Finite Group Databasebeta

← #20251577

Subgroups — #20251577

Order 6016.

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

normal subgroups only

This group has 380 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
1#15689064C213yesmaximal, complemented
2#15689061C213yesmaximal, complemented
3#15689052C213yesmaximal
4#15689042C211yesmaximal, characteristic, complemented
5#15689034C211yesmaximal, characteristic
6#15688994C213yesmaximal
7C47×#395C211yesmaximal, characteristic, complemented
8C22×C4×D47C2211yescharacteristic
9C2×Dic47⋊C4C2213yes—
10C2×Dic47⋊C4C2213yes—
11C2×(C2×D47)⋊C4C2213yes—
12C2×(C2×D47)⋊C4C2213yes—
13C47⋊#95C2213yes—
14C47⋊#95C2213yes—
15C47⋊#95C2213yes—
16C47⋊#95C2213yes—
17C47⋊#95C2213yes—
18C22×Q8×C47C2211yescharacteristic
19C2×C4⋊C4×C47C2213yes—
20#95×C47C2213yes—
21C23×D47C2311yescharacteristic
22C2×Q8×C47—43no—
23C22×C4×C47C2311yescharacteristic
24C22×C4×C47C2313yes—
25C22×C4×C47C2313yes—
26C22×Dic47C2313yes—
27C22×Dic47C2313yes—
28C22×Dic47C2311yescharacteristic
29C2×C4×D47—43no—
30C4⋊C4×C47—43no—
31(C2×D47)⋊C4—26no—
32(C2×D47)⋊C4—43no—
33Dic47⋊C4—43no—
34Dic47⋊C4—43no—
35C23×C47C2411yescharacteristic
36C22×D47—23no—
37C22×D47—23no—
38C22×D47#4112yes—
39Q8×C47—44no—
40C2×C4×C47—23no—
41C2×C4×C47—23no—
42C2×C4×C47—23no—
43C2×C4×C47—23no—
44C2×C4×C47—23no—
45C2×C4×C47—23no—
46C2×C4×C47—23no—
47C2×Dic47—23no—
48C2×Dic47—23no—
49C2×Dic47—23no—
50C2×Dic47—23no—
51C2×Dic47—23no—
52C2×Dic47—26no—
53C4×D47—44no—
54C22×C47C2×#4111yescharacteristic
55C22×C47H(5,𝔽2)13yes—
56C22×C472−1+413yes—
57C2×D47—26no—
58C2×D47—41no—
59C2×D47—43no—
60C4×C47—43no—
61C4×C47—41no—
62C4×C47—43no—
63Dic47—43no—
64Dic47—41no—
65Dic47—43no—
66#2835—471nomaximal, Sylow
67C2×C47#53913yes—
68C2×C47H(3,𝔽4)11yescharacteristic
69C2×C47#56313yes—
70D47—42no—
71#400—473no—
72#400—473no—
73#397—473no—
74#395—471no—
75#395D4711yescharacteristic, complemented
76#393—471no—
77#385—473no—
78C47#283511yescharacteristic, complemented, Sylow
79C22×Q8C2×D4711yescharacteristic
80C23×C4—471no—
81C2×C4⋊C4—473no—
82C2×C4⋊C4—473no—
83C2×C4⋊C4C2×D4713yes—
84C2×C22⋊C4—473no—
85C2×C22⋊C4—473no—
86#95—473no—
87#95—473no—
88#95—473no—
89#95—473no—
90#95—473no—
91#95C2×D4713yes—
92C24—471no—
93C2×Q8—43no—
94C22×C4—473no—
95C22×C4—473no—
96C22×C4—471no—
97C22×C4—1883no—
98C22×C4C22×D4711yescharacteristic
99C22×C4C22×D4713yes—
100C22×C4C22×D4713yes—
101C4⋊C4—43no—
102C4⋊C4—1883no—
103C4⋊C4—1883no—
104C22⋊C4—946no—
105C22⋊C4—1883no—
106C23—472no—
107C23—943no—
108C23—943no—
109C23C23×D4711yescharacteristic
110Q8—44no—
111C2×C4—23no—
112C2×C4—23no—
113C2×C4—23no—
114C2×C4—23no—
115C2×C4—23no—
116C2×C4—23no—
117C2×C4—23no—
118C2×C4—943no—
119C2×C4—943no—
120C2×C4—943no—
121C2×C4—943no—
122C2×C4—946no—
123C2×C4—943no—
124C2×C4—1884no—
125C22—946no—
126C22—1881no—
127C22—1883no—
128C22#41×D4711yescharacteristic
129C22#1309406913yes—
130C22#1309407213yes—
131C4—41no—
132C4—43no—
133C4—43no—
134C4—1881no—
135C4—1883no—
136C4—1883no—
137C2—1882no—
138C2#1568971913yes—
139C2#1568986611yescharacteristic
140C2#1568987213yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#395C2
hypercenter#395D47
hypocenterC47#2835
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. #15689064C2semidirect
2. #15689061C2semidirect
4. #15689042C2semidirect
7. C47×#395C2semidirect
75. #395D47semidirect
78. C47#2835semidirect