Finite Group Databasebeta

← D39⋊(C3⋊(C7⋊D7)) #37525621

Subgroups — D39⋊(C3⋊(C7⋊D7)) #37525621

Order 22932.

440 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 105 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×C72×D39C211yesmaximal, characteristic, complemented
2C3×C3⋊(C7⋊D91)C211yesmaximal, characteristic, complemented
3C13×C3⋊(C3⋊(C7⋊D7))C211yesmaximal, characteristic, complemented
4D39⋊(C7⋊D7)—31nomaximal
5D13×C3⋊(C7⋊D7)—31nomaximal
6C32×C72×C13C2211yescharacteristic, complemented, Hall
7C3⋊(C7⋊D91)D311yescharacteristic, complemented
8C13×C3⋊(C7⋊D7)—31no—
9C13×C3⋊(C7⋊D7)—31no—
10C13×C3⋊(C7⋊D7)—61no—
11C72×D39D311yescharacteristic, complemented
12C3×C7⋊D91—31no—
13C3×C72×D13—31no—
14D39⋊D21—78nomaximal
15D13×C7⋊D7—91noHall
16C3×C72×C13—21no—
17C3×C72×C13C2×D311yescharacteristic, complemented
18C3×C72×C13C2×D311yescharacteristic, complemented
19D3×C3⋊(C7⋊D7)—131nomaximal, Hall
20C13×C3⋊D21—78no—
21C3×D273—78no—
22C3×C7×D39D718yescomplemented
23C7⋊D91—31no—
24C13×C7⋊D7—91no—
25C72×D13—31no—
26D21⋊D13—218no—
27D13×D21—218no—
28C3⋊(C3⋊(C7⋊D7))D1311yescharacteristic, complemented
29C3×C3⋊(C7⋊D7)—131no—
30C3×D3×C72—131no—
31C32×C7×C13C2×D718yescomplemented
32C72×C13D3211yescharacteristic, complemented, Hall
33C2×C3⋊(C7⋊D7)—391no—
34D3×C7⋊D7—391no—
35D273—78no—
36C13×D21—218no—
37C13×D21—218no—
38C13×D21—428no—
39C7×D39D2118yescomplemented
40C3×D91—218no—
41C3×C7×D13—38no—
42(C3⋊D3)⋊D13—491noHall
43C32×C72C2×D1311yescharacteristic, complemented, Hall
44D7×D13—638no—
45C2×C3×C72—391no—
46C3⋊(C7⋊D7)—31no—
47C3⋊(C7⋊D7)—31no—
48C3⋊(C7⋊D7)—61no—
49C3⋊(C7⋊D7)—131no—
50D3×C72—131no—
51C3×C7⋊D7—391no—
52C3×C7×C13—28no—
53C3×C7×C13D3×D718yescomplemented
54C3×C7×C13C2×D2118yescomplemented
55D3×D21—918no—
56C13×C3⋊D3—491no—
57C3×D39—491no—
58C3×D39C7⋊D711yescharacteristic, complemented
59C2×C7⋊D7—1171noHall
60D91—218no—
61C7×D13—38no—
62C13×D7—638no—
63D3×D13—1471no—
64D3×D13—1471no—
65C3×C72—21no—
66C3×C72D3×D1311yescharacteristic, complemented
67C3×C72D3×D1311yescharacteristic, complemented
68C3⋊D21—78no—
69C3×D21—918no—
70C3×D3×C7—138no—
71C32×C13C2×C7⋊D711yescharacteristic, complemented, Hall
72C2×C72—391no—
73C7⋊D7—91no—
74C7⋊D7—391no—
75C7×C13D3×D2118yescomplemented
76C2×D21—2738no—
77D3×D7—2738no—
78D39—491no—
79D39C3⋊(C7⋊D7)11yescharacteristic, complemented
80C3×D13—31no—
81C3×D13—1471no—
82D3×C13—2941no—
83D3×C13—1471no—
84D3×C13—1471no—
85C32×C7D7×D1318yescomplemented
86C2×D13—4411noHall
87C72(C3⋊D3)⋊D1311yescharacteristic, complemented, Sylow
88C2×C3×C7—398no—
89D21—218no—
90D21—218no—
91D21—428no—
92D21—918no—
93C3×D7—2738no—
94D3×C7—138no—
95C3×C13—21no—
96C3×C13D3×C7⋊D711yescharacteristic, complemented
97C3×C13C2×C3⋊(C7⋊D7)11yescharacteristic, complemented
98D32—6371noHall
99C2×D7—8198no—
100C2×C13—4411no—
101D13—31no—
102D13—1471no—
103C3×C7—28no—
104C3×C7D13×D2118yescomplemented
105C3×C7D21⋊D1318yescomplemented
106C3⋊D3—491no—
107C3×D3—131no—
108C3×D3—6371no—
109C2×C7—398no—
110D7—2738no—
111D7—638no—
112C13D3×C3⋊(C7⋊D7)11yescharacteristic, complemented, Sylow
113C2×D3—19111no—
114C2×D3—19111no—
115C32D13×C7⋊D711yescharacteristic, complemented, Sylow
116C7D39⋊D2118yescomplemented
117C2×C3—391no—
118C2×C3—19111no—
119D3—131no—
120D3—2941no—
121D3—6371no—
122D3—1471no—
123D3—1471no—
124C22—57331noSylow
125C3—21no—
126C3D13×C3⋊(C7⋊D7)11yescharacteristic, complemented
127C3D39⋊(C7⋊D7)11yescharacteristic, complemented
128C2—391no—
129C2—19111no—
130C2—4411no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C72×C13C22
LCSG ▷ C32×C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C72×D39C2semidirect
2. C3×C3⋊(C7⋊D91)C2semidirect
3. C13×C3⋊(C3⋊(C7⋊D7))C2semidirect
6. C32×C72×C13C22semidirect
7. C3⋊(C7⋊D91)D3semidirect
11. C72×D39D3semidirect
17. C3×C72×C13C2×D3semidirect
18. C3×C72×C13C2×D3semidirect
22. C3×C7×D39D7semidirect
28. C3⋊(C3⋊(C7⋊D7))D13semidirect
31. C32×C7×C13C2×D7semidirect
32. C72×C13D32semidirect
39. C7×D39D21semidirect
43. C32×C72C2×D13semidirect
53. C3×C7×C13D3×D7semidirect
54. C3×C7×C13C2×D21semidirect
58. C3×D39C7⋊D7semidirect
66. C3×C72D3×D13semidirect
67. C3×C72D3×D13semidirect
71. C32×C13C2×C7⋊D7semidirect
75. C7×C13D3×D21semidirect
79. D39C3⋊(C7⋊D7)semidirect
85. C32×C7D7×D13semidirect
87. C72(C3⋊D3)⋊D13semidirect
96. C3×C13D3×C7⋊D7semidirect
97. C3×C13C2×C3⋊(C7⋊D7)semidirect
104. C3×C7D13×D21semidirect
105. C3×C7D21⋊D13semidirect
112. C13D3×C3⋊(C7⋊D7)semidirect
115. C32D13×C7⋊D7semidirect
116. C7D39⋊D21semidirect
126. C3D13×C3⋊(C7⋊D7)semidirect
127. C3D39⋊(C7⋊D7)semidirect

Maximal subgroups

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

subgroupindex
C3×C72×D392
C3×C3⋊(C7⋊D91)2
C13×C3⋊(C3⋊(C7⋊D7))2
D39⋊(C7⋊D7)3
D13×C3⋊(C7⋊D7)3
D39⋊D217
D3×C3⋊(C7⋊D7)13