Finite Group Databasebeta

← #15689755

Subgroups — #15689755

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×C22⋊D47C212yesmaximal, complemented
2C2×D4×D47C212yesmaximal, complemented
3#13094020C211yesmaximal, characteristic, complemented
4#13093997C212yesmaximal, complemented
5#13093996C212yesmaximal, complemented
6#13093994C212yesmaximal, complemented
7#13093992C211yesmaximal, characteristic, complemented
8(C22⋊D47)⋊C4C212yesmaximal, complemented
9#120×C47C211yesmaximal, characteristic, complemented
10C24×C47C2211yescharacteristic, complemented
11C23×D47C2211yescharacteristic, complemented
12C23×D47C2212yescomplemented
13C2×D4×C47C2212yescomplemented
14C2×D4×C47C2211yescharacteristic, complemented
15C2×C22⋊D47—28no—
16C2×C22⋊D47C2212yes—
17C2×C22⋊D47C2212yescomplemented
18C2×C22⋊D47C2212yescomplemented
19C2×C22⋊D47C2212yescomplemented
20C2×C22⋊D47C2212yescomplemented
21C22×Dic47C2212yescomplemented
22D4×D47—28no—
23C2×D188C2212yescomplemented
24C2×D188C2211yescharacteristic, complemented
25C2×C4×D47C2212yescomplemented
26C22⋊C4×C47C2212yescomplemented
27C22⋊C4×C47C2211yescharacteristic, complemented
28C22⋊Dic47C2211yescharacteristic, complemented
29(C2×D47)⋊C4C2212yescomplemented
30(C2×D47)⋊C4C2212yescomplemented
31Dic47⋊C4C2212yescomplemented
32C4×Dic47C2211yescharacteristic, complemented
33C23×C47—24no—
34C23×C47—41no—
35C23×C47C2311yescharacteristic
36C23×C47C2311yescharacteristic
37C23×C47C2312yes—
38C22×D47—24no—
39C22×D47—24no—
40C22×D47—24no—
41C22×D47—41no—
42C22×D47—42no—
43C22×D47C2312yes—
44C22×D47C2312yes—
45D4×C47—24no—
46D4×C47—41no—
47C2×C4×C47C2311yescharacteristic
48C2×C4×C47C2312yes—
49C22⋊D47—24no—
50C22⋊D47—24no—
51C22⋊D47—24no—
52C22⋊D47—24no—
53C22⋊D47D418yescomplemented
54C2×Dic47—24no—
55C2×Dic47C2312yes—
56C2×Dic47C2312yes—
57D188—24no—
58D188—41no—
59C4×D47—24no—
60C22×C47—22no—
61C22×C47—22no—
62C22×C47—22no—
63C22×C47—22no—
64C22×C47—21no—
65C22×C47—21no—
66C22×C47—44no—
67C22×C47C2×D414yescomplemented
68C22×C47C2411yescharacteristic
69C2×D47—22no—
70C2×D47—22no—
71C2×D47—22no—
72C2×D47—22no—
73C2×D47—22no—
74C2×D47—44no—
75C2×D47—48no—
76C2×D47C2×D414yescomplemented
77C4×C47—22no—
78C4×C47—21no—
79Dic47—22no—
80Dic47C2×D414yescomplemented
81C2×C47—24no—
82C2×C47—41no—
83C2×C47—41no—
84C2×C47C22×D412yes—
85C2×C47H(5,𝔽2)11yescharacteristic
86D47—24no—
87D47—42no—
88D42—471nomaximal, Sylow
89C47D4211yescharacteristic, complemented, Sylow
90C22×D4—472no—
91C22×D4—472no—
92#127—471no—
93#121—472no—
94#121—472no—
95#120—471no—
96#120—472no—
97#120D4711yescharacteristic, complemented
98C4×D4—472no—
99C24—471no—
100C24—472no—
101C24C2×D4711yescharacteristic, complemented
102C2×D4—472no—
103C2×D4—472no—
104C2×D4—472no—
105C2×D4—472no—
106C2×D4—472no—
107C2×D4—472no—
108C2×D4—471no—
109C2×D4—948no—
110C2×D4—948no—
111C2×D4C2×D4712yescomplemented
112C2×D4C2×D4711yescharacteristic, complemented
113C22×C4—472no—
114C22×C4—472no—
115C4⋊C4—472no—
116C22⋊C4—471no—
117C22⋊C4—472no—
118C22⋊C4—472no—
119C22⋊C4C2×D4712yescomplemented
120C22⋊C4C2×D4711yescharacteristic, complemented
121C42—471no—
122C23—24no—
123C23—41no—
124C23—472no—
125C23—472no—
126C23—944no—
127C23—944no—
128C23—944no—
129C23—1882no—
130C23—1881no—
131C23C22×D4711yescharacteristic
132C23C22×D4711yescharacteristic
133C23C22×D4712yes—
134D4—24no—
135D4—41no—
136D4—478no—
137D4—944no—
138D4—944no—
139D4—944no—
140D4—944no—
141D4—944no—
142D4—1881no—
143C2×C4—472no—
144C2×C4—472no—
145C2×C4—944no—
146C2×C4—944no—
147C2×C4C22×D4711yescharacteristic
148C2×C4C22×D4712yes—
149C22—22no—
150C22—22no—
151C22—22no—
152C22—22no—
153C22—21no—
154C22—21no—
155C22—44no—
156C22—474no—
157C22—942no—
158C22—942no—
159C22—942no—
160C22—942no—
161C22—942no—
162C22—1888no—
163C22—1884no—
164C22D4×D4714yescomplemented
165C22C23×D4711yescharacteristic
166C4—22no—
167C4—21no—
168C4—474no—
169C4—942no—
170C2—24no—
171C2—41no—
172C2—41no—
173C2—944no—
174C2—1882no—
175C2C2×D4×D4712yes—
176C2#1309406911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D47
commutator, socle, cosocleC22×C47C24
Fitting#120×C47C2
hypercenter#120D47
hypocenterC47D42
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D47C2semidirect
2. C2×D4×D47C2semidirect
3. #13094020C2semidirect
4. #13093997C2semidirect
5. #13093996C2semidirect
6. #13093994C2semidirect
7. #13093992C2semidirect
8. (C22⋊D47)⋊C4C2semidirect
9. #120×C47C2semidirect
10. C24×C47C22semidirect
11. C23×D47C22semidirect
12. C23×D47C22semidirect
13. C2×D4×C47C22semidirect
14. C2×D4×C47C22semidirect
17. C2×C22⋊D47C22semidirect
18. C2×C22⋊D47C22semidirect
19. C2×C22⋊D47C22semidirect
20. C2×C22⋊D47C22semidirect
21. C22×Dic47C22semidirect
23. C2×D188C22semidirect
24. C2×D188C22semidirect
25. C2×C4×D47C22semidirect
26. C22⋊C4×C47C22semidirect
27. C22⋊C4×C47C22semidirect
28. C22⋊Dic47C22semidirect
29. (C2×D47)⋊C4C22semidirect
30. (C2×D47)⋊C4C22semidirect
31. Dic47⋊C4C22semidirect
32. C4×Dic47C22semidirect
53. C22⋊D47D4semidirect
67. C22×C47C2×D4semidirect
76. C2×D47C2×D4semidirect
80. Dic47C2×D4semidirect
89. C47D42semidirect
97. #120D47semidirect
101. C24C2×D47semidirect
111. C2×D4C2×D47semidirect
112. C2×D4C2×D47semidirect
119. C22⋊C4C2×D47semidirect
120. C22⋊C4C2×D47semidirect
164. C22D4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D472
C2×D4×D472
#130940202
#130939972
#130939962
#130939942
#130939922
(C22⋊D47)⋊C42
#120×C472
D4247