Finite Group Databasebeta

← #37525624

Subgroups — #37525624

Order 22932.

440 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 97 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×C3⋊(C7⋊D7)C211yesmaximal, characteristic, complemented
2C3×C3⋊(C7⋊D91)C211yesmaximal, characteristic, complemented
3C72×C3⋊D39C211yesmaximal, characteristic, complemented
4D39⋊(C7⋊D7)—31nomaximal
5D39×C7⋊D7—31nomaximal
6C32×C72×C13C2211yescharacteristic, complemented, Hall
7C3⋊(C7⋊D91)D311yescharacteristic, complemented
8C13×C3⋊(C7⋊D7)D311yescharacteristic, complemented
9C72×D39—31no—
10C72×D39—31no—
11C72×D39—61no—
12C3×C7⋊D91—31no—
13C3×C13×C7⋊D7—31no—
14D21⋊D39—78nomaximal
15D13×C7⋊D7—91noHall
16C3×C72×C13—21no—
17C3×C72×C13C2×D311yescharacteristic, complemented
18C3×C72×C13C2×D311yescharacteristic, complemented
19(C3⋊D3)⋊(C7⋊D7)—131nomaximal, Hall
20C7×C3⋊D39D718yescomplemented
21C3×D273—78no—
22C3×C13×D21—78no—
23C7⋊D91—31no—
24C13×C7⋊D7—31no—
25C72×D13—91no—
26D21⋊D13—218no—
27D7×D39—218no—
28C72×C3⋊D3—131no—
29C3×C3⋊(C7⋊D7)—131no—
30C3×C3⋊(C7⋊D7)D1311yescharacteristic, complemented
31C32×C7×C13C2×D718yescomplemented
32C72×C13D3211yescharacteristic, complemented, Hall
33D3×C7⋊D7—391no—
34D3×C7⋊D7—391no—
35D273—78no—
36C13×D21—78no—
37C7×D39—38no—
38C7×D39—38no—
39C7×D39—68no—
40C3×D91—218no—
41C3×C13×D7—218no—
42D3×D39—491noHall
43C32×C72C2×D1311yescharacteristic, complemented, Hall
44D7×D13—638no—
45C3⋊(C7⋊D7)—131no—
46C3⋊(C7⋊D7)D3911yescharacteristic, complemented
47D3×C72—391no—
48D3×C72—391no—
49D3×C72—781no—
50C3×C7⋊D7—31no—
51C3×C7⋊D7—391no—
52C3×C7×C13—28no—
53C3×C7×C13D3×D718yescomplemented
54C3×C7×C13D3×D718yescomplemented
55(C3⋊D3)⋊D7—918no—
56C3⋊D39C7⋊D711yescharacteristic, complemented
57C3×D39—491no—
58C3×D3×C13—491no—
59C2×C7⋊D7—1171noHall
60D91—218no—
61C7×D13—98no—
62C13×D7—218no—
63C2×D39—1471no—
64D3×D13—1471no—
65C3×C72—21no—
66C3×C72D3×D1311yescharacteristic, complemented
67C3×C72C2×D3911yescharacteristic, complemented
68C7×C3⋊D3—138no—
69C3×D21—78no—
70C3×D21—918no—
71C32×C13C2×C7⋊D711yescharacteristic, complemented, Hall
72C2×C72—1171no—
73C7⋊D7—31no—
74C7⋊D7—391no—
75C7×C13(C3⋊D3)⋊D718yescomplemented
76D3×D7—2738no—
77D3×D7—2738no—
78C2×C3×C13—1471no—
79D39—31no—
80D39—31no—
81D39—61no—
82D39—491no—
83C3×D13—1471no—
84D3×C13—491no—
85C32×C7D7×D1318yescomplemented
86C2×D13—4411noHall
87C72D3×D3911yescharacteristic, complemented, Sylow
88D21—78no—
89D21—918no—
90C3×D7—2738no—
91C3×D7—218no—
92D3×C7—398no—
93D3×C7—398no—
94D3×C7—788no—
95C3×C13—21no—
96C3×C13D3×C7⋊D711yescharacteristic, complemented
97C3×C13D3×C7⋊D711yescharacteristic, complemented
98D32—6371noHall
99C2×D7—8198no—
100C2×C13—1471no—
101D13—91no—
102D13—1471no—
103C3×C7—28no—
104C3×C7D7×D3918yescomplemented
105C3×C7D21⋊D1318yescomplemented
106C3⋊D3—131no—
107C3×D3—491no—
108C3×D3—6371no—
109C2×C7—1178no—
110D7—2738no—
111D7—218no—
112C13(C3⋊D3)⋊(C7⋊D7)11yescharacteristic, complemented, Sylow
113C2×D3—19111no—
114C2×D3—19111no—
115C32D13×C7⋊D711yescharacteristic, complemented, Sylow
116C7D21⋊D3918yescomplemented
117C2×C3—19111no—
118C2×C3—1471no—
119D3—391no—
120D3—391no—
121D3—491no—
122D3—781no—
123D3—6371no—
124C22—57331noSylow
125C3—21no—
126C3D39×C7⋊D711yescharacteristic, complemented
127C3D39⋊(C7⋊D7)11yescharacteristic, complemented
128C2—1171no—
129C2—19111no—
130C2—1471no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C72×C13C22
LCSG ▷ C32×C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C13×C3⋊(C7⋊D7)C2semidirect
2. C3×C3⋊(C7⋊D91)C2semidirect
3. C72×C3⋊D39C2semidirect
6. C32×C72×C13C22semidirect
7. C3⋊(C7⋊D91)D3semidirect
8. C13×C3⋊(C7⋊D7)D3semidirect
17. C3×C72×C13C2×D3semidirect
18. C3×C72×C13C2×D3semidirect
20. C7×C3⋊D39D7semidirect
30. C3×C3⋊(C7⋊D7)D13semidirect
31. C32×C7×C13C2×D7semidirect
32. C72×C13D32semidirect
43. C32×C72C2×D13semidirect
46. C3⋊(C7⋊D7)D39semidirect
53. C3×C7×C13D3×D7semidirect
54. C3×C7×C13D3×D7semidirect
56. C3⋊D39C7⋊D7semidirect
66. C3×C72D3×D13semidirect
67. C3×C72C2×D39semidirect
71. C32×C13C2×C7⋊D7semidirect
75. C7×C13(C3⋊D3)⋊D7semidirect
85. C32×C7D7×D13semidirect
87. C72D3×D39semidirect
96. C3×C13D3×C7⋊D7semidirect
97. C3×C13D3×C7⋊D7semidirect
104. C3×C7D7×D39semidirect
105. C3×C7D21⋊D13semidirect
112. C13(C3⋊D3)⋊(C7⋊D7)semidirect
115. C32D13×C7⋊D7semidirect
116. C7D21⋊D39semidirect
126. C3D39×C7⋊D7semidirect
127. C3D39⋊(C7⋊D7)semidirect

Maximal subgroups

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

subgroupindex
C3×C13×C3⋊(C7⋊D7)2
C3×C3⋊(C7⋊D91)2
C72×C3⋊D392
D39⋊(C7⋊D7)3
D39×C7⋊D73
D21⋊D397
(C3⋊D3)⋊(C7⋊D7)13