Finite Group Databasebeta

← #135×D47 #15689901

Subgroups — #135×D47 #15689901

Order 3008.

266 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 101 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#41×D47C212yesmaximal, complemented
2#13094047C211yesmaximal, characteristic, complemented
3#13094046C211yesmaximal, characteristic, complemented
4#13094045C212yesmaximal, complemented
5#13094044C212yesmaximal, complemented
6#13094043C211yesmaximal, characteristic, complemented
7Q16×D47C211yesmaximal, characteristic, complemented
8SD16×D47C212yesmaximal, complemented
9D8×D47C211yesmaximal, characteristic, complemented
10C2×C8×D47C211yesmaximal, characteristic, complemented
11#135×C47C211yesmaximal, characteristic, complemented
12#41×C47C2212yescomplemented
13#10625354C2212yescomplemented
14Q8×D47C2212yes—
15#10625352—22no—
16#10625352C2212yescomplemented
17D4×D47—22no—
18D4×D47C2212yes—
19#10625350—22no—
20#10625350C2212yescomplemented
21C2×C4×D47—22no—
22C2×C4×D47C2211yescharacteristic
23Q16×C47C2211yescharacteristic, complemented
24SD16×C47C2212yescomplemented
25D8×C47C2211yescharacteristic, complemented
26C2×C8×C47C2211yescharacteristic, complemented
27#10625337C2212yescomplemented
28#10625336C2212yescomplemented
29#10625335C2212yescomplemented
30#10625334C2212yescomplemented
31C2×C47⋊C8C2211yescharacteristic, complemented
32Dic188C2211yescharacteristic, complemented
33D376C2211yescharacteristic, complemented
34#10625325C2212yescomplemented
35C8×D47C2211yescharacteristic
36C8×D47C2211yescharacteristic
37C8×D47C2211yescharacteristic, complemented
38C8×D47C2211yescharacteristic, complemented
39C22×D47—22no—
40C22×D47D411yescharacteristic
41Q8×C47C2312yes—
42D4×C47—22no—
43D4×C47C2312yes—
44C2×C4×C47—22no—
45C2×C4×C47C2311yescharacteristic
46C22⋊D47—22no—
47C22⋊D47—22no—
48C22⋊D47—22no—
49C2×Dic47—22no—
50C2×Dic47D411yescharacteristic
51D188—22no—
52D188C2312yes—
53C4×D47—22no—
54C4×D47—22no—
55C4×D47—22no—
56C4×D47D411yescharacteristic
57C4×D47D411yescharacteristic
58C4×D47C2311yescharacteristic
59C4×D47C2311yescharacteristic
60Dic94—22no—
61Dic94C2312yes—
62C8×C47C2311yescharacteristic
63C8×C47C2311yescharacteristic
64C47⋊C8C2311yescharacteristic
65C47⋊C8C2311yescharacteristic
66C22×C47—22no—
67C22×C47C2×D411yescharacteristic
68C2×D47—22no—
69C2×D47—22no—
70C2×D47—44no—
71C2×D47C2×D411yescharacteristic
72C2×D47C2×D411yescharacteristic
73C4×C47—22no—
74C4×C47C2×D411yescharacteristic
75C4×C47C2411yescharacteristic
76Dic47—22no—
77Dic47C2×D411yescharacteristic
78Dic47C2×D411yescharacteristic
79C2×C47—21no—
80C2×C47—42no—
81C2×C47C22×D411yescharacteristic
82D47—21no—
83D47—42no—
84D47#13512yesdirect product factor
85C2×#135—471nomaximal, Sylow
86C47C2×#13511yescharacteristic, complemented, Sylow
87C2×#41—472no—
88#135—472no—
89#135—471no—
90#135—472no—
91#135—471no—
92#135—471no—
93#135D4711yescharacteristic, direct product factor
94C2×Q16—471no—
95C2×SD16—472no—
96C2×D8—471no—
97C22×C8—471no—
98#41—472no—
99#41—472no—
100#41—472no—
101#41—942no—
102#41—942no—
103#41C2×D4712yescomplemented
104C2×Q8—472no—
105C2×D4—472no—
106C2×D4—942no—
107C22×C4—471no—
108C22×C4—942no—
109Q16—472no—
110Q16—471no—
111Q16C2×D4711yescharacteristic, complemented
112SD16—472no—
113SD16—472no—
114SD16—472no—
115SD16C2×D4712yescomplemented
116D8—472no—
117D8—471no—
118D8C2×D4711yescharacteristic, complemented
119C2×C8—471no—
120C2×C8—471no—
121C2×C8—471no—
122C2×C8—471no—
123C2×C8—471no—
124C2×C8C2×D4711yescharacteristic, complemented
125C23—471no—
126C23—942no—
127Q8—472no—
128Q8—942no—
129Q8C22×D4712yes—
130D4—22no—
131D4—472no—
132D4—942no—
133D4—942no—
134D4—942no—
135D4—942no—
136D4C22×D4712yes—
137C2×C4—22no—
138C2×C4—471no—
139C2×C4—471no—
140C2×C4—471no—
141C2×C4—471no—
142C2×C4—471no—
143C2×C4—942no—
144C2×C4—942no—
145C2×C4—942no—
146C2×C4—942no—
147C2×C4C22×D4711yescharacteristic
148C8—471no—
149C8—471no—
150C8C22×D4711yescharacteristic
151C8C22×D4711yescharacteristic
152C22—22no—
153C22—471no—
154C22—471no—
155C22—942no—
156C22—942no—
157C22—1884no—
158C22D4×D4711yescharacteristic
159C4—22no—
160C4—471no—
161C4—471no—
162C4—942no—
163C4D4×D4711yescharacteristic
164C4C23×D4711yescharacteristic
165C2—21no—
166C2—42no—
167C2—472no—
168C2—941no—
169C2—1882no—
170C2C2×D4×D4711yescharacteristic
subgroupG/H
centerC4D4×D47
commutator, cosocleC4×C47C24
FrattiniC4C23×D47
Fitting#135×C47C2
socleC2×C47C22×D4
hypercenter#135D47
hypocenterC47C2×#135
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D47C2semidirect
2. #13094047C2semidirect
3. #13094046C2semidirect
4. #13094045C2semidirect
5. #13094044C2semidirect
6. #13094043C2semidirect
7. Q16×D47C2semidirect
8. SD16×D47C2semidirect
9. D8×D47C2semidirect
10. C2×C8×D47C2semidirect
11. #135×C47C2semidirect
12. #41×C47C22semidirect
13. #10625354C22semidirect
16. #10625352C22semidirect
20. #10625350C22semidirect
23. Q16×C47C22semidirect
24. SD16×C47C22semidirect
25. D8×C47C22semidirect
26. C2×C8×C47C22semidirect
27. #10625337C22semidirect
28. #10625336C22semidirect
29. #10625335C22semidirect
30. #10625334C22semidirect
31. C2×C47⋊C8C22semidirect
32. Dic188C22semidirect
33. D376C22semidirect
34. #10625325C22semidirect
37. C8×D47C22semidirect
38. C8×D47C22semidirect
84. D47#135direct (N × H)
86. C47C2×#135semidirect
93. #135D47direct (N × H)
103. #41C2×D47semidirect
111. Q16C2×D47semidirect
115. SD16C2×D47semidirect
118. D8C2×D47semidirect
124. C2×C8C2×D47semidirect

Maximal subgroups

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

subgroupindex
#41×D472
#130940472
#130940462
#130940452
#130940442
#130940432
Q16×D472
SD16×D472
D8×D472
C2×C8×D472
#135×C472
C2×#13547