Finite Group Databasebeta

← D11×D693 #44478964

Subgroups — D11×D693 #44478964

Order 30492.

180 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 40 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
1C7⋊(C9⋊(C11⋊D11))C211yesmaximal, characteristic, complemented
2C11×D693C211yesmaximal, characteristic, complemented
3C7×C9×C11×D11C211yesmaximal, characteristic, complemented
4D11×D231—31nomaximal
5C7×C9×C112C2211yescharacteristic, complemented, Hall
6C3⋊(C7⋊(C11⋊D11))—31no—
7C11×D231—31no—
8C3×C7×C11×D11D311yescharacteristic
9D11×D99—71nomaximal, Hall
10D11×D77—91noHall
11C2×D693—111nomaximal
12D11×D63—111nomaximal
13C3×C7×C112C2×D311yescharacteristic
14C9⋊(C11⋊D11)—71no—
15C11×D99—71no—
16C9×C11×D11D711yescharacteristic, complemented
17C7⋊(C11⋊D11)—91no—
18C11×D77—91no—
19C7×C11×D11D911yescharacteristic, complemented
20D11×D33—211no—
21C2×C7×C9×C11—111no—
22D693—111no—
23D693—111no—
24D693—225no—
25D693D1111yescharacteristic, direct product factor
26C11×D63—111no—
27C7×C9×D11D1111yescharacteristic, complemented
28C9×C112C2×D711yescharacteristic, complemented, Hall
29C2×D231—331no—
30D11×D21—331no—
31C7×C112C2×D911yescharacteristic, complemented, Hall
32C3⋊(C11⋊D11)—211no—
33C11×D33—211no—
34C3×C11×D11D2111yescharacteristic
35C7×C9×C11—25no—
36C7×C9×C11C2×D1111yescharacteristic, complemented
37C7×C9×C11C2×D1111yescharacteristic, complemented
38D112—631noHall
39C2×C3×C7×C11—111no—
40D231—31no—
41D231—331no—
42D231—331no—
43D231—665no—
44C11×D21—331no—
45C3×C7×D11D3311yescharacteristic
46C2×D99—771no—
47D9×D11—771no—
48C3×C112C2×D2111yescharacteristic
49C2×D77—991no—
50D7×D11—991no—
51C2×D63—1211noHall
52C11⋊D11—631no—
53C11×D11—631no—
54C11×D11D6311yescharacteristic, complemented
55C3×C7×C11—25no—
56C3×C7×C11D3×D1111yescharacteristic
57C3×C7×C11C2×D3311yescharacteristic
58C2×C9×C11—111no—
59D99—71no—
60D99—771no—
61D99—771no—
62D99—1545no—
63C9×D11D7711yescharacteristic, complemented
64C11×D9—771no—
65C2×C7×C11—111no—
66D77—91no—
67D77—991no—
68D77—991no—
69D77—1985no—
70C7×D11D9911yescharacteristic, complemented
71C11×D7—991no—
72C2×D33—2311no—
73D3×D11—2311no—
74C2×C7×C9—111no—
75D63—111no—
76D63—1211no—
77C112C2×D6311yescharacteristic, complemented, Sylow
78C9×C11—25no—
79C9×C11D7×D1111yescharacteristic, complemented
80C9×C11C2×D7711yescharacteristic, complemented
81C2×D21—3631no—
82C7×C11—25no—
83C7×C11D9×D1111yescharacteristic, complemented
84C7×C11C2×D9911yescharacteristic, complemented
85C2×C3×C11—111no—
86D33—211no—
87D33—4625no—
88D33—2311no—
89D33—2311no—
90C3×D11D23111yescharacteristic
91D3×C11—2311no—
92C7×C9D11211yescharacteristic, complemented, Hall
93C2×D11—6931no—
94C2×D11—6931no—
95C2×C3×C7—111no—
96D21—331no—
97D21—3631no—
98C2×D9—8471noHall
99C3×C11—25no—
100C3×C11D11×D2111yescharacteristic
101C3×C11C2×D23111yescharacteristic
102C2×D7—10891noHall
103C2×C11—111no—
104C2×C11—6931no—
105D11—631no—
106D11—13865no—
107D11—6931no—
108D11—6931no—
109D11D69311yescharacteristic, direct product factor
110C3×C7D11×D3311yescharacteristic
111C2×C9—111no—
112D9—771no—
113D9—8471no—
114C2×C7—111no—
115D7—10891no—
116D7—991no—
117C2×D3—25411no—
118C11—25no—
119C11D11×D6311yescharacteristic, complemented
120C11C2×D69311yescharacteristic, complemented
121C9D11×D7711yescharacteristic, complemented, Sylow
122C7D11×D9911yescharacteristic, complemented, Sylow
123C2×C3—111no—
124D3—2311no—
125D3—25411no—
126C22—76231noSylow
127C3D11×D23111yescharacteristic
128C2—111no—
129C2—6931no—
130C2—76231no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC7×C9×C112C22
FrattiniC3D11×D231
socleC3×C7×C112C2×D3
LCSG ▷ C7×C9×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C7⋊(C9⋊(C11⋊D11))C2semidirect
2. C11×D693C2semidirect
3. C7×C9×C11×D11C2semidirect
5. C7×C9×C112C22semidirect
16. C9×C11×D11D7semidirect
19. C7×C11×D11D9semidirect
25. D693D11direct (N × H)
27. C7×C9×D11D11semidirect
28. C9×C112C2×D7semidirect
31. C7×C112C2×D9semidirect
36. C7×C9×C11C2×D11semidirect
37. C7×C9×C11C2×D11semidirect
54. C11×D11D63semidirect
63. C9×D11D77semidirect
70. C7×D11D99semidirect
77. C112C2×D63semidirect
79. C9×C11D7×D11semidirect
80. C9×C11C2×D77semidirect
83. C7×C11D9×D11semidirect
84. C7×C11C2×D99semidirect
92. C7×C9D112semidirect
109. D11D693direct (N × H)
119. C11D11×D63semidirect
120. C11C2×D693semidirect
121. C9D11×D77semidirect
122. C7D11×D99semidirect

Maximal subgroups

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

subgroupindex
C7⋊(C9⋊(C11⋊D11))2
C11×D6932
C7×C9×C11×D112
D11×D2313
D11×D997
C2×D69311
D11×D6311