Finite Group Databasebeta

← C11×C13×(C3⋊D3)⋊D7 #49114958

Subgroups — C11×C13×(C3⋊D3)⋊D7 #49114958

Order 36036.

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

normal subgroups only

This group has 176 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
1C3×C11×C13×D21C212yesmaximal, complemented
2C7×C11×C13×C3⋊D3C211yesmaximal, characteristic, complemented
3D3×C11×C13×D7—32nomaximal
4C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
5C11×C13×D21D312yescomplemented
6D3×C7×C11×C13—32no—
7D3×C7×C11×C13—61no—
8C3×C11×C13×D7—32no—
9D32×C11×C13—71nomaximal, Hall
10C2×C11×C13×D7—91noHall
11C13×(C3⋊D3)⋊D7C1111yesmaximal, characteristic, direct product factor, Hall
12C3×C7×C11×C13—21no—
13C3×C7×C11×C13C2×D312yescomplemented
14C11×(C3⋊D3)⋊D7C1311yesmaximal, characteristic, direct product factor, Hall
15C11×C13×C3⋊D3D711yescharacteristic, complemented
16C3×D3×C11×C13—72no—
17C11×C13×D7—32no—
18C2×C7×C11×C13—91no—
19C2×D3×C11×C13—212no—
20C7×C13×C3⋊D3C2×C1111yescharacteristic, complemented
21C3×C13×D21C2×C1112yescomplemented
22C7×C11×C3⋊D3C2×C1311yescharacteristic, complemented
23C3×C11×D21C2×C1312yescomplemented
24C32×C11×C13C2×D711yescharacteristic, complemented, Hall
25D3×C13×D7—32no—
26C7×C11×C13D3211yescharacteristic, complemented, Hall
27D3×C11×D7—32no—
28C2×C3×C11×C13—212no—
29D3×C11×C13—32no—
30D3×C11×C13—61no—
31D3×C11×C13—72no—
32C32×C7×C13C22×C1111yescharacteristic, complemented, Hall
33C32×C7×C11C22×C1311yescharacteristic, complemented, Hall
34C22×C11×C13—631noHall
35C13×D21D3×C1112yescomplemented
36D3×C7×C13—32no—
37D3×C7×C13—61no—
38C3×C13×D7—32no—
39D32×C13—71noHall
40C11×D21D3×C1312yescomplemented
41D3×C7×C11—32no—
42D3×C7×C11—61no—
43C3×C11×D7—32no—
44C3×C11×C13—21no—
45C3×C11×C13D3×D712yescomplemented
46D32×C11—71noHall
47C2×C13×D7—91noHall
48C2×C11×D7—91noHall
49C2×C11×C13—91no—
50C2×C11×C13—212no—
51C3×C7×C13—21no—
52C3×C7×C13C2×D3×C1112yescomplemented
53(C3⋊D3)⋊D7C11×C1311yescharacteristic, direct product factor, Hall
54C13×C3⋊D3C11×D711yescharacteristic, complemented
55C3×D3×C13—72no—
56C3×C7×C11—21no—
57C3×C7×C11C2×D3×C1312yescomplemented
58C11×C3⋊D3C13×D711yescharacteristic, complemented
59C3×D3×C11—72no—
60C2×C7×C13—91no—
61C13×D7—32no—
62C2×D3×C13—212no—
63C2×C7×C11—91no—
64C11×D7—32no—
65C11×C13(C3⋊D3)⋊D711yescharacteristic, direct product factor, Hall
66C2×D3×C11—212no—
67C7×C3⋊D3C2×C11×C1311yescharacteristic, complemented
68C3×D21C2×C11×C1312yescomplemented
69C32×C13C2×C11×D711yescharacteristic, complemented, Hall
70C32×C11C2×C13×D711yescharacteristic, complemented, Hall
71C7×C13D32×C1111yescharacteristic, complemented, Hall
72D3×D7—32no—
73C2×C3×C13—212no—
74D3×C13—32no—
75D3×C13—61no—
76D3×C13—72no—
77C7×C11D32×C1311yescharacteristic, complemented, Hall
78C2×C3×C11—212no—
79D3×C11—32no—
80D3×C11—61no—
81D3×C11—72no—
82C32×C7C22×C11×C1311yescharacteristic, complemented, Hall
83C22×C13—631noHall
84C22×C11—631noHall
85D21D3×C11×C1312yescomplemented
86C3×D7—32no—
87D3×C7—32no—
88D3×C7—61no—
89C3×C13—21no—
90C3×C13D3×C11×D712yescomplemented
91D32—71noHall
92C3×C11—21no—
93C3×C11D3×C13×D712yescomplemented
94C2×D7—91noHall
95C2×C13—91no—
96C2×C13—212no—
97C2×C11—91no—
98C2×C11—212no—
99C3×C7—21no—
100C3×C7C2×D3×C11×C1312yescomplemented
101C3⋊D3C11×C13×D711yescharacteristic, complemented
102C3×D3—72no—
103C2×C7—91no—
104D7—32no—
105C13C11×(C3⋊D3)⋊D711yescharacteristic, direct product factor, Sylow
106C2×D3—212no—
107C11C13×(C3⋊D3)⋊D711yescharacteristic, direct product factor, Sylow
108C32C2×C11×C13×D711yescharacteristic, complemented, Sylow
109C7D32×C11×C1311yescharacteristic, complemented, Sylow
110C2×C3—212no—
111D3—32no—
112D3—61no—
113D3—72no—
114C22—631noSylow
115C3—21no—
116C3D3×C11×C13×D712yescomplemented
117C2—91no—
118C2—212no—
subgroupG/H
center, hypercenterC11×C13(C3⋊D3)⋊D7
commutator, cosocle, hypocenterC32×C7C22×C11×C13
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C32×C7
UCSC1 ◁ C11×C13

Complements

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

NH ≅ G/Ntype
1. C3×C11×C13×D21C2semidirect
2. C7×C11×C13×C3⋊D3C2semidirect
4. C32×C7×C11×C13C22semidirect
5. C11×C13×D21D3semidirect
11. C13×(C3⋊D3)⋊D7C11direct (N × H)
13. C3×C7×C11×C13C2×D3semidirect
14. C11×(C3⋊D3)⋊D7C13direct (N × H)
15. C11×C13×C3⋊D3D7semidirect
20. C7×C13×C3⋊D3C2×C11semidirect
21. C3×C13×D21C2×C11semidirect
22. C7×C11×C3⋊D3C2×C13semidirect
23. C3×C11×D21C2×C13semidirect
24. C32×C11×C13C2×D7semidirect
26. C7×C11×C13D32semidirect
32. C32×C7×C13C22×C11semidirect
33. C32×C7×C11C22×C13semidirect
35. C13×D21D3×C11semidirect
40. C11×D21D3×C13semidirect
45. C3×C11×C13D3×D7semidirect
52. C3×C7×C13C2×D3×C11semidirect
53. (C3⋊D3)⋊D7C11×C13direct (N × H)
54. C13×C3⋊D3C11×D7semidirect
57. C3×C7×C11C2×D3×C13semidirect
58. C11×C3⋊D3C13×D7semidirect
65. C11×C13(C3⋊D3)⋊D7direct (N × H)
67. C7×C3⋊D3C2×C11×C13semidirect
68. C3×D21C2×C11×C13semidirect
69. C32×C13C2×C11×D7semidirect
70. C32×C11C2×C13×D7semidirect
71. C7×C13D32×C11semidirect
77. C7×C11D32×C13semidirect
82. C32×C7C22×C11×C13semidirect
85. D21D3×C11×C13semidirect
90. C3×C13D3×C11×D7semidirect
93. C3×C11D3×C13×D7semidirect
100. C3×C7C2×D3×C11×C13semidirect
101. C3⋊D3C11×C13×D7semidirect
105. C13C11×(C3⋊D3)⋊D7direct (N × H)
107. C11C13×(C3⋊D3)⋊D7direct (N × H)
108. C32C2×C11×C13×D7semidirect
109. C7D32×C11×C13semidirect
116. C3D3×C11×C13×D7semidirect

Maximal subgroups

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

subgroupindex
C3×C11×C13×D212
C7×C11×C13×C3⋊D32
D3×C11×C13×D73
D32×C11×C137
C13×(C3⋊D3)⋊D711
C11×(C3⋊D3)⋊D713