Finite Group Databasebeta

← C131×#8545 #45694429

Subgroups — C131×#8545 #45694429

Order 33536.

910 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 910 conjugacy classes of subgroups — too many to draw. Only its 150 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
1C22×#126×C131C211yesmaximal, characteristic
2#1819×C131C216yesmaximal
3C2×#126×C131—212no—
4C22×C4⋊C4×C131C413yescomplemented
5C22×C22⋊C4×C131C2213yes—
6C22×C42×C131C411yescharacteristic, complemented
7#379×C131C2214yes—
8#342×C131—212no—
9C25×C131C2311yescharacteristic
10C23×C4×C131C2×C413yes—
11C23×C4×C131C2×C413yes—
12#126×C131—232no—
13C2×C4⋊C4×C131—26no—
14C2×C4⋊C4×C131—26no—
15C2×C4⋊C4×C131—26no—
16C2×C22⋊C4×C131—26no—
17C2×C22⋊C4×C131—26no—
18C2×C22⋊C4×C131—212no—
19C2×C22⋊C4×C131D4112yes—
20C2×C42×C131—26no—
21C24×C131—46no—
22C24×C131C22×C411yescharacteristic
23C24×C131C2×D416yes—
24C22×C4×C131—23no—
25C22×C4×C131—23no—
26C22×C4×C131—23no—
27C22×C4×C131—23no—
28C22×C4×C131—46no—
29C22×C4×C131—46no—
30C22×C4×C131—44no—
31C22×C4×C131C22⋊C416yes—
32C22×C4×C131C22⋊C416yes—
33C4⋊C4×C131—224no—
34C22⋊C4×C131—224no—
35C22⋊C4×C131—424no—
36C42×C131—28no—
37C23×C131—26no—
38C23×C131—212no—
39C23×C131—46no—
40C23×C131—46no—
41C23×C131—88no—
42C23×C131C2×C22⋊C413yes—
43C23×C131#12014yes—
44C2×C4×C131—26no—
45C2×C4×C131—26no—
46C2×C4×C131—46no—
47C2×C4×C131—46no—
48C2×C4×C131—46no—
49C2×C4×C131—46no—
50C2×C4×C131—46no—
51C2×C4×C131—46no—
52C2×C4×C131—812no—
53C22×C131—28no—
54C22×C131—23no—
55C22×C131—23no—
56C22×C131—212no—
57C22×C131—812no—
58C22×C131#37911yescharacteristic
59C22×C131#41016yes—
60C4×C131—46no—
61C4×C131—46no—
62C4×C131—164no—
63C2×C131—26no—
64C2×C131—44no—
65C2×C131#178213yes—
66#8545C13111yesmaximal, characteristic, direct product factor, Sylow
67C131#854511yescharacteristic, direct product factor, Sylow
68C22×#126C2×C13111yescharacteristic
69#1819C2×C13116yes—
70C2×#126—212no—
71C22×C4⋊C4C4×C13113yescomplemented
72C22×C22⋊C4C22×C13113yes—
73C22×C42C4×C13111yescharacteristic, complemented
74#379C22×C13114yes—
75#342—212no—
76C25C23×C13111yescharacteristic
77C23×C4C2×C4×C13113yes—
78C23×C4C2×C4×C13113yes—
79#126—232no—
80C2×C4⋊C4—26no—
81C2×C4⋊C4—26no—
82C2×C4⋊C4—26no—
83C2×C22⋊C4—26no—
84C2×C22⋊C4—26no—
85C2×C22⋊C4—212no—
86C2×C22⋊C4D4×C131112yes—
87C2×C42—26no—
88C24—46no—
89C24C22×C4×C13111yescharacteristic
90C24C2×D4×C13116yes—
91C22×C4—23no—
92C22×C4—23no—
93C22×C4—23no—
94C22×C4—23no—
95C22×C4—46no—
96C22×C4—46no—
97C22×C4—44no—
98C22×C4C22⋊C4×C13116yes—
99C22×C4C22⋊C4×C13116yes—
100C4⋊C4—224no—
101C22⋊C4—224no—
102C22⋊C4—424no—
103C42—28no—
104C23—26no—
105C23—212no—
106C23—46no—
107C23—46no—
108C23—88no—
109C23C2×C22⋊C4×C13113yes—
110C23#120×C13114yes—
111C2×C4—26no—
112C2×C4—26no—
113C2×C4—46no—
114C2×C4—46no—
115C2×C4—46no—
116C2×C4—46no—
117C2×C4—46no—
118C2×C4—46no—
119C2×C4—812no—
120C22—28no—
121C22—23no—
122C22—23no—
123C22—212no—
124C22—812no—
125C22#379×C13111yescharacteristic
126C22#410×C13116yes—
127C4—46no—
128C4—46no—
129C4—164no—
130C2—26no—
131C2—44no—
132C2#1782×C13113yes—
subgroupG/H
center, socleC22×C131#379
commutatorC24C22×C4×C131
Frattini, cosocleC25C23×C131
prime radicalC25×C131C23
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C25×C131 ◁ G

Complements

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

NH ≅ G/Ntype
4. C22×C4⋊C4×C131C4semidirect
6. C22×C42×C131C4semidirect
66. #8545C131direct (N × H)
67. C131#8545direct (N × H)
71. C22×C4⋊C4C4×C131semidirect
73. C22×C42C4×C131semidirect

Maximal subgroups

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

subgroupindex
C22×#126×C1312
#1819×C1312
#8545131