Finite Group Databasebeta

← D3×C13×C3⋊(C7⋊D7) #37525619

Subgroups — D3×C13×C3⋊(C7⋊D7) #37525619

Order 22932.

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

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 128 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
1C3×D3×C72×C13C211yesmaximal, characteristic, complemented
2C3×C13×C3⋊(C7⋊D7)C211yesmaximal, characteristic, complemented
3C13×C3⋊(C3⋊(C7⋊D7))C211yesmaximal, characteristic, complemented
4C2×C13×C3⋊(C7⋊D7)—31nomaximal
5D3×C13×C7⋊D7—31nomaximal
6C32×C72×C13C2211yescharacteristic, complemented, Hall
7C13×C3⋊(C7⋊D7)—31no—
8C13×C3⋊(C7⋊D7)—31no—
9C13×C3⋊(C7⋊D7)—61no—
10C13×C3⋊(C7⋊D7)D311yescharacteristic, direct product factor
11D3×C72×C13D311yescharacteristic, complemented
12C3×C13×C7⋊D7—31no—
13C2×C3×C72×C13—31no—
14D3×C13×D21—78nomaximal
15C2×C13×C7⋊D7—91noHall
16C3×C72×C13—21no—
17C3×C72×C13C2×D311yescharacteristic, complemented
18C3×C72×C13C2×D311yescharacteristic, complemented
19D3×C3⋊(C7⋊D7)C1311yesmaximal, characteristic, direct product factor, Hall
20C13×C3⋊D21—78no—
21C3×C13×D21—78no—
22C3×D3×C7×C13D718yescomplemented
23C2×C72×C13—31no—
24C13×C7⋊D7—31no—
25C13×C7⋊D7—91no—
26C2×C13×D21—218no—
27D3×C13×D7—218no—
28C3⋊(C3⋊(C7⋊D7))C2×C1311yescharacteristic, complemented
29C3×C3⋊(C7⋊D7)C2×C1311yescharacteristic, complemented
30C3×D3×C72C2×C1311yescharacteristic, complemented
31C32×C7×C13C2×D718yescomplemented
32C72×C13D3211yescharacteristic, complemented, Hall
33C2×C3⋊(C7⋊D7)—31no—
34D3×C7⋊D7—31no—
35C2×C3×C7×C13—38no—
36C13×D21—78no—
37C13×D21—218no—
38C13×D21—218no—
39C13×D21—428no—
40D3×C7×C13D2118yescomplemented
41C3×C13×D7—218no—
42D32×C13—491noHall
43C32×C72C22×C1311yescharacteristic, complemented, Hall
44C2×C13×D7—638no—
45C2×C3×C72—31no—
46C3⋊(C7⋊D7)—31no—
47C3⋊(C7⋊D7)—31no—
48C3⋊(C7⋊D7)—61no—
49C3⋊(C7⋊D7)D3×C1311yescharacteristic, direct product factor
50D3×C72D3×C1311yescharacteristic, complemented
51C3×C7⋊D7—31no—
52C3×C7×C13—28no—
53C3×C7×C13D3×D718yescomplemented
54C3×C7×C13C2×D2118yescomplemented
55D3×D21—78no—
56C13×C3⋊D3—491no—
57C3×D3×C13—491no—
58C3×D3×C13C7⋊D711yescharacteristic, complemented
59C2×C7⋊D7—91noHall
60C2×C7×C13—38no—
61C13×D7—218no—
62C13×D7—638no—
63C2×D3×C13—1471no—
64C2×D3×C13—1471no—
65C3×C72—21no—
66C3×C72C2×D3×C1311yescharacteristic, complemented
67C3×C72C2×D3×C1311yescharacteristic, complemented
68C3⋊D21—78no—
69C3×D21—78no—
70C3×D3×C7C13×D718yescomplemented
71C32×C13C2×C7⋊D711yescharacteristic, complemented, Hall
72C2×C72—31no—
73C7⋊D7—31no—
74C7⋊D7—91no—
75C7×C13D3×D2118yescomplemented
76C2×D21—218no—
77D3×D7—218no—
78C2×C3×C13—31no—
79C2×C3×C13—1471no—
80D3×C13—2941no—
81D3×C13—491no—
82D3×C13—1471no—
83D3×C13—1471no—
84D3×C13C3⋊(C7⋊D7)11yescharacteristic, direct product factor
85C32×C7C2×C13×D718yescomplemented
86C22×C13—4411noHall
87C72D32×C1311yescharacteristic, complemented, Sylow
88C2×C3×C7—38no—
89D21—78no—
90D21—218no—
91D21—218no—
92D21—428no—
93C3×D7—218no—
94D3×C7C13×D2118yescomplemented
95C3×C13—21no—
96C3×C13D3×C7⋊D711yescharacteristic, complemented
97C3×C13C2×C3⋊(C7⋊D7)11yescharacteristic, complemented
98D32—491noHall
99C2×D7—638no—
100C2×C13—31no—
101C2×C13—1471no—
102C2×C13—4411no—
103C3×C7—28no—
104C3×C7D3×C13×D718yescomplemented
105C3×C7C2×C13×D2118yescomplemented
106C3⋊D3—491no—
107C3×D3—491no—
108C3×D3C13×C7⋊D711yescharacteristic, complemented
109C2×C7—38no—
110D7—218no—
111D7—638no—
112C13D3×C3⋊(C7⋊D7)11yescharacteristic, direct product factor, Sylow
113C2×D3—1471no—
114C2×D3—1471no—
115C32C2×C13×C7⋊D711yescharacteristic, complemented, Sylow
116C7D3×C13×D2118yescomplemented
117C2×C3—31no—
118C2×C3—1471no—
119D3—2941no—
120D3—491no—
121D3—1471no—
122D3—1471no—
123D3C13×C3⋊(C7⋊D7)11yescharacteristic, direct product factor
124C22—4411noSylow
125C3—21no—
126C3D3×C13×C7⋊D711yescharacteristic, complemented
127C3C2×C13×C3⋊(C7⋊D7)11yescharacteristic, complemented
128C2—31no—
129C2—1471no—
130C2—4411no—
subgroupG/H
center, hypercenterC13D3×C3⋊(C7⋊D7)
commutator, cosocle, hypocenterC32×C72C22×C13
FrattiniC1G
Fitting, socleC32×C72×C13C22
LCSG ▷ C32×C72
UCSC1 ◁ C13

Complements

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

NH ≅ G/Ntype
1. C3×D3×C72×C13C2semidirect
2. C3×C13×C3⋊(C7⋊D7)C2semidirect
3. C13×C3⋊(C3⋊(C7⋊D7))C2semidirect
6. C32×C72×C13C22semidirect
10. C13×C3⋊(C7⋊D7)D3direct (N × H)
11. D3×C72×C13D3semidirect
17. C3×C72×C13C2×D3semidirect
18. C3×C72×C13C2×D3semidirect
19. D3×C3⋊(C7⋊D7)C13direct (N × H)
22. C3×D3×C7×C13D7semidirect
28. C3⋊(C3⋊(C7⋊D7))C2×C13semidirect
29. C3×C3⋊(C7⋊D7)C2×C13semidirect
30. C3×D3×C72C2×C13semidirect
31. C32×C7×C13C2×D7semidirect
32. C72×C13D32semidirect
40. D3×C7×C13D21semidirect
43. C32×C72C22×C13semidirect
49. C3⋊(C7⋊D7)D3×C13direct (N × H)
50. D3×C72D3×C13semidirect
53. C3×C7×C13D3×D7semidirect
54. C3×C7×C13C2×D21semidirect
58. C3×D3×C13C7⋊D7semidirect
66. C3×C72C2×D3×C13semidirect
67. C3×C72C2×D3×C13semidirect
70. C3×D3×C7C13×D7semidirect
71. C32×C13C2×C7⋊D7semidirect
75. C7×C13D3×D21semidirect
84. D3×C13C3⋊(C7⋊D7)direct (N × H)
85. C32×C7C2×C13×D7semidirect
87. C72D32×C13semidirect
94. D3×C7C13×D21semidirect
96. C3×C13D3×C7⋊D7semidirect
97. C3×C13C2×C3⋊(C7⋊D7)semidirect
104. C3×C7D3×C13×D7semidirect
105. C3×C7C2×C13×D21semidirect
108. C3×D3C13×C7⋊D7semidirect
112. C13D3×C3⋊(C7⋊D7)direct (N × H)
115. C32C2×C13×C7⋊D7semidirect
116. C7D3×C13×D21semidirect
123. D3C13×C3⋊(C7⋊D7)direct (N × H)
126. C3D3×C13×C7⋊D7semidirect
127. C3C2×C13×C3⋊(C7⋊D7)semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C72×C132
C3×C13×C3⋊(C7⋊D7)2
C13×C3⋊(C3⋊(C7⋊D7))2
C2×C13×C3⋊(C7⋊D7)3
D3×C13×C7⋊D73
D3×C13×D217
D3×C3⋊(C7⋊D7)13