Finite Group Databasebeta

← #45655796

Subgroups — #45655796

Order 32576.

346 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C2×D4×D509C212yesmaximal, complemented
2#30654200C212yesmaximal, complemented
3#30654197C212yesmaximal, complemented
4#30654189C211yesmaximal, characteristic, complemented
5#30654187C212yesmaximal, complemented
6#30654185C212yesmaximal, complemented
7#30654183C212yesmaximal, complemented
8C2×#22550838C211yesmaximal, characteristic, complemented
9#121×C509C211yesmaximal, characteristic, complemented
10C23×D509C2211yescharacteristic
11C23×D509C2212yescomplemented
12C2×D2036C2212yes—
13C2×D2036C2211yescharacteristic, complemented
14C2×C22⋊D509C2212yes—
15C2×C22⋊D509C2212yescomplemented
16C2×C22⋊D509C2212yescomplemented
17D4×D509—28no—
18C22×Dic509C2211yescharacteristic, complemented
19C2×C4×D509C2212yescomplemented
20C4⋊Dic509C2211yescharacteristic, complemented
21#22550840C2212yescomplemented
22C22⋊Dic509C2212yescomplemented
23#22550838C2212yescomplemented
24#22550838C2212yescomplemented
25#22550838C2212yescomplemented
26#22550838C2212yescomplemented
27C2×D4×C509C2212yescomplemented
28C2×D4×C509C2211yescharacteristic, complemented
29C22×C4×C509C2211yescharacteristic, complemented
30C4⋊C4×C509C2211yescharacteristic, complemented
31C22⋊C4×C509C2212yescomplemented
32C22×D509—24no—
33C22×D509—41no—
34C22×D509—41no—
35C22×D509—42no—
36C22×D509—42no—
37C22×D509D414yescomplemented
38C22×D509C2312yes—
39C22×D509C2312yes—
40D2036—24no—
41D2036—41no—
42C22⋊D509—24no—
43C22⋊D509—24no—
44C22⋊D509—42no—
45C2×Dic509—41no—
46C2×Dic509C2312yes—
47C2×Dic509C2312yes—
48C4×D509—24no—
49C23×C509C2312yes—
50C23×C509C2311yescharacteristic
51D4×C509—24no—
52D4×C509—41no—
53C2×C4×C509—41no—
54C2×C4×C509C2311yescharacteristic
55C2×C4×C509C2312yes—
56C2×C4×C509C2311yescharacteristic
57C22×C509—21no—
58C22×C509—21no—
59C22×C509—22no—
60C22×C509—22no—
61C22×C509—22no—
62C22×C509C2×D412yes—
63C22×C509C2411yescharacteristic
64C2×D509—22no—
65C2×D509—22no—
66C2×D509—22no—
67C2×D509—22no—
68C2×D509—22no—
69C2×D509—44no—
70C2×D509—48no—
71C2×D509C2×D414yes—
72C4×C509—22no—
73C4×C509—21no—
74C4×C509—21no—
75Dic509—22no—
76Dic509—22no—
77C2×C509—22no—
78C2×C509—42no—
79C2×C509C22×D411yescharacteristic
80C2×C509H(5,𝔽2)11yescharacteristic
81C2×C509H(5,𝔽2)11yescharacteristic
82D509—24no—
83D509—42no—
84C509#53411yescharacteristic, complemented, Sylow
85#534—5091nomaximal, Sylow
86C22×D4—5092no—
87#123—5092no—
88#123—5092no—
89#121—5092no—
90#121—5091no—
91#121D50911yescharacteristic, complemented
92#120—5092no—
93#120—5092no—
94C2×C22⋊C4—5091no—
95C24—5092no—
96C24—5091no—
97C2×D4—10188no—
98C2×D4—5092no—
99C2×D4—5092no—
100C2×D4—5092no—
101C2×D4—5091no—
102C2×D4—5092no—
103C2×D4C2×D50912yescomplemented
104C2×D4C2×D50911yescharacteristic, complemented
105C22×C4—5091no—
106C22×C4—5092no—
107C22×C4C2×D50911yescharacteristic, complemented
108C4⋊C4—5092no—
109C4⋊C4—5091no—
110C4⋊C4C2×D50911yescharacteristic, complemented
111C22⋊C4—5092no—
112C22⋊C4—5092no—
113C22⋊C4—5092no—
114C22⋊C4—5092no—
115C22⋊C4—5092no—
116C22⋊C4C2×D50912yescomplemented
117C23—20361no—
118C23—20361no—
119C23—20362no—
120C23—20362no—
121C23—10184no—
122C23—5094no—
123C23—5092no—
124C23—5092no—
125C23C22×D50912yes—
126C23C22×D50911yescharacteristic
127D4—24no—
128D4—41no—
129D4—20361no—
130D4—20362no—
131D4—10184no—
132D4—10184no—
133D4—10184no—
134C2×C4—41no—
135C2×C4—20361no—
136C2×C4—10184no—
137C2×C4—5092no—
138C2×C4—5092no—
139C2×C4C22×D50911yescharacteristic
140C2×C4C22×D50911yescharacteristic
141C2×C4C22×D50912yes—
142C22—21no—
143C22—21no—
144C22—22no—
145C22—22no—
146C22—22no—
147C22—20364no—
148C22—20368no—
149C22—10182no—
150C22—10182no—
151C22—10182no—
152C22—10182no—
153C22—10182no—
154C22—5094no—
155C22D4×D50912yes—
156C22C23×D50911yescharacteristic
157C4—22no—
158C4—21no—
159C4—21no—
160C4—10182no—
161C4—10182no—
162C2—22no—
163C2—42no—
164C2—20362no—
165C2—10184no—
166C2C2×D4×D50911yescharacteristic
167C2#3065426011yescharacteristic
168C2#3065426111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D509
commutator, socle, cosocleC22×C509C24
Fitting#121×C509C2
hypercenter#121D509
hypocenterC509#534
LCSG ▷ C22×C509 ▷ C509
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D4×D509C2semidirect
2. #30654200C2semidirect
3. #30654197C2semidirect
4. #30654189C2semidirect
5. #30654187C2semidirect
6. #30654185C2semidirect
7. #30654183C2semidirect
8. C2×#22550838C2semidirect
9. #121×C509C2semidirect
11. C23×D509C22semidirect
13. C2×D2036C22semidirect
15. C2×C22⋊D509C22semidirect
16. C2×C22⋊D509C22semidirect
18. C22×Dic509C22semidirect
19. C2×C4×D509C22semidirect
20. C4⋊Dic509C22semidirect
21. #22550840C22semidirect
22. C22⋊Dic509C22semidirect
23. #22550838C22semidirect
24. #22550838C22semidirect
25. #22550838C22semidirect
26. #22550838C22semidirect
27. C2×D4×C509C22semidirect
28. C2×D4×C509C22semidirect
29. C22×C4×C509C22semidirect
30. C4⋊C4×C509C22semidirect
31. C22⋊C4×C509C22semidirect
37. C22×D509D4semidirect
84. C509#534semidirect
91. #121D509semidirect
103. C2×D4C2×D509semidirect
104. C2×D4C2×D509semidirect
107. C22×C4C2×D509semidirect
110. C4⋊C4C2×D509semidirect
116. C22⋊C4C2×D509semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D5092
#306542002
#306541972
#306541892
#306541872
#306541852
#306541832
C2×#225508382
#121×C5092
#534509