yescomplemented
50C2×D4C22×C712yescomplemented
51C22×C4C22×C714yescomplemented
52C4⋊C4C22×C712yescomplemented
53C22⋊C4C22×C714yescomplemented
54C22⋊C4C22×C714yescomplemented
55C42C22×C711yescharacteristic, complemented
56C2×C7—28no—
57C2×C7—44no—
58C2×C7C22×D412yes—
59C2×C7H(5,𝔽2)11yescharacteristic
60C23—216no—
61C23—44no—
62C23C23×C714yes—
63C23C23×C714yes—
64D4—216no—
65D4—28no—
66D4—42no—
67D4C7×D418yesdirect product factor
68C2×C4—28no—
69C2×C4C23×C711yescharacteristic
70C2×C4C23×C714yes—
71C2×C4C23×C712yes—
72C7D4211yescharacteristic, direct product factor, Sylow
73C22—24no—
74C22—24no—
75C22—28no—
76C22—24no—
77C22—416no—
78C22C2×C7×D418yescomplemented
79C22C24×C711yescharacteristic
80C4—24no—
81C4—21no—
82C4C2×C7×D414yescomplemented
83C2—28no—
84C2—44no—
85C2C22×C7×D412yes—
86C2C7×H(5,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C7C24
commutator, Frattini, cosocleC22C24×C7
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C7×D4C2semidirect
2. C7×#127C2semidirect
3. C7×#121C2semidirect
4. C7×#120C2semidirect
5. C4×C7×D4C2semidirect
6. C24×C7C22semidirect
9. C2×C7×D4C22semidirect
10. C2×C7×D4C22semidirect
11. C2×C7×D4C22semidirect
12. C22×C4×C7C22semidirect
13. C7×C4⋊C4C22semidirect
14. C7×C22⋊C4C22semidirect
15. C7×C22⋊C4C22semidirect
16. C42×C7C22semidirect
17. D42C7direct (N × H)
25. C7×D4D4direct (N × H)
30. C22×D4C2×C7semidirect
31. #127C2×C7semidirect
32. #121C2×C7semidirect
33. #120C2×C7semidirect
34. C4×D4C2×C7semidirect
40. C22×C7C2×D4semidirect
44. C4×C7C2×D4semidirect
45. C24C22×C7semidirect
48. C2×D4C22×C7semidirect
49. C2×D4C22×C7semidirect
50. C2×D4C22×C7semidirect
51. C22×C4C22×C7semidirect
52. C4⋊C4C22×C7semidirect
53. C22⋊C4C22×C7semidirect
54. C22⋊C4C22×C7semidirect
55. C42C22×C7semidirect
67. D4C7×D4direct (N × H)
72. C7D42direct (N × H)
78. C22C2×C7×D4semidirect
82. C4C2×C7×D4semidirect

Maximal subgroups

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

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