Finite Group Databasebeta

← #20251572

Subgroups — #20251572

Order 6016.

372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C47⋊#401C211yesmaximal, characteristic, complemented
2#15689060C211yesmaximal, characteristic
3#15689057C213yesmaximal, complemented
4#15689055C213yesmaximal, complemented
5#15689052C213yesmaximal
6#15688997C213yesmaximal
7C47×#401C211yesmaximal, characteristic, complemented
8C22×C4×D47C2211yescharacteristic
9C2×C4⋊Dic47C2213yes—
10C2×C4⋊Dic47C2213yes—
11C2×Dic47⋊C4C2213yes—
12C2×Dic47⋊C4C2213yes—
13C2×(C2×D47)⋊C4C2213yes—
14C2×(C2×D47)⋊C4C2213yes—
15C47⋊#95C2213yes—
16C47⋊#95C2213yes—
17C47⋊#95C2213yes—
18#95×C47C2213yes—
19#95×C47C2213yes—
20#95×C47C2211yescharacteristic
21C23×D47C2311yescharacteristic
22C22×C4×C47C2313yes—
23C22×C4×C47C2313yes—
24C22×C4×C47C2311yescharacteristic
25C22×Dic47C2313yes—
26C22×Dic47C2311yescharacteristic
27C22×Dic47C2313yes—
28C2×C4×D47—43no—
29(C2×D47)⋊C4—26no—
30(C2×D47)⋊C4—43no—
31C4⋊Dic47—43no—
32C4⋊Dic47—43no—
33Dic47⋊C4—43no—
34Dic47⋊C4—43no—
35C23×C47C2411yescharacteristic
36C22×D47—23no—
37C22×D47—23no—
38C22×D47#4112yes—
39C2×C4×C47—23no—
40C2×C4×C47—23no—
41C2×C4×C47—23no—
42C2×C4×C47—23no—
43C2×C4×C47—23no—
44C2×C4×C47—26no—
45C2×Dic47—23no—
46C2×Dic47—23no—
47C2×Dic47—23no—
48C2×Dic47—23no—
49C2×Dic47—23no—
50C2×Dic47—23no—
51C2×Dic47—23no—
52C4×D47—44no—
53C22×C47C2×#4111yescharacteristic
54C22×C47H(5,𝔽2)13yes—
55C22×C472−1+413yes—
56C2×D47—26no—
57C2×D47—41no—
58C2×D47—43no—
59C4×C47—43no—
60C4×C47—41no—
61C4×C47—43no—
62Dic47—43no—
63Dic47—41no—
64Dic47—43no—
65#2834—471nomaximal, Sylow
66C2×C47#53913yes—
67C2×C47#56011yescharacteristic
68C2×C47#56313yes—
69D47—42no—
70#401—471no—
71#401D4711yescharacteristic, complemented
72#399—471no—
73#398—473no—
74#398—473no—
75#397—473no—
76#385—473no—
77C47#283411yescharacteristic, complemented, Sylow
78C23×C4—471no—
79C2×C4⋊C4—473no—
80C2×C4⋊C4—473no—
81C2×C4⋊C4—473no—
82C2×C4⋊C4—473no—
83C2×C22⋊C4—473no—
84C2×C22⋊C4—473no—
85#95—473no—
86#95—473no—
87#95—473no—
88#95C2×D4713yes—
89#95C2×D4713yes—
90#95C2×D4711yescharacteristic
91C24—471no—
92C22×C4—473no—
93C22×C4—471no—
94C22×C4—473no—
95C22×C4—1883no—
96C22×C4C22×D4713yes—
97C22×C4C22×D4713yes—
98C22×C4C22×D4711yescharacteristic
99C4⋊C4—1883no—
100C4⋊C4—1883no—
101C4⋊C4—1883no—
102C4⋊C4—1883no—
103C22⋊C4—946no—
104C22⋊C4—1883no—
105C23—472no—
106C23—943no—
107C23—943no—
108C23C23×D4711yescharacteristic
109C2×C4—23no—
110C2×C4—23no—
111C2×C4—23no—
112C2×C4—23no—
113C2×C4—26no—
114C2×C4—23no—
115C2×C4—943no—
116C2×C4—943no—
117C2×C4—943no—
118C2×C4—943no—
119C2×C4—943no—
120C2×C4—943no—
121C2×C4—943no—
122C2×C4—1884no—
123C22—946no—
124C22—1881no—
125C22—1883no—
126C22#41×D4711yescharacteristic
127C22#1309407013yes—
128C22#1309407113yes—
129C4—41no—
130C4—43no—
131C4—43no—
132C4—1881no—
133C4—1883no—
134C4—1883no—
135C2—1882no—
136C2#1568971413yes—
137C2#1568986411yescharacteristic
138C2#1568987513yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#401C2
hypercenter#401D47
hypocenterC47#2834
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #401

Complements

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

NH ≅ G/Ntype
1. C47⋊#401C2semidirect
3. #15689057C2semidirect
4. #15689055C2semidirect
7. C47×#401C2semidirect
71. #401D47semidirect
77. C47#2834semidirect