Finite Group Databasebeta

← C2×C11×D693 #44478985

Subgroups — C2×C11×D693 #44478985

Order 30492.

180 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 54 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
1C11×D693C212yesmaximal, direct product factor
2C2×C7×C9×C112C211yesmaximal, characteristic, complemented
3C2×C11×D231—31nomaximal
4C7×C9×C112C2211yescharacteristic, complemented, Hall
5C11×D231—32no—
6C2×C3×C7×C112D311yescharacteristic
7C2×C11×D99—71nomaximal, Hall
8C2×C11×D77—91noHall
9C2×D693C1111yesmaximal, characteristic, direct product factor
10C2×C11×D63—111nomaximal
11C3×C7×C112C2×D311yescharacteristic
12C11×D99—72no—
13C2×C9×C112D711yescharacteristic, complemented
14C2×C7×C112D911yescharacteristic, complemented
15C11×D77—92no—
16C2×C11×D33—211no—
17C2×C7×C9×C11—25no—
18C2×C7×C9×C11D1111yescharacteristic, complemented
19C2×C7×C9×C11C2×C1111yescharacteristic, complemented
20D693C2×C1112yesdirect product factor
21C11×D63—112no—
22C9×C112C2×D711yescharacteristic, complemented, Hall
23C2×D231—31no—
24C2×C11×D21—331no—
25C7×C112C2×D911yescharacteristic, complemented, Hall
26C2×C3×C112D2111yescharacteristic
27C11×D33—212no—
28C7×C9×C11—25no—
29C7×C9×C11C2×D1111yescharacteristic, complemented
30C7×C9×C11C22×C1111yescharacteristic, complemented
31C2×C11×D11—631noHall
32C2×C3×C7×C11—25no—
33C2×C3×C7×C11D3×C1111yescharacteristic
34C2×C3×C7×C11D3311yescharacteristic
35D231—32no—
36C11×D21—332no—
37C2×D99—71no—
38C2×C11×D9—771no—
39C3×C112C2×D2111yescharacteristic
40C2×D77—91no—
41C2×C11×D7—991no—
42C2×D63—111noHall
43C2×C112D6311yescharacteristic, complemented
44C11×D11—632no—
45C3×C7×C11—25no—
46C3×C7×C11C2×D3×C1111yescharacteristic
47C3×C7×C11C2×D3311yescharacteristic
48C2×C9×C11—25no—
49C2×C9×C11C11×D711yescharacteristic, complemented
50C2×C9×C11D7711yescharacteristic, complemented
51D99—72no—
52C11×D9—772no—
53C2×C7×C11—25no—
54C2×C7×C11C11×D911yescharacteristic, complemented
55C2×C7×C11D9911yescharacteristic, complemented
56D77—92no—
57C11×D7—992no—
58C2×D33—211no—
59C2×D3×C11—2311no—
60C2×C7×C9C11×D1111yescharacteristic, complemented
61D63—112no—
62C112C2×D6311yescharacteristic, complemented, Sylow
63C9×C11—25no—
64C9×C11C2×C11×D711yescharacteristic, complemented
65C9×C11C2×D7711yescharacteristic, complemented
66C2×D21—331no—
67C7×C11—25no—
68C7×C11C2×C11×D911yescharacteristic, complemented
69C7×C11C2×D9911yescharacteristic, complemented
70C2×C3×C11—25no—
71C2×C3×C11C11×D2111yescharacteristic
72C2×C3×C11D23111yescharacteristic
73D33—212no—
74D3×C11—2312no—
75C7×C9C2×C11×D1111yescharacteristic, complemented, Hall
76C22×C11—6931no—
77C2×D11—631no—
78C2×C3×C7C11×D3311yescharacteristic
79D21—332no—
80C2×D9—771noHall
81C3×C11—25no—
82C3×C11C2×C11×D2111yescharacteristic
83C3×C11C2×D23111yescharacteristic
84C2×D7—991noHall
85C2×C11—25no—
86C2×C11—6932no—
87C2×C11C11×D6311yescharacteristic, complemented
88C2×C11D69311yescharacteristic, direct product factor
89D11—632no—
90C3×C7C2×C11×D3311yescharacteristic
91C2×C9C11×D7711yescharacteristic, complemented
92D9—772no—
93C2×C7C11×D9911yescharacteristic, complemented
94D7—992no—
95C2×D3—2311no—
96C11—25no—
97C11C2×C11×D6311yescharacteristic, complemented
98C11C2×D69311yescharacteristic, direct product factor
99C9C2×C11×D7711yescharacteristic, complemented, Sylow
100C7C2×C11×D9911yescharacteristic, complemented, Sylow
101C2×C3C11×D23111yescharacteristic
102D3—2312no—
103C22—6931noSylow
104C3C2×C11×D23111yescharacteristic
105C2—6932no—
106C2C11×D69311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C11D693
commutator, cosocle, hypocenterC7×C9×C11C22×C11
FrattiniC3C2×C11×D231
FittingC2×C7×C9×C112C2
socleC2×C3×C7×C112D3
LCSG ▷ C7×C9×C11
UCSC1 ◁ C2×C11

Complements

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

NH ≅ G/Ntype
1. C11×D693C2direct (N × H)
2. C2×C7×C9×C112C2semidirect
4. C7×C9×C112C22semidirect
9. C2×D693C11direct (N × H)
13. C2×C9×C112D7semidirect
14. C2×C7×C112D9semidirect
18. C2×C7×C9×C11D11semidirect
19. C2×C7×C9×C11C2×C11semidirect
20. D693C2×C11direct (N × H)
22. C9×C112C2×D7semidirect
25. C7×C112C2×D9semidirect
29. C7×C9×C11C2×D11semidirect
30. C7×C9×C11C22×C11semidirect
43. C2×C112D63semidirect
49. C2×C9×C11C11×D7semidirect
50. C2×C9×C11D77semidirect
54. C2×C7×C11C11×D9semidirect
55. C2×C7×C11D99semidirect
60. C2×C7×C9C11×D11semidirect
62. C112C2×D63semidirect
64. C9×C11C2×C11×D7semidirect
65. C9×C11C2×D77semidirect
68. C7×C11C2×C11×D9semidirect
69. C7×C11C2×D99semidirect
75. C7×C9C2×C11×D11semidirect
87. C2×C11C11×D63semidirect
88. C2×C11D693direct (N × H)
91. C2×C9C11×D77semidirect
93. C2×C7C11×D99semidirect
97. C11C2×C11×D63semidirect
98. C11C2×D693direct (N × H)
99. C9C2×C11×D77semidirect
100. C7C2×C11×D99semidirect
106. C2C11×D693direct (N × H)

Maximal subgroups

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

subgroupindex
C11×D6932
C2×C7×C9×C1122
C2×C11×D2313
C2×C11×D997
C2×D69311
C2×C11×D6311