Finite Group Databasebeta

← #37527240

Subgroups — #37527240

Order 22976.

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×D359C212yesmaximal, complemented
2#26040047C212yesmaximal, complemented
3#26040044C212yesmaximal, complemented
4#26040042C212yesmaximal, complemented
5#26040039C212yesmaximal, complemented
6#26040037C211yesmaximal, characteristic, complemented
7#26040035C212yesmaximal, complemented
8C2×#19153324C211yesmaximal, characteristic, complemented
9#135×C359C211yesmaximal, characteristic, complemented
10#19153342C2212yes—
11#19153341—22no—
12#19153341C2212yescomplemented
13#19153340—22no—
14#19153340C2212yes—
15Q8×D359C2212yescomplemented
16D4×D359—22no—
17D4×D359C2212yescomplemented
18C2×C4×D359—22no—
19C2×C4×D359C2211yescharacteristic
20Dic1436C2211yescharacteristic, complemented
21#19153331C2212yescomplemented
22#19153330C2212yescomplemented
23#19153329C2212yescomplemented
24#19153328C2212yescomplemented
25D2872C2211yescharacteristic, complemented
26#19153326C2212yescomplemented
27#19153324C2212yescomplemented
28#19153324C2212yescomplemented
29C2×C359⋊C8C2211yescharacteristic, complemented
30#41×C359C2212yescomplemented
31Q16×C359C2211yescharacteristic, complemented
32SD16×C359C2212yescomplemented
33D8×C359C2211yescharacteristic, complemented
34C2×C8×C359C2211yescharacteristic, complemented
35C22×D359—22no—
36C22×D359D411yescharacteristic
37Dic718—22no—
38Dic718C2312yes—
39D1436—22no—
40D1436C2312yes—
41C22⋊D359—22no—
42C22⋊D359—22no—
43C22⋊D359—22no—
44C2×Dic359—22no—
45C2×Dic359D411yescharacteristic
46C4×D359—22no—
47C4×D359—22no—
48C4×D359—22no—
49C4×D359D412yes—
50C4×D359C2312yes—
51C359⋊C8C2312yes—
52Q8×C359C2312yes—
53D4×C359—22no—
54D4×C359C2312yes—
55C2×C4×C359—22no—
56C2×C4×C359C2311yescharacteristic
57C8×C359C2311yescharacteristic
58C8×C359C2311yescharacteristic
59C22×C359—22no—
60C22×C359C2×D411yescharacteristic
61C2×D359—22no—
62C2×D359—41no—
63C2×D359—44no—
64C2×D359C2×D412yes—
65C4×C359—22no—
66C4×C359C2×D411yescharacteristic
67C4×C359C2411yescharacteristic
68Dic359—22no—
69Dic359C2×D412yes—
70C2×C359—21no—
71C2×C359—42no—
72C2×C359C22×D411yescharacteristic
73D359—22no—
74D359—42no—
75C359#57511yescharacteristic, complemented, Sylow
76#575—3591nomaximal, Sylow
77C2×#41—3592no—
78#137—3592no—
79#137—3592no—
80AGL(1,ℤ/8)—3592no—
81AGL(1,ℤ/8)—3592no—
82#135—3592no—
83#135—3591no—
84#135D35911yescharacteristic, complemented
85C2×M16—3591no—
86#41—3592no—
87#41—3592no—
88#41—3592no—
89#41—7182no—
90#41—7182no—
91#41C2×D35912yescomplemented
92C2×Q8—3592no—
93C2×D4—3592no—
94C2×D4—7182no—
95C22×C4—3591no—
96C22×C4—7182no—
97Q16—3592no—
98Q16—3591no—
99Q16C2×D35911yescharacteristic, complemented
100SD16—3592no—
101SD16—3592no—
102SD16—3592no—
103SD16C2×D35912yescomplemented
104D8—3592no—
105D8—3591no—
106D8C2×D35911yescharacteristic, complemented
107M16—3592no—
108M16—3592no—
109C2×C8—3591no—
110C2×C8C2×D35911yescharacteristic, complemented
111C23—3591no—
112C23—7182no—
113Q8—3592no—
114Q8—7182no—
115Q8C22×D35912yes—
116D4—22no—
117D4—3592no—
118D4—7182no—
119D4—7182no—
120D4—7182no—
121D4—7182no—
122D4C22×D35912yes—
123C2×C4—22no—
124C2×C4—3591no—
125C2×C4—3592no—
126C2×C4—3592no—
127C2×C4—7182no—
128C2×C4—7182no—
129C2×C4—7182no—
130C2×C4—7182no—
131C2×C4C22×D35911yescharacteristic
132C8—3592no—
133C8C22×D35911yescharacteristic
134C8C22×D35911yescharacteristic
135C22—22no—
136C22—3592no—
137C22—14361no—
138C22—14364no—
139C22—7182no—
140C22D4×D35911yescharacteristic
141C4—22no—
142C4—3592no—
143C4—7182no—
144C4D4×D35911yescharacteristic
145C4C23×D35911yescharacteristic
146C2—21no—
147C2—42no—
148C2—14362no—
149C2—7182no—
150C2C2×D4×D35911yescharacteristic
subgroupG/H
centerC4D4×D359
commutator, cosocleC4×C359C24
FrattiniC4C23×D359
Fitting#135×C359C2
socleC2×C359C22×D4
hypercenter#135D359
hypocenterC359#575
LCSG ▷ C4×C359 ▷ C2×C359 ▷ C359
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D359C2semidirect
2. #26040047C2semidirect
3. #26040044C2semidirect
4. #26040042C2semidirect
5. #26040039C2semidirect
6. #26040037C2semidirect
7. #26040035C2semidirect
8. C2×#19153324C2semidirect
9. #135×C359C2semidirect
12. #19153341C22semidirect
15. Q8×D359C22semidirect
17. D4×D359C22semidirect
20. Dic1436C22semidirect
21. #19153331C22semidirect
22. #19153330C22semidirect
23. #19153329C22semidirect
24. #19153328C22semidirect
25. D2872C22semidirect
26. #19153326C22semidirect
27. #19153324C22semidirect
28. #19153324C22semidirect
29. C2×C359⋊C8C22semidirect
30. #41×C359C22semidirect
31. Q16×C359C22semidirect
32. SD16×C359C22semidirect
33. D8×C359C22semidirect
34. C2×C8×C359C22semidirect
75. C359#575semidirect
84. #135D359semidirect
91. #41C2×D359semidirect
99. Q16C2×D359semidirect
103. SD16C2×D359semidirect
106. D8C2×D359semidirect
110. C2×C8C2×D359semidirect

Maximal subgroups

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

subgroupindex
#41×D3592
#260400472
#260400442
#260400422
#260400392
#260400372
#260400352
C2×#191533242
#135×C3592
#575359