Finite Group Databasebeta

← #20241230

Subgroups — #20241230

Order 6016.

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

normal subgroups only

This group has 264 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
1C2×C22⋊(C47⋊C8)C211yesmaximal, characteristic
2C2×C47⋊#95C211yesmaximal, characteristic
3C2×C22⋊C8×C47C211yesmaximal, characteristic
4C23×Dic47C412yes—
5C22×C47⋊C8—21no—
6C22⋊(C47⋊C8)—21no—
7C22⋊(C47⋊C8)C412yescomplemented
8C47⋊#95—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—
23C22×Dic47—22no—
24C22×Dic47—42no—
25C22×Dic47—42no—
26C22×Dic47C814yescomplemented
27C2×C8×C47—22no—
28C2×C8×C47—42no—
29C2×C47⋊C8—22no—
30C2×C47⋊C8—42no—
31C23×C47—22no—
32C23×C47—21no—
33C23×C47—21no—
34C23×C47C4211yescharacteristic
35C23×C47C22⋊C411yescharacteristic
36C23×C47C4⋊C411yescharacteristic
37C23×C47C2×C812yes—
38C23×C47M1612yes—
39C2×C4×C47—22no—
40C2×C4×C47—22no—
41C2×C4×C47—41no—
42C2×C4×C47—41no—
43C2×C4×C47—41no—
44C2×C4×C47—41no—
45C2×C4×C47C22⋊C411yescharacteristic
46C2×C4×C47C22⋊C411yescharacteristic
47C2×C4×C47C4⋊C411yescharacteristic
48C2×C4×C47C4⋊C411yescharacteristic
49C2×Dic47—24no—
50C2×Dic47—44no—
51C2×Dic47—42no—
52C2×Dic47—42no—
53C2×Dic47—44no—
54C8×C47—42no—
55C47⋊C8—42no—
56C22×C47—22no—
57C22×C47—22no—
58C22×C47—22no—
59C22×C47—22no—
60C22×C47—21no—
61C22×C47—21no—
62C22×C47—21no—
63C22×C47—21no—
64C22×C47#9511yescharacteristic
65C22×C47C4×C811yescharacteristic
66C22×C47#9711yescharacteristic
67C22×C47C22⋊C812yes—
68C22×C47#9912yes—
69C22×C47#10011yescharacteristic
70C22×C47#10111yescharacteristic
71C22×C47C4⋊C812yes—
72C4×C47—21no—
73C4×C47—21no—
74C4×C47—21no—
75C4×C47—21no—
76Dic47—44no—
77#1280—471nomaximal, Sylow
78C2×C47—21no—
79C2×C47—21no—
80C2×C47—22no—
81C2×C47#32312yes—
82C2×C47#32412yes—
83C2×C47#33611yescharacteristic
84C2×C47#34211yescharacteristic
85C2×C47#34311yescharacteristic
86C2×C22⋊C8—471no—
87C2×C22⋊C8D4711yescharacteristic
88C2×#95—471no—
89C47#128011yescharacteristic, complemented, Sylow
90C23×C4—472no—
91C23×C4C2×D4711yescharacteristic
92C22×C8—21no—
93C22×C8—941no—
94C22⋊C8—21no—
95C22⋊C8—472no—
96C22⋊C8—941no—
97C22⋊C8Dic4712yescomplemented
98#95—941no—
99#95—941no—
100C24C4×D4711yescharacteristic
101C22×C4—42no—
102C22×C4—474no—
103C22×C4—942no—
104C22×C4—942no—
105C22×C4—1882no—
106C22×C4—1882no—
107C22×C4Dic9411yescharacteristic
108C22×C4C4×D4711yescharacteristic
109C22×C4D18811yescharacteristic
110C22×C4C2×Dic4711yescharacteristic
111C22×C4C22⋊D4711yescharacteristic
112C22×C4C22⋊D4711yescharacteristic
113C2×C8—22no—
114C2×C8—42no—
115C2×C8—942no—
116C2×C8—1882no—
117C23—22no—
118C23—21no—
119C23—21no—
120C23C8×D4712yes—
121C23#1062532412yes—
122C23C4×Dic4711yescharacteristic
123C23Dic47⋊C411yescharacteristic
124C23(C2×D47)⋊C411yescharacteristic
125C2×C4—22no—
126C2×C4—22no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—944no—
132C2×C4—1884no—
133C2×C4—1882no—
134C2×C4—1882no—
135C2×C4—1884no—
136C2×C4Dic47⋊C411yescharacteristic
137C2×C4C4⋊Dic4711yescharacteristic
138C2×C4(C2×D47)⋊C411yescharacteristic
139C2×C4C22⋊Dic4711yescharacteristic
140C8—42no—
141C8—1882no—
142C22—22no—
143C22—22no—
144C22—22no—
145C22—22no—
146C22—21no—
147C22—21no—
148C22—21no—
149C22—21no—
150C22C47⋊#9511yescharacteristic
151C22C8×Dic4711yescharacteristic
152C22#1309393411yescharacteristic
153C22(C2×D47)⋊C812yes—
154C22#1309393812yes—
155C22#1309394011yescharacteristic
156C22#1309394211yescharacteristic
157C22Dic47⋊C812yes—
158C4—21no—
159C4—21no—
160C4—21no—
161C4—21no—
162C4—1884no—
163C2—21no—
164C2—21no—
165C2—22no—
166C2#1568884612yes—
167C2#1568884812yes—
168C2#1568887711yescharacteristic
169C2#1568888911yescharacteristic
170C2#1568889111yescharacteristic
subgroupG/H
centerC23(C2×D47)⋊C4
commutatorC22×C47C4×C8
FrattiniC23×C4C2×D47
FittingC2×C22⋊C8×C47C2
socleC23×C47C22⋊C4
hypercenterC2×C22⋊C8D47
hypocenterC47#1280
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
7. C22⋊(C47⋊C8)C4semidirect
13. C22⋊C8×C47C4semidirect
26. C22×Dic47C8semidirect
89. C47#1280semidirect
97. C22⋊C8Dic47semidirect