Finite Group Databasebeta

← #20241392

Subgroups — #20241392

Order 6016.

168 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 35 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#15689040C211yesmaximal, characteristic
2#15688892C211yesmaximal, characteristic, complemented
3C47×#324C211yesmaximal, characteristic, complemented
4C22×D188C411yescharacteristic
5C2×#10625329—21no—
6C2×(C2×D47)⋊C4—21no—
7C2×(C2×D47)⋊C4—21no—
8C47⋊#95C411yescharacteristic
9C2×C4⋊C4×C47C2211yescharacteristic
10C22⋊C8×C47—21no—
11C23×D47—21no—
12C22×C4×C47C2×C411yescharacteristic
13C22×C4×C47D411yescharacteristic
14C22×C4×C47D411yescharacteristic
15C22×Dic47—21no—
16C2×D188—41no—
17C2×D188—42no—
18C2×C8×C47—41no—
19C4⋊C4×C47—41no—
20(C2×D47)⋊C4—42no—
21(C2×D47)⋊C4—41no—
22(C2×D47)⋊C4—41no—
23#10625329—22no—
24#10625329—41no—
25C2×C47⋊C8—41no—
26C23×C47C22⋊C411yescharacteristic
27C22×D47—22no—
28C22×D47—41no—
29C22×D47—41no—
30C22×D47—41no—
31C22×D47—41no—
32C22×D47—41no—
33C22×D47—41no—
34C2×C4×C47—21no—
35C2×C4×C47—21no—
36C2×C4×C47—21no—
37C2×C4×C47—21no—
38C2×C4×C47—41no—
39C2×C4×C47—41no—
40C2×C4×C47D811yescharacteristic
41C2×C4×C47SD1611yescharacteristic
42C2×Dic47—41no—
43C2×Dic47—41no—
44C2×Dic47—41no—
45D188—42no—
46D188—42no—
47C8×C47—81no—
48C47⋊C8—42no—
49C22×C47—21no—
50C22×C47—21no—
51C22×C47#9911yescharacteristic
52C22×C47#10211yescharacteristic
53C22×C47#10411yescharacteristic
54C2×D47—42no—
55C2×D47—42no—
56C2×D47—42no—
57C2×D47—81no—
58C2×D47—81no—
59C2×D47—81no—
60C2×D47—81no—
61C4×C47—21no—
62C4×C47—21no—
63C4×C47—41no—
64C4×C47—41no—
65Dic47—81no—
66#1345—471nomaximal, Sylow
67C2×C47—21no—
68C2×C47—21no—
69C2×C47#32711yescharacteristic
70C2×C47AΣL(1,𝔽16)11yescharacteristic
71C2×C47#35511yescharacteristic
72D47—82no—
73#394—471no—
74#343—471no—
75#324D4711yescharacteristic, complemented
76C47#134511yescharacteristic, complemented, Sylow
77C22×D4—471no—
78C2×M16—941no—
79C2×C4⋊C4C2×D4711yescharacteristic
80C2×C22⋊C4—941no—
81C2×C22⋊C4—941no—
82C22⋊C8—21no—
83#95—471no—
84C24—941no—
85C2×D4—1881no—
86C2×D4—1882no—
87C22×C4—941no—
88C22×C4C4×D4711yescharacteristic
89C22×C4D18811yescharacteristic
90C22×C4C22⋊D4711yescharacteristic
91M16—942no—
92M16—1881no—
93C2×C8—41no—
94C2×C8—1881no—
95C4⋊C4—41no—
96C22⋊C4—1882no—
97C22⋊C4—1881no—
98C22⋊C4—1881no—
99C23—942no—
100C23—1881no—
101C23—1881no—
102C23—1881no—
103C23—1881no—
104C23—1881no—
105C23—1881no—
106C23(C2×D47)⋊C411yescharacteristic
107D4—1882no—
108D4—1882no—
109C2×C4—21no—
110C2×C4—21no—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—41no—
114C2×C4—41no—
115C2×C4—1881no—
116C2×C4—1881no—
117C2×C4—1881no—
118C2×C4#1062532511yescharacteristic
119C2×C4D37611yescharacteristic
120C8—81no—
121C8—1882no—
122C22—21no—
123C22—21no—
124C22—3761no—
125C22—3761no—
126C22—3761no—
127C22—3761no—
128C22—1882no—
129C22—1882no—
130C22—1882no—
131C22#1309393811yescharacteristic
132C22#1309394611yescharacteristic
133C22#1309395011yescharacteristic
134C4—21no—
135C4—21no—
136C4—41no—
137C4—41no—
138C4—3761no—
139C2—21no—
140C2—21no—
141C2—3762no—
142C2#1568885811yescharacteristic
143C2#1568890911yescharacteristic
144C2#1568891911yescharacteristic
subgroupG/H
centerC22#13093938
commutatorC22×C4×C47C2×C4
FrattiniC2×C4⋊C4C2×D47
FittingC47×#324C2
socleC22×C47#99
hypercenter#324D47
hypocenterC47#1345
LCSG ▷ C22×C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #15688892C2semidirect
3. C47×#324C2semidirect
75. #324D47semidirect
76. C47#1345semidirect