Finite Group Databasebeta

← D39×D147 #37524293

Subgroups — D39×D147 #37524293

Order 22932.

132 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 36 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×C13×D147C211yesmaximal, characteristic, complemented
3C3×C49×D39C211yesmaximal, characteristic, complemented
4D39×D49—31nomaximal
5D13×D147—31nomaximal
6C32×C13×C49C2211yescharacteristic, complemented, Hall
7D1911—31no—
8D1911—31no—
9D1911—61no—
10C13×D147D311yescharacteristic, complemented
11C49×D39D311yescharacteristic, complemented
12C3×C13×D49—31no—
13C3×D13×C49—31no—
14D21×D39—71nomaximal
15D13×D49—91noHall
16C3×C13×C49—21no—
17C3×C13×C49C2×D311yescharacteristic, complemented
18C3×C13×C49C2×D311yescharacteristic, complemented
19D3×D147—131nomaximal, Hall
20C3⋊D273—71no—
21C3×C13×D21—71no—
22C3×C7×D39D711yescharacteristic
23D637—91no—
24D13×C49—31no—
25C13×D49—31no—
26D7×D39—211no—
27D13×D21—211no—
28C3⋊D147—131no—
29C3×D147D1311yescharacteristic, complemented
30C3×D3×C49—131no—
31C32×C7×C13C2×D711yescharacteristic
32C13×C49D3211yescharacteristic, complemented, Hall
33C2×D147—391no—
34D3×D49—391no—
35D273—211no—
36D273—211no—
37D273—421no—
38C13×D21—71no—
39C7×D39D2111yescharacteristic
40C3×C13×D7—211no—
41C3×C7×D13—31no—
42D3×D39—491noHall
43C32×C49C2×D1311yescharacteristic, complemented, Hall
44D7×D13—631no—
45C2×C3×C49—391no—
46D147—391no—
47D147—391no—
48D147—781no—
49D147D3911yescharacteristic, direct product factor
50C3×D49—31no—
51D3×C49—131no—
52C3×C7×C13—21no—
53C3×C7×C13D3×D711yescharacteristic
54C3×C7×C13C2×D2111yescharacteristic
55D3×D21—911no—
56C3⋊D39—491no—
57C3×D39D4911yescharacteristic, complemented
58C3×D3×C13—491no—
59C2×D49—1171noHall
60D91—631no—
61C7×D13—31no—
62C13×D7—211no—
63C2×D39—1471no—
64D3×D13—1471no—
65C3×C49—21no—
66C3×C49D3×D1311yescharacteristic, complemented
67C3×C49C2×D3911yescharacteristic, complemented
68C3⋊D21—911no—
69C3×D21—71no—
70C3×D3×C7—131no—
71C32×C13C2×D4911yescharacteristic, complemented, Hall
72C2×C49—391no—
73D49—31no—
74D49—1171no—
75C7×C13D3×D2111yescharacteristic
76C2×D21—2731no—
77D3×D7—2731no—
78C2×C3×C13—1471no—
79D39—2941no—
80D39—1471no—
81D39—1471no—
82D39D14711yescharacteristic, direct product factor
83C3×D13—31no—
84D3×C13—491no—
85C32×C7D7×D1311yescharacteristic
86C2×D13—4411noHall
87C49D3×D3911yescharacteristic, complemented, Sylow
88C2×C3×C7—391no—
89D21—71no—
90D21—2731no—
91D21—2731no—
92D21—5461no—
93C3×D7—211no—
94D3×C7—131no—
95C3×C13—21no—
96C3×C13D3×D4911yescharacteristic, complemented
97C3×C13C2×D14711yescharacteristic, complemented
98D32—6371noHall
99C2×D7—8191no—
100C2×C13—1471no—
101D13—31no—
102D13—4411no—
103C3×C7—21no—
104C3×C7D13×D2111yescharacteristic
105C3×C7D7×D3911yescharacteristic
106C3⋊D3—6371no—
107C3×D3—131no—
108C3×D3—491no—
109C2×C7—391no—
110D7—211no—
111D7—8191no—
112C13D3×D14711yescharacteristic, complemented, Sylow
113C2×D3—19111no—
114C2×D3—19111no—
115C32D13×D4911yescharacteristic, complemented, Sylow
116C7D21×D3911yescharacteristic
117C2×C3—391no—
118C2×C3—1471no—
119D3—131no—
120D3—491no—
121D3—19111no—
122D3—19111no—
123D3—38221no—
124C22—57331noSylow
125C3—21no—
126C3D13×D14711yescharacteristic, complemented
127C3D39×D4911yescharacteristic, complemented
128C2—391no—
129C2—57331no—
130C2—1471no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC32×C13×C49C22
FrattiniC7D21×D39
socleC32×C7×C13C2×D7
LCSG ▷ C32×C13×C49
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊D1911C2semidirect
2. C3×C13×D147C2semidirect
3. C3×C49×D39C2semidirect
6. C32×C13×C49C22semidirect
10. C13×D147D3semidirect
11. C49×D39D3semidirect
17. C3×C13×C49C2×D3semidirect
18. C3×C13×C49C2×D3semidirect
29. C3×D147D13semidirect
32. C13×C49D32semidirect
43. C32×C49C2×D13semidirect
49. D147D39direct (N × H)
57. C3×D39D49semidirect
66. C3×C49D3×D13semidirect
67. C3×C49C2×D39semidirect
71. C32×C13C2×D49semidirect
82. D39D147direct (N × H)
87. C49D3×D39semidirect
96. C3×C13D3×D49semidirect
97. C3×C13C2×D147semidirect
112. C13D3×D147semidirect
115. C32D13×D49semidirect
126. C3D13×D147semidirect
127. C3D39×D49semidirect

Maximal subgroups

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

subgroupindex
C3⋊D19112
C3×C13×D1472
C3×C49×D392
D39×D493
D13×D1473
D21×D397
D3×D14713