Finite Group Databasebeta

← C7×D77⋊(C3⋊D3) #34085019

Subgroups — C7×D77⋊(C3⋊D3) #34085019

Order 19404.

312 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C7×C11×C3⋊D21C211yesmaximal, characteristic, complemented
2C72×C3⋊D33C211yesmaximal, characteristic, complemented
3C32×C7×D77C211yesmaximal, characteristic, complemented
4C7×D21⋊D11—34nomaximal
5C32×C72×C11C2211yescharacteristic, complemented, Hall
6C7×C11×D21—34no—
7C72×D33—34no—
8C3×C7×D77D314yescomplemented
9D77⋊(C3⋊D3)C711yesmaximal, characteristic, direct product factor
10C7×C3⋊D3×D11—71nomaximal
11C7×D7×D11—91noHall
12C7×D7×C3⋊D3—111nomaximal, Hall
13C3×C72×C11C2×D314yescomplemented
14C11×C3⋊D21C2×C711yescharacteristic, complemented
15C7×C3⋊D33—23no—
16C7×C3⋊D33D711yescharacteristic, complemented
17C7×C3⋊D33C2×C711yescharacteristic, complemented
18C7×C11×C3⋊D3—71no—
19C32×D77C2×C711yescharacteristic, complemented
20C32×C7×D11—71no—
21C7×D77C3⋊D311yescharacteristic, complemented
22C7×C11×D7—91no—
23C72×D11—91no—
24D21⋊D11—34no—
25D3×C7×D11—214no—
26C7×C3⋊D21D1111yescharacteristic, complemented
27C72×C3⋊D3—111no—
28C32×C7×D7—111no—
29C32×C7×C11—23no—
30C32×C7×C11C2×D711yescharacteristic, complemented
31C32×C7×C11C22×C711yescharacteristic, complemented
32D3×C7×D7—334no—
33C72×C11C2×C3⋊D311yescharacteristic, complemented, Hall
34C11×D21—34no—
35C7×D33—34no—
36C7×D33—34no—
37C7×D33—612no—
38D3×C7×C11—214no—
39C3×D77D3×C714yescomplemented
40C3×C7×D11—74no—
41C32×C72C2×D1111yescharacteristic, complemented, Hall
42C3⋊D3×D11—71noHall
43C2×C7×D11—631no—
44D7×D11—91no—
45C7×D21—34no—
46D3×C72—334no—
47C3×C7×D7—114no—
48C2×C7×C3⋊D3—771no—
49D7×C3⋊D3—111no—
50C3×C7×C11—212no—
51C3×C7×C11D3×D714yescomplemented
52C3×C7×C11C2×D3×C714yescomplemented
53C3⋊D33C7×D711yescharacteristic, complemented
54C11×C3⋊D3—71no—
55C32×D11—71no—
56C2×C7×D7—991noHall
57C2×C7×C11—631no—
58D77C7×C3⋊D311yescharacteristic, complemented
59C7×D11—71no—
60C7×D11—91no—
61C7×D11—91no—
62C7×D11—183no—
63C11×D7—91no—
64C3×C72D3×D1114yescomplemented
65D3×D11—214no—
66C2×C32×C7—771no—
67C3⋊D21C7×D1111yescharacteristic, complemented
68C7×C3⋊D3—71no—
69C7×C3⋊D3—111no—
70C7×C3⋊D3—111no—
71C7×C3⋊D3—223no—
72C32×D7—111no—
73C32×C11C2×C7×D711yescharacteristic, complemented, Hall
74C2×C72—991no—
75C7×D7—91no—
76C7×D7—111no—
77C2×D3×C7—2314no—
78D3×D7—334no—
79C7×C11—23no—
80C7×C11D7×C3⋊D311yescharacteristic, complemented
81C7×C11C2×C7×C3⋊D311yescharacteristic, complemented
82D33—34no—
83C3×D11—74no—
84D3×C11—214no—
85C32×C7—23no—
86C32×C7D7×D1111yescharacteristic, complemented
87C32×C7C2×C7×D1111yescharacteristic, complemented
88C72C3⋊D3×D1111yescharacteristic, complemented, Sylow
89C2×D11—631noHall
90C2×C3×C7—774no—
91D21—34no—
92C3×D7—114no—
93D3×C7—214no—
94D3×C7—334no—
95D3×C7—334no—
96D3×C7—6612no—
97C2×C3⋊D3—771noHall
98C3×C11D3×C7×D714yescomplemented
99C22×C7—6931no—
100C2×D7—991no—
101C2×C11—631no—
102D11—71no—
103D11—91no—
104C3×C7—212no—
105C3×C7D3×C7×D1114yescomplemented
106C3×C7D21⋊D1114yescomplemented
107C2×C32—771no—
108C3⋊D3—71no—
109C3⋊D3—111no—
110C2×C7—631no—
111C2×C7—771no—
112C2×C7—991no—
113C2×C7—991no—
114C2×C7—1983no—
115D7—91no—
116D7—111no—
117C2×D3—2314no—
118C11C7×D7×C3⋊D311yescharacteristic, complemented, Sylow
119C32C7×D7×D1111yescharacteristic, complemented, Sylow
120C7—23no—
121C7C7×C3⋊D3×D1111yescharacteristic, complemented
122C7D77⋊(C3⋊D3)11yescharacteristic, direct product factor
123C2×C3—774no—
124D3—214no—
125D3—334no—
126C22—6931noSylow
127C3C7×D21⋊D1114yescomplemented
128C2—631no—
129C2—771no—
130C2—991no—
subgroupG/H
center, hypercenterC7D77⋊(C3⋊D3)
commutator, cosocle, hypocenterC32×C7×C11C22×C7
FrattiniC1G
Fitting, socleC32×C72×C11C22
LCSG ▷ C32×C7×C11
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C7×C11×C3⋊D21C2semidirect
2. C72×C3⋊D33C2semidirect
3. C32×C7×D77C2semidirect
5. C32×C72×C11C22semidirect
8. C3×C7×D77D3semidirect
9. D77⋊(C3⋊D3)C7direct (N × H)
13. C3×C72×C11C2×D3semidirect
14. C11×C3⋊D21C2×C7semidirect
16. C7×C3⋊D33D7semidirect
17. C7×C3⋊D33C2×C7semidirect
19. C32×D77C2×C7semidirect
21. C7×D77C3⋊D3semidirect
26. C7×C3⋊D21D11semidirect
30. C32×C7×C11C2×D7semidirect
31. C32×C7×C11C22×C7semidirect
33. C72×C11C2×C3⋊D3semidirect
39. C3×D77D3×C7semidirect
41. C32×C72C2×D11semidirect
51. C3×C7×C11D3×D7semidirect
52. C3×C7×C11C2×D3×C7semidirect
53. C3⋊D33C7×D7semidirect
58. D77C7×C3⋊D3semidirect
64. C3×C72D3×D11semidirect
67. C3⋊D21C7×D11semidirect
73. C32×C11C2×C7×D7semidirect
80. C7×C11D7×C3⋊D3semidirect
81. C7×C11C2×C7×C3⋊D3semidirect
86. C32×C7D7×D11semidirect
87. C32×C7C2×C7×D11semidirect
88. C72C3⋊D3×D11semidirect
98. C3×C11D3×C7×D7semidirect
105. C3×C7D3×C7×D11semidirect
106. C3×C7D21⋊D11semidirect
118. C11C7×D7×C3⋊D3semidirect
119. C32C7×D7×D11semidirect
121. C7C7×C3⋊D3×D11semidirect
122. C7D77⋊(C3⋊D3)direct (N × H)
127. C3C7×D21⋊D11semidirect

Maximal subgroups

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

subgroupindex
C7×C11×C3⋊D212
C72×C3⋊D332
C32×C7×D772
C7×D21⋊D113
D77⋊(C3⋊D3)7
C7×C3⋊D3×D117
C7×D7×C3⋊D311