Finite Group Databasebeta

← #15689681

Subgroups — #15689681

Order 3008.

346 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 103 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×D4×D47C212yesmaximal, complemented
2#13094009C212yesmaximal, complemented
3#13094006C212yesmaximal, complemented
4#13093998C211yesmaximal, characteristic, complemented
5#13093996C212yesmaximal, complemented
6#13093994C212yesmaximal, complemented
7#13093992C212yesmaximal, complemented
8C2×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
9#121×C47C211yesmaximal, characteristic, complemented
10C23×D47C2211yescharacteristic
11C23×D47C2212yescomplemented
12C2×D4×C47C2212yescomplemented
13C2×D4×C47C2211yescharacteristic, complemented
14C22×C4×C47C2211yescharacteristic, complemented
15C2×C22⋊D47C2212yes—
16C2×C22⋊D47C2212yescomplemented
17C2×C22⋊D47C2212yescomplemented
18C22×Dic47C2211yescharacteristic, complemented
19D4×D47—28no—
20C2×D188C2212yes—
21C2×D188C2211yescharacteristic, complemented
22C2×C4×D47C2212yescomplemented
23C4⋊C4×C47C2211yescharacteristic, complemented
24C22⋊C4×C47C2212yescomplemented
25C22⋊Dic47C2212yescomplemented
26(C2×D47)⋊C4C2212yescomplemented
27(C2×D47)⋊C4C2212yescomplemented
28(C2×D47)⋊C4C2212yescomplemented
29(C2×D47)⋊C4C2212yescomplemented
30C4⋊Dic47C2211yescharacteristic, complemented
31Dic47⋊C4C2212yescomplemented
32C23×C47C2312yes—
33C23×C47C2311yescharacteristic
34C22×D47—24no—
35C22×D47—41no—
36C22×D47—41no—
37C22×D47—42no—
38C22×D47—42no—
39C22×D47D414yescomplemented
40C22×D47C2312yes—
41C22×D47C2312yes—
42D4×C47—24no—
43D4×C47—41no—
44C2×C4×C47—41no—
45C2×C4×C47C2312yes—
46C2×C4×C47C2311yescharacteristic
47C2×C4×C47C2311yescharacteristic
48C22⋊D47—24no—
49C22⋊D47—24no—
50C22⋊D47—42no—
51C2×Dic47—41no—
52C2×Dic47C2312yes—
53C2×Dic47C2312yes—
54D188—24no—
55D188—41no—
56C4×D47—24no—
57C22×C47—21no—
58C22×C47—21no—
59C22×C47—22no—
60C22×C47—22no—
61C22×C47—22no—
62C22×C47C2×D412yes—
63C22×C47C2411yescharacteristic
64C2×D47—22no—
65C2×D47—22no—
66C2×D47—22no—
67C2×D47—22no—
68C2×D47—22no—
69C2×D47—44no—
70C2×D47—48no—
71C2×D47C2×D414yes—
72C4×C47—22no—
73C4×C47—21no—
74C4×C47—21no—
75Dic47—22no—
76Dic47—22no—
77C2×C47—22no—
78C2×C47—42no—
79C2×C47C22×D411yescharacteristic
80C2×C47H(5,𝔽2)11yescharacteristic
81C2×C47H(5,𝔽2)11yescharacteristic
82D47—24no—
83D47—42no—
84#534—471nomaximal, Sylow
85C47#53411yescharacteristic, complemented, Sylow
86C22×D4—472no—
87#123—472no—
88#123—472no—
89#121—472no—
90#121—471no—
91#121D4711yescharacteristic, complemented
92#120—472no—
93#120—472no—
94C2×C22⋊C4—471no—
95C24—471no—
96C24—472no—
97C2×D4—472no—
98C2×D4—472no—
99C2×D4—472no—
100C2×D4—472no—
101C2×D4—471no—
102C2×D4—948no—
103C2×D4C2×D4712yescomplemented
104C2×D4C2×D4711yescharacteristic, complemented
105C22×C4—471no—
106C22×C4—472no—
107C22×C4C2×D4711yescharacteristic, complemented
108C4⋊C4—472no—
109C4⋊C4—471no—
110C4⋊C4C2×D4711yescharacteristic, complemented
111C22⋊C4—472no—
112C22⋊C4—472no—
113C22⋊C4—472no—
114C22⋊C4—472no—
115C22⋊C4—472no—
116C22⋊C4C2×D4712yescomplemented
117C23—472no—
118C23—474no—
119C23—472no—
120C23—944no—
121C23—1881no—
122C23—1881no—
123C23—1882no—
124C23—1882no—
125C23C22×D4712yes—
126C23C22×D4711yescharacteristic
127D4—24no—
128D4—41no—
129D4—944no—
130D4—944no—
131D4—944no—
132D4—1881no—
133D4—1882no—
134C2×C4—41no—
135C2×C4—472no—
136C2×C4—472no—
137C2×C4—944no—
138C2×C4—1881no—
139C2×C4C22×D4711yescharacteristic
140C2×C4C22×D4711yescharacteristic
141C2×C4C22×D4712yes—
142C22—21no—
143C22—21no—
144C22—22no—
145C22—22no—
146C22—22no—
147C22—474no—
148C22—942no—
149C22—942no—
150C22—942no—
151C22—942no—
152C22—942no—
153C22—1884no—
154C22—1888no—
155C22D4×D4712yes—
156C22C23×D4711yescharacteristic
157C4—22no—
158C4—21no—
159C4—21no—
160C4—942no—
161C4—942no—
162C2—22no—
163C2—42no—
164C2—944no—
165C2—1882no—
166C2C2×D4×D4711yescharacteristic
167C2#1309406911yescharacteristic
168C2#1309407011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D47
commutator, socle, cosocleC22×C47C24
Fitting#121×C47C2
hypercenter#121D47
hypocenterC47#534
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D4×D47C2semidirect
2. #13094009C2semidirect
3. #13094006C2semidirect
4. #13093998C2semidirect
5. #13093996C2semidirect
6. #13093994C2semidirect
7. #13093992C2semidirect
8. C2×(C2×D47)⋊C4C2semidirect
9. #121×C47C2semidirect
11. C23×D47C22semidirect
12. C2×D4×C47C22semidirect
13. C2×D4×C47C22semidirect
14. C22×C4×C47C22semidirect
16. C2×C22⋊D47C22semidirect
17. C2×C22⋊D47C22semidirect
18. C22×Dic47C22semidirect
21. C2×D188C22semidirect
22. C2×C4×D47C22semidirect
23. C4⋊C4×C47C22semidirect
24. C22⋊C4×C47C22semidirect
25. C22⋊Dic47C22semidirect
26. (C2×D47)⋊C4C22semidirect
27. (C2×D47)⋊C4C22semidirect
28. (C2×D47)⋊C4C22semidirect
29. (C2×D47)⋊C4C22semidirect
30. C4⋊Dic47C22semidirect
31. Dic47⋊C4C22semidirect
39. C22×D47D4semidirect
85. C47#534semidirect
91. #121D47semidirect
103. C2×D4C2×D47semidirect
104. C2×D4C2×D47semidirect
107. C22×C4C2×D47semidirect
110. C4⋊C4C2×D47semidirect
116. C22⋊C4C2×D47semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D472
#130940092
#130940062
#130939982
#130939962
#130939942
#130939922
C2×(C2×D47)⋊C42
#121×C472
#53447