Finite Group Databasebeta

← #39910044

Subgroups — #39910044

Order 26176.

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

normal subgroups only

This group has 262 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#41×D409C212yesmaximal, complemented
2#27189749C212yesmaximal, complemented
3#27189746C212yesmaximal, complemented
4#27189744C212yesmaximal, complemented
5#27189741C212yesmaximal, complemented
6#27189739C211yesmaximal, characteristic, complemented
7#27189737C212yesmaximal, complemented
8C2×#20266971C211yesmaximal, characteristic, complemented
9#135×C409C211yesmaximal, characteristic, complemented
10#20266989C2212yes—
11#20266988—22no—
12#20266988C2212yescomplemented
13#20266987—22no—
14#20266987C2212yes—
15Q8×D409C2212yescomplemented
16D4×D409—22no—
17D4×D409C2212yescomplemented
18C2×C4×D409—22no—
19C2×C4×D409C2211yescharacteristic
20Dic1636C2211yescharacteristic, complemented
21#20266978C2212yescomplemented
22#20266977C2212yescomplemented
23#20266976C2212yescomplemented
24#20266975C2212yescomplemented
25D3272C2211yescharacteristic, complemented
26#20266973C2212yescomplemented
27#20266971C2212yescomplemented
28#20266971C2212yescomplemented
29C2×#15692543C2211yescharacteristic, complemented
30#41×C409C2212yescomplemented
31Q16×C409C2211yescharacteristic, complemented
32SD16×C409C2212yescomplemented
33D8×C409C2211yescharacteristic, complemented
34C2×C8×C409C2211yescharacteristic, complemented
35C22×D409—22no—
36C22×D409D411yescharacteristic
37Dic818—22no—
38Dic818C2312yes—
39D1636—22no—
40D1636C2312yes—
41C22⋊D409—22no—
42C22⋊D409—22no—
43C22⋊D409—22no—
44C2×Dic409—22no—
45C2×Dic409D411yescharacteristic
46C4×D409—22no—
47C4×D409—22no—
48C4×D409—22no—
49C4×D409D412yes—
50C4×D409C2312yes—
51#15692543C2312yes—
52Q8×C409C2312yes—
53D4×C409—22no—
54D4×C409C2312yes—
55C2×C4×C409—22no—
56C2×C4×C409C2311yescharacteristic
57C8×C409C2311yescharacteristic
58C8×C409C2311yescharacteristic
59C22×C409—22no—
60C22×C409C2×D411yescharacteristic
61C2×D409—22no—
62C2×D409—41no—
63C2×D409—44no—
64C2×D409C2×D412yes—
65C4×C409—22no—
66C4×C409C2×D411yescharacteristic
67C4×C409C2411yescharacteristic
68Dic409—22no—
69Dic409C2×D412yes—
70C2×C409—21no—
71C2×C409—42no—
72C2×C409C22×D411yescharacteristic
73D409—22no—
74D409—42no—
75C409#57511yescharacteristic, complemented, Sylow
76#575—4091nomaximal, Sylow
77C2×#41—4092no—
78#137—4092no—
79#137—4092no—
80AGL(1,ℤ/8)—4092no—
81AGL(1,ℤ/8)—4092no—
82#135—4092no—
83#135—4091no—
84#135D40911yescharacteristic, complemented
85C2×M16—4091no—
86#41—8182no—
87#41—8182no—
88#41—4092no—
89#41—4092no—
90#41—4092no—
91#41C2×D40912yescomplemented
92C2×Q8—4092no—
93C2×D4—8182no—
94C2×D4—4092no—
95C22×C4—8182no—
96C22×C4—4091no—
97Q16—4092no—
98Q16—4091no—
99Q16C2×D40911yescharacteristic, complemented
100SD16—4092no—
101SD16—4092no—
102SD16—4092no—
103SD16C2×D40912yescomplemented
104D8—4092no—
105D8—4091no—
106D8C2×D40911yescharacteristic, complemented
107M16—4092no—
108M16—4092no—
109C2×C8—4091no—
110C2×C8C2×D40911yescharacteristic, complemented
111C23—8182no—
112C23—4091no—
113Q8—8182no—
114Q8—4092no—
115Q8C22×D40912yes—
116D4—22no—
117D4—8182no—
118D4—8182no—
119D4—8182no—
120D4—8182no—
121D4—4092no—
122D4C22×D40912yes—
123C2×C4—22no—
124C2×C4—8182no—
125C2×C4—8182no—
126C2×C4—8182no—
127C2×C4—8182no—
128C2×C4—4091no—
129C2×C4—4092no—
130C2×C4—4092no—
131C2×C4C22×D40911yescharacteristic
132C8—4092no—
133C8C22×D40911yescharacteristic
134C8C22×D40911yescharacteristic
135C22—22no—
136C22—8182no—
137C22—16361no—
138C22—16364no—
139C22—4092no—
140C22D4×D40911yescharacteristic
141C4—22no—
142C4—8182no—
143C4—4092no—
144C4D4×D40911yescharacteristic
145C4C23×D40911yescharacteristic
146C2—21no—
147C2—42no—
148C2—8182no—
149C2—16362no—
150C2C2×D4×D40911yescharacteristic
subgroupG/H
centerC4D4×D409
commutator, cosocleC4×C409C24
FrattiniC4C23×D409
Fitting#135×C409C2
socleC2×C409C22×D4
hypercenter#135D409
hypocenterC409#575
LCSG ▷ C4×C409 ▷ C2×C409 ▷ C409
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D409C2semidirect
2. #27189749C2semidirect
3. #27189746C2semidirect
4. #27189744C2semidirect
5. #27189741C2semidirect
6. #27189739C2semidirect
7. #27189737C2semidirect
8. C2×#20266971C2semidirect
9. #135×C409C2semidirect
12. #20266988C22semidirect
15. Q8×D409C22semidirect
17. D4×D409C22semidirect
20. Dic1636C22semidirect
21. #20266978C22semidirect
22. #20266977C22semidirect
23. #20266976C22semidirect
24. #20266975C22semidirect
25. D3272C22semidirect
26. #20266973C22semidirect
27. #20266971C22semidirect
28. #20266971C22semidirect
29. C2×#15692543C22semidirect
30. #41×C409C22semidirect
31. Q16×C409C22semidirect
32. SD16×C409C22semidirect
33. D8×C409C22semidirect
34. C2×C8×C409C22semidirect
75. C409#575semidirect
84. #135D409semidirect
91. #41C2×D409semidirect
99. Q16C2×D409semidirect
103. SD16C2×D409semidirect
106. D8C2×D409semidirect
110. C2×C8C2×D409semidirect

Maximal subgroups

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

subgroupindex
#41×D4092
#271897492
#271897462
#271897442
#271897412
#271897392
#271897372
C2×#202669712
#135×C4092
#575409