Finite Group Databasebeta

← C7×C3⋊D3×D91 #37525635

Subgroups — C7×C3⋊D3×D91 #37525635

Order 22932.

312 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 72 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
2C72×C13×C3⋊D3C211yesmaximal, characteristic, complemented
3C7×C3⋊D273C211yesmaximal, characteristic, complemented
4D3×C7×D91—34nomaximal
5C32×C72×C13C2211yescharacteristic, complemented, Hall
6C7×D273—34no—
7D3×C72×C13—34no—
8C3×C7×D91D314yescomplemented
9C3⋊D3×D91C711yesmaximal, characteristic, direct product factor
10C7×C3⋊D3×D13—71nomaximal
11C2×C7×D91—91noHall
12C3×C72×C13C2×D314yescomplemented
13C7×D7×C3⋊D3—131nomaximal, Hall
14C3⋊D273C2×C711yescharacteristic, complemented
15C7×C3⋊D39—71no—
16C7×C13×C3⋊D3—23no—
17C7×C13×C3⋊D3D711yescharacteristic, complemented
18C7×C13×C3⋊D3C2×C711yescharacteristic, complemented
19C32×D91C2×C711yescharacteristic, complemented
20C32×C7×D13—71no—
21C2×C72×C13—91no—
22C7×D91—91no—
23C7×D91C3⋊D311yescharacteristic, direct product factor
24D3×D91—34no—
25D3×C7×D13—214no—
26C7×C3⋊D21—131no—
27C72×C3⋊D3D1311yescharacteristic, complemented
28C32×C7×D7—131no—
29C32×C7×C13—23no—
30C32×C7×C13C2×D711yescharacteristic, complemented
31C32×C7×C13C22×C711yescharacteristic, complemented
32C72×C13C2×C3⋊D311yescharacteristic, complemented, Hall
33D3×C7×D7—394no—
34D273—34no—
35C7×D39—214no—
36D3×C7×C13—34no—
37D3×C7×C13—34no—
38D3×C7×C13—612no—
39C3×D91D3×C714yescomplemented
40C3×C7×D13—74no—
41C3⋊D3×D13—71noHall
42C32×C72C2×D1311yescharacteristic, complemented, Hall
43C2×D91—91no—
44C2×C7×D13—631no—
45C7×D21—394no—
46D3×C72—34no—
47C3×C7×D7—134no—
48C3×C7×C13—212no—
49C3×C7×C13D3×D714yescomplemented
50C3×C7×C13C2×D3×C714yescomplemented
51C2×C7×C3⋊D3—911no—
52D7×C3⋊D3—131no—
53C3⋊D39—71no—
54C13×C3⋊D3C7×D711yescharacteristic, complemented
55C32×D13—71no—
56C2×C7×D7—1171noHall
57C2×C7×C13—91no—
58C2×C7×C13—91no—
59C2×C7×C13—183no—
60D91—91no—
61D91C7×C3⋊D311yescharacteristic, direct product factor
62C7×D13—71no—
63C7×D13—631no—
64D3×D13—214no—
65C3×C72D3×D1314yescomplemented
66C2×C32×C7—911no—
67C3⋊D21—131no—
68C7×C3⋊D3—23no—
69C7×C3⋊D3—911no—
70C7×C3⋊D3C7×D1311yescharacteristic, complemented
71C7×C3⋊D3D9111yescharacteristic, direct product factor
72C32×D7—131no—
73C32×C13C2×C7×D711yescharacteristic, complemented, Hall
74C2×C72—91no—
75C7×D7—131no—
76C7×D7—1171no—
77C7×C13—23no—
78C7×C13D7×C3⋊D311yescharacteristic, complemented
79C7×C13C2×C7×C3⋊D311yescharacteristic, complemented
80C2×D3×C7—2734no—
81D3×D7—394no—
82D39—214no—
83C3×D13—74no—
84D3×C13—34no—
85C32×C7—23no—
86C32×C7C2×C7×D1311yescharacteristic, complemented
87C32×C7C2×D9111yescharacteristic, complemented
88C2×D13—631noHall
89C72C3⋊D3×D1311yescharacteristic, complemented, Sylow
90C2×C3×C7—914no—
91D21—394no—
92C3×D7—134no—
93D3×C7—34no—
94D3×C7—34no—
95D3×C7—612no—
96D3×C7—2734no—
97C3×C13D3×C7×D714yescomplemented
98C2×C3⋊D3—911noHall
99C22×C7—8191no—
100C2×D7—1171no—
101C2×C13—91no—
102D13—71no—
103D13—631no—
104C3×C7—212no—
105C3×C7D3×C7×D1314yescomplemented
106C3×C7D3×D9114yescomplemented
107C2×C32—911no—
108C3⋊D3—911no—
109C3⋊D3C7×D9111yescharacteristic, direct product factor
110C2×C7—91no—
111C2×C7—91no—
112C2×C7—183no—
113C2×C7—8191no—
114C2×C7—911no—
115D7—131no—
116D7—1171no—
117C13C7×D7×C3⋊D311yescharacteristic, complemented, Sylow
118C2×D3—2734no—
119C32C2×C7×D9111yescharacteristic, complemented, Sylow
120C7—23no—
121C7C7×C3⋊D3×D1311yescharacteristic, complemented
122C7C3⋊D3×D9111yescharacteristic, direct product factor
123C2×C3—914no—
124D3—34no—
125D3—2734no—
126C22—8191noSylow
127C3D3×C7×D9114yescomplemented
128C2—91no—
129C2—8191no—
130C2—911no—
subgroupG/H
center, hypercenterC7C3⋊D3×D91
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×D91C2semidirect
2. C72×C13×C3⋊D3C2semidirect
3. C7×C3⋊D273C2semidirect
5. C32×C72×C13C22semidirect
8. C3×C7×D91D3semidirect
9. C3⋊D3×D91C7direct (N × H)
12. C3×C72×C13C2×D3semidirect
14. C3⋊D273C2×C7semidirect
17. C7×C13×C3⋊D3D7semidirect
18. C7×C13×C3⋊D3C2×C7semidirect
19. C32×D91C2×C7semidirect
23. C7×D91C3⋊D3direct (N × H)
27. C72×C3⋊D3D13semidirect
30. C32×C7×C13C2×D7semidirect
31. C32×C7×C13C22×C7semidirect
32. C72×C13C2×C3⋊D3semidirect
39. C3×D91D3×C7semidirect
42. C32×C72C2×D13semidirect
49. C3×C7×C13D3×D7semidirect
50. C3×C7×C13C2×D3×C7semidirect
54. C13×C3⋊D3C7×D7semidirect
61. D91C7×C3⋊D3direct (N × H)
65. C3×C72D3×D13semidirect
70. C7×C3⋊D3C7×D13semidirect
71. C7×C3⋊D3D91direct (N × H)
73. C32×C13C2×C7×D7semidirect
78. C7×C13D7×C3⋊D3semidirect
79. C7×C13C2×C7×C3⋊D3semidirect
86. C32×C7C2×C7×D13semidirect
87. C32×C7C2×D91semidirect
89. C72C3⋊D3×D13semidirect
97. C3×C13D3×C7×D7semidirect
105. C3×C7D3×C7×D13semidirect
106. C3×C7D3×D91semidirect
109. C3⋊D3C7×D91direct (N × H)
117. C13C7×D7×C3⋊D3semidirect
119. C32C2×C7×D91semidirect
121. C7C7×C3⋊D3×D13semidirect
122. C7C3⋊D3×D91direct (N × H)
127. C3D3×C7×D91semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D912
C72×C13×C3⋊D32
C7×C3⋊D2732
D3×C7×D913
C3⋊D3×D917
C7×C3⋊D3×D137
C7×D7×C3⋊D313