Finite Group Databasebeta

← C2×C11×(C7⋊C9)⋊D7 #34084692

Subgroups — C2×C11×(C7⋊C9)⋊D7 #34084692

Order 19404.

160 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 58 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
1C2×C7×C11×C7⋊C9C211yesmaximal, characteristic, complemented
2C11×(C7⋊C9)⋊D7C212yesmaximal, direct product factor
3C2×C3×C11×C7⋊D7C311yesmaximal, characteristic
4C7×C11×C7⋊C9C2211yescharacteristic, complemented, Hall
5C3×C11×C7⋊D7C2×C312yes—
6C2×C3×C72×C11C2×C311yescharacteristic
7C2×C9×C11×D7—71nomaximal
8C2×C11×D7⋊C9—71nomaximal
9C2×C11×C7⋊D7C911yescharacteristic, complemented, Hall
10C2×(C7⋊C9)⋊D7C1111yesmaximal, characteristic, direct product factor, Hall
11C3×C72×C11C22×C311yescharacteristic
12C2×C7×C9×C11—71no—
13C9×C11×D7—72no—
14C2×C11×C7⋊C9D711yescharacteristic, complemented
15C11×D7⋊C9—72no—
16C2×C72×C11C2×C911yescharacteristic, complemented
17C11×C7⋊D7C2×C912yescomplemented
18C2×C3×C11×D7—71no—
19C2×C3×C11×D7—71no—
20C2×C3×C11×D7—212no—
21C2×C7×C7⋊C9C2×C1111yescharacteristic, complemented
22(C7⋊C9)⋊D7C2×C1112yesdirect product factor
23C7×C9×C11—71no—
24C11×C7⋊C9C2×D711yescharacteristic, complemented
25C2×C3×C7⋊D7C3×C1111yescharacteristic
26C72×C11C22×C911yescharacteristic, complemented, Hall
27C2×C3×C7×C11—32no—
28C2×C3×C7×C11AGL(1,𝔽7)11yescharacteristic
29C2×C3×C7×C11C3×D711yescharacteristic
30C3×C11×D7—72no—
31C3×C11×D7—72no—
32C3×C11×D7—214no—
33C7×C7⋊C9C22×C1111yescharacteristic, complemented, Hall
34C22×C9×C11—491noHall
35C2×C11×D7—71no—
36C2×C11×D7—71no—
37C2×C11×D7—212no—
38C2×C3×C72C2×C3×C1111yescharacteristic
39C3×C7⋊D7C2×C3×C1112yes—
40C2×C9×D7—71no—
41C2×D7⋊C9—71no—
42C3×C7×C11—32no—
43C3×C7×C11C2×AGL(1,𝔽7)11yescharacteristic
44C3×C7×C11C2×C3×D711yescharacteristic
45C2×C9×C11—71no—
46C2×C9×C11—492no—
47C2×C7⋊D7C9×C1111yescharacteristic, complemented, Hall
48C2×C7×C11—32no—
49C2×C7×C11D7⋊C911yescharacteristic, complemented
50C2×C7×C11C9×D711yescharacteristic, complemented
51C11×D7—72no—
52C11×D7—72no—
53C11×D7—214no—
54C3×C72C22×C3×C1111yescharacteristic
55C22×C3×C11—491no—
56C2×C7×C9—71no—
57C9×D7—72no—
58C2×C7⋊C9C11×D711yescharacteristic, complemented
59D7⋊C9—72no—
60C9×C11—71noHall
61C2×C72C2×C9×C1111yescharacteristic, complemented
62C7⋊D7C2×C9×C1112yescomplemented
63C2×C3×D7—71no—
64C2×C3×D7—71no—
65C2×C3×D7—212no—
66C7×C11—32no—
67C7×C11C2×D7⋊C911yescharacteristic, complemented
68C7×C11C2×C9×D711yescharacteristic, complemented
69C2×C3×C11—492no—
70C2×C3×C11ΓL(1,𝔽8)⋊D711yescharacteristic
71C7×C9—71no—
72C7⋊C9C2×C11×D711yescharacteristic, complemented
73C72C22×C9×C1111yescharacteristic, complemented, Sylow
74C22×C11—491noHall
75C2×C3×C7—32no—
76C2×C3×C7C11×AGL(1,𝔽7)11yescharacteristic
77C2×C3×C7C3×C11×D711yescharacteristic
78C3×D7—72no—
79C3×D7—72no—
80C3×D7—214no—
81C22×C9—491noHall
82C3×C11C2×ΓL(1,𝔽8)⋊D711yescharacteristic
83C2×D7—71no—
84C2×D7—71no—
85C2×D7—212no—
86C2×C11—492no—
87C2×C11(C7⋊C9)⋊D711yescharacteristic, direct product factor
88C3×C7—32no—
89C3×C7C2×C11×AGL(1,𝔽7)11yescharacteristic
90C3×C7C2×C3×C11×D711yescharacteristic
91C2×C9—71no—
92C2×C9—492no—
93C2×C7—32no—
94C2×C7C11×D7⋊C911yescharacteristic, complemented
95C2×C7C9×C11×D711yescharacteristic, complemented
96D7—72no—
97D7—72no—
98D7—214no—
99C22×C3—491no—
100C11C2×(C7⋊C9)⋊D711yescharacteristic, direct product factor, Sylow
101C9—71noSylow
102C7—32no—
103C7C2×C11×D7⋊C911yescharacteristic, complemented
104C7C2×C9×C11×D711yescharacteristic, complemented
105C2×C3—492no—
106C2×C3C11×ΓL(1,𝔽8)⋊D711yescharacteristic
107C22—491noSylow
108C3C2×C11×ΓL(1,𝔽8)⋊D711yescharacteristic
109C2—492no—
110C2C11×(C7⋊C9)⋊D711yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C11ΓL(1,𝔽8)⋊D7
commutator, hypocenterC72C22×C9×C11
FrattiniC3C2×C11×ΓL(1,𝔽8)⋊D7
Fitting, socleC2×C3×C72×C11C2×C3
prime radicalC2×C3×C11×C7⋊D7C3
cosocleC3×C72C22×C3×C11
LCSG ▷ C72
UCSC1 ◁ C2×C3×C11

Complements

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

NH ≅ G/Ntype
1. C2×C7×C11×C7⋊C9C2semidirect
2. C11×(C7⋊C9)⋊D7C2direct (N × H)
4. C7×C11×C7⋊C9C22semidirect
9. C2×C11×C7⋊D7C9semidirect
10. C2×(C7⋊C9)⋊D7C11direct (N × H)
14. C2×C11×C7⋊C9D7semidirect
16. C2×C72×C11C2×C9semidirect
17. C11×C7⋊D7C2×C9semidirect
21. C2×C7×C7⋊C9C2×C11semidirect
22. (C7⋊C9)⋊D7C2×C11direct (N × H)
24. C11×C7⋊C9C2×D7semidirect
26. C72×C11C22×C9semidirect
33. C7×C7⋊C9C22×C11semidirect
47. C2×C7⋊D7C9×C11semidirect
49. C2×C7×C11D7⋊C9semidirect
50. C2×C7×C11C9×D7semidirect
58. C2×C7⋊C9C11×D7semidirect
61. C2×C72C2×C9×C11semidirect
62. C7⋊D7C2×C9×C11semidirect
67. C7×C11C2×D7⋊C9semidirect
68. C7×C11C2×C9×D7semidirect
72. C7⋊C9C2×C11×D7semidirect
73. C72C22×C9×C11semidirect
87. C2×C11(C7⋊C9)⋊D7direct (N × H)
94. C2×C7C11×D7⋊C9semidirect
95. C2×C7C9×C11×D7semidirect
100. C11C2×(C7⋊C9)⋊D7direct (N × H)
103. C7C2×C11×D7⋊C9semidirect
104. C7C2×C9×C11×D7semidirect
110. C2C11×(C7⋊C9)⋊D7direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×C11×C7⋊C92
C11×(C7⋊C9)⋊D72
C2×C3×C11×C7⋊D73
C2×C9×C11×D77
C2×C11×D7⋊C97
C2×(C7⋊C9)⋊D711