Finite Group Databasebeta

← #20241904

Subgroups — #20241904

Order 6016.

346 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 85 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#15689087C211yesmaximal, characteristic, complemented
2C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
3#15688857C214yesmaximal, complemented
4C2×#121×C47C211yesmaximal, characteristic
5C2×#10625329—21no—
6C2×C22⋊Dic47—21no—
7C2×C4×Dic47—21no—
8C22⋊(C47⋊C8)—21no—
9C22⋊(C47⋊C8)C2212yescomplemented
10C47⋊#95C2212yescomplemented
11C22×D4×C47—21no—
12C22×D4×C47C411yescharacteristic, complemented
13C23×C4×C47C2211yescharacteristic
14#121×C47—21no—
15#121×C47—21no—
16#121×C47C412yescomplemented
17#121×C47C2212yes—
18C2×C4⋊C4×C47C411yescharacteristic, complemented
19C2×C22⋊C4×C47—21no—
20C24×C47—21no—
21C24×C47D411yescharacteristic
22C2×D4×C47—22no—
23C2×D4×C47—22no—
24C2×D4×C47—21no—
25C2×D4×C47—42no—
26C2×D4×C47—44no—
27C2×D4×C47C2×C412yes—
28C22×C4×C47—21no—
29C22×C4×C47—42no—
30C22×C4×C47C2×C411yescharacteristic
31C22×C4×C47C2×C411yescharacteristic
32C22×C4×C47D411yescharacteristic
33C22×C4×C47D411yescharacteristic
34C22×C4×C47D411yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C22×Dic47—22no—
37C4⋊C4×C47—21no—
38C4⋊C4×C47C2×C412yes—
39C22⋊C4×C47—22no—
40C22⋊C4×C47—22no—
41C22⋊Dic47—24no—
42C4×Dic47—42no—
43#10625329—42no—
44C2×C47⋊C8—22no—
45C23×C47—22no—
46C23×C47—22no—
47C23×C47—22no—
48C23×C47—41no—
49C23×C47—42no—
50C23×C47—42no—
51C23×C47—42no—
52C23×C47C22⋊C411yescharacteristic
53C23×C47C22⋊C411yescharacteristic
54C23×C47C2×D411yescharacteristic
55D4×C47—42no—
56D4×C47—44no—
57D4×C47—44no—
58D4×C47—42no—
59C2×C4×C47—22no—
60C2×C4×C47—22no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—41no—
64C2×C4×C47—41no—
65C2×C4×C47—41no—
66C2×C4×C47—42no—
67C2×C4×C47C22⋊C411yescharacteristic
68C2×C4×C47C22⋊C411yescharacteristic
69C2×C4×C47C22×C411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×Dic47—24no—
72C2×Dic47—42no—
73C2×Dic47—42no—
74C47⋊C8—42no—
75C22×C47—21no—
76C22×C47—21no—
77C22×C47—21no—
78C22×C47—21no—
79C22×C47—21no—
80C22×C47—21no—
81C22×C47—21no—
82C22×C47—44no—
83C22×C47—42no—
84C22×C47—42no—
85C22×C47—42no—
86C22×C47—84no—
87C22×C47#10412yes—
88C22×C47C2×C22⋊C411yescharacteristic
89C22×C47AGL(1,ℤ/8)12yes—
90C4×C47—21no—
91C4×C47—21no—
92C4×C47—21no—
93C4×C47—42no—
94C4×C47#9912yes—
95Dic47—44no—
96#1507—471nomaximal, Sylow
97C2×C47—22no—
98C2×C47—22no—
99C2×C47—41no—
100C2×C47—82no—
101C2×C47C2×#9911yescharacteristic
102C2×C47#41811yescharacteristic
103C2×C47C2×#10411yescharacteristic
104C2×#121D4711yescharacteristic
105#407—471no—
106C4×C22⋊C4—471no—
107#327—474no—
108C47#150711yescharacteristic, complemented, Sylow
109C22×D4—21no—
110C22×D4Dic4711yescharacteristic, complemented
111C23×C4C2×D4711yescharacteristic
112C2×M16—941no—
113#121—21no—
114#121—21no—
115#121Dic4712yescomplemented
116#121C2×D4712yes—
117C2×C4⋊C4Dic4711yescharacteristic, complemented
118C2×C22⋊C4—21no—
119C2×C22⋊C4—941no—
120C2×C42—941no—
121C22⋊C8—472no—
122C22⋊C8—941no—
123#95—472no—
124C24—21no—
125C24C22⋊D4711yescharacteristic
126C2×D4—22no—
127C2×D4—22no—
128C2×D4—21no—
129C2×D4—42no—
130C2×D4—44no—
131C2×D4C2×Dic4712yes—
132C22×C4—21no—
133C22×C4—42no—
134C22×C4—942no—
135C22×C4C2×Dic4711yescharacteristic
136C22×C4C2×Dic4711yescharacteristic
137C22×C4C22⋊D4711yescharacteristic
138C22×C4C22⋊D4711yescharacteristic
139C22×C4C22⋊D4711yescharacteristic
140C22×C4C22×D4711yescharacteristic
141M16—1882no—
142C2×C8—942no—
143C4⋊C4—21no—
144C4⋊C4C2×Dic4712yes—
145C22⋊C4—22no—
146C22⋊C4—22no—
147C22⋊C4—944no—
148C42—1882no—
149C23—22no—
150C23—22no—
151C23—22no—
152C23—41no—
153C23—42no—
154C23—42no—
155C23—42no—
156C23C22⋊Dic4711yescharacteristic
157C23C22⋊Dic4711yescharacteristic
158C23C2×C22⋊D4711yescharacteristic
159D4—42no—
160D4—44no—
161D4—44no—
162D4—42no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—42no—
171C2×C4—944no—
172C2×C4—1882no—
173C2×C4—1882no—
174C2×C4C22⋊Dic4711yescharacteristic
175C2×C4C22⋊Dic4711yescharacteristic
176C2×C4C22×Dic4711yescharacteristic
177C2×C4C2×C22⋊D4711yescharacteristic
178C8—1882no—
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—44no—
187C22—42no—
188C22—42no—
189C22—42no—
190C22—84no—
191C22#1309395112yes—
192C22C2×C22⋊Dic4711yescharacteristic
193C22#1309405012yes—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—42no—
198C4—1884no—
199C4#1309393912yes—
200C2—22no—
201C2—22no—
202C2—41no—
203C2—82no—
204C2C2×#1309393911yescharacteristic
205C2#1568912811yescharacteristic
206C2C2×#1309395111yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#121×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC2×#121D47
hypocenterC47#1507
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #15689087C2semidirect
2. C4×C22⋊Dic47C2semidirect
3. #15688857C2semidirect
9. C22⋊(C47⋊C8)C22semidirect
10. C47⋊#95C22semidirect
12. C22×D4×C47C4semidirect
16. #121×C47C4semidirect
18. C2×C4⋊C4×C47C4semidirect
108. C47#1507semidirect
110. C22×D4Dic47semidirect
115. #121Dic47semidirect
117. C2×C4⋊C4Dic47semidirect