Finite Group Databasebeta

← C3×C13×D21⋊D7 #37525593

Subgroups — C3×C13×D21⋊D7 #37525593

Order 22932.

248 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 60 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×C13×C7⋊D7C211yesmaximal, characteristic, complemented
2C3×C7×C13×D21C212yesmaximal, complemented
3C13×D21⋊D7C311yesmaximal, characteristic, direct product factor
4C3×C13×D72—31nomaximal
5C32×C72×C13C2211yescharacteristic, complemented, Hall
6C7×C13×D21C2×C312yescomplemented
7C3×C13×C7⋊D7—21no—
8C3×C13×C7⋊D7D311yescharacteristic, complemented
9C3×C13×C7⋊D7C2×C311yescharacteristic, complemented
10C3×C7×C13×D7—32no—
11C3×D3×C13×D7—72nomaximal
12C13×D72—31noHall
13C3×C72×C13—21no—
14C3×C72×C13C2×D311yescharacteristic, complemented
15C3×C72×C13C22×C311yescharacteristic, complemented
16C3×D21⋊D7C1311yesmaximal, characteristic, direct product factor, Hall
17C3×C13×D21D712yescomplemented
18C3×D3×C7×C13—72no—
19C32×C13×D7—72no—
20C32×C13×D7—143no—
21C13×C7⋊D7C3×D311yescharacteristic, complemented
22C7×C13×D7—32no—
23C2×C3×C13×D7—212no—
24D3×C13×D7—72no—
25C3×C7×D21C2×C1312yescomplemented
26C32×C7⋊D7C2×C1311yescharacteristic, complemented
27C32×C7×C13—23no—
28C32×C7×C13C2×D712yescomplemented
29C72×C13C2×C3×D311yescharacteristic, complemented, Hall
30D21⋊D7C3×C1311yescharacteristic, direct product factor
31C3×D72—31no—
32C2×C3×C7×C13—212no—
33C13×D21C3×D712yescomplemented
34D3×C7×C13—72no—
35C3×C13×D7—32no—
36C3×C13×D7—72no—
37C3×C13×D7—72no—
38C3×C13×D7—142no—
39C3×C13×D7—143no—
40C3×C13×D7—143no—
41C3×C13×D7—146no—
42C2×C3×D3×C13—491noHall
43C32×C72C22×C1311yescharacteristic, complemented, Hall
44C2×C13×D7—212no—
45C7×D21C2×C3×C1312yescomplemented
46C3×C7⋊D7—21no—
47C3×C7⋊D7D3×C1311yescharacteristic, complemented
48C3×C7⋊D7C2×C3×C1311yescharacteristic, complemented
49C3×C7×D7—32no—
50C3×C7×C13—26no—
51C3×C7×C13—23no—
52C3×C7×C13—23no—
53C3×C7×C13—22no—
54C3×C7×C13D3×D712yescomplemented
55C3×C7×C13C2×C3×D712yescomplemented
56C3×D3×D7—72no—
57C2×C32×C13—491no—
58C3×D3×C13—72no—
59D72—31noHall
60C2×C7×C13—212no—
61C13×D7—32no—
62C13×D7—72no—
63C13×D7—143no—
64C22×C3×C13—1471no—
65C2×D3×C13—491no—
66C3×C72—21no—
67C3×C72C2×D3×C1311yescharacteristic, complemented
68C3×C72C22×C3×C1311yescharacteristic, complemented
69C3×D21C13×D712yescomplemented
70C3×D3×C7—72no—
71C32×D7—72no—
72C32×D7—143no—
73C32×C13D7211yescharacteristic, complemented, Hall
74C7⋊D7C3×D3×C1311yescharacteristic, complemented
75C7×D7—32no—
76C7×C13—23no—
77C7×C13C3×D3×D712yescomplemented
78C2×C3×D7—212no—
79D3×D7—72no—
80C2×C3×C13—212no—
81C2×C3×C13—491no—
82C2×C3×C13—491no—
83C2×C3×C13—981no—
84D3×C13—72no—
85C32×C7—23no—
86C32×C7C2×C13×D712yescomplemented
87C22×C13—1471noHall
88C72C2×C3×D3×C1311yescharacteristic, complemented, Sylow
89C2×C3×C7—212no—
90D21C3×C13×D712yescomplemented
91C3×D7—32no—
92C3×D7—72no—
93C3×D7—72no—
94C3×D7—143no—
95C3×D7—143no—
96C3×D7—142no—
97C3×D7—146no—
98D3×C7—72no—
99C3×C13—21no—
100C3×C13C3×D7211yescharacteristic, complemented
101C3×C13D21⋊D711yescharacteristic, direct product factor
102C2×C3×D3—491noHall
103C2×D7—212no—
104C2×C13—212no—
105C2×C13—491no—
106C3×C7—26no—
107C3×C7—22no—
108C3×C7—23no—
109C3×C7—23no—
110C3×C7D3×C13×D712yescomplemented
111C3×C7C2×C3×C13×D712yescomplemented
112C2×C32—491no—
113C3×D3—72no—
114C2×C7—212no—
115D7—32no—
116D7—72no—
117D7—143no—
118C13C3×D21⋊D711yescharacteristic, direct product factor, Sylow
119C22×C3—1471no—
120C2×D3—491no—
121C32C13×D7211yescharacteristic, complemented, Sylow
122C7—23no—
123C7C3×D3×C13×D712yescomplemented
124C2×C3—212no—
125C2×C3—491no—
126C2×C3—491no—
127C2×C3—981no—
128D3—72no—
129C22—1471noSylow
130C3—21no—
131C3C3×C13×D7211yescharacteristic, complemented
132C3C13×D21⋊D711yescharacteristic, direct product factor
133C2—212no—
134C2—491no—
subgroupG/H
center, hypercenterC3×C13D21⋊D7
commutator, cosocle, hypocenterC3×C72C22×C3×C13
FrattiniC1G
Fitting, socleC32×C72×C13C22
LCSG ▷ C3×C72
UCSC1 ◁ C3×C13

Complements

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

NH ≅ G/Ntype
1. C32×C13×C7⋊D7C2semidirect
2. C3×C7×C13×D21C2semidirect
3. C13×D21⋊D7C3direct (N × H)
5. C32×C72×C13C22semidirect
6. C7×C13×D21C2×C3semidirect
8. C3×C13×C7⋊D7D3semidirect
9. C3×C13×C7⋊D7C2×C3semidirect
14. C3×C72×C13C2×D3semidirect
15. C3×C72×C13C22×C3semidirect
16. C3×D21⋊D7C13direct (N × H)
17. C3×C13×D21D7semidirect
21. C13×C7⋊D7C3×D3semidirect
25. C3×C7×D21C2×C13semidirect
26. C32×C7⋊D7C2×C13semidirect
28. C32×C7×C13C2×D7semidirect
29. C72×C13C2×C3×D3semidirect
30. D21⋊D7C3×C13direct (N × H)
33. C13×D21C3×D7semidirect
43. C32×C72C22×C13semidirect
45. C7×D21C2×C3×C13semidirect
47. C3×C7⋊D7D3×C13semidirect
48. C3×C7⋊D7C2×C3×C13semidirect
54. C3×C7×C13D3×D7semidirect
55. C3×C7×C13C2×C3×D7semidirect
67. C3×C72C2×D3×C13semidirect
68. C3×C72C22×C3×C13semidirect
69. C3×D21C13×D7semidirect
73. C32×C13D72semidirect
74. C7⋊D7C3×D3×C13semidirect
77. C7×C13C3×D3×D7semidirect
86. C32×C7C2×C13×D7semidirect
88. C72C2×C3×D3×C13semidirect
90. D21C3×C13×D7semidirect
100. C3×C13C3×D72semidirect
101. C3×C13D21⋊D7direct (N × H)
110. C3×C7D3×C13×D7semidirect
111. C3×C7C2×C3×C13×D7semidirect
118. C13C3×D21⋊D7direct (N × H)
121. C32C13×D72semidirect
123. C7C3×D3×C13×D7semidirect
131. C3C3×C13×D72semidirect
132. C3C13×D21⋊D7direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C13×C7⋊D72
C3×C7×C13×D212
C13×D21⋊D73
C3×C13×D723
C3×D3×C13×D77
C3×D21⋊D713