Finite Group Databasebeta

← #37527001

Subgroups — #37527001

Order 22976.

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×D359C212yesmaximal, complemented
2#26040000C212yesmaximal, complemented
3#26039997C212yesmaximal, complemented
4#26039989C211yesmaximal, characteristic, complemented
5#26039987C212yesmaximal, complemented
6#26039985C212yesmaximal, complemented
7#26039983C212yesmaximal, complemented
8C2×(C2×D359)⋊C4C211yesmaximal, characteristic, complemented
9#121×C359C211yesmaximal, characteristic, complemented
10C23×D359C2211yescharacteristic
11C23×D359C2212yescomplemented
12C2×D1436C2212yes—
13C2×D1436C2211yescharacteristic, complemented
14C2×C22⋊D359C2212yes—
15C2×C22⋊D359C2212yescomplemented
16C2×C22⋊D359C2212yescomplemented
17D4×D359—28no—
18C22×Dic359C2211yescharacteristic, complemented
19C2×C4×D359C2212yescomplemented
20C4⋊Dic359C2211yescharacteristic, complemented
21Dic359⋊C4C2212yescomplemented
22C22⋊Dic359C2212yescomplemented
23(C2×D359)⋊C4C2212yescomplemented
24(C2×D359)⋊C4C2212yescomplemented
25(C2×D359)⋊C4C2212yescomplemented
26(C2×D359)⋊C4C2212yescomplemented
27C2×D4×C359C2212yescomplemented
28C2×D4×C359C2211yescharacteristic, complemented
29C22×C4×C359C2211yescharacteristic, complemented
30C4⋊C4×C359C2211yescharacteristic, complemented
31C22⋊C4×C359C2212yescomplemented
32C22×D359—24no—
33C22×D359—41no—
34C22×D359—41no—
35C22×D359—42no—
36C22×D359—42no—
37C22×D359D414yescomplemented
38C22×D359C2312yes—
39C22×D359C2312yes—
40D1436—24no—
41D1436—41no—
42C22⋊D359—24no—
43C22⋊D359—24no—
44C22⋊D359—42no—
45C2×Dic359—41no—
46C2×Dic359C2312yes—
47C2×Dic359C2312yes—
48C4×D359—24no—
49C23×C359C2312yes—
50C23×C359C2311yescharacteristic
51D4×C359—24no—
52D4×C359—41no—
53C2×C4×C359—41no—
54C2×C4×C359C2311yescharacteristic
55C2×C4×C359C2312yes—
56C2×C4×C359C2311yescharacteristic
57C22×C359—21no—
58C22×C359—21no—
59C22×C359—22no—
60C22×C359—22no—
61C22×C359—22no—
62C22×C359C2×D412yes—
63C22×C359C2411yescharacteristic
64C2×D359—22no—
65C2×D359—22no—
66C2×D359—22no—
67C2×D359—22no—
68C2×D359—22no—
69C2×D359—44no—
70C2×D359—48no—
71C2×D359C2×D414yes—
72C4×C359—22no—
73C4×C359—21no—
74C4×C359—21no—
75Dic359—22no—
76Dic359—22no—
77C2×C359—22no—
78C2×C359—42no—
79C2×C359C22×D411yescharacteristic
80C2×C359H(5,𝔽2)11yescharacteristic
81C2×C359H(5,𝔽2)11yescharacteristic
82D359—24no—
83D359—42no—
84C359#53411yescharacteristic, complemented, Sylow
85#534—3591nomaximal, Sylow
86C22×D4—3592no—
87#123—3592no—
88#123—3592no—
89#121—3592no—
90#121—3591no—
91#121D35911yescharacteristic, complemented
92#120—3592no—
93#120—3592no—
94C2×C22⋊C4—3591no—
95C24—3591no—
96C24—3592no—
97C2×D4—3592no—
98C2×D4—3592no—
99C2×D4—3592no—
100C2×D4—3591no—
101C2×D4—3592no—
102C2×D4—7188no—
103C2×D4C2×D35912yescomplemented
104C2×D4C2×D35911yescharacteristic, complemented
105C22×C4—3591no—
106C22×C4—3592no—
107C22×C4C2×D35911yescharacteristic, complemented
108C4⋊C4—3592no—
109C4⋊C4—3591no—
110C4⋊C4C2×D35911yescharacteristic, complemented
111C22⋊C4—3592no—
112C22⋊C4—3592no—
113C22⋊C4—3592no—
114C22⋊C4—3592no—
115C22⋊C4—3592no—
116C22⋊C4C2×D35912yescomplemented
117C23—3594no—
118C23—3592no—
119C23—3592no—
120C23—14361no—
121C23—14361no—
122C23—14362no—
123C23—14362no—
124C23—7184no—
125C23C22×D35912yes—
126C23C22×D35911yescharacteristic
127D4—24no—
128D4—41no—
129D4—14361no—
130D4—14362no—
131D4—7184no—
132D4—7184no—
133D4—7184no—
134C2×C4—41no—
135C2×C4—3592no—
136C2×C4—3592no—
137C2×C4—14361no—
138C2×C4—7184no—
139C2×C4C22×D35911yescharacteristic
140C2×C4C22×D35911yescharacteristic
141C2×C4C22×D35912yes—
142C22—21no—
143C22—21no—
144C22—22no—
145C22—22no—
146C22—22no—
147C22—3594no—
148C22—14364no—
149C22—14368no—
150C22—7182no—
151C22—7182no—
152C22—7182no—
153C22—7182no—
154C22—7182no—
155C22D4×D35912yes—
156C22C23×D35911yescharacteristic
157C4—22no—
158C4—21no—
159C4—21no—
160C4—7182no—
161C4—7182no—
162C2—22no—
163C2—42no—
164C2—14362no—
165C2—7184no—
166C2C2×D4×D35911yescharacteristic
167C2#2604006011yescharacteristic
168C2#2604006111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D359
commutator, socle, cosocleC22×C359C24
Fitting#121×C359C2
hypercenter#121D359
hypocenterC359#534
LCSG ▷ C22×C359 ▷ C359
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D4×D359C2semidirect
2. #26040000C2semidirect
3. #26039997C2semidirect
4. #26039989C2semidirect
5. #26039987C2semidirect
6. #26039985C2semidirect
7. #26039983C2semidirect
8. C2×(C2×D359)⋊C4C2semidirect
9. #121×C359C2semidirect
11. C23×D359C22semidirect
13. C2×D1436C22semidirect
15. C2×C22⋊D359C22semidirect
16. C2×C22⋊D359C22semidirect
18. C22×Dic359C22semidirect
19. C2×C4×D359C22semidirect
20. C4⋊Dic359C22semidirect
21. Dic359⋊C4C22semidirect
22. C22⋊Dic359C22semidirect
23. (C2×D359)⋊C4C22semidirect
24. (C2×D359)⋊C4C22semidirect
25. (C2×D359)⋊C4C22semidirect
26. (C2×D359)⋊C4C22semidirect
27. C2×D4×C359C22semidirect
28. C2×D4×C359C22semidirect
29. C22×C4×C359C22semidirect
30. C4⋊C4×C359C22semidirect
31. C22⋊C4×C359C22semidirect
37. C22×D359D4semidirect
84. C359#534semidirect
91. #121D359semidirect
103. C2×D4C2×D359semidirect
104. C2×D4C2×D359semidirect
107. C22×C4C2×D359semidirect
110. C4⋊C4C2×D359semidirect
116. C22⋊C4C2×D359semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D3592
#260400002
#260399972
#260399892
#260399872
#260399852
#260399832
C2×(C2×D359)⋊C42
#121×C3592
#534359