Finite Group Databasebeta

← C9×D11×D77 #44478954

Subgroups — C9×D11×D77 #44478954

Order 30492.

180 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 48 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
1C9×C7⋊(C11⋊D11)C211yesmaximal, characteristic, complemented
2C9×C11×D77C211yesmaximal, characteristic, complemented
3C7×C9×C11×D11C211yesmaximal, characteristic, complemented
4C3×D11×D77C311yesmaximal, characteristic
5C7×C9×C112C2211yescharacteristic, complemented, Hall
6C3×C7⋊(C11⋊D11)C2×C311yescharacteristic
7C3×C11×D77C2×C311yescharacteristic
8C3×C7×C11×D11C2×C311yescharacteristic
9C9×D112—71nomaximal, Hall
10D11×D77C911yescharacteristic, direct product factor, Hall
11C2×C9×D77—111nomaximal
12C9×D7×D11—111nomaximal
13C3×C7×C112C22×C311yescharacteristic
14C9×C11⋊D11—71no—
15C9×C11×D11—71no—
16C9×C11×D11D711yescharacteristic, complemented
17C7⋊(C11⋊D11)C2×C911yescharacteristic, complemented
18C11×D77C2×C911yescharacteristic, complemented
19C7×C11×D11C2×C911yescharacteristic, complemented
20C3×D112—71no—
21C2×C7×C9×C11—111no—
22C9×D77—111no—
23C9×D77—111no—
24C9×D77—225no—
25C9×D77D1111yescharacteristic, direct product factor
26C9×C11×D7—111no—
27C7×C9×D11D1111yescharacteristic, complemented
28C9×C112C2×D711yescharacteristic, complemented, Hall
29C2×C3×D77—111no—
30C3×D7×D11—111no—
31C7×C112C22×C911yescharacteristic, complemented, Hall
32C3×C11⋊D11—71no—
33C3×C11×D11—71no—
34C3×C11×D11C3×D711yescharacteristic
35C7×C9×C11—25no—
36C7×C9×C11C2×D1111yescharacteristic, complemented
37C7×C9×C11C2×D1111yescharacteristic, complemented
38D112—71noHall
39C2×C3×C7×C11—111no—
40C3×D77—111no—
41C3×D77—111no—
42C3×D77—225no—
43C3×D77C3×D1111yescharacteristic
44C3×C11×D7—111no—
45C3×C7×D11C3×D1111yescharacteristic
46C2×C9×D11—771no—
47C2×C9×D11—771no—
48C3×C112C2×C3×D711yescharacteristic
49C2×D77—111no—
50D7×D11—111no—
51C2×C9×D7—1211noHall
52C11⋊D11—71no—
53C11×D11—71no—
54C11×D11C9×D711yescharacteristic, complemented
55C3×C7×C11—25no—
56C3×C7×C11C2×C3×D1111yescharacteristic
57C3×C7×C11C2×C3×D1111yescharacteristic
58C2×C9×C11—111no—
59C2×C9×C11—771no—
60C9×D11—71no—
61C9×D11—771no—
62C9×D11—771no—
63C9×D11—1545no—
64C9×D11D7711yescharacteristic, direct product factor
65C2×C7×C11—111no—
66D77—111no—
67D77—111no—
68D77—225no—
69D77C9×D1111yescharacteristic, direct product factor
70C7×D11C9×D1111yescharacteristic, complemented
71C11×D7—111no—
72C2×C3×D11—771no—
73C2×C3×D11—771no—
74C2×C7×C9—111no—
75C9×D7—111no—
76C9×D7—1211no—
77C112C2×C9×D711yescharacteristic, complemented, Sylow
78C9×C11—25no—
79C9×C11D7×D1111yescharacteristic, complemented
80C9×C11C2×D7711yescharacteristic, complemented
81C2×C3×D7—1211no—
82C7×C11—25no—
83C7×C11C2×C9×D1111yescharacteristic, complemented
84C7×C11C2×C9×D1111yescharacteristic, complemented
85C2×C3×C11—111no—
86C2×C3×C11—771no—
87C3×D11—71no—
88C3×D11—771no—
89C3×D11—771no—
90C3×D11—1545no—
91C3×D11C3×D7711yescharacteristic
92C7×C9D11211yescharacteristic, complemented, Hall
93C2×D11—771no—
94C2×D11—771no—
95C2×C3×C7—111no—
96C3×D7—111no—
97C3×D7—1211no—
98C22×C9—8471noHall
99C3×C11—25no—
100C3×C11C3×D7×D1111yescharacteristic
101C3×C11C2×C3×D7711yescharacteristic
102C2×D7—1211noHall
103C2×C11—111no—
104C2×C11—771no—
105D11—71no—
106D11—771no—
107D11—771no—
108D11—1545no—
109D11C9×D7711yescharacteristic, direct product factor
110C3×C7C3×D11211yescharacteristic
111C2×C9—111no—
112C2×C9—771no—
113C2×C9—8471no—
114C2×C7—111no—
115D7—111no—
116D7—1211no—
117C22×C3—8471no—
118C11—25no—
119C11C9×D7×D1111yescharacteristic, complemented
120C11C2×C9×D7711yescharacteristic, complemented
121C9D11×D7711yescharacteristic, direct product factor, Sylow
122C7C9×D11211yescharacteristic, complemented, Sylow
123C2×C3—111no—
124C2×C3—771no—
125C2×C3—8471no—
126C22—8471noSylow
127C3C3×D11×D7711yescharacteristic
128C2—111no—
129C2—771no—
130C2—8471no—
subgroupG/H
center, hypercenterC9D11×D77
commutator, hypocenterC7×C112C22×C9
FrattiniC3C3×D11×D77
FittingC7×C9×C112C22
socle, cosocleC3×C7×C112C22×C3
prime radicalC3×D11×D77C3
LCSG ▷ C7×C112
UCSC1 ◁ C9

Complements

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

NH ≅ G/Ntype
1. C9×C7⋊(C11⋊D11)C2semidirect
2. C9×C11×D77C2semidirect
3. C7×C9×C11×D11C2semidirect
5. C7×C9×C112C22semidirect
10. D11×D77C9direct (N × H)
16. C9×C11×D11D7semidirect
17. C7⋊(C11⋊D11)C2×C9semidirect
18. C11×D77C2×C9semidirect
19. C7×C11×D11C2×C9semidirect
25. C9×D77D11direct (N × H)
27. C7×C9×D11D11semidirect
28. C9×C112C2×D7semidirect
31. C7×C112C22×C9semidirect
36. C7×C9×C11C2×D11semidirect
37. C7×C9×C11C2×D11semidirect
54. C11×D11C9×D7semidirect
64. C9×D11D77direct (N × H)
69. D77C9×D11direct (N × H)
70. C7×D11C9×D11semidirect
77. C112C2×C9×D7semidirect
79. C9×C11D7×D11semidirect
80. C9×C11C2×D77semidirect
83. C7×C11C2×C9×D11semidirect
84. C7×C11C2×C9×D11semidirect
92. C7×C9D112semidirect
109. D11C9×D77direct (N × H)
119. C11C9×D7×D11semidirect
120. C11C2×C9×D77semidirect
121. C9D11×D77direct (N × H)
122. C7C9×D112semidirect

Maximal subgroups

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

subgroupindex
C9×C7⋊(C11⋊D11)2
C9×C11×D772
C7×C9×C11×D112
C3×D11×D773
C9×D1127
C2×C9×D7711
C9×D7×D1111