Finite Group Databasebeta

← #15689757

Subgroups — #15689757

Order 3008.

428 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C22×D188C211yesmaximal, characteristic, complemented
2C2×D4×D47C211yesmaximal, characteristic, complemented
3C2×D4×D47C212yesmaximal, complemented
4#13094020C211yesmaximal, characteristic, complemented
5#13093999C211yesmaximal, characteristic, complemented
6#13093997C212yesmaximal, complemented
7#13093994C212yesmaximal, complemented
8#13093992C212yesmaximal, complemented
9#13093986C211yesmaximal, characteristic, complemented
10C4×C22⋊D47C211yesmaximal, characteristic, complemented
11#121×C47C211yesmaximal, characteristic, complemented
12C23×D47C2212yescomplemented
13C23×D47C2212yescomplemented
14C2×D4×C47C2212yescomplemented
15C2×D4×C47C2211yescharacteristic, complemented
16C22×C4×C47C2211yescharacteristic, complemented
17C2×C22⋊D47C2211yescharacteristic
18C2×C22⋊D47C2212yescomplemented
19C2×C22⋊D47C2212yescomplemented
20C2×C22⋊D47C2212yescomplemented
21D4×D47—28no—
22D4×D47—24no—
23C2×D188—24no—
24C2×D188C2211yescharacteristic
25C2×D188C2212yescomplemented
26C2×D188C2212yescomplemented
27C2×D188C2211yescharacteristic, complemented
28C2×C4×D47C2211yescharacteristic, complemented
29C2×C4×D47C2212yescomplemented
30C4⋊C4×C47C2211yescharacteristic, complemented
31C22⋊C4×C47C2212yescomplemented
32C22⋊Dic47C2211yescharacteristic, complemented
33(C2×D47)⋊C4C2211yescharacteristic, complemented
34(C2×D47)⋊C4C2212yescomplemented
35(C2×D47)⋊C4C2212yescomplemented
36Dic47⋊C4C2211yescharacteristic, complemented
37C4×Dic47C2211yescharacteristic, complemented
38C23×C47C2312yes—
39C23×C47C2311yescharacteristic
40C22×D47—24no—
41C22×D47—24no—
42C22×D47—24no—
43C22×D47—24no—
44C22×D47—42no—
45C22×D47—42no—
46C22×D47C2312yes—
47C22×D47C2312yes—
48C22×D47C2311yescharacteristic
49D4×C47—24no—
50D4×C47—22no—
51C2×C4×C47—22no—
52C2×C4×C47C2311yescharacteristic
53C2×C4×C47C2312yes—
54C2×C4×C47C2311yescharacteristic
55C22⋊D47—24no—
56C22⋊D47—24no—
57C22⋊D47—42no—
58C22⋊D47D414yescomplemented
59C2×Dic47C2311yescharacteristic
60C2×Dic47C2311yescharacteristic
61C2×Dic47C2311yescharacteristic
62D188—24no—
63D188—24no—
64D188—22no—
65D188D414yescomplemented
66C4×D47—22no—
67C4×D47—24no—
68C22×C47—21no—
69C22×C47—21no—
70C22×C47—22no—
71C22×C47—22no—
72C22×C47—22no—
73C22×C47C2×D412yescomplemented
74C22×C47C2411yescharacteristic
75C2×D47—21no—
76C2×D47—22no—
77C2×D47—22no—
78C2×D47—21no—
79C2×D47—22no—
80C2×D47—22no—
81C2×D47—22no—
82C2×D47—48no—
83C2×D47—48no—
84C2×D47C2×D412yescomplemented
85C2×D47C2×D414yescomplemented
86C4×C47—22no—
87C4×C47—21no—
88C4×C47C2×D412yescomplemented
89Dic47—21no—
90Dic47—21no—
91Dic47C2×D412yescomplemented
92C2×C47—22no—
93C2×C47—42no—
94C2×C47C22×D411yescharacteristic
95C2×C47C22×D411yescharacteristic
96C2×C47H(5,𝔽2)11yescharacteristic
97D47—22no—
98D47—24no—
99D47—42no—
100D42—471nomaximal, Sylow
101C47D4211yescharacteristic, complemented, Sylow
102C22×D4—472no—
103C22×D4—471no—
104C22×D4—471no—
105#127—471no—
106#121—471no—
107#121—472no—
108#121D4711yescharacteristic, complemented
109#120—472no—
110#120—472no—
111C4×D4—471no—
112C4×D4—471no—
113C24—472no—
114C24—472no—
115C2×D4—471no—
116C2×D4—472no—
117C2×D4—472no—
118C2×D4—472no—
119C2×D4—471no—
120C2×D4—472no—
121C2×D4—472no—
122C2×D4—471no—
123C2×D4—944no—
124C2×D4—948no—
125C2×D4—944no—
126C2×D4C2×D4712yescomplemented
127C2×D4C2×D4711yescharacteristic, complemented
128C22×C4—472no—
129C22×C4—471no—
130C22×C4C2×D4711yescharacteristic, complemented
131C4⋊C4—471no—
132C4⋊C4C2×D4711yescharacteristic, complemented
133C22⋊C4—471no—
134C22⋊C4—472no—
135C22⋊C4—471no—
136C22⋊C4—472no—
137C22⋊C4C2×D4712yescomplemented
138C42—471no—
139C23—472no—
140C23—471no—
141C23—472no—
142C23—944no—
143C23—944no—
144C23—944no—
145C23—944no—
146C23—1882no—
147C23—1882no—
148C23C22×D4712yes—
149C23C22×D4711yescharacteristic
150D4—24no—
151D4—22no—
152D4—474no—
153D4—474no—
154D4—944no—
155D4—944no—
156D4—944no—
157D4—944no—
158D4—942no—
159D4—1882no—
160C2×C4—22no—
161C2×C4—471no—
162C2×C4—471no—
163C2×C4—471no—
164C2×C4—944no—
165C2×C4—942no—
166C2×C4C22×D4712yes—
167C2×C4C22×D4711yescharacteristic
168C2×C4C22×D4711yescharacteristic
169C22—21no—
170C22—21no—
171C22—22no—
172C22—22no—
173C22—22no—
174C22—472no—
175C22—474no—
176C22—942no—
177C22—941no—
178C22—942no—
179C22—941no—
180C22—942no—
181C22—942no—
182C22—942no—
183C22—1888no—
184C22—1888no—
185C22D4×D4712yescomplemented
186C22C23×D4711yescharacteristic
187C4—21no—
188C4—22no—
189C4—472no—
190C4—941no—
191C4—941no—
192C4D4×D4712yescomplemented
193C2—22no—
194C2—42no—
195C2—944no—
196C2—942no—
197C2—1882no—
198C2C2×D4×D4711yescharacteristic
199C2C2×D4×D4711yescharacteristic
200C2#1309407011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D47
commutator, socle, cosocleC22×C47C24
Fitting#121×C47C2
hypercenter#121D47
hypocenterC47D42
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C22×D188C2semidirect
2. C2×D4×D47C2semidirect
3. C2×D4×D47C2semidirect
4. #13094020C2semidirect
5. #13093999C2semidirect
6. #13093997C2semidirect
7. #13093994C2semidirect
8. #13093992C2semidirect
9. #13093986C2semidirect
10. C4×C22⋊D47C2semidirect
11. #121×C47C2semidirect
12. C23×D47C22semidirect
13. C23×D47C22semidirect
14. C2×D4×C47C22semidirect
15. C2×D4×C47C22semidirect
16. C22×C4×C47C22semidirect
18. C2×C22⋊D47C22semidirect
19. C2×C22⋊D47C22semidirect
20. C2×C22⋊D47C22semidirect
25. C2×D188C22semidirect
26. C2×D188C22semidirect
27. C2×D188C22semidirect
28. C2×C4×D47C22semidirect
29. C2×C4×D47C22semidirect
30. C4⋊C4×C47C22semidirect
31. C22⋊C4×C47C22semidirect
32. C22⋊Dic47C22semidirect
33. (C2×D47)⋊C4C22semidirect
34. (C2×D47)⋊C4C22semidirect
35. (C2×D47)⋊C4C22semidirect
36. Dic47⋊C4C22semidirect
37. C4×Dic47C22semidirect
58. C22⋊D47D4semidirect
65. D188D4semidirect
73. C22×C47C2×D4semidirect
84. C2×D47C2×D4semidirect
85. C2×D47C2×D4semidirect
88. C4×C47C2×D4semidirect
91. Dic47C2×D4semidirect
101. C47D42semidirect
108. #121D47semidirect
126. C2×D4C2×D47semidirect
127. C2×D4C2×D47semidirect
130. C22×C4C2×D47semidirect
132. C4⋊C4C2×D47semidirect
137. C22⋊C4C2×D47semidirect
185. C22D4×D47semidirect
192. C4D4×D47semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×D1882
C2×D4×D472
#130940202
#130939992
#130939972
#130939942
#130939922
#130939862
C4×C22⋊D472
#121×C472
D4247