Finite Group Databasebeta

← #15689925

Subgroups — #15689925

Order 3008.

268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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#13094070C212yesmaximal, complemented
2#13094051C214yesmaximal, complemented
3#13094049C212yesmaximal, complemented
4#13094047C212yesmaximal, complemented
5C2×D376C211yesmaximal, characteristic, complemented
6D8×D47C212yesmaximal, complemented
7#13094030C211yesmaximal, characteristic, complemented
8#135×C47C211yesmaximal, characteristic, complemented
9#41×C47C2212yescomplemented
10#10625354C2214yescomplemented
11D4×D47—24no—
12D4×D47C2214yescomplemented
13#10625350—22no—
14#10625350C2211yescharacteristic
15C2×D188—22no—
16C2×D188C2212yescomplemented
17Q16×C47C2211yescharacteristic, complemented
18SD16×C47C2212yescomplemented
19D8×C47C2211yescharacteristic, complemented
20C2×C8×C47C2211yescharacteristic, complemented
21#10625336C2214yescomplemented
22#10625334C2214yescomplemented
23#10625329C2211yescharacteristic, complemented
24D376C2212yescomplemented
25D376C2212yescomplemented
26#10625324C2212yescomplemented
27C8×D47C2212yescomplemented
28C22×D47—22no—
29C22×D47—24no—
30Q8×C47C2312yes—
31D4×C47—22no—
32D4×C47C2312yes—
33C2×C4×C47—22no—
34C2×C4×C47C2311yescharacteristic
35C22⋊D47—24no—
36C22⋊D47D412yes—
37D188—24no—
38D188—22no—
39D188D411yescharacteristic
40D188C2314yes—
41C4×D47—24no—
42C4×D47C2312yes—
43Dic94D411yescharacteristic
44C8×C47C2311yescharacteristic
45C8×C47C2311yescharacteristic
46C47⋊C8C2312yes—
47C22×C47—22no—
48C22×C47C2×D411yescharacteristic
49C2×D47—24no—
50C2×D47—84no—
51C2×D47—82no—
52C2×D47C2×D412yes—
53C4×C47—22no—
54C4×C47C2×D411yescharacteristic
55C4×C47C2411yescharacteristic
56Dic47C2×D412yes—
57C2×C47—21no—
58C2×C47—42no—
59C2×C47C22×D411yescharacteristic
60D47—22no—
61D47—44no—
62#576—471nomaximal, Sylow
63C47#57611yescharacteristic, complemented, Sylow
64H(5,𝔽2)—472no—
65AGL(1,ℤ/8)—472no—
66AGL(1,ℤ/8)—474no—
67#135—472no—
68#135D4711yescharacteristic, complemented
69C2×D8—472no—
70C2×D8—471no—
71#131—471no—
72#41—471no—
73#41—474no—
74#41—942no—
75#41C2×D4712yescomplemented
76C2×D4—474no—
77C2×D4—472no—
78C2×D4—942no—
79C2×D4—944no—
80Q16C2×D4711yescharacteristic, complemented
81SD16—474no—
82SD16C2×D4712yescomplemented
83D8—474no—
84D8—472no—
85D8—472no—
86D8C2×D4711yescharacteristic, complemented
87M16—471no—
88M16—472no—
89C2×C8—472no—
90C2×C8C2×D4711yescharacteristic, complemented
91C23—944no—
92C23—942no—
93Q8—471no—
94Q8C22×D4712yes—
95D4—22no—
96D4—472no—
97D4—471no—
98D4—474no—
99D4—944no—
100D4—944no—
101D4—942no—
102D4C22×D4712yes—
103C2×C4—22no—
104C2×C4—472no—
105C2×C4—944no—
106C2×C4C22×D4711yescharacteristic
107C8—472no—
108C8C22×D4711yescharacteristic
109C8C22×D4711yescharacteristic
110C22—22no—
111C22—472no—
112C22—944no—
113C22—3762no—
114C22—3764no—
115C22D4×D4711yescharacteristic
116C4—22no—
117C4—472no—
118C4D4×D4711yescharacteristic
119C4C23×D4711yescharacteristic
120C2—21no—
121C2—42no—
122C2—942no—
123C2—1884no—
124C2C2×D4×D4711yescharacteristic
subgroupG/H
centerC2C2×D4×D47
commutator, cosocleC4×C47C24
FrattiniC4C23×D47
Fitting#135×C47C2
socleC2×C47C22×D4
hypercenter#135D47
hypocenterC47#576
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #13094070C2semidirect
2. #13094051C2semidirect
3. #13094049C2semidirect
4. #13094047C2semidirect
5. C2×D376C2semidirect
6. D8×D47C2semidirect
7. #13094030C2semidirect
8. #135×C47C2semidirect
9. #41×C47C22semidirect
10. #10625354C22semidirect
12. D4×D47C22semidirect
16. C2×D188C22semidirect
17. Q16×C47C22semidirect
18. SD16×C47C22semidirect
19. D8×C47C22semidirect
20. C2×C8×C47C22semidirect
21. #10625336C22semidirect
22. #10625334C22semidirect
23. #10625329C22semidirect
24. D376C22semidirect
25. D376C22semidirect
26. #10625324C22semidirect
27. C8×D47C22semidirect
63. C47#576semidirect
68. #135D47semidirect
75. #41C2×D47semidirect
80. Q16C2×D47semidirect
82. SD16C2×D47semidirect
86. D8C2×D47semidirect
90. C2×C8C2×D47semidirect

Maximal subgroups

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

subgroupindex
#130940702
#130940512
#130940492
#130940472
C2×D3762
D8×D472
#130940302
#135×C472
#57647