Finite Group Databasebeta

← C2×C3×C13×D147 #37524317

Subgroups — C2×C3×C13×D147 #37524317

Order 22932.

132 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C3×C13×D147C212yesmaximal, direct product factor
2C2×C32×C13×C49C211yesmaximal, characteristic, complemented
3C2×C13×D147C311yesmaximal, characteristic, direct product factor
4C2×C3×C13×D49—31nomaximal
5C32×C13×C49C2211yescharacteristic, complemented, Hall
6C13×D147C2×C312yesdirect product factor
7C3×C13×D49—32no—
8C2×C3×C13×C49—21no—
9C2×C3×C13×C49D311yescharacteristic, complemented
10C2×C3×C13×C49C2×C311yescharacteristic, complemented
11C2×C3×C13×D21—71nomaximal
12C2×C13×D49—31noHall
13C3×C13×C49—21no—
14C3×C13×C49C2×D311yescharacteristic, complemented
15C3×C13×C49C22×C311yescharacteristic, complemented
16C2×C3×D147C1311yesmaximal, characteristic, direct product factor, Hall
17C2×C32×C7×C13D711yescharacteristic
18C3×C13×D21—72no—
19C2×C13×C49C3×D311yescharacteristic, complemented
20C13×D49—32no—
21C2×C13×D21—71no—
22C2×C3×C13×D7—211no—
23C2×C32×C49C2×C1311yescharacteristic, complemented
24C3×D147C2×C1312yesdirect product factor
25C32×C7×C13C2×D711yescharacteristic
26C13×C49C2×C3×D311yescharacteristic, complemented, Hall
27C2×D147C3×C1311yescharacteristic, direct product factor
28C2×C3×D49—31no—
29C2×C3×C7×C13—21no—
30C2×C3×C7×C13C3×D711yescharacteristic
31C2×C3×C7×C13D2111yescharacteristic
32C13×D21—72no—
33C3×C13×D7—212no—
34C2×C3×D3×C13—491noHall
35C32×C49C22×C1311yescharacteristic, complemented, Hall
36C2×C13×D7—211no—
37C2×C3×C49—21no—
38C2×C3×C49D3×C1311yescharacteristic, complemented
39C2×C3×C49C2×C3×C1311yescharacteristic, complemented
40D147C2×C3×C1312yesdirect product factor
41C3×D49—32no—
42C3×C7×C13—21no—
43C3×C7×C13C2×C3×D711yescharacteristic
44C3×C7×C13C2×D2111yescharacteristic
45C2×C3×D21—71no—
46C2×C32×C13D4911yescharacteristic, complemented
47C3×D3×C13—492no—
48C2×D49—31noHall
49C2×C7×C13C3×D2111yescharacteristic
50C13×D7—212no—
51C22×C3×C13—1471no—
52C2×D3×C13—491no—
53C3×C49—21no—
54C3×C49C2×D3×C1311yescharacteristic, complemented
55C3×C49C22×C3×C1311yescharacteristic, complemented
56C2×C32×C7C13×D711yescharacteristic
57C3×D21—72no—
58C32×C13C2×D4911yescharacteristic, complemented, Hall
59C2×C49C3×D3×C1311yescharacteristic, complemented
60D49—32no—
61C7×C13C2×C3×D2111yescharacteristic
62C2×D21—71no—
63C2×C3×D7—211no—
64C2×C3×C13—21no—
65C2×C3×C13—1472no—
66C2×C3×C13C3×D4911yescharacteristic, complemented
67C2×C3×C13D14711yescharacteristic, direct product factor
68D3×C13—492no—
69C32×C7C2×C13×D711yescharacteristic
70C22×C13—1471noHall
71C49C2×C3×D3×C1311yescharacteristic, complemented, Sylow
72C2×C3×C7—21no—
73C2×C3×C7C3×C13×D711yescharacteristic
74C2×C3×C7C13×D2111yescharacteristic
75D21—72no—
76C3×D7—212no—
77C3×C13—21no—
78C3×C13C2×C3×D4911yescharacteristic, complemented
79C3×C13C2×D14711yescharacteristic, direct product factor
80C2×C3×D3—491noHall
81C2×D7—211no—
82C2×C13—1472no—
83C2×C13C3×D14711yescharacteristic, direct product factor
84C3×C7—21no—
85C3×C7C2×C3×C13×D711yescharacteristic
86C3×C7C2×C13×D2111yescharacteristic
87C2×C32C13×D4911yescharacteristic, complemented
88C3×D3—492no—
89C2×C7C3×C13×D2111yescharacteristic
90D7—212no—
91C13C2×C3×D14711yescharacteristic, direct product factor, Sylow
92C22×C3—1471no—
93C2×D3—491no—
94C32C2×C13×D4911yescharacteristic, complemented, Sylow
95C7C2×C3×C13×D2111yescharacteristic
96C2×C3—21no—
97C2×C3—1472no—
98C2×C3C3×C13×D4911yescharacteristic, complemented
99C2×C3C13×D14711yescharacteristic, direct product factor
100D3—492no—
101C22—1471noSylow
102C3—21no—
103C3C2×C3×C13×D4911yescharacteristic, complemented
104C3C2×C13×D14711yescharacteristic, direct product factor
105C2—1472no—
106C2C3×C13×D14711yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C13D147
commutator, cosocle, hypocenterC3×C49C22×C3×C13
FrattiniC7C2×C3×C13×D21
FittingC2×C32×C13×C49C2
socleC2×C32×C7×C13D7
LCSG ▷ C3×C49
UCSC1 ◁ C2×C3×C13

Complements

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

NH ≅ G/Ntype
1. C3×C13×D147C2direct (N × H)
2. C2×C32×C13×C49C2semidirect
3. C2×C13×D147C3direct (N × H)
5. C32×C13×C49C22semidirect
6. C13×D147C2×C3direct (N × H)
9. C2×C3×C13×C49D3semidirect
10. C2×C3×C13×C49C2×C3semidirect
14. C3×C13×C49C2×D3semidirect
15. C3×C13×C49C22×C3semidirect
16. C2×C3×D147C13direct (N × H)
19. C2×C13×C49C3×D3semidirect
23. C2×C32×C49C2×C13semidirect
24. C3×D147C2×C13direct (N × H)
26. C13×C49C2×C3×D3semidirect
27. C2×D147C3×C13direct (N × H)
35. C32×C49C22×C13semidirect
38. C2×C3×C49D3×C13semidirect
39. C2×C3×C49C2×C3×C13semidirect
40. D147C2×C3×C13direct (N × H)
46. C2×C32×C13D49semidirect
54. C3×C49C2×D3×C13semidirect
55. C3×C49C22×C3×C13semidirect
58. C32×C13C2×D49semidirect
59. C2×C49C3×D3×C13semidirect
66. C2×C3×C13C3×D49semidirect
67. C2×C3×C13D147direct (N × H)
71. C49C2×C3×D3×C13semidirect
78. C3×C13C2×C3×D49semidirect
79. C3×C13C2×D147direct (N × H)
83. C2×C13C3×D147direct (N × H)
87. C2×C32C13×D49semidirect
91. C13C2×C3×D147direct (N × H)
94. C32C2×C13×D49semidirect
98. C2×C3C3×C13×D49semidirect
99. C2×C3C13×D147direct (N × H)
103. C3C2×C3×C13×D49semidirect
104. C3C2×C13×D147direct (N × H)
106. C2C3×C13×D147direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C13×D1472
C2×C32×C13×C492
C2×C13×D1473
C2×C3×C13×D493
C2×C3×C13×D217
C2×C3×D14713