Finite Group Databasebeta

← C7×D7×C3⋊D39 #37525634

Subgroups — C7×D7×C3⋊D39 #37525634

Order 22932.

312 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 80 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×C13×D7C211yesmaximal, characteristic, complemented
2C72×C3⋊D39C211yesmaximal, characteristic, complemented
3C7×C3⋊D273C211yesmaximal, characteristic, complemented
4C7×D7×D39—34nomaximal
5C32×C72×C13C2211yescharacteristic, complemented, Hall
6C7×D273—34no—
7C72×D39—34no—
8C3×C7×C13×D7D314yescomplemented
9C2×C7×C3⋊D39—71nomaximal
10D7×C3⋊D39C711yesmaximal, characteristic, direct product factor
11C7×D7×D13—91noHall
12C3×C72×C13C2×D314yescomplemented
13C7×D7×C3⋊D3—131nomaximal, Hall
14C2×C32×C7×C13—71no—
15C3⋊D273C2×C711yescharacteristic, complemented
16C7×C3⋊D39—23no—
17C7×C3⋊D39—71no—
18C7×C3⋊D39D711yescharacteristic, direct product factor
19C7×C3⋊D39C2×C711yescharacteristic, complemented
20C32×C13×D7C2×C711yescharacteristic, complemented
21C7×D91—91no—
22C7×C13×D7C3⋊D311yescharacteristic, complemented
23C72×D13—91no—
24C2×C7×D39—214no—
25D7×D39—34no—
26C7×C3⋊D21—131no—
27C72×C3⋊D3—131no—
28C32×C7×D7D1311yescharacteristic, complemented
29C32×C7×C13—23no—
30C32×C7×C13C2×D711yescharacteristic, complemented
31C32×C7×C13C22×C711yescharacteristic, complemented
32C72×C13C2×C3⋊D311yescharacteristic, complemented, Hall
33D3×C7×D7—394no—
34C2×C3×C7×C13—74no—
35D273—34no—
36C7×D39—34no—
37C7×D39—34no—
38C7×D39—612no—
39C7×D39—214no—
40C3×C13×D7D3×C714yescomplemented
41C2×C3⋊D39—71noHall
42C32×C72C2×D1311yescharacteristic, complemented, Hall
43C2×C7×D13—631no—
44D7×D13—91no—
45C7×D21—394no—
46D3×C72—394no—
47C3×C7×D7D3914yescomplemented
48C3×C7×C13—212no—
49C3×C7×C13D3×D714yescomplemented
50C3×C7×C13C2×D3×C714yescomplemented
51C2×C7×C3⋊D3—911no—
52D7×C3⋊D3—131no—
53C2×C32×C13—71no—
54C3⋊D39—71no—
55C3⋊D39C7×D711yescharacteristic, direct product factor
56C2×C7×D7—1171noHall
57C2×C7×C13—71no—
58D91—91no—
59C7×D13—91no—
60C7×D13—91no—
61C7×D13—183no—
62C7×D13—631no—
63C13×D7C7×C3⋊D311yescharacteristic, complemented
64C2×D39—214no—
65C3×C72C2×D3914yescomplemented
66C2×C32×C7—71no—
67C3⋊D21—131no—
68C7×C3⋊D3—131no—
69C7×C3⋊D3—131no—
70C7×C3⋊D3—263no—
71C7×C3⋊D3—911no—
72C32×D7C7×D1311yescharacteristic, complemented
73C32×C13C2×C7×D711yescharacteristic, complemented, Hall
74C2×C72—1171no—
75C7×D7—1171no—
76C7×D7C3⋊D3911yescharacteristic, direct product factor
77C7×C13—23no—
78C7×C13D7×C3⋊D311yescharacteristic, complemented
79C7×C13C2×C7×C3⋊D311yescharacteristic, complemented
80C2×D3×C7—2734no—
81D3×D7—394no—
82C2×C3×C13—74no—
83D39—34no—
84D39—214no—
85C32×C7—23no—
86C32×C7D7×D1311yescharacteristic, complemented
87C32×C7C2×C7×D1311yescharacteristic, complemented
88C2×D13—631noHall
89C72C2×C3⋊D3911yescharacteristic, complemented, Sylow
90C2×C3×C7—74no—
91D21—394no—
92C3×D7C7×D3914yescomplemented
93D3×C7—2734no—
94D3×C7—394no—
95D3×C7—394no—
96D3×C7—7812no—
97C3×C13D3×C7×D714yescomplemented
98C2×C3⋊D3—911noHall
99C22×C7—8191no—
100C2×D7—1171no—
101C2×C13—71no—
102D13—91no—
103D13—631no—
104C3×C7—212no—
105C3×C7D7×D3914yescomplemented
106C3×C7C2×C7×D3914yescomplemented
107C2×C32—71no—
108C3⋊D3—131no—
109C3⋊D3—911no—
110C2×C7—71no—
111C2×C7—8191no—
112C2×C7—1171no—
113C2×C7—1171no—
114C2×C7—2343no—
115D7—1171no—
116D7C7×C3⋊D3911yescharacteristic, direct product factor
117C13C7×D7×C3⋊D311yescharacteristic, complemented, Sylow
118C2×D3—2734no—
119C32C7×D7×D1311yescharacteristic, complemented, Sylow
120C7—23no—
121C7D7×C3⋊D3911yescharacteristic, direct product factor
122C7C2×C7×C3⋊D3911yescharacteristic, complemented
123C2×C3—74no—
124D3—2734no—
125D3—394no—
126C22—8191noSylow
127C3C7×D7×D3914yescomplemented
128C2—71no—
129C2—8191no—
130C2—1171no—
subgroupG/H
center, hypercenterC7D7×C3⋊D39
commutator, cosocle, hypocenterC32×C7×C13C22×C7
FrattiniC1G
Fitting, socleC32×C72×C13C22
LCSG ▷ C32×C7×C13
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C32×C7×C13×D7C2semidirect
2. C72×C3⋊D39C2semidirect
3. C7×C3⋊D273C2semidirect
5. C32×C72×C13C22semidirect
8. C3×C7×C13×D7D3semidirect
10. D7×C3⋊D39C7direct (N × H)
12. C3×C72×C13C2×D3semidirect
15. C3⋊D273C2×C7semidirect
18. C7×C3⋊D39D7direct (N × H)
19. C7×C3⋊D39C2×C7semidirect
20. C32×C13×D7C2×C7semidirect
22. C7×C13×D7C3⋊D3semidirect
28. C32×C7×D7D13semidirect
30. C32×C7×C13C2×D7semidirect
31. C32×C7×C13C22×C7semidirect
32. C72×C13C2×C3⋊D3semidirect
40. C3×C13×D7D3×C7semidirect
42. C32×C72C2×D13semidirect
47. C3×C7×D7D39semidirect
49. C3×C7×C13D3×D7semidirect
50. C3×C7×C13C2×D3×C7semidirect
55. C3⋊D39C7×D7direct (N × H)
63. C13×D7C7×C3⋊D3semidirect
65. C3×C72C2×D39semidirect
72. C32×D7C7×D13semidirect
73. C32×C13C2×C7×D7semidirect
76. C7×D7C3⋊D39direct (N × H)
78. C7×C13D7×C3⋊D3semidirect
79. C7×C13C2×C7×C3⋊D3semidirect
86. C32×C7D7×D13semidirect
87. C32×C7C2×C7×D13semidirect
89. C72C2×C3⋊D39semidirect
92. C3×D7C7×D39semidirect
97. C3×C13D3×C7×D7semidirect
105. C3×C7D7×D39semidirect
106. C3×C7C2×C7×D39semidirect
116. D7C7×C3⋊D39direct (N × H)
117. C13C7×D7×C3⋊D3semidirect
119. C32C7×D7×D13semidirect
121. C7D7×C3⋊D39direct (N × H)
122. C7C2×C7×C3⋊D39semidirect
127. C3C7×D7×D39semidirect

Maximal subgroups

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

subgroupindex
C32×C7×C13×D72
C72×C3⋊D392
C7×C3⋊D2732
C7×D7×D393
C2×C7×C3⋊D397
D7×C3⋊D397
C7×D7×C3⋊D313