Finite Group Databasebeta

← C3×D39⋊(C7⋊D7) #37525601

Subgroups — C3×D39⋊(C7⋊D7) #37525601

Order 22932.

440 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C32×C7⋊D91C211yesmaximal, characteristic, complemented
2C3×C72×D39C211yesmaximal, characteristic, complemented
3C3×C13×C3⋊(C7⋊D7)C211yesmaximal, characteristic, complemented
4D39⋊(C7⋊D7)C311yesmaximal, characteristic, direct product factor
5C3×D13×C7⋊D7—31nomaximal
6C32×C72×C13C2211yescharacteristic, complemented, Hall
7C13×C3⋊(C7⋊D7)C2×C311yescharacteristic, complemented
8C72×D39C2×C311yescharacteristic, complemented
9C3×C7⋊D91—21no—
10C3×C7⋊D91D311yescharacteristic, complemented
11C3×C7⋊D91C2×C311yescharacteristic, complemented
12C3×C13×C7⋊D7—31no—
13C3×C72×D13—31no—
14C3×D21⋊D13—78nomaximal
15D13×C7⋊D7—31noHall
16C3×C72×C13—21no—
17C3×C72×C13C2×D311yescharacteristic, complemented
18C3×C72×C13C22×C311yescharacteristic, complemented
19C3×D3×C7⋊D7—131nomaximal, Hall
20C3×C13×D21—78no—
21C3×C7×D39D718yescomplemented
22C32×D91—78no—
23C7⋊D91C3×D311yescharacteristic, complemented
24C13×C7⋊D7—31no—
25C72×D13—31no—
26D21⋊D13—78no—
27C3×D7×D13—218no—
28C3×C3⋊(C7⋊D7)D1311yescharacteristic, complemented
29C3×D3×C72—131no—
30C32×C7⋊D7—131no—
31C32×C7×C13C2×D718yescomplemented
32C72×C13C2×C3×D311yescharacteristic, complemented, Hall
33C2×C3×C7⋊D7—391no—
34D3×C7⋊D7—131no—
35C13×D21—78no—
36C7×D39C3×D718yescomplemented
37C3×D91—78no—
38C3×D91—78no—
39C3×D91—148no—
40C3×C13×D7—218no—
41C3×C7×D13—38no—
42C3×D3×D13—491noHall
43C32×C72C2×D1311yescharacteristic, complemented, Hall
44D7×D13—218no—
45C2×C3×C72—391no—
46C3⋊(C7⋊D7)C3×D1311yescharacteristic, complemented
47D3×C72—131no—
48C3×C7⋊D7—31no—
49C3×C7⋊D7—131no—
50C3×C7⋊D7—131no—
51C3×C7⋊D7—261no—
52C3×C7×C13—28no—
53C3×C7×C13D3×D718yescomplemented
54C3×C7×C13C2×C3×D718yescomplemented
55C3×D3×D7—918no—
56C3×D39C7⋊D711yescharacteristic, complemented
57C3×D3×C13—491no—
58C32×D13—491no—
59C2×C7⋊D7—391noHall
60D91—78no—
61C7×D13—38no—
62C13×D7—218no—
63C2×C3×D13—1471no—
64D3×D13—491no—
65C3×C72—21no—
66C3×C72D3×D1311yescharacteristic, complemented
67C3×C72C2×C3×D1311yescharacteristic, complemented
68C3×D21—78no—
69C3×D3×C7—138no—
70C32×D7—918no—
71C32×C13C2×C7⋊D711yescharacteristic, complemented, Hall
72C2×C72—391no—
73C7⋊D7—31no—
74C7⋊D7—131no—
75C7×C13C3×D3×D718yescomplemented
76C2×C3×D7—2738no—
77D3×D7—918no—
78C2×C3×C13—1471no—
79D39C3×C7⋊D711yescharacteristic, complemented
80C3×D13—31no—
81C3×D13—491no—
82C3×D13—491no—
83C3×D13—981no—
84D3×C13—491no—
85C32×C7D7×D1318yescomplemented
86C2×D13—1471noHall
87C72C3×D3×D1311yescharacteristic, complemented, Sylow
88C2×C3×C7—398no—
89D21—78no—
90C3×D7—218no—
91C3×D7—918no—
92C3×D7—918no—
93C3×D7—1828no—
94D3×C7—138no—
95C3×C13—21no—
96C3×C13D3×C7⋊D711yescharacteristic, complemented
97C3×C13C2×C3×C7⋊D711yescharacteristic, complemented
98C2×C3×D3—6371noHall
99C2×D7—2738no—
100C2×C13—1471no—
101D13—31no—
102D13—491no—
103C3×C7—28no—
104C3×C7C3×D7×D1318yescomplemented
105C3×C7D21⋊D1318yescomplemented
106C2×C32—6371no—
107C3×D3—131no—
108C3×D3—491no—
109C2×C7—398no—
110D7—218no—
111D7—918no—
112C13C3×D3×C7⋊D711yescharacteristic, complemented, Sylow
113C22×C3—19111no—
114C2×D3—6371no—
115C32D13×C7⋊D711yescharacteristic, complemented, Sylow
116C7C3×D21⋊D1318yescomplemented
117C2×C3—391no—
118C2×C3—6371no—
119C2×C3—6371no—
120C2×C3—1471no—
121C2×C3—12741no—
122D3—131no—
123D3—491no—
124C22—19111noSylow
125C3—21no—
126C3C3×D13×C7⋊D711yescharacteristic, complemented
127C3D39⋊(C7⋊D7)11yescharacteristic, direct product factor
128C2—391no—
129C2—6371no—
130C2—1471no—
subgroupG/H
center, hypercenterC3D39⋊(C7⋊D7)
commutator, cosocle, hypocenterC3×C72×C13C22×C3
FrattiniC1G
Fitting, socleC32×C72×C13C22
LCSG ▷ C3×C72×C13
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C7⋊D91C2semidirect
2. C3×C72×D39C2semidirect
3. C3×C13×C3⋊(C7⋊D7)C2semidirect
4. D39⋊(C7⋊D7)C3direct (N × H)
6. C32×C72×C13C22semidirect
7. C13×C3⋊(C7⋊D7)C2×C3semidirect
8. C72×D39C2×C3semidirect
10. C3×C7⋊D91D3semidirect
11. C3×C7⋊D91C2×C3semidirect
17. C3×C72×C13C2×D3semidirect
18. C3×C72×C13C22×C3semidirect
21. C3×C7×D39D7semidirect
23. C7⋊D91C3×D3semidirect
28. C3×C3⋊(C7⋊D7)D13semidirect
31. C32×C7×C13C2×D7semidirect
32. C72×C13C2×C3×D3semidirect
36. C7×D39C3×D7semidirect
43. C32×C72C2×D13semidirect
46. C3⋊(C7⋊D7)C3×D13semidirect
53. C3×C7×C13D3×D7semidirect
54. C3×C7×C13C2×C3×D7semidirect
56. C3×D39C7⋊D7semidirect
66. C3×C72D3×D13semidirect
67. C3×C72C2×C3×D13semidirect
71. C32×C13C2×C7⋊D7semidirect
75. C7×C13C3×D3×D7semidirect
79. D39C3×C7⋊D7semidirect
85. C32×C7D7×D13semidirect
87. C72C3×D3×D13semidirect
96. C3×C13D3×C7⋊D7semidirect
97. C3×C13C2×C3×C7⋊D7semidirect
104. C3×C7C3×D7×D13semidirect
105. C3×C7D21⋊D13semidirect
112. C13C3×D3×C7⋊D7semidirect
115. C32D13×C7⋊D7semidirect
116. C7C3×D21⋊D13semidirect
126. C3C3×D13×C7⋊D7semidirect
127. C3D39⋊(C7⋊D7)direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C7⋊D912
C3×C72×D392
C3×C13×C3⋊(C7⋊D7)2
D39⋊(C7⋊D7)3
C3×D13×C7⋊D73
C3×D21⋊D137
C3×D3×C7⋊D713