Finite Group Databasebeta

← #20241234

Subgroups — #20241234

Order 6016.

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

normal subgroups only

This group has 228 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
1C2×C22⋊(C47⋊C8)C211yesmaximal, characteristic
2C4×C22⋊Dic47C211yesmaximal, characteristic
3C2×C22⋊C8×C47C211yesmaximal, characteristic
4C22×C47⋊C8C412yescomplemented
5C2×C22⋊Dic47C412yes—
6C2×C4×Dic47—21no—
7C22⋊(C47⋊C8)—21no—
8C22⋊(C47⋊C8)—21no—
9C47⋊#95—21no—
10C23×C4×C47C2211yescharacteristic
11C22×C8×C47—21no—
12C22⋊C8×C47—21no—
13C22⋊C8×C47C412yescomplemented
14C24×C47C2×C411yescharacteristic
15C22×C4×C47—42no—
16C22×C4×C47C2×C411yescharacteristic
17C22×C4×C47C2×C411yescharacteristic
18C22×C4×C47D411yescharacteristic
19C22×C4×C47D411yescharacteristic
20C22×C4×C47D411yescharacteristic
21C22×C4×C47Q811yescharacteristic
22C22×Dic47—22no—
23C2×C8×C47—22no—
24C2×C8×C47—42no—
25C22⋊Dic47—22no—
26C22⋊Dic47C814yescomplemented
27C4×Dic47—42no—
28C2×C47⋊C8—22no—
29C2×C47⋊C8—42no—
30C23×C47—41no—
31C23×C47—41no—
32C23×C47C4211yescharacteristic
33C23×C47C22⋊C411yescharacteristic
34C23×C47C4⋊C411yescharacteristic
35C23×C47C2×C812yes—
36C23×C47M1612yes—
37C2×C4×C47—22no—
38C2×C4×C47—22no—
39C2×C4×C47—22no—
40C2×C4×C47—41no—
41C2×C4×C47—41no—
42C2×C4×C47—41no—
43C2×C4×C47C22⋊C411yescharacteristic
44C2×C4×C47C22⋊C411yescharacteristic
45C2×C4×C47C4⋊C411yescharacteristic
46C2×C4×C47C4⋊C411yescharacteristic
47C2×Dic47—24no—
48C2×Dic47—42no—
49C2×Dic47—42no—
50C8×C47—42no—
51C47⋊C8—42no—
52C22×C47—21no—
53C22×C47—21no—
54C22×C47—21no—
55C22×C47—21no—
56C22×C47—21no—
57C22×C47—21no—
58C22×C47—42no—
59C22×C47—42no—
60C22×C47#9511yescharacteristic
61C22×C47C4×C811yescharacteristic
62C22×C47#9711yescharacteristic
63C22×C47C22⋊C812yes—
64C22×C47C4⋊C812yes—
65C4×C47—21no—
66C4×C47—21no—
67C4×C47—21no—
68C4×C47#9912yes—
69Dic47—44no—
70#1282—471nomaximal, Sylow
71C2×C47—22no—
72C2×C47—21no—
73C2×C47—21no—
74C2×C47—22no—
75C2×C47#33611yescharacteristic
76C2×C47#34211yescharacteristic
77C2×C47#34411yescharacteristic
78C2×C22⋊C8—471no—
79C2×C22⋊C8D4711yescharacteristic
80C4×C22⋊C4—471no—
81C47#128211yescharacteristic, complemented, Sylow
82C23×C4C2×D4711yescharacteristic
83C22×C8—21no—
84C22×C8—472no—
85C2×C22⋊C4—472no—
86C2×C42—941no—
87C22⋊C8—21no—
88C22⋊C8—941no—
89C22⋊C8—941no—
90C22⋊C8Dic4712yescomplemented
91#95—941no—
92C24C4×D4711yescharacteristic
93C22×C4—42no—
94C22×C4—942no—
95C22×C4Dic9411yescharacteristic
96C22×C4C4×D4711yescharacteristic
97C22×C4D18811yescharacteristic
98C22×C4C2×Dic4711yescharacteristic
99C22×C4C22⋊D4711yescharacteristic
100C22×C4C22⋊D4711yescharacteristic
101C2×C8—22no—
102C2×C8—42no—
103C2×C8—942no—
104C2×C8—1882no—
105C22⋊C4—474no—
106C22⋊C4—942no—
107C42—1882no—
108C23—41no—
109C23—41no—
110C23C8×D4712yes—
111C23#1062532412yes—
112C23C4×Dic4711yescharacteristic
113C23Dic47⋊C411yescharacteristic
114C23(C2×D47)⋊C411yescharacteristic
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—944no—
122C2×C4—1882no—
123C2×C4—1882no—
124C2×C4Dic47⋊C411yescharacteristic
125C2×C4C4⋊Dic4711yescharacteristic
126C2×C4(C2×D47)⋊C411yescharacteristic
127C2×C4C22⋊Dic4711yescharacteristic
128C8—42no—
129C8—1882no—
130C22—21no—
131C22—21no—
132C22—21no—
133C22—21no—
134C22—21no—
135C22—21no—
136C22—42no—
137C22—42no—
138C22C47⋊#9511yescharacteristic
139C22C8×Dic4711yescharacteristic
140C22#1309393411yescharacteristic
141C22(C2×D47)⋊C812yes—
142C22Dic47⋊C812yes—
143C4—21no—
144C4—21no—
145C4—21no—
146C4—1884no—
147C4#1309393812yes—
148C2—22no—
149C2—21no—
150C2—21no—
151C2—22no—
152C2#1568887711yescharacteristic
153C2#1568888911yescharacteristic
154C2#1568889511yescharacteristic
subgroupG/H
centerC2×C4(C2×D47)⋊C4
commutatorC22×C47C4×C8
FrattiniC23×C4C2×D47
FittingC2×C22⋊C8×C47C2
socleC22×C47#95
hypercenterC2×C22⋊C8D47
hypocenterC47#1282
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
4. C22×C47⋊C8C4semidirect
13. C22⋊C8×C47C4semidirect
26. C22⋊Dic47C8semidirect
81. C47#1282semidirect
90. C22⋊C8Dic47semidirect