Finite Group Databasebeta

← C7×D13×C3⋊D21 #37525632

Subgroups — C7×D13×C3⋊D21 #37525632

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×C72×D13C211yesmaximal, characteristic, complemented
2C7×C13×C3⋊D21C211yesmaximal, characteristic, complemented
3C7×C3⋊D273C211yesmaximal, characteristic, complemented
4C7×D13×D21—34nomaximal
5C32×C72×C13C2211yescharacteristic, complemented, Hall
6C7×D273—34no—
7C7×C13×D21—34no—
8C3×C72×D13D314yescomplemented
9D13×C3⋊D21C711yesmaximal, characteristic, direct product factor
10C7×C3⋊D3×D13—71nomaximal
11C7×D7×D13—91noHall
12C3×C72×C13C2×D314yescomplemented
13C2×C7×C3⋊D21—131nomaximal, Hall
14C3⋊D273C2×C711yescharacteristic, complemented
15C13×C3⋊D21C2×C711yescharacteristic, complemented
16C7×C3⋊D39—71no—
17C7×C13×C3⋊D3—71no—
18C32×C7×D13—23no—
19C32×C7×D13D711yescharacteristic, complemented
20C32×C7×D13C2×C711yescharacteristic, complemented
21C7×D91—91no—
22C7×C13×D7—91no—
23C72×D13C3⋊D311yescharacteristic, complemented
24D13×D21—34no—
25D3×C7×D13—214no—
26C2×C32×C72—131no—
27C7×C3⋊D21—131no—
28C7×C3⋊D21D1311yescharacteristic, direct product factor
29C32×C7×C13—23no—
30C32×C7×C13C2×D711yescharacteristic, complemented
31C32×C7×C13C22×C711yescharacteristic, complemented
32C72×C13C2×C3⋊D311yescharacteristic, complemented, Hall
33C2×C7×D21—394no—
34D273—34no—
35C13×D21—34no—
36C7×D39—214no—
37D3×C7×C13—214no—
38C3×C7×D13—212no—
39C3×C7×D13D3×C714yescomplemented
40C3×C7×D13D2114yescomplemented
41C3⋊D3×D13—71noHall
42C32×C72C2×D1311yescharacteristic, complemented, Hall
43C2×C7×D13—631no—
44D7×D13—91no—
45C2×C3×C72—134no—
46C7×D21—34no—
47C7×D21—394no—
48C3×C7×C13—212no—
49C3×C7×C13C2×D3×C714yescomplemented
50C3×C7×C13C2×D2114yescomplemented
51C2×C3⋊D21—131no—
52C2×C7×C3⋊D3—911no—
53C3⋊D39—71no—
54C13×C3⋊D3—71no—
55C32×D13C7×D711yescharacteristic, complemented
56C2×C7×D7—1171noHall
57C2×C7×C13—631no—
58D91—91no—
59C7×D13—23no—
60C7×D13—631no—
61C7×D13C7×C3⋊D311yescharacteristic, complemented
62C7×D13C3⋊D2111yescharacteristic, direct product factor
63C13×D7—91no—
64D3×D13—214no—
65C3×C72D3×D1314yescomplemented
66C2×C32×C7—131no—
67C2×C32×C7—131no—
68C2×C32×C7—263no—
69C3⋊D21—131no—
70C3⋊D21C7×D1311yescharacteristic, direct product factor
71C7×C3⋊D3—71no—
72C7×C3⋊D3—911no—
73C32×C13C2×C7×D711yescharacteristic, complemented, Hall
74C2×C72—131no—
75C7×D7—91no—
76C7×D7—1171no—
77C7×C13—23no—
78C7×C13C2×C7×C3⋊D311yescharacteristic, complemented
79C7×C13C2×C3⋊D2111yescharacteristic, complemented
80C2×D21—394no—
81C2×D3×C7—2734no—
82D39—214no—
83C3×D13C7×D2114yescomplemented
84D3×C13—214no—
85C32×C7—23no—
86C32×C7D7×D1311yescharacteristic, complemented
87C32×C7C2×C7×D1311yescharacteristic, complemented
88C2×D13—631noHall
89C72C3⋊D3×D1311yescharacteristic, complemented, Sylow
90C2×C3×C7—134no—
91C2×C3×C7—134no—
92C2×C3×C7—2612no—
93D21—34no—
94D21—394no—
95D3×C7—2734no—
96D3×C7—214no—
97C3×C13C2×C7×D2114yescomplemented
98C2×C3⋊D3—911noHall
99C22×C7—8191no—
100C2×D7—1171no—
101C2×C13—631no—
102D13—631no—
103D13C7×C3⋊D2111yescharacteristic, direct product factor
104C3×C7—212no—
105C3×C7D3×C7×D1314yescomplemented
106C3×C7D13×D2114yescomplemented
107C2×C32—131no—
108C3⋊D3—71no—
109C3⋊D3—911no—
110C2×C7—131no—
111C2×C7—131no—
112C2×C7—263no—
113C2×C7—8191no—
114C2×C7—631no—
115D7—91no—
116D7—1171no—
117C13C2×C7×C3⋊D2111yescharacteristic, complemented, Sylow
118C2×D3—2734no—
119C32C7×D7×D1311yescharacteristic, complemented, Sylow
120C7—23no—
121C7C7×C3⋊D3×D1311yescharacteristic, complemented
122C7D13×C3⋊D2111yescharacteristic, direct product factor
123C2×C3—134no—
124D3—2734no—
125D3—214no—
126C22—8191noSylow
127C3C7×D13×D2114yescomplemented
128C2—131no—
129C2—8191no—
130C2—631no—
subgroupG/H
center, hypercenterC7D13×C3⋊D21
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×C72×D13C2semidirect
2. C7×C13×C3⋊D21C2semidirect
3. C7×C3⋊D273C2semidirect
5. C32×C72×C13C22semidirect
8. C3×C72×D13D3semidirect
9. D13×C3⋊D21C7direct (N × H)
12. C3×C72×C13C2×D3semidirect
14. C3⋊D273C2×C7semidirect
15. C13×C3⋊D21C2×C7semidirect
19. C32×C7×D13D7semidirect
20. C32×C7×D13C2×C7semidirect
23. C72×D13C3⋊D3semidirect
28. C7×C3⋊D21D13direct (N × H)
30. C32×C7×C13C2×D7semidirect
31. C32×C7×C13C22×C7semidirect
32. C72×C13C2×C3⋊D3semidirect
39. C3×C7×D13D3×C7semidirect
40. C3×C7×D13D21semidirect
42. C32×C72C2×D13semidirect
49. C3×C7×C13C2×D3×C7semidirect
50. C3×C7×C13C2×D21semidirect
55. C32×D13C7×D7semidirect
61. C7×D13C7×C3⋊D3semidirect
62. C7×D13C3⋊D21direct (N × H)
65. C3×C72D3×D13semidirect
70. C3⋊D21C7×D13direct (N × H)
73. C32×C13C2×C7×D7semidirect
78. C7×C13C2×C7×C3⋊D3semidirect
79. C7×C13C2×C3⋊D21semidirect
83. C3×D13C7×D21semidirect
86. C32×C7D7×D13semidirect
87. C32×C7C2×C7×D13semidirect
89. C72C3⋊D3×D13semidirect
97. C3×C13C2×C7×D21semidirect
103. D13C7×C3⋊D21direct (N × H)
105. C3×C7D3×C7×D13semidirect
106. C3×C7D13×D21semidirect
117. C13C2×C7×C3⋊D21semidirect
119. C32C7×D7×D13semidirect
121. C7C7×C3⋊D3×D13semidirect
122. C7D13×C3⋊D21direct (N × H)
127. C3C7×D13×D21semidirect

Maximal subgroups

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

subgroupindex
C32×C72×D132
C7×C13×C3⋊D212
C7×C3⋊D2732
C7×D13×D213
D13×C3⋊D217
C7×C3⋊D3×D137
C2×C7×C3⋊D2113