Finite Group Databasebeta

← #135×D487 #44529828

Subgroups — #135×D487 #44529828

Order 31168.

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×D487C212yesmaximal, complemented
2#29510238C211yesmaximal, characteristic, complemented
3#29510237C211yesmaximal, characteristic, complemented
4#29510236C212yesmaximal, complemented
5#29510235C212yesmaximal, complemented
6#29510234C211yesmaximal, characteristic, complemented
7Q16×D487C211yesmaximal, characteristic, complemented
8SD16×D487C212yesmaximal, complemented
9D8×D487C211yesmaximal, characteristic, complemented
10C2×C8×D487C211yesmaximal, characteristic, complemented
11#135×C487C211yesmaximal, characteristic, complemented
12#21441262C2212yescomplemented
13#21441261—22no—
14#21441261C2212yescomplemented
15#21441260—22no—
16#21441260C2212yescomplemented
17Q8×D487C2212yes—
18D4×D487—22no—
19D4×D487C2212yes—
20C2×C4×D487—22no—
21C2×C4×D487C2211yescharacteristic
22Dic1948C2211yescharacteristic, complemented
23#21441251C2212yescomplemented
24#21441250C2212yescomplemented
25#21441249C2212yescomplemented
26#21441248C2212yescomplemented
27D3896C2211yescharacteristic, complemented
28#21441246C2212yescomplemented
29C2×C487⋊C8C2211yescharacteristic, complemented
30C8×D487C2211yescharacteristic
31C8×D487C2211yescharacteristic
32C8×D487C2211yescharacteristic, complemented
33C8×D487C2211yescharacteristic, complemented
34#41×C487C2212yescomplemented
35Q16×C487C2211yescharacteristic, complemented
36SD16×C487C2212yescomplemented
37D8×C487C2211yescharacteristic, complemented
38C2×C8×C487C2211yescharacteristic, complemented
39C22×D487—22no—
40C22×D487D411yescharacteristic
41Dic974—22no—
42Dic974C2312yes—
43D1948—22no—
44D1948C2312yes—
45C22⋊D487—22no—
46C22⋊D487—22no—
47C22⋊D487—22no—
48C2×Dic487—22no—
49C2×Dic487D411yescharacteristic
50C4×D487—22no—
51C4×D487—22no—
52C4×D487—22no—
53C4×D487D411yescharacteristic
54C4×D487D411yescharacteristic
55C4×D487C2311yescharacteristic
56C4×D487C2311yescharacteristic
57C487⋊C8C2311yescharacteristic
58C487⋊C8C2311yescharacteristic
59Q8×C487C2312yes—
60D4×C487—22no—
61D4×C487C2312yes—
62C2×C4×C487—22no—
63C2×C4×C487C2311yescharacteristic
64C8×C487C2311yescharacteristic
65C8×C487C2311yescharacteristic
66C22×C487—22no—
67C22×C487C2×D411yescharacteristic
68C2×D487—22no—
69C2×D487—22no—
70C2×D487—44no—
71C2×D487C2×D411yescharacteristic
72C2×D487C2×D411yescharacteristic
73C4×C487—22no—
74C4×C487C2×D411yescharacteristic
75C4×C487C2411yescharacteristic
76Dic487—22no—
77Dic487C2×D411yescharacteristic
78Dic487C2×D411yescharacteristic
79C2×C487—21no—
80C2×C487—42no—
81C2×C487C22×D411yescharacteristic
82D487—21no—
83D487—42no—
84D487#13512yesdirect product factor
85C487C2×#13511yescharacteristic, complemented, Sylow
86C2×#135—4871nomaximal, Sylow
87C2×#41—4872no—
88#135—4872no—
89#135—4871no—
90#135—4872no—
91#135—4871no—
92#135—4871no—
93#135D48711yescharacteristic, direct product factor
94C2×Q16—4871no—
95C2×SD16—4872no—
96C2×D8—4871no—
97C22×C8—4871no—
98#41—9742no—
99#41—9742no—
100#41—4872no—
101#41—4872no—
102#41—4872no—
103#41C2×D48712yescomplemented
104C2×Q8—4872no—
105C2×D4—9742no—
106C2×D4—4872no—
107C22×C4—9742no—
108C22×C4—4871no—
109Q16—4872no—
110Q16—4871no—
111Q16C2×D48711yescharacteristic, complemented
112SD16—4872no—
113SD16—4872no—
114SD16—4872no—
115SD16C2×D48712yescomplemented
116D8—4872no—
117D8—4871no—
118D8C2×D48711yescharacteristic, complemented
119C2×C8—4871no—
120C2×C8—4871no—
121C2×C8—4871no—
122C2×C8—4871no—
123C2×C8—4871no—
124C2×C8C2×D48711yescharacteristic, complemented
125C23—9742no—
126C23—4871no—
127Q8—9742no—
128Q8—4872no—
129Q8C22×D48712yes—
130D4—22no—
131D4—9742no—
132D4—9742no—
133D4—9742no—
134D4—9742no—
135D4—4872no—
136D4C22×D48712yes—
137C2×C4—22no—
138C2×C4—9742no—
139C2×C4—9742no—
140C2×C4—9742no—
141C2×C4—9742no—
142C2×C4—4871no—
143C2×C4—4871no—
144C2×C4—4871no—
145C2×C4—4871no—
146C2×C4—4871no—
147C2×C4C22×D48711yescharacteristic
148C8—4871no—
149C8—4871no—
150C8C22×D48711yescharacteristic
151C8C22×D48711yescharacteristic
152C22—22no—
153C22—19484no—
154C22—9742no—
155C22—9742no—
156C22—4871no—
157C22—4871no—
158C22D4×D48711yescharacteristic
159C4—22no—
160C4—9742no—
161C4—4871no—
162C4—4871no—
163C4D4×D48711yescharacteristic
164C4C23×D48711yescharacteristic
165C2—21no—
166C2—42no—
167C2—19482no—
168C2—9741no—
169C2—4872no—
170C2C2×D4×D48711yescharacteristic
subgroupG/H
centerC4D4×D487
commutator, cosocleC4×C487C24
FrattiniC4C23×D487
Fitting#135×C487C2
socleC2×C487C22×D4
hypercenter#135D487
hypocenterC487C2×#135
LCSG ▷ C4×C487 ▷ C2×C487 ▷ C487
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D487C2semidirect
2. #29510238C2semidirect
3. #29510237C2semidirect
4. #29510236C2semidirect
5. #29510235C2semidirect
6. #29510234C2semidirect
7. Q16×D487C2semidirect
8. SD16×D487C2semidirect
9. D8×D487C2semidirect
10. C2×C8×D487C2semidirect
11. #135×C487C2semidirect
12. #21441262C22semidirect
14. #21441261C22semidirect
16. #21441260C22semidirect
22. Dic1948C22semidirect
23. #21441251C22semidirect
24. #21441250C22semidirect
25. #21441249C22semidirect
26. #21441248C22semidirect
27. D3896C22semidirect
28. #21441246C22semidirect
29. C2×C487⋊C8C22semidirect
32. C8×D487C22semidirect
33. C8×D487C22semidirect
34. #41×C487C22semidirect
35. Q16×C487C22semidirect
36. SD16×C487C22semidirect
37. D8×C487C22semidirect
38. C2×C8×C487C22semidirect
84. D487#135direct (N × H)
85. C487C2×#135semidirect
93. #135D487direct (N × H)
103. #41C2×D487semidirect
111. Q16C2×D487semidirect
115. SD16C2×D487semidirect
118. D8C2×D487semidirect
124. C2×C8C2×D487semidirect

Maximal subgroups

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

subgroupindex
#41×D4872
#295102382
#295102372
#295102362
#295102352
#295102342
Q16×D4872
SD16×D4872
D8×D4872
C2×C8×D4872
#135×C4872
C2×#135487