Finite Group Databasebeta

← D3×C13×D147 #37524290

Subgroups — D3×C13×D147 #37524290

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
1C13×C3⋊D147C211yesmaximal, characteristic, complemented
2C3×C13×D147C211yesmaximal, characteristic, complemented
3C3×D3×C13×C49C211yesmaximal, characteristic, complemented
4C2×C13×D147—31nomaximal
5D3×C13×D49—31nomaximal
6C32×C13×C49C2211yescharacteristic, complemented, Hall
7C13×D147—31no—
8C13×D147—31no—
9C13×D147—61no—
10C13×D147D311yescharacteristic, direct product factor
11D3×C13×C49D311yescharacteristic, complemented
12C3×C13×D49—31no—
13C2×C3×C13×C49—31no—
14D3×C13×D21—71nomaximal
15C2×C13×D49—91noHall
16C3×C13×C49—21no—
17C3×C13×C49C2×D311yescharacteristic, complemented
18C3×C13×C49C2×D311yescharacteristic, complemented
19D3×D147C1311yesmaximal, characteristic, direct product factor, Hall
20C13×C3⋊D21—71no—
21C3×C13×D21—71no—
22C3×D3×C7×C13D711yescharacteristic
23C2×C13×C49—31no—
24C13×D49—31no—
25C13×D49—91no—
26C2×C13×D21—211no—
27D3×C13×D7—211no—
28C3⋊D147C2×C1311yescharacteristic, complemented
29C3×D147C2×C1311yescharacteristic, complemented
30C3×D3×C49C2×C1311yescharacteristic, complemented
31C32×C7×C13C2×D711yescharacteristic
32C13×C49D3211yescharacteristic, complemented, Hall
33C2×D147—31no—
34D3×D49—31no—
35C2×C3×C7×C13—31no—
36C13×D21—71no—
37C13×D21—211no—
38C13×D21—211no—
39C13×D21—421no—
40D3×C7×C13D2111yescharacteristic
41C3×C13×D7—211no—
42D32×C13—491noHall
43C32×C49C22×C1311yescharacteristic, complemented, Hall
44C2×C13×D7—631no—
45C2×C3×C49—31no—
46D147—31no—
47D147—31no—
48D147—61no—
49D147D3×C1311yescharacteristic, direct product factor
50C3×D49—31no—
51D3×C49D3×C1311yescharacteristic, complemented
52C3×C7×C13—21no—
53C3×C7×C13D3×D711yescharacteristic
54C3×C7×C13C2×D2111yescharacteristic
55D3×D21—71no—
56C13×C3⋊D3—491no—
57C3×D3×C13—491no—
58C3×D3×C13D4911yescharacteristic, complemented
59C2×D49—91noHall
60C2×C7×C13—31no—
61C13×D7—211no—
62C13×D7—631no—
63C2×D3×C13—1471no—
64C2×D3×C13—1471no—
65C3×C49—21no—
66C3×C49C2×D3×C1311yescharacteristic, complemented
67C3×C49C2×D3×C1311yescharacteristic, complemented
68C3⋊D21—71no—
69C3×D21—71no—
70C3×D3×C7C13×D711yescharacteristic
71C32×C13C2×D4911yescharacteristic, complemented, Hall
72C2×C49—31no—
73D49—31no—
74D49—91no—
75C7×C13D3×D2111yescharacteristic
76C2×D21—211no—
77D3×D7—211no—
78C2×C3×C13—31no—
79C2×C3×C13—1471no—
80D3×C13—2941no—
81D3×C13—491no—
82D3×C13—1471no—
83D3×C13—1471no—
84D3×C13D14711yescharacteristic, direct product factor
85C32×C7C2×C13×D711yescharacteristic
86C22×C13—4411noHall
87C49D32×C1311yescharacteristic, complemented, Sylow
88C2×C3×C7—31no—
89D21—71no—
90D21—211no—
91D21—211no—
92D21—421no—
93C3×D7—211no—
94D3×C7C13×D2111yescharacteristic
95C3×C13—21no—
96C3×C13D3×D4911yescharacteristic, complemented
97C3×C13C2×D14711yescharacteristic, complemented
98D32—491noHall
99C2×D7—631no—
100C2×C13—31no—
101C2×C13—1471no—
102C2×C13—4411no—
103C3×C7—21no—
104C3×C7D3×C13×D711yescharacteristic
105C3×C7C2×C13×D2111yescharacteristic
106C3⋊D3—491no—
107C3×D3—491no—
108C3×D3C13×D4911yescharacteristic, complemented
109C2×C7—31no—
110D7—211no—
111D7—631no—
112C13D3×D14711yescharacteristic, direct product factor, Sylow
113C2×D3—1471no—
114C2×D3—1471no—
115C32C2×C13×D4911yescharacteristic, complemented, Sylow
116C7D3×C13×D2111yescharacteristic
117C2×C3—31no—
118C2×C3—1471no—
119D3—2941no—
120D3—491no—
121D3—1471no—
122D3—1471no—
123D3C13×D14711yescharacteristic, direct product factor
124C22—4411noSylow
125C3—21no—
126C3D3×C13×D4911yescharacteristic, complemented
127C3C2×C13×D14711yescharacteristic, complemented
128C2—31no—
129C2—1471no—
130C2—4411no—
subgroupG/H
center, hypercenterC13D3×D147
commutator, cosocle, hypocenterC32×C49C22×C13
FrattiniC7D3×C13×D21
FittingC32×C13×C49C22
socleC32×C7×C13C2×D7
LCSG ▷ C32×C49
UCSC1 ◁ C13

Complements

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

NH ≅ G/Ntype
1. C13×C3⋊D147C2semidirect
2. C3×C13×D147C2semidirect
3. C3×D3×C13×C49C2semidirect
6. C32×C13×C49C22semidirect
10. C13×D147D3direct (N × H)
11. D3×C13×C49D3semidirect
17. C3×C13×C49C2×D3semidirect
18. C3×C13×C49C2×D3semidirect
19. D3×D147C13direct (N × H)
28. C3⋊D147C2×C13semidirect
29. C3×D147C2×C13semidirect
30. C3×D3×C49C2×C13semidirect
32. C13×C49D32semidirect
43. C32×C49C22×C13semidirect
49. D147D3×C13direct (N × H)
51. D3×C49D3×C13semidirect
58. C3×D3×C13D49semidirect
66. C3×C49C2×D3×C13semidirect
67. C3×C49C2×D3×C13semidirect
71. C32×C13C2×D49semidirect
84. D3×C13D147direct (N × H)
87. C49D32×C13semidirect
96. C3×C13D3×D49semidirect
97. C3×C13C2×D147semidirect
108. C3×D3C13×D49semidirect
112. C13D3×D147direct (N × H)
115. C32C2×C13×D49semidirect
123. D3C13×D147direct (N × H)
126. C3D3×C13×D49semidirect
127. C3C2×C13×D147semidirect

Maximal subgroups

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

subgroupindex
C13×C3⋊D1472
C3×C13×D1472
C3×D3×C13×C492
C2×C13×D1473
D3×C13×D493
D3×C13×D217
D3×D14713