Finite Group Databasebeta

← #20241391

Subgroups — #20241391

Order 6016.

168 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 37 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#15688892C211yesmaximal, characteristic, complemented
2#15688849C211yesmaximal, characteristic, complemented
3C47×#394C211yesmaximal, characteristic
4C2×#10625329—21no—
5C22⋊(C47⋊C8)—21no—
6C22×D4×C47C411yescharacteristic
7C2×C4⋊C4×C47C2211yescharacteristic
8C2×C22⋊C4×C47—21no—
9C2×C22⋊C4×C47—21no—
10#95×C47C411yescharacteristic
11C24×C47—21no—
12C2×D4×C47—41no—
13C2×D4×C47—42no—
14C22×C4×C47—21no—
15C22×C4×C47C2×C411yescharacteristic
16C22×C4×C47D411yescharacteristic
17C22×C4×C47D411yescharacteristic
18C4⋊C4×C47—41no—
19C22⋊C4×C47—42no—
20C22⋊C4×C47—41no—
21C22⋊C4×C47—41no—
22#10625329—22no—
23#10625329—41no—
24C2×C47⋊C8—41no—
25C2×C47⋊C8—41no—
26C23×C47—22no—
27C23×C47—41no—
28C23×C47—41no—
29C23×C47—41no—
30C23×C47—41no—
31C23×C47—41no—
32C23×C47—41no—
33C23×C47C22⋊C411yescharacteristic
34D4×C47—42no—
35D4×C47—42no—
36C2×C4×C47—21no—
37C2×C4×C47—21no—
38C2×C4×C47—21no—
39C2×C4×C47—21no—
40C2×C4×C47—41no—
41C2×C4×C47—41no—
42C2×C4×C47—41no—
43C2×C4×C47—41no—
44C2×C4×C47—41no—
45C2×C4×C47D811yescharacteristic
46C2×C4×C47SD1611yescharacteristic
47C47⋊C8—42no—
48C47⋊C8—81no—
49C22×C47—21no—
50C22×C47—21no—
51C22×C47—42no—
52C22×C47—42no—
53C22×C47—42no—
54C22×C47—81no—
55C22×C47—81no—
56C22×C47—81no—
57C22×C47—81no—
58C22×C47#9911yescharacteristic
59C22×C47#10211yescharacteristic
60C22×C47#10411yescharacteristic
61C4×C47—21no—
62C4×C47—21no—
63C4×C47—41no—
64C4×C47—41no—
65C4×C47—81no—
66#1345—471nomaximal, Sylow
67C2×C47—21no—
68C2×C47—21no—
69C2×C47—82no—
70C2×C47#32711yescharacteristic
71C2×C47AΣL(1,𝔽16)11yescharacteristic
72C2×C47#35511yescharacteristic
73#394D4711yescharacteristic
74#343—471no—
75#324—471no—
76C47#134511yescharacteristic, complemented, Sylow
77C22×D4Dic4711yescharacteristic
78C2×M16—941no—
79C2×C4⋊C4C2×D4711yescharacteristic
80C2×C22⋊C4—21no—
81C2×C22⋊C4—21no—
82C22⋊C8—941no—
83#95Dic4711yescharacteristic
84C24—21no—
85C2×D4—41no—
86C2×D4—42no—
87C22×C4—21no—
88C22×C4C2×Dic4711yescharacteristic
89C22×C4C22⋊D4711yescharacteristic
90C22×C4C22⋊D4711yescharacteristic
91M16—942no—
92M16—1881no—
93C2×C8—1881no—
94C2×C8—1881no—
95C4⋊C4—41no—
96C22⋊C4—42no—
97C22⋊C4—41no—
98C22⋊C4—41no—
99C23—22no—
100C23—41no—
101C23—41no—
102C23—41no—
103C23—41no—
104C23—41no—
105C23—41no—
106C23C22⋊Dic4711yescharacteristic
107D4—42no—
108D4—42no—
109C2×C4—21no—
110C2×C4—21no—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—41no—
114C2×C4—41no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4#1062533411yescharacteristic
119C2×C4#1062533511yescharacteristic
120C8—3761no—
121C8—1882no—
122C22—21no—
123C22—21no—
124C22—42no—
125C22—42no—
126C22—42no—
127C22—81no—
128C22—81no—
129C22—81no—
130C22—81no—
131C22#1309393911yescharacteristic
132C22#1309394511yescharacteristic
133C22#1309395111yescharacteristic
134C4—21no—
135C4—21no—
136C4—41no—
137C4—41no—
138C4—81no—
139C2—21no—
140C2—21no—
141C2—82no—
142C2#1568885711yescharacteristic
143C2#1568891011yescharacteristic
144C2#1568892011yescharacteristic
subgroupG/H
centerC22#13093939
commutatorC22×C4×C47C2×C4
FrattiniC2×C4⋊C4C2×D47
FittingC47×#394C2
socleC22×C47#99
hypercenter#394D47
hypocenterC47#1345
LCSG ▷ C22×C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #15688892C2semidirect
2. #15688849C2semidirect
76. C47#1345semidirect