Finite Group Databasebeta

← C2×C7×D819 #37524615

Subgroups — C2×C7×D819 #37524615

Order 22932.

156 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×D819C212yesmaximal, direct product factor
2C2×C72×C9×C13C211yesmaximal, characteristic, complemented
3C2×C7×D273—31nomaximal
4C72×C9×C13C2211yescharacteristic, complemented, Hall
5C7×D273—32no—
6C2×C3×C72×C13D311yescharacteristic
7C2×D819C711yesmaximal, characteristic, direct product factor
8C2×C7×D117—71nomaximal
9C2×C7×D91—91noHall
10C3×C72×C13C2×D311yescharacteristic
11C2×C7×D63—131nomaximal, Hall
12C2×C7×C9×C13—23no—
13C2×C7×C9×C13D711yescharacteristic, complemented
14C2×C7×C9×C13C2×C711yescharacteristic, complemented
15D819C2×C712yesdirect product factor
16C7×D117—72no—
17C2×C72×C13D911yescharacteristic, complemented
18C7×D91—92no—
19C2×D273—31no—
20C2×C7×D39—211no—
21C2×C72×C9D1311yescharacteristic, complemented
22C7×D63—132no—
23C7×C9×C13—23no—
24C7×C9×C13C2×D711yescharacteristic, complemented
25C7×C9×C13C22×C711yescharacteristic, complemented
26C72×C13C2×D911yescharacteristic, complemented, Hall
27C2×C7×D21—391no—
28C2×C3×C7×C13—23no—
29C2×C3×C7×C13D3×C711yescharacteristic
30C2×C3×C7×C13D2111yescharacteristic
31D273—32no—
32C7×D39—212no—
33C2×D117—71noHall
34C72×C9C2×D1311yescharacteristic, complemented, Hall
35C2×D91—91no—
36C2×C7×D13—631no—
37C2×C3×C72D3911yescharacteristic
38C7×D21—392no—
39C3×C7×C13—23no—
40C3×C7×C13C2×D3×C711yescharacteristic
41C3×C7×C13C2×D2111yescharacteristic
42C2×D63—131no—
43C2×C7×D9—911no—
44C2×C9×C13C7×D711yescharacteristic, complemented
45D117—72no—
46C2×C7×D7—1171noHall
47C2×C7×C13—23no—
48C2×C7×C13C7×D911yescharacteristic, complemented
49C2×C7×C13D6311yescharacteristic, complemented
50D91—92no—
51C7×D13—632no—
52C2×D39—211no—
53C3×C72C2×D3911yescharacteristic
54C2×C7×C9—23no—
55C2×C7×C9C7×D1311yescharacteristic, complemented
56C2×C7×C9D9111yescharacteristic, complemented
57D63—132no—
58C7×D9—912no—
59C9×C13C2×C7×D711yescharacteristic, complemented, Hall
60C2×C72D11711yescharacteristic, complemented
61C7×D7—1172no—
62C7×C13—23no—
63C7×C13C2×C7×D911yescharacteristic, complemented
64C7×C13C2×D6311yescharacteristic, complemented
65C2×D21—391no—
66C2×D3×C7—2731no—
67C2×C3×C13C7×D2111yescharacteristic
68D39—212no—
69C7×C9—23no—
70C7×C9C2×C7×D1311yescharacteristic, complemented
71C7×C9C2×D9111yescharacteristic, complemented
72C2×D13—631noHall
73C72C2×D11711yescharacteristic, complemented, Sylow
74C2×C3×C7—23no—
75C2×C3×C7C7×D3911yescharacteristic
76C2×C3×C7D27311yescharacteristic
77D21—392no—
78D3×C7—2732no—
79C3×C13C2×C7×D2111yescharacteristic
80C2×D9—911noHall
81C22×C7—8191no—
82C2×D7—1171no—
83C2×C13C7×D6311yescharacteristic, complemented
84D13—632no—
85C3×C7—23no—
86C3×C7C2×C7×D3911yescharacteristic
87C3×C7C2×D27311yescharacteristic
88C2×C9C7×D9111yescharacteristic, complemented
89D9—912no—
90C2×C7—23no—
91C2×C7—8192no—
92C2×C7C7×D11711yescharacteristic, complemented
93C2×C7D81911yescharacteristic, direct product factor
94D7—1172no—
95C13C2×C7×D6311yescharacteristic, complemented, Sylow
96C2×D3—2731no—
97C9C2×C7×D9111yescharacteristic, complemented, Sylow
98C7—23no—
99C7C2×C7×D11711yescharacteristic, complemented
100C7C2×D81911yescharacteristic, direct product factor
101C2×C3C7×D27311yescharacteristic
102D3—2732no—
103C22—8191noSylow
104C3C2×C7×D27311yescharacteristic
105C2—8192no—
106C2C7×D81911yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C7D819
commutator, cosocle, hypocenterC7×C9×C13C22×C7
FrattiniC3C2×C7×D273
FittingC2×C72×C9×C13C2
socleC2×C3×C72×C13D3
LCSG ▷ C7×C9×C13
UCSC1 ◁ C2×C7

Complements

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

NH ≅ G/Ntype
1. C7×D819C2direct (N × H)
2. C2×C72×C9×C13C2semidirect
4. C72×C9×C13C22semidirect
7. C2×D819C7direct (N × H)
13. C2×C7×C9×C13D7semidirect
14. C2×C7×C9×C13C2×C7semidirect
15. D819C2×C7direct (N × H)
17. C2×C72×C13D9semidirect
21. C2×C72×C9D13semidirect
24. C7×C9×C13C2×D7semidirect
25. C7×C9×C13C22×C7semidirect
26. C72×C13C2×D9semidirect
34. C72×C9C2×D13semidirect
44. C2×C9×C13C7×D7semidirect
48. C2×C7×C13C7×D9semidirect
49. C2×C7×C13D63semidirect
55. C2×C7×C9C7×D13semidirect
56. C2×C7×C9D91semidirect
59. C9×C13C2×C7×D7semidirect
60. C2×C72D117semidirect
63. C7×C13C2×C7×D9semidirect
64. C7×C13C2×D63semidirect
70. C7×C9C2×C7×D13semidirect
71. C7×C9C2×D91semidirect
73. C72C2×D117semidirect
83. C2×C13C7×D63semidirect
88. C2×C9C7×D91semidirect
92. C2×C7C7×D117semidirect
93. C2×C7D819direct (N × H)
95. C13C2×C7×D63semidirect
97. C9C2×C7×D91semidirect
99. C7C2×C7×D117semidirect
100. C7C2×D819direct (N × H)
106. C2C7×D819direct (N × H)

Maximal subgroups

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

subgroupindex
C7×D8192
C2×C72×C9×C132
C2×C7×D2733
C2×D8197
C2×C7×D1177
C2×C7×D6313