Finite Group Databasebeta

← #20241926

Subgroups — #20241926

Order 6016.

222 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 77 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#15689180C211yesmaximal, characteristic, complemented
2#15688989C211yesmaximal, characteristic, complemented
3#15688860C212yesmaximal, complemented
4#15688857C212yesmaximal
5C47×#529C211yesmaximal, characteristic
6C2×C4⋊Dic47—21no—
7C4⋊(C47⋊C8)—21no—
8C22⋊(C47⋊C8)C2212yes—
9#13093935—21no—
10C47⋊#95—21no—
11C47⋊#95C2212yes—
12#126×C47—21no—
13#125×C47C411yescharacteristic, complemented
14#124×C47C411yescharacteristic, complemented
15#123×C47—21no—
16C22⋊Q8×C47C2211yescharacteristic
17#121×C47C2211yescharacteristic
18C4×Q8×C47C411yescharacteristic, complemented
19C4×D4×C47—21no—
20C4×D4×C47C411yescharacteristic, complemented
21#117×C47—21no—
22C2×C42×C47C2211yescharacteristic
23C2×Q8×C47C2×C411yescharacteristic
24C2×D4×C47—21no—
25C2×D4×C47C2×C411yescharacteristic
26C22×C4×C47—21no—
27C22×C4×C47D411yescharacteristic
28C22×C4×C47D411yescharacteristic
29C22×C4×C47C2311yescharacteristic
30C22×Dic47—22no—
31C4⋊C4×C47—21no—
32C4⋊C4×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47—21no—
35C4⋊C4×C47C2×C411yescharacteristic
36C4⋊C4×C47C2×C411yescharacteristic
37C22⋊C4×C47—21no—
38C22⋊C4×C47—21no—
39C22⋊C4×C47—21no—
40C22⋊C4×C47—21no—
41C22⋊C4×C47—21no—
42C42×C47—21no—
43C42×C47C2×C411yescharacteristic
44C42×C47C2×C411yescharacteristic
45C42×C47D411yescharacteristic
46C42×C47D411yescharacteristic
47C4⋊Dic47—42no—
48C2×C47⋊C8—22no—
49C23×C47—21no—
50C23×C47C2×D411yescharacteristic
51Q8×C47—41no—
52D4×C47—41no—
53D4×C47—41no—
54D4×C47—41no—
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47—42no—
63C2×C4×C47C22⋊C411yescharacteristic
64C2×C4×C47C22⋊C411yescharacteristic
65C2×C4×C47C22⋊C411yescharacteristic
66C2×C4×C47C22⋊C411yescharacteristic
67C2×C4×C47C22×C411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C2×Dic47—42no—
70C2×Dic47—42no—
71C2×Dic47—42no—
72C47⋊C8—42no—
73C22×C47—21no—
74C22×C47—21no—
75C22×C47—41no—
76C22×C47—41no—
77C22×C47—41no—
78C22×C47C2×C22⋊C411yescharacteristic
79C22×C47AGL(1,ℤ/8)11yescharacteristic
80C22×C47#13711yescharacteristic
81C4×C47—21no—
82C4×C47—21no—
83C4×C47—21no—
84C4×C47—21no—
85C4×C47—21no—
86C4×C47—21no—
87C4×C47—41no—
88C4×C47—41no—
89C4×C47—41no—
90Dic47—82no—
91#1512—471nomaximal, Sylow
92C2×C47—21no—
93C2×C47—21no—
94C2×C47—81no—
95C2×C47#41011yescharacteristic
96C2×C47#41711yescharacteristic
97C2×C47#42111yescharacteristic
98#529D4711yescharacteristic
99#432—471no—
100#382—471no—
101#328—472no—
102#327—472no—
103C47#151211yescharacteristic, complemented, Sylow
104#126—21no—
105#125Dic4711yescharacteristic, complemented
106#124Dic4711yescharacteristic, complemented
107#123—21no—
108C22⋊Q8C2×D4711yescharacteristic
109#121C2×D4711yescharacteristic
110C4×Q8Dic4711yescharacteristic, complemented
111C4×D4—21no—
112C4×D4Dic4711yescharacteristic, complemented
113#117—21no—
114C2×C4⋊C4—941no—
115C2×C42C2×D4711yescharacteristic
116C4⋊C8—941no—
117C22⋊C8—472no—
118#97—941no—
119#95—472no—
120#95—941no—
121C2×Q8C2×Dic4711yescharacteristic
122C2×D4—21no—
123C2×D4C2×Dic4711yescharacteristic
124C22×C4—21no—
125C22×C4—942no—
126C22×C4C22⋊D4711yescharacteristic
127C22×C4C22⋊D4711yescharacteristic
128C22×C4C22×D4711yescharacteristic
129C2×C8—942no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—1882no—
135C4⋊C4C2×Dic4711yescharacteristic
136C4⋊C4C2×Dic4711yescharacteristic
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—21no—
141C22⋊C4—21no—
142C42—21no—
143C42C2×Dic4711yescharacteristic
144C42C2×Dic4711yescharacteristic
145C42C22⋊D4711yescharacteristic
146C42C22⋊D4711yescharacteristic
147C23—21no—
148C23C2×C22⋊D4711yescharacteristic
149Q8—41no—
150D4—41no—
151D4—41no—
152D4—41no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—1882no—
162C2×C4—1882no—
163C2×C4—1882no—
164C2×C4C22⋊Dic4711yescharacteristic
165C2×C4C22⋊Dic4711yescharacteristic
166C2×C4C22⋊Dic4711yescharacteristic
167C2×C4C22⋊Dic4711yescharacteristic
168C2×C4C22×Dic4711yescharacteristic
169C2×C4C2×C22⋊D4711yescharacteristic
170C8—1882no—
171C22—21no—
172C22—21no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22C2×C22⋊Dic4711yescharacteristic
177C22#1309404911yescharacteristic
178C22#1309405411yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—41no—
188C4—3762no—
189C2—21no—
190C2—21no—
191C2—81no—
192C2#1568909711yescharacteristic
193C2#1568912411yescharacteristic
194C2#1568914011yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#529C2
socleC22×C47C2×C22⋊C4
hypercenter#529D47
hypocenterC47#1512
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #15689180C2semidirect
2. #15688989C2semidirect
3. #15688860C2semidirect
13. #125×C47C4semidirect
14. #124×C47C4semidirect
18. C4×Q8×C47C4semidirect
20. C4×D4×C47C4semidirect
103. C47#1512semidirect
105. #125Dic47semidirect
106. #124Dic47semidirect
110. C4×Q8Dic47semidirect
112. C4×D4Dic47semidirect