Finite Group Databasebeta

← C47×#8545 #26048243

Subgroups — C47×#8545 #26048243

Order 12032.

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×C47C211yesmaximal, characteristic
2C47×#1819C216yesmaximal
3C2×#126×C47—212no—
4C22×C4⋊C4×C47C413yescomplemented
5C22×C22⋊C4×C47C2213yes—
6C22×C42×C47C411yescharacteristic, complemented
7C47×#379C2214yes—
8C47×#342—212no—
9C25×C47C2311yescharacteristic
10C23×C4×C47C2×C413yes—
11C23×C4×C47C2×C413yes—
12#126×C47—232no—
13C2×C4⋊C4×C47—26no—
14C2×C4⋊C4×C47—26no—
15C2×C4⋊C4×C47—26no—
16C2×C22⋊C4×C47—26no—
17C2×C22⋊C4×C47—26no—
18C2×C22⋊C4×C47—212no—
19C2×C22⋊C4×C47D4112yes—
20C2×C42×C47—26no—
21C24×C47—46no—
22C24×C47C22×C411yescharacteristic
23C24×C47C2×D416yes—
24C22×C4×C47—23no—
25C22×C4×C47—23no—
26C22×C4×C47—23no—
27C22×C4×C47—23no—
28C22×C4×C47—46no—
29C22×C4×C47—46no—
30C22×C4×C47—44no—
31C22×C4×C47C22⋊C416yes—
32C22×C4×C47C22⋊C416yes—
33C4⋊C4×C47—224no—
34C22⋊C4×C47—224no—
35C22⋊C4×C47—424no—
36C42×C47—28no—
37C23×C47—26no—
38C23×C47—212no—
39C23×C47—46no—
40C23×C47—46no—
41C23×C47—88no—
42C23×C47C2×C22⋊C413yes—
43C23×C47#12014yes—
44C2×C4×C47—26no—
45C2×C4×C47—26no—
46C2×C4×C47—46no—
47C2×C4×C47—46no—
48C2×C4×C47—46no—
49C2×C4×C47—46no—
50C2×C4×C47—46no—
51C2×C4×C47—46no—
52C2×C4×C47—812no—
53#8545C4711yesmaximal, characteristic, direct product factor, Sylow
54C22×C47—28no—
55C22×C47—23no—
56C22×C47—23no—
57C22×C47—212no—
58C22×C47—812no—
59C22×C47#37911yescharacteristic
60C22×C47#41016yes—
61C4×C47—46no—
62C4×C47—46no—
63C4×C47—164no—
64C22×#126C2×C4711yescharacteristic
65#1819C2×C4716yes—
66C2×C47—26no—
67C2×C47—44no—
68C2×C47#178213yes—
69C2×#126—212no—
70C22×C4⋊C4C4×C4713yescomplemented
71C22×C22⋊C4C22×C4713yes—
72C22×C42C4×C4711yescharacteristic, complemented
73#379C22×C4714yes—
74#342—212no—
75C47#854511yescharacteristic, direct product factor, Sylow
76C25C23×C4711yescharacteristic
77C23×C4C2×C4×C4713yes—
78C23×C4C2×C4×C4713yes—
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×C47112yes—
87C2×C42—26no—
88C24—46no—
89C24C22×C4×C4711yescharacteristic
90C24C2×D4×C4716yes—
91C22×C4—23no—
92C22×C4—23no—
93C22×C4—23no—
94C22×C4—23no—
95C22×C4—46no—
96C22×C4—46no—
97C22×C4—44no—
98C22×C4C22⋊C4×C4716yes—
99C22×C4C22⋊C4×C4716yes—
100C4⋊C4—224no—
101C22⋊C4—224no—
102C22⋊C4—424no—
103C42—28no—
104C23—26no—
105C23—212no—
106C23—46no—
107C23—46no—
108C23—88no—
109C23C2×C22⋊C4×C4713yes—
110C23#120×C4714yes—
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—
125C22C47×#37911yescharacteristic
126C22C47×#41016yes—
127C4—46no—
128C4—46no—
129C4—164no—
130C2—26no—
131C2—44no—
132C2C47×#178213yes—
subgroupG/H
center, socleC22×C47#379
commutatorC24C22×C4×C47
Frattini, cosocleC25C23×C47
prime radicalC25×C47C23
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C25×C47 ◁ G

Complements

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

NH ≅ G/Ntype
4. C22×C4⋊C4×C47C4semidirect
6. C22×C42×C47C4semidirect
53. #8545C47direct (N × H)
70. C22×C4⋊C4C4×C47semidirect
72. C22×C42C4×C47semidirect
75. C47#8545direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#126×C472
C47×#18192
#854547