Finite Group Databasebeta

← C7×D13×D7⋊C9 #37524406

Subgroups — C7×D13×D7⋊C9 #37524406

Order 22932.

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

normal subgroups only

This group has 128 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×D13×C7⋊C9C211yesmaximal, characteristic, complemented
2C7×(C7⋊C9)⋊D13C211yesmaximal, characteristic, complemented
3C7×C13×D7⋊C9C211yesmaximal, characteristic, complemented
4C3×C7×D7×D13C311yesmaximal, characteristic
5C7×C13×C7⋊C9C2211yescharacteristic, complemented, Hall
6C3×C7×D91C2×C311yescharacteristic
7C3×C7×C13×D7C2×C311yescharacteristic
8C3×C72×D13C2×C311yescharacteristic
9C2×C7×C9×D13—71nomaximal
10D13×D7⋊C9C711yesmaximal, characteristic, direct product factor
11C7×D7×D13C911yescharacteristic, complemented, Hall
12C3×C72×C13C22×C311yescharacteristic
13C2×C7×D7⋊C9—131nomaximal, Hall
14C2×C7×C9×C13—71no—
15C7×C9×D13—71no—
16C7×C9×D13—71no—
17(C7⋊C9)⋊D13C2×C711yescharacteristic, complemented
18C13×D7⋊C9C2×C711yescharacteristic, complemented
19D13×C7⋊C9C2×C711yescharacteristic, complemented
20C7×D91C2×C911yescharacteristic, complemented
21C7×C13×D7C2×C911yescharacteristic, complemented
22C72×D13C2×C911yescharacteristic, complemented
23C2×C3×C7×D13—211no—
24C3×D7×D13C3×C711yescharacteristic
25C2×C7×C7⋊C9—131no—
26C7×D7⋊C9—131no—
27C7×D7⋊C9D1311yescharacteristic, direct product factor
28C7×C9×C13—71no—
29C13×C7⋊C9C22×C711yescharacteristic, complemented
30C72×C13C22×C911yescharacteristic, complemented, Hall
31C2×C3×C7×D7—131no—
32C2×C3×C7×C13—211no—
33C3×D91C2×C3×C711yescharacteristic
34C3×C13×D7C2×C3×C711yescharacteristic
35C3×C7×D13—61no—
36C3×C7×D13—71no—
37C3×C7×D13AGL(1,𝔽7)11yescharacteristic
38C3×C7×D13C2×C3×C711yescharacteristic
39C2×C9×D13—71noHall
40C7×C7⋊C9C2×D1311yescharacteristic, complemented, Hall
41C2×C7×D13—211no—
42D7×D13C7×C911yescharacteristic, complemented
43C2×C3×C72—131no—
44C3×C7×D7—131no—
45C3×C7×D7C3×D1311yescharacteristic
46C3×C7×C13—61no—
47C3×C7×C13C2×AGL(1,𝔽7)11yescharacteristic
48C3×C7×C13C22×C3×C711yescharacteristic
49C22×C7×C9—911no—
50C2×D7⋊C9—131no—
51C2×C9×C13—71no—
52C9×D13—71no—
53C9×D13—71no—
54C2×C7×D7—131noHall
55C2×C7×C13—211no—
56D91C2×C7×C911yescharacteristic, complemented
57C7×D13—61no—
58C7×D13—71no—
59C7×D13D7⋊C911yescharacteristic, direct product factor
60C7×D13C2×C7×C911yescharacteristic, complemented
61C13×D7C2×C7×C911yescharacteristic, complemented
62C2×C3×D13—211no—
63C3×C72C2×C3×D1311yescharacteristic
64C2×C7×C9—71no—
65C2×C7×C9—911no—
66C2×C7×C9—911no—
67C2×C7⋊C9—131no—
68D7⋊C9—131no—
69D7⋊C9C7×D1311yescharacteristic, direct product factor
70C9×C13—71noHall
71C2×C72—131no—
72C7×D7—131no—
73C7×D7C9×D1311yescharacteristic, complemented
74C7×C13—61no—
75C7×C13C2×D7⋊C911yescharacteristic, complemented
76C7×C13C22×C7×C911yescharacteristic, complemented
77C22×C3×C7—2731no—
78C2×C3×D7—131no—
79C2×C3×C13—211no—
80C3×D13—211no—
81C3×D13C7×AGL(1,𝔽7)11yescharacteristic
82C7×C9—71no—
83C7⋊C9C2×C7×D1311yescharacteristic, complemented
84C2×D13—211noHall
85C72C2×C9×D1311yescharacteristic, complemented, Sylow
86C2×C3×C7—131no—
87C2×C3×C7—131no—
88C2×C3×C7—2731no—
89C2×C3×C7—211no—
90C2×C3×C7—781no—
91C3×D7—131no—
92C3×D7C3×C7×D1311yescharacteristic
93C3×C13C2×C7×AGL(1,𝔽7)11yescharacteristic
94C22×C9—911noHall
95C22×C7—2731no—
96C2×D7—131no—
97C2×C13—211no—
98D13—211no—
99D13C7×D7⋊C911yescharacteristic, direct product factor
100C3×C7—61no—
101C3×C7D13×AGL(1,𝔽7)11yescharacteristic
102C3×C7C2×C3×C7×D1311yescharacteristic
103C2×C9—71no—
104C2×C9—911no—
105C2×C9—911no—
106C2×C7—131no—
107C2×C7—131no—
108C2×C7—2731no—
109C2×C7—211no—
110C2×C7—781no—
111D7—131no—
112D7C7×C9×D1311yescharacteristic, complemented
113C13C2×C7×D7⋊C911yescharacteristic, complemented, Sylow
114C22×C3—2731no—
115C9—71noSylow
116C7—61no—
117C7D13×D7⋊C911yescharacteristic, direct product factor
118C7C2×C7×C9×D1311yescharacteristic, complemented
119C2×C3—71no—
120C2×C3—131no—
121C2×C3—2731no—
122C22—2731noSylow
123C3C7×D13×AGL(1,𝔽7)11yescharacteristic
124C2—71no—
125C2—131no—
126C2—2731no—
subgroupG/H
center, hypercenterC3×C7D13×AGL(1,𝔽7)
commutator, hypocenterC7×C13C22×C7×C9
FrattiniC3C7×D13×AGL(1,𝔽7)
Fitting, socleC3×C72×C13C22×C3
prime radicalC3×C7×D7×D13C3
cosocleC3×C7×C13C22×C3×C7
LCSG ▷ C7×C13
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
1. C7×D13×C7⋊C9C2semidirect
2. C7×(C7⋊C9)⋊D13C2semidirect
3. C7×C13×D7⋊C9C2semidirect
5. C7×C13×C7⋊C9C22semidirect
10. D13×D7⋊C9C7direct (N × H)
11. C7×D7×D13C9semidirect
17. (C7⋊C9)⋊D13C2×C7semidirect
18. C13×D7⋊C9C2×C7semidirect
19. D13×C7⋊C9C2×C7semidirect
20. C7×D91C2×C9semidirect
21. C7×C13×D7C2×C9semidirect
22. C72×D13C2×C9semidirect
27. C7×D7⋊C9D13direct (N × H)
29. C13×C7⋊C9C22×C7semidirect
30. C72×C13C22×C9semidirect
40. C7×C7⋊C9C2×D13semidirect
42. D7×D13C7×C9semidirect
56. D91C2×C7×C9semidirect
59. C7×D13D7⋊C9direct (N × H)
60. C7×D13C2×C7×C9semidirect
61. C13×D7C2×C7×C9semidirect
69. D7⋊C9C7×D13direct (N × H)
73. C7×D7C9×D13semidirect
75. C7×C13C2×D7⋊C9semidirect
76. C7×C13C22×C7×C9semidirect
83. C7⋊C9C2×C7×D13semidirect
85. C72C2×C9×D13semidirect
99. D13C7×D7⋊C9direct (N × H)
112. D7C7×C9×D13semidirect
113. C13C2×C7×D7⋊C9semidirect
117. C7D13×D7⋊C9direct (N × H)
118. C7C2×C7×C9×D13semidirect

Maximal subgroups

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

subgroupindex
C7×D13×C7⋊C92
C7×(C7⋊C9)⋊D132
C7×C13×D7⋊C92
C3×C7×D7×D133
C2×C7×C9×D137
D13×D7⋊C97
C2×C7×D7⋊C913