Finite Group Databasebeta

← C11×D7×D99 #44478968

Subgroups — C11×D7×D99 #44478968

Order 30492.

180 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 44 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×D693C211yesmaximal, characteristic, complemented
2C7×C11×D99C211yesmaximal, characteristic, complemented
3C9×C112×D7C211yesmaximal, characteristic, complemented
4C11×D7×D33—31nomaximal
5C7×C9×C112C2211yescharacteristic, complemented, Hall
6C11×D231—31no—
7C7×C11×D33—31no—
8C3×C112×D7D311yescharacteristic
9C2×C11×D99—71nomaximal, Hall
10C11×D7×D11—91noHall
11D7×D99C1111yesmaximal, characteristic, direct product factor
12C11×D7×D9—111nomaximal
13C3×C7×C112C2×D311yescharacteristic
14C11×D99—71no—
15C11×D99D711yescharacteristic, direct product factor
16C2×C9×C112—71no—
17C11×D77—91no—
18C112×D7D911yescharacteristic, complemented
19C7×C11×D11—91no—
20C2×C11×D33—211no—
21D693C2×C1111yescharacteristic, complemented
22C11×D63—111no—
23C7×D99C2×C1111yescharacteristic, complemented
24C7×C11×D9—111no—
25C9×C11×D7—25no—
26C9×C11×D7D1111yescharacteristic, complemented
27C9×C11×D7C2×C1111yescharacteristic, complemented
28C9×C112C2×D711yescharacteristic, complemented, Hall
29D7×D33—31no—
30D3×C11×D7—331no—
31C7×C112C2×D911yescharacteristic, complemented, Hall
32C2×C3×C112—71no—
33C11×D33—31no—
34C11×D33—211no—
35C7×C9×C11—25no—
36C7×C9×C11C2×D1111yescharacteristic, complemented
37C7×C9×C11C22×C1111yescharacteristic, complemented
38C2×C11×D11—631noHall
39D231—31no—
40C11×D21—331no—
41C7×D33—31no—
42D3×C7×C11—331no—
43C3×C11×D7—25no—
44C3×C11×D7D3×C1111yescharacteristic
45C3×C11×D7D3311yescharacteristic
46C2×D99—71no—
47C2×C11×D9—771no—
48C3×C112D3×D711yescharacteristic
49C2×C11×D7—991no—
50D7×D11—91no—
51D7×D9—111noHall
52C2×C112—71no—
53C11×D11—91no—
54C11×D11—631no—
55C3×C7×C11—25no—
56C3×C7×C11C2×D3×C1111yescharacteristic
57C3×C7×C11C2×D3311yescharacteristic
58C2×C9×C11—71no—
59C2×C9×C11—71no—
60C2×C9×C11—145no—
61D99—71no—
62D99C11×D711yescharacteristic, direct product factor
63C11×D9—111no—
64C11×D9—771no—
65C2×C7×C11—991no—
66D77—91no—
67C7×D11—91no—
68C11×D7—25no—
69C11×D7—991no—
70C11×D7C11×D911yescharacteristic, complemented
71C11×D7D9911yescharacteristic, direct product factor
72C2×D33—211no—
73C2×D3×C11—2311no—
74D63—111no—
75C9×D7C11×D1111yescharacteristic, complemented
76C7×D9—111no—
77C112D7×D911yescharacteristic, complemented, Sylow
78C9×C11—25no—
79C9×C11D7×D1111yescharacteristic, complemented
80C9×C11C2×C11×D711yescharacteristic, complemented
81D3×D7—331no—
82C7×C11—25no—
83C7×C11C2×C11×D911yescharacteristic, complemented
84C7×C11C2×D9911yescharacteristic, complemented
85C2×C3×C11—71no—
86C2×C3×C11—71no—
87C2×C3×C11—145no—
88D33—31no—
89D33—211no—
90D3×C11—331no—
91D3×C11—2311no—
92C7×C9C2×C11×D1111yescharacteristic, complemented, Hall
93C22×C11—6931no—
94C2×D11—631no—
95D21—331no—
96C3×D7C11×D3311yescharacteristic
97D3×C7—331no—
98C2×D9—771noHall
99C3×C11—25no—
100C3×C11D3×C11×D711yescharacteristic
101C3×C11D7×D3311yescharacteristic
102C2×D7—991noHall
103C2×C11—71no—
104C2×C11—71no—
105C2×C11—145no—
106C2×C11—991no—
107C2×C11—6931no—
108D11—91no—
109D11—631no—
110C3×C7C2×C11×D3311yescharacteristic
111C2×C9—71no—
112D9—111no—
113D9—771no—
114C2×C7—991no—
115D7—991no—
116D7C11×D9911yescharacteristic, direct product factor
117C2×D3—2311no—
118C11—25no—
119C11C11×D7×D911yescharacteristic, complemented
120C11D7×D9911yescharacteristic, direct product factor
121C9C11×D7×D1111yescharacteristic, complemented, Sylow
122C7C2×C11×D9911yescharacteristic, complemented, Sylow
123C2×C3—71no—
124D3—331no—
125D3—2311no—
126C22—6931noSylow
127C3C11×D7×D3311yescharacteristic
128C2—71no—
129C2—991no—
130C2—6931no—
subgroupG/H
center, hypercenterC11D7×D99
commutator, cosocle, hypocenterC7×C9×C11C22×C11
FrattiniC3C11×D7×D33
FittingC7×C9×C112C22
socleC3×C7×C112C2×D3
LCSG ▷ C7×C9×C11
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C11×D693C2semidirect
2. C7×C11×D99C2semidirect
3. C9×C112×D7C2semidirect
5. C7×C9×C112C22semidirect
11. D7×D99C11direct (N × H)
15. C11×D99D7direct (N × H)
18. C112×D7D9semidirect
21. D693C2×C11semidirect
23. C7×D99C2×C11semidirect
26. C9×C11×D7D11semidirect
27. C9×C11×D7C2×C11semidirect
28. C9×C112C2×D7semidirect
31. C7×C112C2×D9semidirect
36. C7×C9×C11C2×D11semidirect
37. C7×C9×C11C22×C11semidirect
62. D99C11×D7direct (N × H)
70. C11×D7C11×D9semidirect
71. C11×D7D99direct (N × H)
75. C9×D7C11×D11semidirect
77. C112D7×D9semidirect
79. C9×C11D7×D11semidirect
80. C9×C11C2×C11×D7semidirect
83. C7×C11C2×C11×D9semidirect
84. C7×C11C2×D99semidirect
92. C7×C9C2×C11×D11semidirect
116. D7C11×D99direct (N × H)
119. C11C11×D7×D9semidirect
120. C11D7×D99direct (N × H)
121. C9C11×D7×D11semidirect
122. C7C2×C11×D99semidirect

Maximal subgroups

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

subgroupindex
C11×D6932
C7×C11×D992
C9×C112×D72
C11×D7×D333
C2×C11×D997
D7×D9911
C11×D7×D911