Finite Group Databasebeta

← #20241718

Subgroups — #20241718

Order 6016.

312 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 93 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#15689087C212yesmaximal
2#15688849C214yesmaximal, complemented
3C22×C4⋊C4×C47C211yesmaximal, characteristic
4C2×#10625329—22no—
5C22⋊(C47⋊C8)—22no—
6C22⋊(C47⋊C8)C2214yes—
7C23×C4×C47C411yescharacteristic
8C23×C4×C47C411yescharacteristic
9C23×C4×C47C2211yescharacteristic
10C2×C4⋊C4×C47—22no—
11C2×C4⋊C4×C47—22no—
12C2×C4⋊C4×C47C412yes—
13C2×C4⋊C4×C47C2212yes—
14C24×C47C2×C411yescharacteristic
15C22×C4×C47—21no—
16C22×C4×C47—21no—
17C22×C4×C47—24no—
18C22×C4×C47—21no—
19C22×C4×C47—21no—
20C22×C4×C47—42no—
21C22×C4×C47—42no—
22C22×C4×C47C2×C412yes—
23C22×C4×C47C2×C412yes—
24C22×C4×C47C2×C411yescharacteristic
25C22×C4×C47D412yes—
26C22×C4×C47D412yes—
27C22×C4×C47C2311yescharacteristic
28C4⋊C4×C47—24no—
29C4⋊C4×C47—24no—
30#10625329—44no—
31C2×C47⋊C8—24no—
32C23×C47—22no—
33C23×C47—22no—
34C23×C47—22no—
35C23×C47C22⋊C411yescharacteristic
36C23×C47C22⋊C411yescharacteristic
37C23×C47C22×C411yescharacteristic
38C2×C4×C47—24no—
39C2×C4×C47—24no—
40C2×C4×C47—24no—
41C2×C4×C47—22no—
42C2×C4×C47—22no—
43C2×C4×C47—22no—
44C2×C4×C47—41no—
45C2×C4×C47—42no—
46C2×C4×C47—41no—
47C2×C4×C47—42no—
48C2×C4×C47—42no—
49C2×C4×C47—42no—
50C2×C4×C47C22⋊C412yes—
51C2×C4×C47M1614yescomplemented
52C2×C4×C47C2×D412yes—
53C47⋊C8—44no—
54C22×C47—28no—
55C22×C47—21no—
56C22×C47—21no—
57C22×C47—21no—
58C22×C47—21no—
59C22×C47—21no—
60C22×C47—21no—
61C22×C47#9912yes—
62C22×C47#10112yes—
63C22×C47C2×C22⋊C411yescharacteristic
64C22×C47C2×M1612yes—
65C4×C47—24no—
66C4×C47—22no—
67C4×C47—22no—
68C4×C47—42no—
69#1463—471nomaximal, Sylow
70C2×C47—22no—
71C2×C47—22no—
72C2×C47—22no—
73C2×C47#40711yescharacteristic
74C2×C47C2×#9911yescharacteristic
75C2×C47C2×#10111yescharacteristic
76C22×C4⋊C4D4711yescharacteristic
77#407—472no—
78#324—474no—
79C47#146311yescharacteristic, complemented, Sylow
80C23×C4Dic4711yescharacteristic
81C23×C4Dic4711yescharacteristic
82C23×C4C2×D4711yescharacteristic
83C2×M16—942no—
84C2×C4⋊C4—22no—
85C2×C4⋊C4—22no—
86C2×C4⋊C4Dic4712yes—
87C2×C4⋊C4C2×D4712yes—
88C22⋊C8—474no—
89C22⋊C8—942no—
90C24C2×Dic4711yescharacteristic
91C22×C4—21no—
92C22×C4—21no—
93C22×C4—24no—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4—42no—
97C22×C4—42no—
98C22×C4C2×Dic4712yes—
99C22×C4C2×Dic4712yes—
100C22×C4C2×Dic4711yescharacteristic
101C22×C4C22⋊D4712yes—
102C22×C4C22⋊D4712yes—
103C22×C4C22×D4711yescharacteristic
104M16—1884no—
105C2×C8—944no—
106C4⋊C4—24no—
107C4⋊C4—24no—
108C23—22no—
109C23—22no—
110C23—22no—
111C23C22⋊Dic4711yescharacteristic
112C23C22⋊Dic4711yescharacteristic
113C23C22×Dic4711yescharacteristic
114C2×C4—24no—
115C2×C4—24no—
116C2×C4—24no—
117C2×C4—22no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—41no—
121C2×C4—42no—
122C2×C4—41no—
123C2×C4—42no—
124C2×C4—42no—
125C2×C4—42no—
126C2×C4#1062532914yescomplemented
127C2×C4C22⋊Dic4712yes—
128C2×C4C2×C22⋊D4712yes—
129C8—1884no—
130C22—28no—
131C22—21no—
132C22—21no—
133C22—21no—
134C22—21no—
135C22—21no—
136C22—21no—
137C22#1309393912yes—
138C22#1309394312yes—
139C22C2×C22⋊Dic4711yescharacteristic
140C22C2×#1062532912yes—
141C4—24no—
142C4—22no—
143C4—22no—
144C4—42no—
145C2—22no—
146C2—22no—
147C2—22no—
148C2#1568908711yescharacteristic
149C2C2×#1309393911yescharacteristic
150C2C2×#1309394311yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic47
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC22×C4⋊C4×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC22×C4⋊C4D47
hypocenterC47#1463
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #15688849C2semidirect
51. C2×C4×C47M16semidirect
79. C47#1463semidirect
126. C2×C4#10625329semidirect