Finite Group Databasebeta

← C23×#131×C47 #26102771

Subgroups — C23×#131×C47 #26102771

Order 12032.

11422 conjugacy classes of subgroups.

The subgroup lattice has 138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#41×C47C211yesmaximal, characteristic
2C22×#131×C47C2156yesmaximal, direct product factor
3C23×M16×C47C213yesmaximal, complemented
4C24×C8×C47C213yesmaximal, complemented
5C22×#41×C47C4128yes—
6C22×#41×C47C22128yes—
7C23×Q8×C47C411yescharacteristic
8C23×D4×C47C413yes—
9C24×C4×C47C2213yes—
10C2×#131×C47C221448yesdirect product factor
11C22×M16×C47C22184yescomplemented
12C23×C8×C47C2213yes—
13C23×C8×C47C2211yescharacteristic
14C23×C8×C47C22184yescomplemented
15C25×C47C2×C413yes—
16C2×#41×C47C2×C41336yes—
17C2×#41×C47C231112yes—
18C22×Q8×C47C2×C4128yes—
19C22×D4×C47C2×C4184yes—
20C23×C4×C47C2×C413yes—
21C23×C4×C47C2×C4142yes—
22C23×C4×C47C2311yescharacteristic
23C23×C4×C47C23142yes—
24#131×C47C231512yesdirect product factor
25C2×M16×C47C231336yescomplemented
26C22×C8×C47C23142yes—
27C22×C8×C47C23114yes—
28C22×C8×C47C231336yescomplemented
29C24×C47—224no—
30C24×C47C22×C4142yes—
31C24×C47C22×C411yescharacteristic
32#41×C47C22×C41448yes—
33#41×C47C24164yes—
34C2×Q8×C47C22×C41112yes—
35C2×D4×C47C22×C41336yes—
36C22×C4×C47C22×C417yes—
37C22×C4×C47C22×C4142yes—
38C22×C4×C47C22×C41252yes—
39C22×C4×C47C2417yes—
40C22×C4×C47C24184yes—
41M16×C47C241192yescomplemented
42C2×C8×C47C24128yes—
43C2×C8×C47C24184yes—
44C2×C8×C47C241192yescomplemented
45C23×C47—2168no—
46C23×C47#13118yesdirect product factor
47C23×C47C23×C4184yes—
48C23×C47C23×C417yes—
49Q8×C47C23×C4164yes—
50D4×C47C23×C41192yes—
51C2×C4×C47C23×C4121yes—
52C2×C4×C47C23×C4184yes—
53C2×C4×C47C23×C41168yes—
54C2×C4×C47C2517yes—
55C2×C4×C47C25124yes—
56C8×C47C2518yes—
57C8×C47C25124yes—
58C23×#131C4711yesmaximal, characteristic, direct product factor, Sylow
59C22×C47—2168no—
60C22×C47C2×#131128yesdirect product factor
61C22×C47C24×C4124yes—
62C22×C47C24×C417yes—
63C4×C47C24×C417yes—
64C4×C47C24×C4124yes—
65C4×C47C2611yescharacteristic
66C23×#41C2×C4711yescharacteristic
67C22×#131C2×C47156yesdirect product factor
68C23×M16C2×C4713yescomplemented
69C24×C8C2×C4713yescomplemented
70C2×C47—224no—
71C2×C47C22×#131114yesdirect product factor
72C2×C47C25×C411yescharacteristic
73C22×#41C4×C47128yes—
74C22×#41C22×C47128yes—
75C23×Q8C4×C4711yescharacteristic
76C23×D4C4×C4713yes—
77C24×C4C22×C4713yes—
78C2×#131C22×C471448yesdirect product factor
79C22×M16C22×C47184yescomplemented
80C23×C8C22×C4713yes—
81C23×C8C22×C4711yescharacteristic
82C23×C8C22×C47184yescomplemented
83C47C23×#13111yescharacteristic, direct product factor, Sylow
84C25C2×C4×C4713yes—
85C2×#41C2×C4×C471336yes—
86C2×#41C23×C471112yes—
87C22×Q8C2×C4×C47128yes—
88C22×D4C2×C4×C47184yes—
89C23×C4C2×C4×C4713yes—
90C23×C4C2×C4×C47142yes—
91C23×C4C23×C4711yescharacteristic
92C23×C4C23×C47142yes—
93#131C23×C471512yesdirect product factor
94C2×M16C23×C471336yescomplemented
95C22×C8C23×C47114yes—
96C22×C8C23×C47142yes—
97C22×C8C23×C471336yescomplemented
98C24—224no—
99C24C22×C4×C47142yes—
100C24C22×C4×C4711yescharacteristic
101#41C22×C4×C471448yes—
102#41C24×C47164yes—
103C2×Q8C22×C4×C471112yes—
104C2×D4C22×C4×C471336yes—
105C22×C4C22×C4×C4717yes—
106C22×C4C22×C4×C47142yes—
107C22×C4C22×C4×C471252yes—
108C22×C4C24×C4717yes—
109C22×C4C24×C47184yes—
110M16C24×C471192yescomplemented
111C2×C8C24×C47128yes—
112C2×C8C24×C47184yes—
113C2×C8C24×C471192yescomplemented
114C23—2168no—
115C23#131×C4718yesdirect product factor
116C23C23×C4×C47184yes—
117C23C23×C4×C4717yes—
118Q8C23×C4×C47164yes—
119D4C23×C4×C471192yes—
120C2×C4C23×C4×C47121yes—
121C2×C4C23×C4×C47184yes—
122C2×C4C23×C4×C471168yes—
123C2×C4C25×C4717yes—
124C2×C4C25×C47124yes—
125C8C25×C4718yes—
126C8C25×C47124yes—
127C22—2168no—
128C22C2×#131×C47128yesdirect product factor
129C22C24×C4×C47124yes—
130C22C24×C4×C4717yes—
131C4C24×C4×C4717yes—
132C4C24×C4×C47124yes—
133C4C26×C4711yescharacteristic
134C2—224no—
135C2C22×#131×C47114yesdirect product factor
136C2C25×C4×C4711yescharacteristic
subgroupG/H
centerC23×C8×C47C22
commutatorC2C25×C4×C47
Frattini, cosocleC4C26×C47
socleC24×C47C22×C4
prime radicalC23×#41×C47C2
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C23×C8×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#131×C47C2direct (N × H)
3. C23×M16×C47C2semidirect
4. C24×C8×C47C2semidirect
10. C2×#131×C47C22direct (N × H)
11. C22×M16×C47C22semidirect
14. C23×C8×C47C22semidirect
24. #131×C47C23direct (N × H)
25. C2×M16×C47C23semidirect
28. C22×C8×C47C23semidirect
41. M16×C47C24semidirect
44. C2×C8×C47C24semidirect
46. C23×C47#131direct (N × H)
58. C23×#131C47direct (N × H)
60. C22×C47C2×#131direct (N × H)
67. C22×#131C2×C47direct (N × H)
68. C23×M16C2×C47semidirect
69. C24×C8C2×C47semidirect
71. C2×C47C22×#131direct (N × H)
78. C2×#131C22×C47direct (N × H)
79. C22×M16C22×C47semidirect
82. C23×C8C22×C47semidirect
83. C47C23×#131direct (N × H)
93. #131C23×C47direct (N × H)
94. C2×M16C23×C47semidirect
97. C22×C8C23×C47semidirect
110. M16C24×C47semidirect
113. C2×C8C24×C47semidirect
115. C23#131×C47direct (N × H)
128. C22C2×#131×C47direct (N × H)
135. C2C22×#131×C47direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#41×C472
C22×#131×C472
C23×M16×C472
C24×C8×C472
C23×#13147