Finite Group Databasebeta

← C3×D3×D637 #37524277

Subgroups — C3×D3×D637 #37524277

Order 22932.

132 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 44 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×D1911C211yesmaximal, characteristic, complemented
2C3×D3×C13×C49C211yesmaximal, characteristic, complemented
3C32×D637C211yesmaximal, characteristic, complemented
4C2×C3×D637—31nomaximal
5D3×D637C311yesmaximal, characteristic, direct product factor
6C32×C13×C49C2211yescharacteristic, complemented, Hall
7D1911C2×C311yescharacteristic, complemented
8D3×C13×C49C2×C311yescharacteristic, complemented
9C3×D637—21no—
10C3×D637—31no—
11C3×D637D311yescharacteristic, direct product factor
12C3×D637C2×C311yescharacteristic, complemented
13C2×C3×C13×C49—31no—
14C3×D3×D91—71nomaximal
15C2×D637—31noHall
16C3×C13×C49—21no—
17C3×C13×C49C2×D311yescharacteristic, complemented
18C3×C13×C49C22×C311yescharacteristic, complemented
19C3×D3×D49—131nomaximal, Hall
20C3×D273—71no—
21C3×D3×C7×C13D711yescharacteristic
22C32×D91—71no—
23C2×C13×C49—31no—
24D637—31no—
25D637C3×D311yescharacteristic, direct product factor
26C2×C3×D91—211no—
27D3×D91—71no—
28C3×D147—131no—
29C3×D3×C49D1311yescharacteristic, complemented
30C32×D49—131no—
31C32×C7×C13C2×D711yescharacteristic
32C13×C49C2×C3×D311yescharacteristic, complemented, Hall
33C2×C3×D49—391no—
34D3×D49—131no—
35C2×C3×C7×C13—31no—
36D273—71no—
37D3×C7×C13C3×D711yescharacteristic
38C3×D91—71no—
39C3×D91—71no—
40C3×D91—141no—
41C3×D91—211no—
42C3×D3×D13—491noHall
43C32×C49C2×D1311yescharacteristic, complemented, Hall
44C2×D91—211no—
45C2×C3×C49—31no—
46D147—131no—
47C3×D49—131no—
48C3×D49—131no—
49C3×D49—261no—
50C3×D49—391no—
51D3×C49C3×D1311yescharacteristic, complemented
52C3×C7×C13—21no—
53C3×C7×C13D3×D711yescharacteristic
54C3×C7×C13C2×C3×D711yescharacteristic
55C3×D3×D7—911no—
56C3×D39—491no—
57C3×D3×C13D4911yescharacteristic, complemented
58C32×D13—491no—
59C2×D49—391noHall
60C2×C7×C13—31no—
61D91—71no—
62D91—211no—
63C2×C3×D13—1471no—
64D3×D13—491no—
65C3×C49—21no—
66C3×C49D3×D1311yescharacteristic, complemented
67C3×C49C2×C3×D1311yescharacteristic, complemented
68C3×D21—911no—
69C3×D3×C7D9111yescharacteristic
70C32×D7—911no—
71C32×C13C2×D4911yescharacteristic, complemented, Hall
72C2×C49—31no—
73D49—131no—
74D49—391no—
75C7×C13C3×D3×D711yescharacteristic
76C2×C3×D7—2731no—
77D3×D7—911no—
78C2×C3×C13—31no—
79D39—491no—
80C3×D13—491no—
81C3×D13—491no—
82C3×D13—981no—
83C3×D13—1471no—
84D3×C13C3×D4911yescharacteristic, complemented
85C32×C7C2×D9111yescharacteristic
86C2×D13—1471noHall
87C49C3×D3×D1311yescharacteristic, complemented, Sylow
88C2×C3×C7—31no—
89D21—911no—
90C3×D7—2731no—
91C3×D7—911no—
92C3×D7—911no—
93C3×D7—1821no—
94D3×C7C3×D9111yescharacteristic
95C3×C13—21no—
96C3×C13D3×D4911yescharacteristic, complemented
97C3×C13C2×C3×D4911yescharacteristic, complemented
98C2×C3×D3—6371noHall
99C2×D7—2731no—
100C2×C13—31no—
101D13—491no—
102D13—1471no—
103C3×C7—21no—
104C3×C7D3×D9111yescharacteristic
105C3×C7C2×C3×D9111yescharacteristic
106C2×C32—6371no—
107C3×D3—6371no—
108C3×D3D63711yescharacteristic, direct product factor
109C2×C7—31no—
110D7—2731no—
111D7—911no—
112C13C3×D3×D4911yescharacteristic, complemented, Sylow
113C22×C3—19111no—
114C2×D3—6371no—
115C32C2×D63711yescharacteristic, complemented, Sylow
116C7C3×D3×D9111yescharacteristic
117C2×C3—31no—
118C2×C3—19111no—
119C2×C3—6371no—
120C2×C3—6371no—
121C2×C3—12741no—
122D3—6371no—
123D3C3×D63711yescharacteristic, direct product factor
124C22—19111noSylow
125C3—21no—
126C3D3×D63711yescharacteristic, direct product factor
127C3C2×C3×D63711yescharacteristic, complemented
128C2—31no—
129C2—19111no—
130C2—6371no—
subgroupG/H
center, hypercenterC3D3×D637
commutator, cosocle, hypocenterC3×C13×C49C22×C3
FrattiniC7C3×D3×D91
FittingC32×C13×C49C22
socleC32×C7×C13C2×D7
LCSG ▷ C3×C13×C49
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×D1911C2semidirect
2. C3×D3×C13×C49C2semidirect
3. C32×D637C2semidirect
5. D3×D637C3direct (N × H)
6. C32×C13×C49C22semidirect
7. D1911C2×C3semidirect
8. D3×C13×C49C2×C3semidirect
11. C3×D637D3direct (N × H)
12. C3×D637C2×C3semidirect
17. C3×C13×C49C2×D3semidirect
18. C3×C13×C49C22×C3semidirect
25. D637C3×D3direct (N × H)
29. C3×D3×C49D13semidirect
32. C13×C49C2×C3×D3semidirect
43. C32×C49C2×D13semidirect
51. D3×C49C3×D13semidirect
57. C3×D3×C13D49semidirect
66. C3×C49D3×D13semidirect
67. C3×C49C2×C3×D13semidirect
71. C32×C13C2×D49semidirect
84. D3×C13C3×D49semidirect
87. C49C3×D3×D13semidirect
96. C3×C13D3×D49semidirect
97. C3×C13C2×C3×D49semidirect
108. C3×D3D637direct (N × H)
112. C13C3×D3×D49semidirect
115. C32C2×D637semidirect
123. D3C3×D637direct (N × H)
126. C3D3×D637direct (N × H)
127. C3C2×C3×D637semidirect

Maximal subgroups

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

subgroupindex
C3×D19112
C3×D3×C13×C492
C32×D6372
C2×C3×D6373
D3×D6373
C3×D3×D917
C3×D3×D4913