Finite Group Databasebeta

← #38786672

Subgroups — #38786672

Order 25664.

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×D401C212yesmaximal, complemented
2#27165722C212yesmaximal, complemented
3#27165719C212yesmaximal, complemented
4#27165711C211yesmaximal, characteristic, complemented
5#27165709C212yesmaximal, complemented
6#27165707C212yesmaximal, complemented
7#27165705C212yesmaximal, complemented
8C2×#20264343C211yesmaximal, characteristic, complemented
9#121×C401C211yesmaximal, characteristic, complemented
10C23×D401C2211yescharacteristic
11C23×D401C2212yescomplemented
12C2×D1604C2212yes—
13C2×D1604C2211yescharacteristic, complemented
14C2×C22⋊D401C2212yes—
15C2×C22⋊D401C2212yescomplemented
16C2×C22⋊D401C2212yescomplemented
17D4×D401—28no—
18C22×Dic401C2211yescharacteristic, complemented
19C2×C4×D401C2212yescomplemented
20C4⋊Dic401C2211yescharacteristic, complemented
21#20264345C2212yescomplemented
22C22⋊Dic401C2212yescomplemented
23#20264343C2212yescomplemented
24#20264343C2212yescomplemented
25#20264343C2212yescomplemented
26#20264343C2212yescomplemented
27C2×D4×C401C2212yescomplemented
28C2×D4×C401C2211yescharacteristic, complemented
29C22×C4×C401C2211yescharacteristic, complemented
30C4⋊C4×C401C2211yescharacteristic, complemented
31C22⋊C4×C401C2212yescomplemented
32C22×D401—24no—
33C22×D401—41no—
34C22×D401—41no—
35C22×D401—42no—
36C22×D401—42no—
37C22×D401D414yescomplemented
38C22×D401C2312yes—
39C22×D401C2312yes—
40D1604—24no—
41D1604—41no—
42C22⋊D401—24no—
43C22⋊D401—24no—
44C22⋊D401—42no—
45C2×Dic401—41no—
46C2×Dic401C2312yes—
47C2×Dic401C2312yes—
48C4×D401—24no—
49C23×C401C2312yes—
50C23×C401C2311yescharacteristic
51D4×C401—24no—
52D4×C401—41no—
53C2×C4×C401—41no—
54C2×C4×C401C2311yescharacteristic
55C2×C4×C401C2312yes—
56C2×C4×C401C2311yescharacteristic
57C22×C401—21no—
58C22×C401—21no—
59C22×C401—22no—
60C22×C401—22no—
61C22×C401—22no—
62C22×C401C2×D412yes—
63C22×C401C2411yescharacteristic
64C2×D401—22no—
65C2×D401—22no—
66C2×D401—22no—
67C2×D401—22no—
68C2×D401—22no—
69C2×D401—44no—
70C2×D401—48no—
71C2×D401C2×D414yes—
72C4×C401—22no—
73C4×C401—21no—
74C4×C401—21no—
75Dic401—22no—
76Dic401—22no—
77C2×C401—22no—
78C2×C401—42no—
79C2×C401C22×D411yescharacteristic
80C2×C401H(5,𝔽2)11yescharacteristic
81C2×C401H(5,𝔽2)11yescharacteristic
82D401—24no—
83D401—42no—
84C401#53411yescharacteristic, complemented, Sylow
85#534—4011nomaximal, Sylow
86C22×D4—4012no—
87#123—4012no—
88#123—4012no—
89#121—4012no—
90#121—4011no—
91#121D40111yescharacteristic, complemented
92#120—4012no—
93#120—4012no—
94C2×C22⋊C4—4011no—
95C24—4012no—
96C24—4011no—
97C2×D4—8028no—
98C2×D4—4012no—
99C2×D4—4012no—
100C2×D4—4012no—
101C2×D4—4012no—
102C2×D4—4011no—
103C2×D4C2×D40112yescomplemented
104C2×D4C2×D40111yescharacteristic, complemented
105C22×C4—4012no—
106C22×C4—4011no—
107C22×C4C2×D40111yescharacteristic, complemented
108C4⋊C4—4012no—
109C4⋊C4—4011no—
110C4⋊C4C2×D40111yescharacteristic, complemented
111C22⋊C4—4012no—
112C22⋊C4—4012no—
113C22⋊C4—4012no—
114C22⋊C4—4012no—
115C22⋊C4—4012no—
116C22⋊C4C2×D40112yescomplemented
117C23—8024no—
118C23—16041no—
119C23—16041no—
120C23—16042no—
121C23—16042no—
122C23—4012no—
123C23—4012no—
124C23—4014no—
125C23C22×D40112yes—
126C23C22×D40111yescharacteristic
127D4—24no—
128D4—41no—
129D4—8024no—
130D4—8024no—
131D4—8024no—
132D4—16041no—
133D4—16042no—
134C2×C4—41no—
135C2×C4—8024no—
136C2×C4—16041no—
137C2×C4—4012no—
138C2×C4—4012no—
139C2×C4C22×D40111yescharacteristic
140C2×C4C22×D40111yescharacteristic
141C2×C4C22×D40112yes—
142C22—21no—
143C22—21no—
144C22—22no—
145C22—22no—
146C22—22no—
147C22—8022no—
148C22—8022no—
149C22—8022no—
150C22—8022no—
151C22—8022no—
152C22—16044no—
153C22—16048no—
154C22—4014no—
155C22D4×D40112yes—
156C22C23×D40111yescharacteristic
157C4—22no—
158C4—21no—
159C4—21no—
160C4—8022no—
161C4—8022no—
162C2—22no—
163C2—42no—
164C2—8024no—
165C2—16042no—
166C2C2×D4×D40111yescharacteristic
167C2#2716578211yescharacteristic
168C2#2716578311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D401
commutator, socle, cosocleC22×C401C24
Fitting#121×C401C2
hypercenter#121D401
hypocenterC401#534
LCSG ▷ C22×C401 ▷ C401
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D4×D401C2semidirect
2. #27165722C2semidirect
3. #27165719C2semidirect
4. #27165711C2semidirect
5. #27165709C2semidirect
6. #27165707C2semidirect
7. #27165705C2semidirect
8. C2×#20264343C2semidirect
9. #121×C401C2semidirect
11. C23×D401C22semidirect
13. C2×D1604C22semidirect
15. C2×C22⋊D401C22semidirect
16. C2×C22⋊D401C22semidirect
18. C22×Dic401C22semidirect
19. C2×C4×D401C22semidirect
20. C4⋊Dic401C22semidirect
21. #20264345C22semidirect
22. C22⋊Dic401C22semidirect
23. #20264343C22semidirect
24. #20264343C22semidirect
25. #20264343C22semidirect
26. #20264343C22semidirect
27. C2×D4×C401C22semidirect
28. C2×D4×C401C22semidirect
29. C22×C4×C401C22semidirect
30. C4⋊C4×C401C22semidirect
31. C22⋊C4×C401C22semidirect
37. C22×D401D4semidirect
84. C401#534semidirect
91. #121D401semidirect
103. C2×D4C2×D401semidirect
104. C2×D4C2×D401semidirect
107. C22×C4C2×D401semidirect
110. C4⋊C4C2×D401semidirect
116. C22⋊C4C2×D401semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D4012
#271657222
#271657192
#271657112
#271657092
#271657072
#271657052
C2×#202643432
#121×C4012
#534401