Finite Group Databasebeta

← #20242098

Subgroups — #20242098

Order 6016.

198 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 81 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#15689180C211yesmaximal, characteristic
2#15689176C211yesmaximal, characteristic
3#15688872C212yesmaximal, complemented
4#15688869C212yesmaximal, complemented
5C47×#533C211yesmaximal, characteristic
6C4⋊(C47⋊C8)C2212yes—
7C4⋊(C47⋊C8)C2212yes—
8C22⋊(C47⋊C8)—21no—
9C22⋊(C47⋊C8)—21no—
10#13093935—21no—
11C4×C47⋊C8—21no—
12C4⋊Q8×C47C2211yescharacteristic
13C4⋊Q8×C47C2211yescharacteristic
14#125×C47—21no—
15C22⋊Q8×C47—21no—
16C22⋊Q8×C47C412yes—
17C4×Q8×C47—21no—
18C4×Q8×C47C412yes—
19#117×C47—21no—
20C2×C42×C47C2211yescharacteristic
21C2×Q8×C47—21no—
22C2×Q8×C47C2×C412yes—
23C22×C4×C47C2×C411yescharacteristic
24C22×C4×C47D411yescharacteristic
25C22×C4×C47D411yescharacteristic
26C4⋊C4×C47—22no—
27C4⋊C4×C47—22no—
28C4⋊C4×C47—21no—
29C4⋊C4×C47—21no—
30C4⋊C4×C47—21no—
31C4⋊C4×C47C2×C412yes—
32C22⋊C4×C47—22no—
33C42×C47—22no—
34C42×C47C2×C411yescharacteristic
35C42×C47D411yescharacteristic
36C42×C47D411yescharacteristic
37C42×C47C2311yescharacteristic
38C2×C47⋊C8—22no—
39C2×C47⋊C8—22no—
40C23×C47C22⋊C411yescharacteristic
41Q8×C47—42no—
42Q8×C47—42no—
43C2×C4×C47—22no—
44C2×C4×C47—22no—
45C2×C4×C47—22no—
46C2×C4×C47—22no—
47C2×C4×C47—41no—
48C2×C4×C47C22⋊C411yescharacteristic
49C2×C4×C47C22⋊C411yescharacteristic
50C2×C4×C47C22⋊C411yescharacteristic
51C2×C4×C47C22×C411yescharacteristic
52C2×C4×C47C2×D411yescharacteristic
53C2×C4×C47C2×D411yescharacteristic
54C47⋊C8—42no—
55C47⋊C8—42no—
56C22×C47—21no—
57C22×C47—21no—
58C22×C47—21no—
59C22×C47C2×C22⋊C411yescharacteristic
60C4×C47—21no—
61C4×C47—21no—
62C4×C47—21no—
63C4×C47—21no—
64C4×C47—42no—
65C4×C47—42no—
66C4×C47#13512yes—
67C4×C47#13712yes—
68#1554—471nomaximal, Sylow
69C2×C47—41no—
70C2×C47#41311yescharacteristic
71C2×C47#41611yescharacteristic
72C2×C47#41911yescharacteristic
73#533D4711yescharacteristic
74#432—471no—
75#431—471no—
76#333—472no—
77#332—472no—
78C47#155411yescharacteristic, complemented, Sylow
79C4⋊Q8C2×D4711yescharacteristic
80C4⋊Q8C2×D4711yescharacteristic
81#125—21no—
82C22⋊Q8—21no—
83C22⋊Q8Dic4712yes—
84C4×Q8—21no—
85C4×Q8Dic4712yes—
86#117—21no—
87C2×C42C2×D4711yescharacteristic
88C4⋊C8—472no—
89C4⋊C8—472no—
90C22⋊C8—941no—
91C22⋊C8—941no—
92#97—941no—
93C4×C8—941no—
94C2×Q8—21no—
95C2×Q8C2×Dic4712yes—
96C22×C4C2×Dic4711yescharacteristic
97C22×C4C22⋊D4711yescharacteristic
98C22×C4C22⋊D4711yescharacteristic
99C2×C8—942no—
100C2×C8—942no—
101C4⋊C4—22no—
102C4⋊C4—22no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—21no—
106C4⋊C4C2×Dic4712yes—
107C22⋊C4—22no—
108C42—22no—
109C42C2×Dic4711yescharacteristic
110C42C22⋊D4711yescharacteristic
111C42C22⋊D4711yescharacteristic
112C42C22×D4711yescharacteristic
113C23C22⋊Dic4711yescharacteristic
114Q8—42no—
115Q8—42no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—41no—
121C2×C4C22⋊Dic4711yescharacteristic
122C2×C4C22⋊Dic4711yescharacteristic
123C2×C4C22⋊Dic4711yescharacteristic
124C2×C4C22×Dic4711yescharacteristic
125C2×C4C2×C22⋊D4711yescharacteristic
126C2×C4C2×C22⋊D4711yescharacteristic
127C8—1882no—
128C8—1882no—
129C22—21no—
130C22—21no—
131C22—21no—
132C22C2×C22⋊Dic4711yescharacteristic
133C4—21no—
134C4—21no—
135C4—21no—
136C4—21no—
137C4—42no—
138C4—42no—
139C4#1309404412yes—
140C4#1309405512yes—
141C2—41no—
142C2#1568910711yescharacteristic
143C2#1568911911yescharacteristic
144C2#1568913211yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#533C2
socleC22×C47C2×C22⋊C4
hypercenter#533D47
hypocenterC47#1554
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
3. #15688872C2semidirect
4. #15688869C2semidirect
78. C47#1554semidirect