Finite Group Databasebeta

← #43272804

Subgroups — #43272804

Order 28736.

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×D449C212yesmaximal, complemented
2#28385372C212yesmaximal, complemented
3#28385369C212yesmaximal, complemented
4#28385367C212yesmaximal, complemented
5#28385364C212yesmaximal, complemented
6#28385362C211yesmaximal, characteristic, complemented
7#28385360C212yesmaximal, complemented
8C2×#20297719C211yesmaximal, characteristic, complemented
9#135×C449C211yesmaximal, characteristic, complemented
10#20297737C2212yes—
11#20297736—22no—
12#20297736C2212yescomplemented
13#20297735—22no—
14#20297735C2212yes—
15Q8×D449C2212yescomplemented
16D4×D449—22no—
17D4×D449C2212yescomplemented
18C2×C4×D449—22no—
19C2×C4×D449C2211yescharacteristic
20Dic1796C2211yescharacteristic, complemented
21#20297726C2212yescomplemented
22#20297725C2212yescomplemented
23#20297724C2212yescomplemented
24#20297723C2212yescomplemented
25D3592C2211yescharacteristic, complemented
26#20297721C2212yescomplemented
27#20297719C2212yescomplemented
28#20297719C2212yescomplemented
29C2×#16813311C2211yescharacteristic, complemented
30#41×C449C2212yescomplemented
31Q16×C449C2211yescharacteristic, complemented
32SD16×C449C2212yescomplemented
33D8×C449C2211yescharacteristic, complemented
34C2×C8×C449C2211yescharacteristic, complemented
35C22×D449—22no—
36C22×D449D411yescharacteristic
37Dic898—22no—
38Dic898C2312yes—
39D1796—22no—
40D1796C2312yes—
41C22⋊D449—22no—
42C22⋊D449—22no—
43C22⋊D449—22no—
44C2×Dic449—22no—
45C2×Dic449D411yescharacteristic
46C4×D449—22no—
47C4×D449—22no—
48C4×D449—22no—
49C4×D449D412yes—
50C4×D449C2312yes—
51#16813311C2312yes—
52Q8×C449C2312yes—
53D4×C449—22no—
54D4×C449C2312yes—
55C2×C4×C449—22no—
56C2×C4×C449C2311yescharacteristic
57C8×C449C2311yescharacteristic
58C8×C449C2311yescharacteristic
59C22×C449—22no—
60C22×C449C2×D411yescharacteristic
61C2×D449—22no—
62C2×D449—41no—
63C2×D449—44no—
64C2×D449C2×D412yes—
65C4×C449—22no—
66C4×C449C2×D411yescharacteristic
67C4×C449C2411yescharacteristic
68Dic449—22no—
69Dic449C2×D412yes—
70C2×C449—21no—
71C2×C449—42no—
72C2×C449C22×D411yescharacteristic
73D449—22no—
74D449—42no—
75C449#57511yescharacteristic, complemented, Sylow
76#575—4491nomaximal, Sylow
77C2×#41—4492no—
78#137—4492no—
79#137—4492no—
80AGL(1,ℤ/8)—4492no—
81AGL(1,ℤ/8)—4492no—
82#135—4492no—
83#135—4491no—
84#135D44911yescharacteristic, complemented
85C2×M16—4491no—
86#41—8982no—
87#41—8982no—
88#41—4492no—
89#41—4492no—
90#41—4492no—
91#41C2×D44912yescomplemented
92C2×Q8—4492no—
93C2×D4—8982no—
94C2×D4—4492no—
95C22×C4—8982no—
96C22×C4—4491no—
97Q16—4492no—
98Q16—4491no—
99Q16C2×D44911yescharacteristic, complemented
100SD16—4492no—
101SD16—4492no—
102SD16—4492no—
103SD16C2×D44912yescomplemented
104D8—4492no—
105D8—4491no—
106D8C2×D44911yescharacteristic, complemented
107M16—4492no—
108M16—4492no—
109C2×C8—4491no—
110C2×C8C2×D44911yescharacteristic, complemented
111C23—8982no—
112C23—4491no—
113Q8—8982no—
114Q8—4492no—
115Q8C22×D44912yes—
116D4—22no—
117D4—8982no—
118D4—8982no—
119D4—8982no—
120D4—8982no—
121D4—4492no—
122D4C22×D44912yes—
123C2×C4—22no—
124C2×C4—8982no—
125C2×C4—8982no—
126C2×C4—8982no—
127C2×C4—8982no—
128C2×C4—4491no—
129C2×C4—4492no—
130C2×C4—4492no—
131C2×C4C22×D44911yescharacteristic
132C8—4492no—
133C8C22×D44911yescharacteristic
134C8C22×D44911yescharacteristic
135C22—22no—
136C22—17961no—
137C22—17964no—
138C22—8982no—
139C22—4492no—
140C22D4×D44911yescharacteristic
141C4—22no—
142C4—8982no—
143C4—4492no—
144C4D4×D44911yescharacteristic
145C4C23×D44911yescharacteristic
146C2—21no—
147C2—42no—
148C2—17962no—
149C2—8982no—
150C2C2×D4×D44911yescharacteristic
subgroupG/H
centerC4D4×D449
commutator, cosocleC4×C449C24
FrattiniC4C23×D449
Fitting#135×C449C2
socleC2×C449C22×D4
hypercenter#135D449
hypocenterC449#575
LCSG ▷ C4×C449 ▷ C2×C449 ▷ C449
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D449C2semidirect
2. #28385372C2semidirect
3. #28385369C2semidirect
4. #28385367C2semidirect
5. #28385364C2semidirect
6. #28385362C2semidirect
7. #28385360C2semidirect
8. C2×#20297719C2semidirect
9. #135×C449C2semidirect
12. #20297736C22semidirect
15. Q8×D449C22semidirect
17. D4×D449C22semidirect
20. Dic1796C22semidirect
21. #20297726C22semidirect
22. #20297725C22semidirect
23. #20297724C22semidirect
24. #20297723C22semidirect
25. D3592C22semidirect
26. #20297721C22semidirect
27. #20297719C22semidirect
28. #20297719C22semidirect
29. C2×#16813311C22semidirect
30. #41×C449C22semidirect
31. Q16×C449C22semidirect
32. SD16×C449C22semidirect
33. D8×C449C22semidirect
34. C2×C8×C449C22semidirect
75. C449#575semidirect
84. #135D449semidirect
91. #41C2×D449semidirect
99. Q16C2×D449semidirect
103. SD16C2×D449semidirect
106. D8C2×D449semidirect
110. C2×C8C2×D449semidirect

Maximal subgroups

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

subgroupindex
#41×D4492
#283853722
#283853692
#283853672
#283853642
#283853622
#283853602
C2×#202977192
#135×C4492
#575449