Finite Group Databasebeta

← D3×C7⋊(C7⋊AGL(1,𝔽11)) #44568608

Subgroups — D3×C7⋊(C7⋊AGL(1,𝔽11)) #44568608

Order 32340.

400 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 98 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⋊(C7⋊AGL(1,𝔽11)))C211yesmaximal, characteristic, complemented
2D3×C72×C11⋊C5C211yesmaximal, characteristic, complemented
3C3×C7⋊(C7⋊AGL(1,𝔽11))C211yesmaximal, characteristic, complemented
4C2×C7⋊(C7⋊AGL(1,𝔽11))—31nomaximal, Hall
5C3×C72×C11⋊C5C2211yescharacteristic, complemented, Hall
6D3×C7⋊D77C511yesmaximal, characteristic, complemented, Hall
7C2×C72×C11⋊C5—31no—
8C7⋊(C7⋊AGL(1,𝔽11))—31no—
9C7⋊(C7⋊AGL(1,𝔽11))D311yescharacteristic, direct product factor
10D3×C7⋊AGL(1,𝔽11)—78nomaximal
11C3⋊(C7⋊D77)C2×C511yescharacteristic, complemented
12D3×C72×C11C2×C511yescharacteristic, complemented
13C3×C7⋊D77C2×C511yescharacteristic, complemented
14C5×D3×C7⋊D7—111nomaximal, Hall
15C72×C11⋊C5C2×D311yescharacteristic, complemented, Hall
16C3⋊(C7⋊AGL(1,𝔽11))—78no—
17D3×C7×C11⋊C5D718yescomplemented
18C3×C7⋊AGL(1,𝔽11)—78no—
19C2×C7⋊D77—31noHall
20C3×C72×C11C22×C511yescharacteristic, complemented, Hall
21C2×C7⋊AGL(1,𝔽11)—218no—
22C5×C3⋊(C7⋊D7)—111no—
23C5×D3×C72—111no—
24C3×C5×C7⋊D7—111no—
25C3×C7×C11⋊C5C2×D718yescomplemented
26C2×C72×C11—31no—
27C7⋊D77—31no—
28C7⋊D77C5×D311yescharacteristic, complemented
29C2×C5×C7⋊D7—331noHall
30D3×D77—78no—
31C2×C7×C11⋊C5—38no—
32C7⋊AGL(1,𝔽11)—78no—
33C7⋊AGL(1,𝔽11)—218no—
34C3×C5×C72—111noHall
35D3×AGL(1,𝔽11)—491noHall
36D3×C7⋊D7—111noHall
37C72×C11C2×C5×D311yescharacteristic, complemented, Hall
38C2×C5×C72—331no—
39C5×C7⋊D7—111no—
40C5×C7⋊D7—331no—
41D231—78no—
42D3×C7×C11C5×D718yescomplemented
43C3×D77—78no—
44C5×D3×D7—778no—
45C7×C11⋊C5D3×D718yescomplemented
46C3⋊AGL(1,𝔽11)—491no—
47D3×C11⋊C5C7⋊D711yescharacteristic, complemented
48C3×AGL(1,𝔽11)—491no—
49C2×D77—218no—
50C3⋊(C7⋊D7)—111no—
51D3×C72AGL(1,𝔽11)11yescharacteristic, complemented
52C3×C7⋊D7—111no—
53C5×C72—111noHall
54C3×C7×C11C2×C5×D718yescomplemented
55C2×AGL(1,𝔽11)—1471noHall
56C5×D21—778no—
57C5×D3×C7—118no—
58C3×C5×D7—778no—
59C2×C7⋊D7—331noHall
60C3×C11⋊C5C2×C7⋊D711yescharacteristic, complemented, Hall
61C2×C7×C11—38no—
62D77—78no—
63D77—218no—
64C3×C72C2×AGL(1,𝔽11)11yescharacteristic, complemented, Hall
65C2×C5×D7—2318no—
66D3×D11—491noHall
67C2×C11⋊C5—31no—
68AGL(1,𝔽11)—491no—
69AGL(1,𝔽11)—1471no—
70C3×C5×C7—118no—
71C2×C72—31no—
72C7⋊D7—111no—
73C7⋊D7—331no—
74D3×D7—778no—
75C7×C11C5×D3×D718yescomplemented
76C2×C5×C7—338no—
77C5×D7—778no—
78C5×D7—2318no—
79D33—491no—
80C3×D11—491no—
81D3×C11C5×C7⋊D711yescharacteristic, complemented
82C2×C5×D3—5391noHall
83C11⋊C5D3×C7⋊D711yescharacteristic, complemented, Hall
84C72D3×AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
85C2×D11—1471noHall
86D21—778no—
87C3×D7—778no—
88D3×C7C7⋊AGL(1,𝔽11)18yescomplemented
89C5×C7—118no—
90C3×C11C2×C5×C7⋊D711yescharacteristic, complemented, Hall
91C2×C3×C5—5391no—
92C5×D3—111no—
93C5×D3—5391no—
94C2×D7—2318no—
95C2×C11—31no—
96D11—491no—
97D11—1471no—
98C3×C7C2×C7⋊AGL(1,𝔽11)18yescomplemented
99C22×C5—16171noHall
100C3×C5—111noHall
101C2×C7—38no—
102D7—778no—
103D7—2318no—
104C2×D3—5391noHall
105C11C5×D3×C7⋊D711yescharacteristic, complemented, Sylow
106C2×C5—5391no—
107C2×C5—331no—
108C2×C5—16171no—
109C7D3×C7⋊AGL(1,𝔽11)18yescomplemented
110C2×C3—5391no—
111D3—5391no—
112D3C7⋊(C7⋊AGL(1,𝔽11))11yescharacteristic, direct product factor
113C5—111noSylow
114C22—16171noSylow
115C3C2×C7⋊(C7⋊AGL(1,𝔽11))11yescharacteristic, complemented, Sylow
116C2—31no—
117C2—5391no—
118C2—16171no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C72×C11C22×C5
LCSG ▷ C3×C72×C11
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(C7⋊(C7⋊AGL(1,𝔽11)))C2semidirect
2. D3×C72×C11⋊C5C2semidirect
3. C3×C7⋊(C7⋊AGL(1,𝔽11))C2semidirect
5. C3×C72×C11⋊C5C22semidirect
6. D3×C7⋊D77C5semidirect
9. C7⋊(C7⋊AGL(1,𝔽11))D3direct (N × H)
11. C3⋊(C7⋊D77)C2×C5semidirect
12. D3×C72×C11C2×C5semidirect
13. C3×C7⋊D77C2×C5semidirect
15. C72×C11⋊C5C2×D3semidirect
17. D3×C7×C11⋊C5D7semidirect
20. C3×C72×C11C22×C5semidirect
25. C3×C7×C11⋊C5C2×D7semidirect
28. C7⋊D77C5×D3semidirect
37. C72×C11C2×C5×D3semidirect
42. D3×C7×C11C5×D7semidirect
45. C7×C11⋊C5D3×D7semidirect
47. D3×C11⋊C5C7⋊D7semidirect
51. D3×C72AGL(1,𝔽11)semidirect
54. C3×C7×C11C2×C5×D7semidirect
60. C3×C11⋊C5C2×C7⋊D7semidirect
64. C3×C72C2×AGL(1,𝔽11)semidirect
75. C7×C11C5×D3×D7semidirect
81. D3×C11C5×C7⋊D7semidirect
83. C11⋊C5D3×C7⋊D7semidirect
84. C72D3×AGL(1,𝔽11)semidirect
88. D3×C7C7⋊AGL(1,𝔽11)semidirect
90. C3×C11C2×C5×C7⋊D7semidirect
98. C3×C7C2×C7⋊AGL(1,𝔽11)semidirect
105. C11C5×D3×C7⋊D7semidirect
109. C7D3×C7⋊AGL(1,𝔽11)semidirect
112. D3C7⋊(C7⋊AGL(1,𝔽11))direct (N × H)
115. C3C2×C7⋊(C7⋊AGL(1,𝔽11))semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C7⋊(C7⋊AGL(1,𝔽11)))2
D3×C72×C11⋊C52
C3×C7⋊(C7⋊AGL(1,𝔽11))2
C2×C7⋊(C7⋊AGL(1,𝔽11))3
D3×C7⋊D775
D3×C7⋊AGL(1,𝔽11)7
C5×D3×C7⋊D711