Finite Group Databasebeta

← C13×D7×C3⋊D21 #37525637

Subgroups — C13×D7×C3⋊D21 #37525637

Order 22932.

312 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C32×C7×C13×D7C211yesmaximal, characteristic, complemented
2C7×C13×C3⋊D21C211yesmaximal, characteristic, complemented
3C13×C3⋊(C3⋊(C7⋊D7))C211yesmaximal, characteristic, complemented
4C13×D7×D21—34nomaximal
5C32×C72×C13C2211yescharacteristic, complemented, Hall
6C13×C3⋊(C7⋊D7)—34no—
7C7×C13×D21—34no—
8C3×C7×C13×D7D314yescomplemented
9C2×C13×C3⋊D21—71nomaximal
10C13×D7×C3⋊D3—71nomaximal
11C13×D72—91noHall
12C3×C72×C13C2×D314yescomplemented
13D7×C3⋊D21C1311yesmaximal, characteristic, direct product factor, Hall
14C2×C32×C7×C13—71no—
15C13×C3⋊D21—71no—
16C13×C3⋊D21—71no—
17C13×C3⋊D21—143no—
18C13×C3⋊D21D711yescharacteristic, direct product factor
19C7×C13×C3⋊D3—71no—
20C32×C13×D7D711yescharacteristic, complemented
21C13×C7⋊D7—91no—
22C7×C13×D7—91no—
23C7×C13×D7C3⋊D311yescharacteristic, complemented
24C2×C13×D21—214no—
25D3×C13×D7—214no—
26C3⋊(C3⋊(C7⋊D7))C2×C1311yescharacteristic, complemented
27C7×C3⋊D21C2×C1311yescharacteristic, complemented
28C32×C7×D7C2×C1311yescharacteristic, complemented
29C32×C7×C13—23no—
30C32×C7×C13C2×D711yescharacteristic, complemented
31C32×C7×C13C2×D711yescharacteristic, complemented
32C72×C13C2×C3⋊D311yescharacteristic, complemented, Hall
33D7×D21—34no—
34C2×C3×C7×C13—74no—
35C13×D21—34no—
36C13×D21—214no—
37C13×D21—214no—
38C13×D21—4212no—
39D3×C7×C13—214no—
40C3×C13×D7D2114yescomplemented
41C2×C13×C3⋊D3—491noHall
42C32×C72C22×C1311yescharacteristic, complemented, Hall
43C2×C13×D7—631no—
44C2×C13×D7—631no—
45C3⋊(C7⋊D7)—34no—
46C7×D21—34no—
47C3×C7×D7D3×C1314yescomplemented
48C3×C7×C13—212no—
49C3×C7×C13D3×D714yescomplemented
50C3×C7×C13C2×D2114yescomplemented
51C2×C3⋊D21—71no—
52D7×C3⋊D3—71no—
53C2×C32×C13—71no—
54C13×C3⋊D3—71no—
55C13×C3⋊D3—491no—
56D72—91noHall
57C2×C7×C13—71no—
58C2×C7×C13—631no—
59C13×D7—91no—
60C13×D7—631no—
61C13×D7—631no—
62C13×D7—1263no—
63C13×D7C3⋊D2111yescharacteristic, direct product factor
64C2×D3×C13—1474no—
65C3×C72C2×D3×C1314yescomplemented
66C2×C32×C7—71no—
67C3⋊D21—71no—
68C3⋊D21—71no—
69C3⋊D21—143no—
70C3⋊D21C13×D711yescharacteristic, direct product factor
71C7×C3⋊D3—71no—
72C32×D7C13×D711yescharacteristic, complemented
73C32×C13D7211yescharacteristic, complemented, Hall
74C7⋊D7—91no—
75C7×D7—91no—
76C7×D7C13×C3⋊D311yescharacteristic, complemented
77C7×C13—23no—
78C7×C13D7×C3⋊D311yescharacteristic, complemented
79C7×C13C2×C3⋊D2111yescharacteristic, complemented
80C2×D21—214no—
81D3×D7—214no—
82C2×C3×C13—74no—
83D3×C13—214no—
84D3×C13—1474no—
85C32×C7—23no—
86C32×C7C2×C13×D711yescharacteristic, complemented
87C32×C7C2×C13×D711yescharacteristic, complemented
88C22×C13—4411noHall
89C72C2×C13×C3⋊D311yescharacteristic, complemented, Sylow
90C2×C3×C7—74no—
91D21—34no—
92D21—214no—
93D21—214no—
94D21—4212no—
95C3×D7C13×D2114yescomplemented
96D3×C7—214no—
97C3×C13D7×D2114yescomplemented
98C2×C3⋊D3—491noHall
99C2×D7—631no—
100C2×D7—631no—
101C2×C13—71no—
102C2×C13—631no—
103C2×C13—4411no—
104C3×C7—212no—
105C3×C7D3×C13×D714yescomplemented
106C3×C7C2×C13×D2114yescomplemented
107C2×C32—71no—
108C3⋊D3—71no—
109C3⋊D3—491no—
110C2×C7—71no—
111C2×C7—631no—
112D7—91no—
113D7—631no—
114D7—631no—
115D7—1263no—
116D7C13×C3⋊D2111yescharacteristic, direct product factor
117C13D7×C3⋊D2111yescharacteristic, direct product factor, Sylow
118C2×D3—1474no—
119C32C13×D7211yescharacteristic, complemented, Sylow
120C7—23no—
121C7C13×D7×C3⋊D311yescharacteristic, complemented
122C7C2×C13×C3⋊D2111yescharacteristic, complemented
123C2×C3—74no—
124D3—214no—
125D3—1474no—
126C22—4411noSylow
127C3C13×D7×D2114yescomplemented
128C2—71no—
129C2—631no—
130C2—4411no—
subgroupG/H
center, hypercenterC13D7×C3⋊D21
commutator, cosocle, hypocenterC32×C72C22×C13
FrattiniC1G
Fitting, socleC32×C72×C13C22
LCSG ▷ C32×C72
UCSC1 ◁ C13

Complements

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

NH ≅ G/Ntype
1. C32×C7×C13×D7C2semidirect
2. C7×C13×C3⋊D21C2semidirect
3. C13×C3⋊(C3⋊(C7⋊D7))C2semidirect
5. C32×C72×C13C22semidirect
8. C3×C7×C13×D7D3semidirect
12. C3×C72×C13C2×D3semidirect
13. D7×C3⋊D21C13direct (N × H)
18. C13×C3⋊D21D7direct (N × H)
20. C32×C13×D7D7semidirect
23. C7×C13×D7C3⋊D3semidirect
26. C3⋊(C3⋊(C7⋊D7))C2×C13semidirect
27. C7×C3⋊D21C2×C13semidirect
28. C32×C7×D7C2×C13semidirect
30. C32×C7×C13C2×D7semidirect
31. C32×C7×C13C2×D7semidirect
32. C72×C13C2×C3⋊D3semidirect
40. C3×C13×D7D21semidirect
42. C32×C72C22×C13semidirect
47. C3×C7×D7D3×C13semidirect
49. C3×C7×C13D3×D7semidirect
50. C3×C7×C13C2×D21semidirect
63. C13×D7C3⋊D21direct (N × H)
65. C3×C72C2×D3×C13semidirect
70. C3⋊D21C13×D7direct (N × H)
72. C32×D7C13×D7semidirect
73. C32×C13D72semidirect
76. C7×D7C13×C3⋊D3semidirect
78. C7×C13D7×C3⋊D3semidirect
79. C7×C13C2×C3⋊D21semidirect
86. C32×C7C2×C13×D7semidirect
87. C32×C7C2×C13×D7semidirect
89. C72C2×C13×C3⋊D3semidirect
95. C3×D7C13×D21semidirect
97. C3×C13D7×D21semidirect
105. C3×C7D3×C13×D7semidirect
106. C3×C7C2×C13×D21semidirect
116. D7C13×C3⋊D21direct (N × H)
117. C13D7×C3⋊D21direct (N × H)
119. C32C13×D72semidirect
121. C7C13×D7×C3⋊D3semidirect
122. C7C2×C13×C3⋊D21semidirect
127. C3C13×D7×D21semidirect

Maximal subgroups

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

subgroupindex
C32×C7×C13×D72
C7×C13×C3⋊D212
C13×C3⋊(C3⋊(C7⋊D7))2
C13×D7×D213
C2×C13×C3⋊D217
C13×D7×C3⋊D37
D7×C3⋊D2113