Finite Group Databasebeta

← C7×D91⋊(C3⋊D3) #37525636

Subgroups — C7×D91⋊(C3⋊D3) #37525636

Order 22932.

312 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 70 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×C3⋊D39C211yesmaximal, characteristic, complemented
3C7×C13×C3⋊D21C211yesmaximal, characteristic, complemented
4C7×D21⋊D13—34nomaximal
5C32×C72×C13C2211yescharacteristic, complemented, Hall
6C7×C13×D21—34no—
7C72×D39—34no—
8C3×C7×D91D314yescomplemented
9D91⋊(C3⋊D3)C711yesmaximal, characteristic, direct product factor
10C7×C3⋊D3×D13—71nomaximal
11C7×D7×D13—91noHall
12C3×C72×C13C2×D314yescomplemented
13C7×D7×C3⋊D3—131nomaximal, Hall
14C13×C3⋊D21C2×C711yescharacteristic, complemented
15C7×C3⋊D39—23no—
16C7×C3⋊D39D711yescharacteristic, complemented
17C7×C3⋊D39C2×C711yescharacteristic, complemented
18C7×C13×C3⋊D3—71no—
19C32×D91C2×C711yescharacteristic, complemented
20C32×C7×D13—71no—
21C7×D91C3⋊D311yescharacteristic, complemented
22C7×C13×D7—91no—
23C72×D13—91no—
24D21⋊D13—34no—
25D3×C7×D13—214no—
26C7×C3⋊D21D1311yescharacteristic, complemented
27C72×C3⋊D3—131no—
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—
34C13×D21—34no—
35C7×D39—34no—
36C7×D39—34no—
37C7×D39—612no—
38D3×C7×C13—214no—
39C3×D91D3×C714yescomplemented
40C3×C7×D13—74no—
41C3⋊D3×D13—71noHall
42C32×C72C2×D1311yescharacteristic, complemented, Hall
43C2×C7×D13—631no—
44D7×D13—91no—
45C7×D21—34no—
46D3×C72—394no—
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⋊D39C7×D711yescharacteristic, complemented
54C13×C3⋊D3—71no—
55C32×D13—71no—
56C2×C7×D7—1171noHall
57C2×C7×C13—631no—
58D91C7×C3⋊D311yescharacteristic, complemented
59C7×D13—71no—
60C7×D13—91no—
61C7×D13—91no—
62C7×D13—183no—
63C13×D7—91no—
64D3×D13—214no—
65C3×C72D3×D1314yescomplemented
66C2×C32×C7—911no—
67C3⋊D21C7×D1311yescharacteristic, complemented
68C7×C3⋊D3—71no—
69C7×C3⋊D3—131no—
70C7×C3⋊D3—131no—
71C7×C3⋊D3—263no—
72C32×D7—131no—
73C32×C13C2×C7×D711yescharacteristic, complemented, Hall
74C2×C72—1171no—
75C7×D7—91no—
76C7×D7—131no—
77C7×C13—23no—
78C7×C13D7×C3⋊D311yescharacteristic, complemented
79C7×C13C2×C7×C3⋊D311yescharacteristic, complemented
80C2×D3×C7—2734no—
81D3×D7—394no—
82D39—34no—
83C3×D13—74no—
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—914no—
91D21—34no—
92C3×D7—134no—
93D3×C7—214no—
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—631no—
102D13—71no—
103D13—91no—
104C3×C7—212no—
105C3×C7D3×C7×D1314yescomplemented
106C3×C7D21⋊D1314yescomplemented
107C2×C32—911no—
108C3⋊D3—71no—
109C3⋊D3—131no—
110C2×C7—631no—
111C2×C7—911no—
112C2×C7—1171no—
113C2×C7—1171no—
114C2×C7—2343no—
115D7—91no—
116D7—131no—
117C13C7×D7×C3⋊D311yescharacteristic, complemented, Sylow
118C2×D3—2734no—
119C32C7×D7×D1311yescharacteristic, complemented, Sylow
120C7—23no—
121C7C7×C3⋊D3×D1311yescharacteristic, complemented
122C7D91⋊(C3⋊D3)11yescharacteristic, direct product factor
123C2×C3—914no—
124D3—214no—
125D3—394no—
126C22—8191noSylow
127C3C7×D21⋊D1314yescomplemented
128C2—631no—
129C2—911no—
130C2—1171no—
subgroupG/H
center, hypercenterC7D91⋊(C3⋊D3)
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×C3⋊D39C2semidirect
3. C7×C13×C3⋊D21C2semidirect
5. C32×C72×C13C22semidirect
8. C3×C7×D91D3semidirect
9. D91⋊(C3⋊D3)C7direct (N × H)
12. C3×C72×C13C2×D3semidirect
14. C13×C3⋊D21C2×C7semidirect
16. C7×C3⋊D39D7semidirect
17. C7×C3⋊D39C2×C7semidirect
19. C32×D91C2×C7semidirect
21. C7×D91C3⋊D3semidirect
26. C7×C3⋊D21D13semidirect
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
53. C3⋊D39C7×D7semidirect
58. D91C7×C3⋊D3semidirect
65. C3×C72D3×D13semidirect
67. C3⋊D21C7×D13semidirect
73. C32×C13C2×C7×D7semidirect
78. C7×C13D7×C3⋊D3semidirect
79. C7×C13C2×C7×C3⋊D3semidirect
86. C32×C7D7×D13semidirect
87. C32×C7C2×C7×D13semidirect
89. C72C3⋊D3×D13semidirect
97. C3×C13D3×C7×D7semidirect
105. C3×C7D3×C7×D13semidirect
106. C3×C7D21⋊D13semidirect
117. C13C7×D7×C3⋊D3semidirect
119. C32C7×D7×D13semidirect
121. C7C7×C3⋊D3×D13semidirect
122. C7D91⋊(C3⋊D3)direct (N × H)
127. C3C7×D21⋊D13semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D912
C72×C3⋊D392
C7×C13×C3⋊D212
C7×D21⋊D133
D91⋊(C3⋊D3)7
C7×C3⋊D3×D137
C7×D7×C3⋊D313