Finite Group Databasebeta

← #14580894

Subgroups — #14580894

Order 2624.

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×D41C212yesmaximal, complemented
2#13050149C212yesmaximal, complemented
3#13050146C212yesmaximal, complemented
4#13050138C211yesmaximal, characteristic, complemented
5#13050136C212yesmaximal, complemented
6#13050134C212yesmaximal, complemented
7#13050132C212yesmaximal, complemented
8C2×#10620281C211yesmaximal, characteristic, complemented
9#121×C41C211yesmaximal, characteristic, complemented
10C23×D41C2211yescharacteristic
11C23×D41C2212yescomplemented
12C2×D4×C41C2212yescomplemented
13C2×D4×C41C2211yescharacteristic, complemented
14C22×C4×C41C2211yescharacteristic, complemented
15C2×C22⋊D41C2212yes—
16C2×C22⋊D41C2212yescomplemented
17C2×C22⋊D41C2212yescomplemented
18C22×Dic41C2211yescharacteristic, complemented
19D4×D41—28no—
20C2×D164C2212yes—
21C2×D164C2211yescharacteristic, complemented
22C2×C4×D41C2212yescomplemented
23C4⋊C4×C41C2211yescharacteristic, complemented
24C22⋊C4×C41C2212yescomplemented
25C22⋊Dic41C2212yescomplemented
26#10620281C2212yescomplemented
27#10620281C2212yescomplemented
28#10620281C2212yescomplemented
29#10620281C2212yescomplemented
30C4⋊Dic41C2211yescharacteristic, complemented
31#10620279C2212yescomplemented
32C23×C41C2312yes—
33C23×C41C2311yescharacteristic
34C22×D41—24no—
35C22×D41—41no—
36C22×D41—41no—
37C22×D41—42no—
38C22×D41—42no—
39C22×D41D414yescomplemented
40C22×D41C2312yes—
41C22×D41C2312yes—
42D4×C41—24no—
43D4×C41—41no—
44C2×C4×C41—41no—
45C2×C4×C41C2312yes—
46C2×C4×C41C2311yescharacteristic
47C2×C4×C41C2311yescharacteristic
48C22⋊D41—24no—
49C22⋊D41—24no—
50C22⋊D41—42no—
51C2×Dic41—41no—
52C2×Dic41C2312yes—
53C2×Dic41C2312yes—
54D164—24no—
55D164—41no—
56C4×D41—24no—
57C22×C41—21no—
58C22×C41—21no—
59C22×C41—22no—
60C22×C41—22no—
61C22×C41—22no—
62C22×C41C2×D412yes—
63C22×C41C2411yescharacteristic
64C2×D41—22no—
65C2×D41—22no—
66C2×D41—22no—
67C2×D41—22no—
68C2×D41—22no—
69C2×D41—44no—
70C2×D41—48no—
71C2×D41C2×D414yes—
72C4×C41—22no—
73C4×C41—21no—
74C4×C41—21no—
75Dic41—22no—
76Dic41—22no—
77C2×C41—22no—
78C2×C41—42no—
79C2×C41C22×D411yescharacteristic
80C2×C41H(5,𝔽2)11yescharacteristic
81C2×C41H(5,𝔽2)11yescharacteristic
82D41—24no—
83D41—42no—
84#534—411nomaximal, Sylow
85C41#53411yescharacteristic, complemented, Sylow
86C22×D4—412no—
87#123—412no—
88#123—412no—
89#121—412no—
90#121—411no—
91#121D4111yescharacteristic, complemented
92#120—412no—
93#120—412no—
94C2×C22⋊C4—411no—
95C24—411no—
96C24—412no—
97C2×D4—412no—
98C2×D4—412no—
99C2×D4—412no—
100C2×D4—412no—
101C2×D4—411no—
102C2×D4—828no—
103C2×D4C2×D4112yescomplemented
104C2×D4C2×D4111yescharacteristic, complemented
105C22×C4—411no—
106C22×C4—412no—
107C22×C4C2×D4111yescharacteristic, complemented
108C4⋊C4—412no—
109C4⋊C4—411no—
110C4⋊C4C2×D4111yescharacteristic, complemented
111C22⋊C4—412no—
112C22⋊C4—412no—
113C22⋊C4—412no—
114C22⋊C4—412no—
115C22⋊C4—412no—
116C22⋊C4C2×D4112yescomplemented
117C23—412no—
118C23—414no—
119C23—412no—
120C23—824no—
121C23—1641no—
122C23—1641no—
123C23—1642no—
124C23—1642no—
125C23C22×D4112yes—
126C23C22×D4111yescharacteristic
127D4—24no—
128D4—41no—
129D4—824no—
130D4—824no—
131D4—824no—
132D4—1641no—
133D4—1642no—
134C2×C4—41no—
135C2×C4—412no—
136C2×C4—412no—
137C2×C4—824no—
138C2×C4—1641no—
139C2×C4C22×D4111yescharacteristic
140C2×C4C22×D4111yescharacteristic
141C2×C4C22×D4112yes—
142C22—21no—
143C22—21no—
144C22—22no—
145C22—22no—
146C22—22no—
147C22—414no—
148C22—822no—
149C22—822no—
150C22—822no—
151C22—822no—
152C22—822no—
153C22—1644no—
154C22—1648no—
155C22D4×D4112yes—
156C22C23×D4111yescharacteristic
157C4—22no—
158C4—21no—
159C4—21no—
160C4—822no—
161C4—822no—
162C2—22no—
163C2—42no—
164C2—824no—
165C2—1642no—
166C2C2×D4×D4111yescharacteristic
167C2#1305020911yescharacteristic
168C2#1305021011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D41
commutator, socle, cosocleC22×C41C24
Fitting#121×C41C2
hypercenter#121D41
hypocenterC41#534
LCSG ▷ C22×C41 ▷ C41
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D4×D41C2semidirect
2. #13050149C2semidirect
3. #13050146C2semidirect
4. #13050138C2semidirect
5. #13050136C2semidirect
6. #13050134C2semidirect
7. #13050132C2semidirect
8. C2×#10620281C2semidirect
9. #121×C41C2semidirect
11. C23×D41C22semidirect
12. C2×D4×C41C22semidirect
13. C2×D4×C41C22semidirect
14. C22×C4×C41C22semidirect
16. C2×C22⋊D41C22semidirect
17. C2×C22⋊D41C22semidirect
18. C22×Dic41C22semidirect
21. C2×D164C22semidirect
22. C2×C4×D41C22semidirect
23. C4⋊C4×C41C22semidirect
24. C22⋊C4×C41C22semidirect
25. C22⋊Dic41C22semidirect
26. #10620281C22semidirect
27. #10620281C22semidirect
28. #10620281C22semidirect
29. #10620281C22semidirect
30. C4⋊Dic41C22semidirect
31. #10620279C22semidirect
39. C22×D41D4semidirect
85. C41#534semidirect
91. #121D41semidirect
103. C2×D4C2×D41semidirect
104. C2×D4C2×D41semidirect
107. C22×C4C2×D41semidirect
110. C4⋊C4C2×D41semidirect
116. C22⋊C4C2×D41semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D412
#130501492
#130501462
#130501382
#130501362
#130501342
#130501322
C2×#106202812
#121×C412
#53441