Finite Group Databasebeta

← C2×C7×D13×C7⋊C9 #37524513

Subgroups — C2×C7×D13×C7⋊C9 #37524513

Order 22932.

160 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C2×C7×C13×C7⋊C9C211yesmaximal, characteristic, complemented
2C7×D13×C7⋊C9C212yesmaximal, direct product factor
3C2×C3×C72×D13C311yesmaximal, characteristic
4C7×C13×C7⋊C9C2211yescharacteristic, complemented, Hall
5C3×C72×D13C2×C312yes—
6C2×C3×C72×C13C2×C311yescharacteristic
7C2×C7×C9×D13—71nomaximal
8C2×D13×C7⋊C9C711yesmaximal, characteristic, direct product factor
9C2×C72×D13C911yescharacteristic, complemented, Hall
10C3×C72×C13C22×C311yescharacteristic
11C22×C7×C7⋊C9—131nomaximal, Hall
12C2×C7×C9×C13—71no—
13C7×C9×D13—72no—
14C2×C13×C7⋊C9C2×C711yescharacteristic, complemented
15D13×C7⋊C9C2×C712yesdirect product factor
16C2×C72×C13C2×C911yescharacteristic, complemented
17C72×D13C2×C912yescomplemented
18C2×C3×C7×D13—32no—
19C2×C3×C7×D13ΓL(1,𝔽8)11yescharacteristic
20C2×C3×C7×D13C3×C711yescharacteristic
21C2×C7×C7⋊C9—132no—
22C2×C7×C7⋊C9D1311yescharacteristic, direct product factor
23C7×C9×C13—71no—
24C13×C7⋊C9C22×C711yescharacteristic, complemented
25C72×C13C22×C911yescharacteristic, complemented, Hall
26C22×C3×C72—131no—
27C2×C3×C7×C13—32no—
28C2×C3×C7×C13C2×ΓL(1,𝔽8)11yescharacteristic
29C2×C3×C7×C13C2×C3×C711yescharacteristic
30C3×C7×D13—34no—
31C3×C7×D13C2×ΓL(1,𝔽8)12yes—
32C3×C7×D13C2×C3×C712yes—
33C2×C9×D13—71noHall
34C7×C7⋊C9C2×D1311yescharacteristic, direct product factor, Hall
35C2×C7×D13—32no—
36C2×C7×D13C7⋊C911yescharacteristic, direct product factor
37C2×C7×D13C7×C911yescharacteristic, complemented
38C2×C3×C72—132no—
39C2×C3×C72C3×D1311yescharacteristic
40C3×C7×C13—32no—
41C3×C7×C13C22×ΓL(1,𝔽8)11yescharacteristic
42C3×C7×C13C22×C3×C711yescharacteristic
43C22×C7×C9—911no—
44C22×C7⋊C9—131no—
45C2×C9×C13—71no—
46C9×D13—72no—
47C22×C72—131noHall
48C2×C7×C13—32no—
49C2×C7×C13C2×C7⋊C911yescharacteristic, complemented
50C2×C7×C13C2×C7×C911yescharacteristic, complemented
51C7×D13—34no—
52C7×D13C2×C7⋊C912yesdirect product factor
53C7×D13C2×C7×C912yescomplemented
54C2×C3×D13C7×ΓL(1,𝔽8)11yescharacteristic
55C3×C72C2×C3×D1311yescharacteristic
56C2×C7×C9—71no—
57C2×C7×C9—912no—
58C2×C7⋊C9—132no—
59C2×C7⋊C9C7×D1311yescharacteristic, direct product factor
60C9×C13—71noHall
61C2×C72—132no—
62C2×C72C9×D1311yescharacteristic, complemented
63C7×C13—32no—
64C7×C13C22×C7⋊C911yescharacteristic, complemented
65C7×C13C22×C7×C911yescharacteristic, complemented
66C22×C3×C7—131no—
67C22×C3×C7—131no—
68C22×C3×C7—392no—
69C2×C3×C13C2×C7×ΓL(1,𝔽8)11yescharacteristic
70C3×D13C2×C7×ΓL(1,𝔽8)12yes—
71C7×C9—71no—
72C7⋊C9C2×C7×D1311yescharacteristic, direct product factor
73C2×D13C7×C7⋊C911yescharacteristic, direct product factor, Hall
74C72C2×C9×D1311yescharacteristic, complemented, Sylow
75C2×C3×C7—32no—
76C2×C3×C7—132no—
77C2×C3×C7—132no—
78C2×C3×C7—394no—
79C2×C3×C7ΓL(1,𝔽8)×D1311yescharacteristic
80C2×C3×C7C3×C7×D1311yescharacteristic
81C3×C13C22×C7×ΓL(1,𝔽8)11yescharacteristic
82C22×C9—911noHall
83C22×C7—131no—
84C22×C7—131no—
85C22×C7—392no—
86C2×C13C2×C7×C7⋊C911yescharacteristic, complemented
87D13C2×C7×C7⋊C912yesdirect product factor
88C3×C7—32no—
89C3×C7C2×ΓL(1,𝔽8)×D1311yescharacteristic
90C3×C7C2×C3×C7×D1311yescharacteristic
91C2×C9—71no—
92C2×C9—912no—
93C2×C7—32no—
94C2×C7—132no—
95C2×C7—132no—
96C2×C7—394no—
97C2×C7D13×C7⋊C911yescharacteristic, direct product factor
98C2×C7C7×C9×D1311yescharacteristic, complemented
99C13C22×C7×C7⋊C911yescharacteristic, complemented, Sylow
100C22×C3—131no—
101C9—71noSylow
102C7—32no—
103C7C2×D13×C7⋊C911yescharacteristic, direct product factor
104C7C2×C7×C9×D1311yescharacteristic, complemented
105C2×C3—132no—
106C2×C3C7×ΓL(1,𝔽8)×D1311yescharacteristic
107C22—131noSylow
108C3C2×C7×ΓL(1,𝔽8)×D1311yescharacteristic
109C2—132no—
110C2C7×D13×C7⋊C911yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C7ΓL(1,𝔽8)×D13
commutator, hypocenterC7×C13C22×C7×C9
FrattiniC3C2×C7×ΓL(1,𝔽8)×D13
Fitting, socleC2×C3×C72×C13C2×C3
prime radicalC2×C3×C72×D13C3
cosocleC3×C7×C13C22×C3×C7
LCSG ▷ C7×C13
UCSC1 ◁ C2×C3×C7

Complements

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

NH ≅ G/Ntype
1. C2×C7×C13×C7⋊C9C2semidirect
2. C7×D13×C7⋊C9C2direct (N × H)
4. C7×C13×C7⋊C9C22semidirect
8. C2×D13×C7⋊C9C7direct (N × H)
9. C2×C72×D13C9semidirect
14. C2×C13×C7⋊C9C2×C7semidirect
15. D13×C7⋊C9C2×C7direct (N × H)
16. C2×C72×C13C2×C9semidirect
17. C72×D13C2×C9semidirect
22. C2×C7×C7⋊C9D13direct (N × H)
24. C13×C7⋊C9C22×C7semidirect
25. C72×C13C22×C9semidirect
34. C7×C7⋊C9C2×D13direct (N × H)
36. C2×C7×D13C7⋊C9direct (N × H)
37. C2×C7×D13C7×C9semidirect
49. C2×C7×C13C2×C7⋊C9semidirect
50. C2×C7×C13C2×C7×C9semidirect
52. C7×D13C2×C7⋊C9direct (N × H)
53. C7×D13C2×C7×C9semidirect
59. C2×C7⋊C9C7×D13direct (N × H)
62. C2×C72C9×D13semidirect
64. C7×C13C22×C7⋊C9semidirect
65. C7×C13C22×C7×C9semidirect
72. C7⋊C9C2×C7×D13direct (N × H)
73. C2×D13C7×C7⋊C9direct (N × H)
74. C72C2×C9×D13semidirect
86. C2×C13C2×C7×C7⋊C9semidirect
87. D13C2×C7×C7⋊C9direct (N × H)
97. C2×C7D13×C7⋊C9direct (N × H)
98. C2×C7C7×C9×D13semidirect
99. C13C22×C7×C7⋊C9semidirect
103. C7C2×D13×C7⋊C9direct (N × H)
104. C7C2×C7×C9×D13semidirect
110. C2C7×D13×C7⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×C13×C7⋊C92
C7×D13×C7⋊C92
C2×C3×C72×D133
C2×C7×C9×D137
C2×D13×C7⋊C97
C22×C7×C7⋊C913