Finite Group Databasebeta

← C7×C13×D7×C3⋊D3 #37525633

Subgroups — C7×C13×D7×C3⋊D3 #37525633

Order 22932.

312 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 88 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×C13×C3⋊D3C211yesmaximal, characteristic, complemented
3C7×C13×C3⋊D21C211yesmaximal, characteristic, complemented
4D3×C7×C13×D7—34nomaximal
5C32×C72×C13C2211yescharacteristic, complemented, Hall
6C7×C13×D21—34no—
7D3×C72×C13—34no—
8C3×C7×C13×D7D314yescomplemented
9C2×C7×C13×C3⋊D3—71nomaximal
10C13×D7×C3⋊D3C711yesmaximal, characteristic, direct product factor
11C2×C7×C13×D7—91noHall
12C3×C72×C13C2×D314yescomplemented
13C7×D7×C3⋊D3C1311yesmaximal, characteristic, direct product factor, Hall
14C2×C32×C7×C13—71no—
15C13×C3⋊D21C2×C711yescharacteristic, complemented
16C7×C13×C3⋊D3—23no—
17C7×C13×C3⋊D3—71no—
18C7×C13×C3⋊D3D711yescharacteristic, direct product factor
19C7×C13×C3⋊D3C2×C711yescharacteristic, complemented
20C32×C13×D7C2×C711yescharacteristic, complemented
21C2×C72×C13—91no—
22C7×C13×D7—91no—
23C7×C13×D7C3⋊D311yescharacteristic, direct product factor
24C2×D3×C7×C13—214no—
25D3×C13×D7—34no—
26C7×C3⋊D21C2×C1311yescharacteristic, complemented
27C72×C3⋊D3C2×C1311yescharacteristic, complemented
28C32×C7×D7C2×C1311yescharacteristic, complemented
29C32×C7×C13—23no—
30C32×C7×C13C2×D711yescharacteristic, complemented
31C32×C7×C13C22×C711yescharacteristic, complemented
32C72×C13C2×C3⋊D311yescharacteristic, complemented, Hall
33D3×C7×D7—34no—
34C2×C3×C7×C13—74no—
35C13×D21—34no—
36D3×C7×C13—34no—
37D3×C7×C13—34no—
38D3×C7×C13—612no—
39D3×C7×C13—214no—
40C3×C13×D7D3×C714yescomplemented
41C2×C13×C3⋊D3—71noHall
42C32×C72C22×C1311yescharacteristic, complemented, Hall
43C22×C7×C13—631no—
44C2×C13×D7—91no—
45C7×D21—34no—
46D3×C72—34no—
47C3×C7×D7D3×C1314yescomplemented
48C3×C7×C13—212no—
49C3×C7×C13D3×D714yescomplemented
50C3×C7×C13C2×D3×C714yescomplemented
51C2×C7×C3⋊D3—71no—
52D7×C3⋊D3C7×C1311yescharacteristic, direct product factor
53C2×C32×C13—71no—
54C13×C3⋊D3—71no—
55C13×C3⋊D3C7×D711yescharacteristic, direct product factor
56C2×C7×D7—91noHall
57C2×C7×C13—71no—
58C2×C7×C13—91no—
59C2×C7×C13—91no—
60C2×C7×C13—183no—
61C2×C7×C13—631no—
62C13×D7—91no—
63C13×D7C7×C3⋊D311yescharacteristic, direct product factor
64C2×D3×C13—214no—
65C3×C72C2×D3×C1314yescomplemented
66C2×C32×C7—71no—
67C3⋊D21C2×C7×C1311yescharacteristic, complemented
68C7×C3⋊D3—23no—
69C7×C3⋊D3—71no—
70C7×C3⋊D3C13×D711yescharacteristic, direct product factor
71C7×C3⋊D3C2×C7×C1311yescharacteristic, complemented
72C32×D7C2×C7×C1311yescharacteristic, complemented
73C32×C13C2×C7×D711yescharacteristic, complemented, Hall
74C2×C72—91no—
75C7×D7—91no—
76C7×D7C13×C3⋊D311yescharacteristic, direct product factor
77C7×C13—23no—
78C7×C13D7×C3⋊D311yescharacteristic, direct product factor
79C7×C13C2×C7×C3⋊D311yescharacteristic, complemented
80C2×D3×C7—214no—
81D3×D7—34no—
82C2×C3×C13—74no—
83D3×C13—34no—
84D3×C13—214no—
85C32×C7—23no—
86C32×C7C2×C13×D711yescharacteristic, complemented
87C32×C7C22×C7×C1311yescharacteristic, complemented
88C22×C13—631noHall
89C72C2×C13×C3⋊D311yescharacteristic, complemented, Sylow
90C2×C3×C7—74no—
91D21—34no—
92C3×D7D3×C7×C1314yescomplemented
93D3×C7—34no—
94D3×C7—34no—
95D3×C7—612no—
96D3×C7—214no—
97C3×C13D3×C7×D714yescomplemented
98C2×C3⋊D3—71noHall
99C22×C7—631no—
100C2×D7—91no—
101C2×C13—71no—
102C2×C13—91no—
103C2×C13—631no—
104C3×C7—212no—
105C3×C7D3×C13×D714yescomplemented
106C3×C7C2×D3×C7×C1314yescomplemented
107C2×C32—71no—
108C3⋊D3—71no—
109C3⋊D3C7×C13×D711yescharacteristic, direct product factor
110C2×C7—71no—
111C2×C7—91no—
112C2×C7—91no—
113C2×C7—183no—
114C2×C7—631no—
115D7—91no—
116D7C7×C13×C3⋊D311yescharacteristic, direct product factor
117C13C7×D7×C3⋊D311yescharacteristic, direct product factor, Sylow
118C2×D3—214no—
119C32C2×C7×C13×D711yescharacteristic, complemented, Sylow
120C7—23no—
121C7C13×D7×C3⋊D311yescharacteristic, direct product factor
122C7C2×C7×C13×C3⋊D311yescharacteristic, complemented
123C2×C3—74no—
124D3—34no—
125D3—214no—
126C22—631noSylow
127C3D3×C7×C13×D714yescomplemented
128C2—71no—
129C2—91no—
130C2—631no—
subgroupG/H
center, hypercenterC7×C13D7×C3⋊D3
commutator, cosocle, hypocenterC32×C7C22×C7×C13
FrattiniC1G
Fitting, socleC32×C72×C13C22
LCSG ▷ C32×C7
UCSC1 ◁ C7×C13

Complements

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

NH ≅ G/Ntype
1. C32×C7×C13×D7C2semidirect
2. C72×C13×C3⋊D3C2semidirect
3. C7×C13×C3⋊D21C2semidirect
5. C32×C72×C13C22semidirect
8. C3×C7×C13×D7D3semidirect
10. C13×D7×C3⋊D3C7direct (N × H)
12. C3×C72×C13C2×D3semidirect
13. C7×D7×C3⋊D3C13direct (N × H)
15. C13×C3⋊D21C2×C7semidirect
18. C7×C13×C3⋊D3D7direct (N × H)
19. C7×C13×C3⋊D3C2×C7semidirect
20. C32×C13×D7C2×C7semidirect
23. C7×C13×D7C3⋊D3direct (N × H)
26. C7×C3⋊D21C2×C13semidirect
27. C72×C3⋊D3C2×C13semidirect
28. C32×C7×D7C2×C13semidirect
30. C32×C7×C13C2×D7semidirect
31. C32×C7×C13C22×C7semidirect
32. C72×C13C2×C3⋊D3semidirect
40. C3×C13×D7D3×C7semidirect
42. C32×C72C22×C13semidirect
47. C3×C7×D7D3×C13semidirect
49. C3×C7×C13D3×D7semidirect
50. C3×C7×C13C2×D3×C7semidirect
52. D7×C3⋊D3C7×C13direct (N × H)
55. C13×C3⋊D3C7×D7direct (N × H)
63. C13×D7C7×C3⋊D3direct (N × H)
65. C3×C72C2×D3×C13semidirect
67. C3⋊D21C2×C7×C13semidirect
70. C7×C3⋊D3C13×D7direct (N × H)
71. C7×C3⋊D3C2×C7×C13semidirect
72. C32×D7C2×C7×C13semidirect
73. C32×C13C2×C7×D7semidirect
76. C7×D7C13×C3⋊D3direct (N × H)
78. C7×C13D7×C3⋊D3direct (N × H)
79. C7×C13C2×C7×C3⋊D3semidirect
86. C32×C7C2×C13×D7semidirect
87. C32×C7C22×C7×C13semidirect
89. C72C2×C13×C3⋊D3semidirect
92. C3×D7D3×C7×C13semidirect
97. C3×C13D3×C7×D7semidirect
105. C3×C7D3×C13×D7semidirect
106. C3×C7C2×D3×C7×C13semidirect
109. C3⋊D3C7×C13×D7direct (N × H)
116. D7C7×C13×C3⋊D3direct (N × H)
117. C13C7×D7×C3⋊D3direct (N × H)
119. C32C2×C7×C13×D7semidirect
121. C7C13×D7×C3⋊D3direct (N × H)
122. C7C2×C7×C13×C3⋊D3semidirect
127. C3D3×C7×C13×D7semidirect

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×C13×C3⋊D32
C7×C13×C3⋊D212
D3×C7×C13×D73
C2×C7×C13×C3⋊D37
C13×D7×C3⋊D37
C7×D7×C3⋊D313