Finite Group Databasebeta

← C23×C4×C11×C81 #72205481

Subgroups — C23×C4×C11×C81 #72205481

Order 28512.

1180 conjugacy classes of subgroups.

The subgroup lattice has 120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C11×C81C211yesmaximal, characteristic
2C22×C4×C11×C81C2114yesmaximal, direct product factor
3C23×C4×C11×C27C311yesmaximal, characteristic
4C23×C11×C81C418yesdirect product factor
5C23×C11×C81C2217yes—
6C2×C4×C11×C81C22128yesdirect product factor
7C24×C11×C27C2×C311yescharacteristic
8C22×C4×C11×C27C2×C3114yes—
9C22×C11×C81C2×C4128yesdirect product factor
10C22×C11×C81C2317yes—
11C4×C11×C81C2318yesdirect product factor
12C23×C4×C9×C11C911yescharacteristic
13C23×C4×C81C1111yesmaximal, characteristic, direct product factor, Hall
14C23×C11×C27C3×C418yes—
15C23×C11×C27C22×C317yes—
16C2×C4×C11×C27C22×C3128yes—
17C2×C11×C81C22×C4114yesdirect product factor
18C2×C11×C81C2411yescharacteristic
19C24×C9×C11C2×C911yescharacteristic
20C22×C4×C9×C11C2×C9114yes—
21C24×C81C2×C1111yescharacteristic
22C22×C4×C81C2×C11114yesdirect product factor
23C22×C11×C27C2×C3×C4128yes—
24C22×C11×C27C23×C317yes—
25C4×C11×C27C23×C318yes—
26C23×C3×C4×C11C2711yescharacteristic
27C11×C81C23×C411yescharacteristic, direct product factor, Hall
28C23×C4×C27C3×C1111yescharacteristic
29C23×C9×C11C4×C918yes—
30C23×C9×C11C22×C917yes—
31C2×C4×C9×C11C22×C9128yes—
32C23×C81C4×C1118yesdirect product factor
33C23×C81C22×C1117yes—
34C2×C4×C81C22×C11128yesdirect product factor
35C2×C11×C27C22×C3×C4114yes—
36C2×C11×C27C24×C311yescharacteristic
37C24×C3×C11C2×C2711yescharacteristic
38C22×C3×C4×C11C2×C27114yes—
39C24×C27C2×C3×C1111yescharacteristic
40C22×C4×C27C2×C3×C11114yes—
41C22×C9×C11C2×C4×C9128yes—
42C22×C9×C11C23×C917yes—
43C4×C9×C11C23×C918yes—
44C23×C4×C11C8111yescharacteristic, direct product factor, Hall
45C22×C81C2×C4×C11128yesdirect product factor
46C22×C81C23×C1117yes—
47C4×C81C23×C1118yesdirect product factor
48C11×C27C23×C3×C411yescharacteristic
49C23×C4×C9C9×C1111yescharacteristic
50C23×C3×C11C4×C2718yes—
51C23×C3×C11C22×C2717yes—
52C2×C3×C4×C11C22×C27128yes—
53C23×C27C3×C4×C1118yes—
54C23×C27C22×C3×C1117yes—
55C2×C4×C27C22×C3×C11128yes—
56C2×C9×C11C22×C4×C9114yes—
57C2×C9×C11C24×C911yescharacteristic
58C24×C11C2×C8111yescharacteristic
59C22×C4×C11C2×C81114yesdirect product factor
60C2×C81C22×C4×C11114yesdirect product factor
61C2×C81C24×C1111yescharacteristic
62C24×C9C2×C9×C1111yescharacteristic
63C22×C4×C9C2×C9×C11114yes—
64C22×C3×C11C2×C4×C27128yes—
65C22×C3×C11C23×C2717yes—
66C3×C4×C11C23×C2718yes—
67C22×C27C2×C3×C4×C11128yes—
68C22×C27C23×C3×C1117yes—
69C4×C27C23×C3×C1118yes—
70C9×C11C23×C4×C911yescharacteristic
71C23×C3×C4C11×C2711yescharacteristic
72C23×C11C4×C8118yesdirect product factor
73C23×C11C22×C8117yes—
74C2×C4×C11C22×C81128yesdirect product factor
75C81C23×C4×C1111yescharacteristic, direct product factor, Sylow
76C23×C9C4×C9×C1118yes—
77C23×C9C22×C9×C1117yes—
78C2×C4×C9C22×C9×C11128yes—
79C2×C3×C11C22×C4×C27114yes—
80C2×C3×C11C24×C2711yescharacteristic
81C2×C27C22×C3×C4×C11114yes—
82C2×C27C24×C3×C1111yescharacteristic
83C24×C3C2×C11×C2711yescharacteristic
84C22×C3×C4C2×C11×C27114yes—
85C22×C11C2×C4×C81128yesdirect product factor
86C22×C11C23×C8117yes—
87C4×C11C23×C8118yesdirect product factor
88C22×C9C2×C4×C9×C11128yes—
89C22×C9C23×C9×C1117yes—
90C4×C9C23×C9×C1118yes—
91C3×C11C23×C4×C2711yescharacteristic
92C23×C4C11×C8111yescharacteristic, direct product factor, Sylow
93C27C23×C3×C4×C1111yescharacteristic
94C23×C3C4×C11×C2718yes—
95C23×C3C22×C11×C2717yes—
96C2×C3×C4C22×C11×C27128yes—
97C2×C11C22×C4×C81114yesdirect product factor
98C2×C11C24×C8111yescharacteristic
99C2×C9C22×C4×C9×C11114yes—
100C2×C9C24×C9×C1111yescharacteristic
101C24C2×C11×C8111yescharacteristic
102C22×C4C2×C11×C81114yesdirect product factor
103C22×C3C2×C4×C11×C27128yes—
104C22×C3C23×C11×C2717yes—
105C3×C4C23×C11×C2718yes—
106C11C23×C4×C8111yescharacteristic, direct product factor, Sylow
107C9C23×C4×C9×C1111yescharacteristic
108C23C4×C11×C8118yesdirect product factor
109C23C22×C11×C8117yes—
110C2×C4C22×C11×C81128yesdirect product factor
111C2×C3C22×C4×C11×C27114yes—
112C2×C3C24×C11×C2711yescharacteristic
113C22C2×C4×C11×C81128yesdirect product factor
114C22C23×C11×C8117yes—
115C4C23×C11×C8118yesdirect product factor
116C3C23×C4×C11×C2711yescharacteristic
117C2C22×C4×C11×C81114yesdirect product factor
118C2C24×C11×C8111yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C27C24×C3×C11
socle, prime radicalC24×C3×C11C2×C27
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4×C11×C81C2direct (N × H)
4. C23×C11×C81C4direct (N × H)
6. C2×C4×C11×C81C22direct (N × H)
9. C22×C11×C81C2×C4direct (N × H)
11. C4×C11×C81C23direct (N × H)
13. C23×C4×C81C11direct (N × H)
17. C2×C11×C81C22×C4direct (N × H)
22. C22×C4×C81C2×C11direct (N × H)
27. C11×C81C23×C4direct (N × H)
32. C23×C81C4×C11direct (N × H)
34. C2×C4×C81C22×C11direct (N × H)
44. C23×C4×C11C81direct (N × H)
45. C22×C81C2×C4×C11direct (N × H)
47. C4×C81C23×C11direct (N × H)
59. C22×C4×C11C2×C81direct (N × H)
60. C2×C81C22×C4×C11direct (N × H)
72. C23×C11C4×C81direct (N × H)
74. C2×C4×C11C22×C81direct (N × H)
75. C81C23×C4×C11direct (N × H)
85. C22×C11C2×C4×C81direct (N × H)
87. C4×C11C23×C81direct (N × H)
92. C23×C4C11×C81direct (N × H)
97. C2×C11C22×C4×C81direct (N × H)
102. C22×C4C2×C11×C81direct (N × H)
106. C11C23×C4×C81direct (N × H)
108. C23C4×C11×C81direct (N × H)
110. C2×C4C22×C11×C81direct (N × H)
113. C22C2×C4×C11×C81direct (N × H)
115. C4C23×C11×C81direct (N × H)
117. C2C22×C4×C11×C81direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C11×C812
C22×C4×C11×C812
C23×C4×C11×C273
C23×C4×C8111