Finite Group Databasebeta

← #20241266

Subgroups — #20241266

Order 6016.

276 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 89 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
3C47×#380C211yesmaximal, characteristic
4C23×Dic47—21no—
5C22×C47⋊C8—21no—
6C22⋊(C47⋊C8)—21no—
7C22⋊(C47⋊C8)C412yescomplemented
8C47⋊#95—21no—
9C47⋊#95C412yescomplemented
10C23×C4×C47C2211yescharacteristic
11C2×C4⋊C4×C47C412yescomplemented
12C2×C22⋊C4×C47—21no—
13#95×C47—21no—
14C24×C47D411yescharacteristic
15C22×C4×C47—22no—
16C22×C4×C47—42no—
17C22×C4×C47C2×C411yescharacteristic
18C22×C4×C47C2×C411yescharacteristic
19C22×C4×C47C2×C411yescharacteristic
20C22×C4×C47D411yescharacteristic
21C22×C4×C47D411yescharacteristic
22C22×C4×C47Q811yescharacteristic
23C22×Dic47—24no—
24C22×Dic47—22no—
25C22×Dic47—42no—
26C22×Dic47—41no—
27C22×Dic47—41no—
28C4⋊C4×C47—42no—
29C22⋊C4×C47—41no—
30C22⋊C4×C47—41no—
31C2×C47⋊C8—22no—
32C2×C47⋊C8—42no—
33C23×C47—22no—
34C23×C47—22no—
35C23×C47C22⋊C411yescharacteristic
36C23×C47C22⋊C411yescharacteristic
37C23×C47C4⋊C411yescharacteristic
38C23×C47D811yescharacteristic
39C23×C47SD1611yescharacteristic
40C23×C47SD1611yescharacteristic
41C23×C47Q1611yescharacteristic
42C2×C4×C47—22no—
43C2×C4×C47—22no—
44C2×C4×C47—41no—
45C2×C4×C47—41no—
46C2×C4×C47—41no—
47C2×C4×C47—41no—
48C2×C4×C47—42no—
49C2×C4×C47—42no—
50C2×C4×C47—42no—
51C2×C4×C47C4211yescharacteristic
52C2×C4×C47C22⋊C411yescharacteristic
53C2×C4×C47C4⋊C411yescharacteristic
54C2×C4×C47C4⋊C411yescharacteristic
55C2×Dic47—24no—
56C2×Dic47—44no—
57C2×Dic47—44no—
58C2×Dic47—42no—
59C2×Dic47—42no—
60C47⋊C8—42no—
61C22×C47—22no—
62C22×C47—22no—
63C22×C47—22no—
64C22×C47—22no—
65C22×C47—21no—
66C22×C47—21no—
67C22×C47—21no—
68C22×C47—21no—
69C22×C47#9511yescharacteristic
70C22×C47#9912yes—
71C22×C47#10211yescharacteristic
72C22×C47#10211yescharacteristic
73C22×C47#10311yescharacteristic
74C22×C47#10311yescharacteristic
75C22×C47#10412yes—
76C22×C47#10611yescharacteristic
77C22×C47#10711yescharacteristic
78C4×C47—21no—
79C4×C47—21no—
80C4×C47—21no—
81C4×C47—21no—
82C4×C47—82no—
83Dic47—44no—
84#1294—471nomaximal, Sylow
85C2×C47—21no—
86C2×C47—21no—
87C2×C47—21no—
88C2×C47—21no—
89C2×C47#32712yes—
90C2×C47#32812yes—
91C2×C47#33911yescharacteristic
92C2×C47#34011yescharacteristic
93C2×C47#34211yescharacteristic
94C2×C22⋊C8—471no—
95#380D4711yescharacteristic
96C2×#95—471no—
97C47#129411yescharacteristic, complemented, Sylow
98C23×C4—941no—
99C23×C4C2×D4711yescharacteristic
100C22×C8—941no—
101C2×C4⋊C4Dic4712yescomplemented
102C2×C22⋊C4—21no—
103C22⋊C8—472no—
104C22⋊C8—941no—
105#95—21no—
106#95—472no—
107#95—941no—
108C24C22⋊D4711yescharacteristic
109C22×C4—22no—
110C22×C4—42no—
111C22×C4—944no—
112C22×C4—942no—
113C22×C4—1882no—
114C22×C4—1881no—
115C22×C4—1881no—
116C22×C4Dic9411yescharacteristic
117C22×C4C4×D4711yescharacteristic
118C22×C4C4×D4711yescharacteristic
119C22×C4D18811yescharacteristic
120C22×C4C2×Dic4711yescharacteristic
121C22×C4C22⋊D4711yescharacteristic
122C2×C8—942no—
123C2×C8—1882no—
124C4⋊C4—42no—
125C22⋊C4—41no—
126C22⋊C4—41no—
127C23—22no—
128C23—22no—
129C23Dic47⋊C411yescharacteristic
130C23(C2×D47)⋊C411yescharacteristic
131C23#1062533411yescharacteristic
132C23#1062533511yescharacteristic
133C23#1062533611yescharacteristic
134C23#1062533711yescharacteristic
135C23C22⋊Dic4711yescharacteristic
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—42no—
143C2×C4—42no—
144C2×C4—42no—
145C2×C4—944no—
146C2×C4—1884no—
147C2×C4—1884no—
148C2×C4—1882no—
149C2×C4—1882no—
150C2×C4C4×Dic4711yescharacteristic
151C2×C4Dic47⋊C411yescharacteristic
152C2×C4C4⋊Dic4711yescharacteristic
153C2×C4(C2×D47)⋊C411yescharacteristic
154C8—1882no—
155C22—22no—
156C22—22no—
157C22—22no—
158C22—22no—
159C22—21no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22C47⋊#9511yescharacteristic
164C22#1309393912yes—
165C22#1309394411yescharacteristic
166C22#1309394511yescharacteristic
167C22#1309394711yescharacteristic
168C22#1309394811yescharacteristic
169C22#1309395112yes—
170C22#1309395511yescharacteristic
171C22#1309395711yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—82no—
177C4—1884no—
178C2—21no—
179C2—21no—
180C2—21no—
181C2—21no—
182C2#1568885712yes—
183C2#1568886012yes—
184C2#1568888211yescharacteristic
185C2#1568888511yescharacteristic
186C2#1568889011yescharacteristic
subgroupG/H
centerC23C22⋊Dic47
commutatorC2×C4×C47C42
FrattiniC23×C4C2×D47
FittingC47×#380C2
socleC23×C47C22⋊C4
hypercenter#380D47
hypocenterC47#1294
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
7. C22⋊(C47⋊C8)C4semidirect
9. C47⋊#95C4semidirect
11. C2×C4⋊C4×C47C4semidirect
97. C47#1294semidirect
101. C2×C4⋊C4Dic47semidirect