Finite Group Databasebeta

← C7×D332 #44479209

Subgroups — C7×D332 #44479209

Order 30492.

296 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 52 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×C7×C11×D33C212yesmaximal, complemented
2C7×C3⋊(C3⋊(C11⋊D11))C211yesmaximal, characteristic, complemented
3C7×D11×D33—32nomaximal
4C32×C7×C112C2211yescharacteristic, complemented, Hall
5C7×C3⋊(C11⋊D11)—32no—
6C7×C3⋊(C11⋊D11)—61no—
7C7×C11×D33D312yescomplemented
8C3×C7×C11×D11—32no—
9D332C711yesmaximal, characteristic, direct product factor, Hall
10C7×D112—91noHall
11D3×C7×D33—112nomaximal
12C3×C7×C112—21no—
13C3×C7×C112C2×D312yescomplemented
14C3⋊(C3⋊(C11⋊D11))C2×C711yescharacteristic, complemented
15C3×C11×D33C2×C712yescomplemented
16C7×C11⋊D11—91no—
17C7×C11×D11—32no—
18D11×D33—32no—
19C7×C3⋊D33—112no—
20C7×C3⋊D33—225no—
21C3×C7×D33D1112yescomplemented
22C3×D3×C7×C11—112no—
23C32×C112C22×C711yescharacteristic, complemented, Hall
24C2×C7×D33—332no—
25D3×C7×D11—332no—
26C7×C112D3211yescharacteristic, complemented, Hall
27C3⋊(C11⋊D11)—32no—
28C3⋊(C11⋊D11)—61no—
29C11×D33D3×C712yescomplemented
30C3×C11×D11—32no—
31C32×C7×C11—25no—
32C32×C7×C11C2×D1112yescomplemented
33D112—91noHall
34C2×C3×C7×C11—332no—
35C7×D33—332no—
36C7×D33—332no—
37C7×D33—662no—
38C7×D33—6610no—
39C7×D33—6610no—
40C7×D33D3312yesdirect product factor
41D3×C7×C11—112no—
42C3×C7×D11—32no—
43D3×D33—112no—
44C3×C112—21no—
45C3×C112C2×D3×C712yescomplemented
46C2×C7×D11—992no—
47D32×C7—1211noHall
48C11⋊D11—91no—
49C11×D11—32no—
50C3×C7×C11—210no—
51C3×C7×C11—22no—
52C3×C7×C11—210no—
53C3×C7×C11D3×D1112yescomplemented
54C3×C7×C11C2×D3312yescomplemented
55C3⋊D33—112no—
56C3⋊D33—225no—
57C3×D33C7×D1112yescomplemented
58C3×D3×C11—112no—
59C2×C7×C11—332no—
60C7×D11—32no—
61C7×D11—992no—
62C7×D11—1985no—
63C2×D33—332no—
64D3×D11—332no—
65C7×C3⋊D3—1211no—
66C3×D3×C7—112no—
67C112D32×C711yescharacteristic, complemented, Sylow
68C32×C11—25no—
69C32×C11C2×C7×D1112yescomplemented
70C2×D3×C7—3632no—
71C7×C11—25no—
72C7×C11D3×D3312yescomplemented
73C2×C3×C11—332no—
74D33—332no—
75D33—332no—
76D33—6610no—
77D33—662no—
78D33—6610no—
79D33C7×D3312yesdirect product factor
80C3×D11—32no—
81D3×C11—112no—
82C32×C7D11211yescharacteristic, complemented, Hall
83C2×D11—992no—
84C2×C3×C7—332no—
85D3×C7—112no—
86D3×C7—3632no—
87D3×C7—7261no—
88D32—1211noHall
89C3×C11—210no—
90C3×C11—22no—
91C3×C11—210no—
92C3×C11D3×C7×D1112yescomplemented
93C3×C11C2×C7×D3312yescomplemented
94C22×C7—10891noHall
95C2×C11—332no—
96D11—32no—
97D11—992no—
98D11—1985no—
99C3×C7—21no—
100C3×C7D11×D3312yescomplemented
101C3⋊D3—1211no—
102C3×D3—112no—
103C2×C7—332no—
104C2×C7—10891no—
105C2×D3—3632no—
106C11—25no—
107C11D3×C7×D3312yescomplemented
108C32C7×D11211yescharacteristic, complemented, Sylow
109C7D33211yescharacteristic, direct product factor, Sylow
110C2×C3—332no—
111D3—112no—
112D3—3632no—
113D3—7261no—
114C22—10891noSylow
115C3—21no—
116C3C7×D11×D3312yescomplemented
117C2—332no—
118C2—10891no—
subgroupG/H
center, hypercenterC7D332
commutator, cosocle, hypocenterC32×C112C22×C7
FrattiniC1G
Fitting, socleC32×C7×C112C22
LCSG ▷ C32×C112
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C3×C7×C11×D33C2semidirect
2. C7×C3⋊(C3⋊(C11⋊D11))C2semidirect
4. C32×C7×C112C22semidirect
7. C7×C11×D33D3semidirect
9. D332C7direct (N × H)
13. C3×C7×C112C2×D3semidirect
14. C3⋊(C3⋊(C11⋊D11))C2×C7semidirect
15. C3×C11×D33C2×C7semidirect
21. C3×C7×D33D11semidirect
23. C32×C112C22×C7semidirect
26. C7×C112D32semidirect
29. C11×D33D3×C7semidirect
32. C32×C7×C11C2×D11semidirect
40. C7×D33D33direct (N × H)
45. C3×C112C2×D3×C7semidirect
53. C3×C7×C11D3×D11semidirect
54. C3×C7×C11C2×D33semidirect
57. C3×D33C7×D11semidirect
67. C112D32×C7semidirect
69. C32×C11C2×C7×D11semidirect
72. C7×C11D3×D33semidirect
79. D33C7×D33direct (N × H)
82. C32×C7D112semidirect
92. C3×C11D3×C7×D11semidirect
93. C3×C11C2×C7×D33semidirect
100. C3×C7D11×D33semidirect
107. C11D3×C7×D33semidirect
108. C32C7×D112semidirect
109. C7D332direct (N × H)
116. C3C7×D11×D33semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C11×D332
C7×C3⋊(C3⋊(C11⋊D11))2
C7×D11×D333
D3327
D3×C7×D3311