Finite Group Databasebeta

← D77⋊D99 #44478975

Subgroups — D77⋊D99 #44478975

Order 30492.

180 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 35 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×C9⋊(C11⋊D11)C211yesmaximal, characteristic, complemented
3C9×C11×D77C211yesmaximal, characteristic, complemented
4D77⋊D33—31nomaximal
5C7×C9×C112C2211yescharacteristic, complemented, Hall
6C11×D231—31no—
7C7×C3⋊(C11⋊D11)—31no—
8C3×C11×D77D311yescharacteristic
9D11×D99—71nomaximal, Hall
10D77⋊D11—91noHall
11D63⋊D11—111nomaximal
12D7×D99—111nomaximal
13C3×C7×C112C2×D311yescharacteristic
14C9⋊(C11⋊D11)D711yescharacteristic, complemented
15C11×D99—71no—
16C9×C11×D11—71no—
17C11×D77—91no—
18C11×D77D911yescharacteristic, complemented
19C7×C11⋊D11—91no—
20D11×D33—211no—
21D693D1111yescharacteristic, complemented
22C11×D63—111no—
23C7×D99—111no—
24C7×D99—111no—
25C7×D99—225no—
26C9×D77D1111yescharacteristic, complemented
27C9×C11×D7—111no—
28C9×C112C2×D711yescharacteristic, complemented, Hall
29D21⋊D11—331no—
30D7×D33—331no—
31C7×C112C2×D911yescharacteristic, complemented, Hall
32C3⋊(C11⋊D11)—31no—
33C11×D33—211no—
34C3×C11×D11—71no—
35C7×C9×C11—25no—
36C7×C9×C11C2×D1111yescharacteristic, complemented
37C7×C9×C11C2×D1111yescharacteristic, complemented
38D112—631noHall
39D231—31no—
40C11×D21—331no—
41C7×D33—331no—
42C7×D33—331no—
43C7×D33—665no—
44C3×D77D3311yescharacteristic
45C3×C11×D7—111no—
46C2×D99—771no—
47D9×D11—771no—
48C3×C112D3×D711yescharacteristic
49D7×D11—991no—
50D7×D11—991no—
51D7×D9—1211noHall
52C11⋊D11—91no—
53C11×D11—71no—
54C11×D11—631no—
55C3×C7×C11—25no—
56C3×C7×C11D3×D1111yescharacteristic
57C3×C7×C11C2×D3311yescharacteristic
58C2×C9×C11—771no—
59D99—71no—
60D99—111no—
61D99—111no—
62D99—225no—
63C9×D11—71no—
64C11×D9—771no—
65D77—91no—
66D77D9911yescharacteristic, complemented
67C7×D11—991no—
68C7×D11—991no—
69C7×D11—1985no—
70C11×D7—111no—
71C11×D7—991no—
72C2×D33—2311no—
73D3×D11—2311no—
74D63—111no—
75C9×D7—111no—
76C7×D9—1211no—
77C112D7×D911yescharacteristic, complemented, Sylow
78C9×C11—25no—
79C9×C11D7×D1111yescharacteristic, complemented
80C9×C11D7×D1111yescharacteristic, complemented
81D3×D7—3631no—
82C7×C11—25no—
83C7×C11D9×D1111yescharacteristic, complemented
84C7×C11C2×D9911yescharacteristic, complemented
85C2×C3×C11—771no—
86D33—211no—
87D33—331no—
88D33—331no—
89D33—665no—
90C3×D11—71no—
91D3×C11—2311no—
92C7×C9D11211yescharacteristic, complemented, Hall
93C2×D11—6931no—
94C2×D11—6931no—
95D21—331no—
96C3×D7—111no—
97D3×C7—3631no—
98C2×D9—8471noHall
99C3×C11—25no—
100C3×C11D7×D3311yescharacteristic
101C3×C11D21⋊D1111yescharacteristic
102C2×D7—10891noHall
103C2×C11—771no—
104C2×C11—6931no—
105D11—71no—
106D11—631no—
107D11—991no—
108D11—991no—
109D11—1985no—
110C3×C7D11×D3311yescharacteristic
111C2×C9—771no—
112D9—771no—
113D9—1211no—
114C2×C7—10891no—
115D7—111no—
116D7—991no—
117C2×D3—25411no—
118C11—25no—
119C11D7×D9911yescharacteristic, complemented
120C11D63⋊D1111yescharacteristic, complemented
121C9D77⋊D1111yescharacteristic, complemented, Sylow
122C7D11×D9911yescharacteristic, complemented, Sylow
123C2×C3—771no—
124D3—3631no—
125D3—2311no—
126C22—76231noSylow
127C3D77⋊D3311yescharacteristic
128C2—10891no—
129C2—771no—
130C2—6931no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC7×C9×C112C22
FrattiniC3D77⋊D33
socleC3×C7×C112C2×D3
LCSG ▷ C7×C9×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C11×D693C2semidirect
2. C7×C9⋊(C11⋊D11)C2semidirect
3. C9×C11×D77C2semidirect
5. C7×C9×C112C22semidirect
14. C9⋊(C11⋊D11)D7semidirect
18. C11×D77D9semidirect
21. D693D11semidirect
26. C9×D77D11semidirect
28. C9×C112C2×D7semidirect
31. C7×C112C2×D9semidirect
36. C7×C9×C11C2×D11semidirect
37. C7×C9×C11C2×D11semidirect
66. D77D99semidirect
77. C112D7×D9semidirect
79. C9×C11D7×D11semidirect
80. C9×C11D7×D11semidirect
83. C7×C11D9×D11semidirect
84. C7×C11C2×D99semidirect
92. C7×C9D112semidirect
119. C11D7×D99semidirect
120. C11D63⋊D11semidirect
121. C9D77⋊D11semidirect
122. C7D11×D99semidirect

Maximal subgroups

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

subgroupindex
C11×D6932
C7×C9⋊(C11⋊D11)2
C9×C11×D772
D77⋊D333
D11×D997
D63⋊D1111
D7×D9911