Finite Group Databasebeta

← C2×C3×D1911 #37524316

Subgroups — C2×C3×D1911 #37524316

Order 22932.

132 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 54 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×D1911C212yesmaximal, direct product factor
2C2×C32×C13×C49C211yesmaximal, characteristic, complemented
3C2×D1911C311yesmaximal, characteristic, direct product factor
4C2×C3×D637—31nomaximal
5C32×C13×C49C2211yescharacteristic, complemented, Hall
6D1911C2×C312yesdirect product factor
7C3×D637—32no—
8C2×C3×C13×C49—21no—
9C2×C3×C13×C49D311yescharacteristic, complemented
10C2×C3×C13×C49C2×C311yescharacteristic, complemented
11C2×C3×D273—71nomaximal
12C2×D637—31noHall
13C3×C13×C49—21no—
14C3×C13×C49C2×D311yescharacteristic, complemented
15C3×C13×C49C22×C311yescharacteristic, complemented
16C2×C3×D147—131nomaximal, Hall
17C2×C32×C7×C13D711yescharacteristic
18C3×D273—72no—
19C2×C13×C49C3×D311yescharacteristic, complemented
20D637—32no—
21C2×D273—71no—
22C2×C3×D91—211no—
23C2×C32×C49D1311yescharacteristic, complemented
24C3×D147—132no—
25C32×C7×C13C2×D711yescharacteristic
26C13×C49C2×C3×D311yescharacteristic, complemented, Hall
27C2×D147—131no—
28C2×C3×D49—391no—
29C2×C3×C7×C13—21no—
30C2×C3×C7×C13C3×D711yescharacteristic
31C2×C3×C7×C13D2111yescharacteristic
32D273—72no—
33C3×D91—212no—
34C2×C3×D39—491noHall
35C32×C49C2×D1311yescharacteristic, complemented, Hall
36C2×D91—211no—
37C2×C3×C49—21no—
38C2×C3×C49C3×D1311yescharacteristic, complemented
39C2×C3×C49D3911yescharacteristic, complemented
40D147—132no—
41C3×D49—392no—
42C3×C7×C13—21no—
43C3×C7×C13C2×C3×D711yescharacteristic
44C3×C7×C13C2×D2111yescharacteristic
45C2×C3×D21—911no—
46C2×C32×C13D4911yescharacteristic, complemented
47C3×D39—492no—
48C2×D49—391noHall
49C2×C7×C13C3×D2111yescharacteristic
50D91—212no—
51C2×D39—491no—
52C2×C3×D13—1471no—
53C3×C49—21no—
54C3×C49C2×C3×D1311yescharacteristic, complemented
55C3×C49C2×D3911yescharacteristic, complemented
56C2×C32×C7D9111yescharacteristic
57C3×D21—912no—
58C32×C13C2×D4911yescharacteristic, complemented, Hall
59C2×C49C3×D3911yescharacteristic, complemented
60D49—392no—
61C7×C13C2×C3×D2111yescharacteristic
62C2×D21—911no—
63C2×C3×D7—2731no—
64C2×C3×C13—21no—
65C2×C3×C13C3×D4911yescharacteristic, complemented
66C2×C3×C13D14711yescharacteristic, complemented
67D39—492no—
68C3×D13—1472no—
69C32×C7C2×D9111yescharacteristic
70C2×D13—1471noHall
71C49C2×C3×D3911yescharacteristic, complemented, Sylow
72C2×C3×C7—21no—
73C2×C3×C7C3×D9111yescharacteristic
74C2×C3×C7D27311yescharacteristic
75D21—912no—
76C3×D7—2732no—
77C3×C13—21no—
78C3×C13C2×C3×D4911yescharacteristic, complemented
79C3×C13C2×D14711yescharacteristic, complemented
80C2×C3×D3—6371noHall
81C2×D7—2731no—
82C2×C13C3×D14711yescharacteristic, complemented
83D13—1472no—
84C3×C7—21no—
85C3×C7C2×C3×D9111yescharacteristic
86C3×C7C2×D27311yescharacteristic
87C2×C32D63711yescharacteristic, complemented
88C3×D3—6372no—
89C2×C7C3×D27311yescharacteristic
90D7—2732no—
91C13C2×C3×D14711yescharacteristic, complemented, Sylow
92C22×C3—19111no—
93C2×D3—6371no—
94C32C2×D63711yescharacteristic, complemented, Sylow
95C7C2×C3×D27311yescharacteristic
96C2×C3—21no—
97C2×C3—19112no—
98C2×C3C3×D63711yescharacteristic, complemented
99C2×C3D191111yescharacteristic, direct product factor
100D3—6372no—
101C22—19111noSylow
102C3—21no—
103C3C2×C3×D63711yescharacteristic, complemented
104C3C2×D191111yescharacteristic, direct product factor
105C2—19112no—
106C2C3×D191111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3D1911
commutator, cosocle, hypocenterC3×C13×C49C22×C3
FrattiniC7C2×C3×D273
FittingC2×C32×C13×C49C2
socleC2×C32×C7×C13D7
LCSG ▷ C3×C13×C49
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C3×D1911C2direct (N × H)
2. C2×C32×C13×C49C2semidirect
3. C2×D1911C3direct (N × H)
5. C32×C13×C49C22semidirect
6. D1911C2×C3direct (N × H)
9. C2×C3×C13×C49D3semidirect
10. C2×C3×C13×C49C2×C3semidirect
14. C3×C13×C49C2×D3semidirect
15. C3×C13×C49C22×C3semidirect
19. C2×C13×C49C3×D3semidirect
23. C2×C32×C49D13semidirect
26. C13×C49C2×C3×D3semidirect
35. C32×C49C2×D13semidirect
38. C2×C3×C49C3×D13semidirect
39. C2×C3×C49D39semidirect
46. C2×C32×C13D49semidirect
54. C3×C49C2×C3×D13semidirect
55. C3×C49C2×D39semidirect
58. C32×C13C2×D49semidirect
59. C2×C49C3×D39semidirect
65. C2×C3×C13C3×D49semidirect
66. C2×C3×C13D147semidirect
71. C49C2×C3×D39semidirect
78. C3×C13C2×C3×D49semidirect
79. C3×C13C2×D147semidirect
82. C2×C13C3×D147semidirect
87. C2×C32D637semidirect
91. C13C2×C3×D147semidirect
94. C32C2×D637semidirect
98. C2×C3C3×D637semidirect
99. C2×C3D1911direct (N × H)
103. C3C2×C3×D637semidirect
104. C3C2×D1911direct (N × H)
106. C2C3×D1911direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D19112
C2×C32×C13×C492
C2×D19113
C2×C3×D6373
C2×C3×D2737
C2×C3×D14713