Finite Group Databasebeta

← #14583531

Subgroups — #14583531

Order 2752.

428 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C22×C22⋊D43C212yesmaximal, complemented
2C2×D4×D43C212yesmaximal, complemented
3#13063321C211yesmaximal, characteristic, complemented
4#13063298C212yesmaximal, complemented
5#13063297C212yesmaximal, complemented
6#13063295C212yesmaximal, complemented
7#13063293C211yesmaximal, characteristic, complemented
8(C22⋊D43)⋊C4C212yesmaximal, complemented
9#120×C43C211yesmaximal, characteristic, complemented
10C24×C43C2211yescharacteristic, complemented
11C23×D43C2211yescharacteristic, complemented
12C23×D43C2212yescomplemented
13C2×D4×C43C2212yescomplemented
14C2×D4×C43C2211yescharacteristic, complemented
15C2×C22⋊D43—28no—
16C2×C22⋊D43C2212yes—
17C2×C22⋊D43C2212yescomplemented
18C2×C22⋊D43C2212yescomplemented
19C2×C22⋊D43C2212yescomplemented
20C2×C22⋊D43C2212yescomplemented
21C22×Dic43C2212yescomplemented
22D4×D43—28no—
23C2×D172C2212yescomplemented
24C2×D172C2211yescharacteristic, complemented
25C2×C4×D43C2212yescomplemented
26C22⋊C4×C43C2212yescomplemented
27C22⋊C4×C43C2211yescharacteristic, complemented
28C22⋊Dic43C2211yescharacteristic, complemented
29(C2×D43)⋊C4C2212yescomplemented
30(C2×D43)⋊C4C2212yescomplemented
31Dic43⋊C4C2212yescomplemented
32C4×Dic43C2211yescharacteristic, complemented
33C23×C43—24no—
34C23×C43—41no—
35C23×C43C2311yescharacteristic
36C23×C43C2311yescharacteristic
37C23×C43C2312yes—
38C22×D43—24no—
39C22×D43—24no—
40C22×D43—24no—
41C22×D43—41no—
42C22×D43—42no—
43C22×D43C2312yes—
44C22×D43C2312yes—
45D4×C43—24no—
46D4×C43—41no—
47C2×C4×C43C2311yescharacteristic
48C2×C4×C43C2312yes—
49C22⋊D43—24no—
50C22⋊D43—24no—
51C22⋊D43—24no—
52C22⋊D43—24no—
53C22⋊D43D418yescomplemented
54C2×Dic43—24no—
55C2×Dic43C2312yes—
56C2×Dic43C2312yes—
57D172—24no—
58D172—41no—
59C4×D43—24no—
60C22×C43—22no—
61C22×C43—22no—
62C22×C43—22no—
63C22×C43—22no—
64C22×C43—21no—
65C22×C43—21no—
66C22×C43—44no—
67C22×C43C2×D414yescomplemented
68C22×C43C2411yescharacteristic
69C2×D43—22no—
70C2×D43—22no—
71C2×D43—22no—
72C2×D43—22no—
73C2×D43—22no—
74C2×D43—44no—
75C2×D43—48no—
76C2×D43C2×D414yescomplemented
77C4×C43—22no—
78C4×C43—21no—
79Dic43—22no—
80Dic43C2×D414yescomplemented
81C2×C43—24no—
82C2×C43—41no—
83C2×C43—41no—
84C2×C43C22×D412yes—
85C2×C43H(5,𝔽2)11yescharacteristic
86D43—24no—
87D43—42no—
88D42—431nomaximal, Sylow
89C43D4211yescharacteristic, complemented, Sylow
90C22×D4—432no—
91C22×D4—432no—
92#127—431no—
93#121—432no—
94#121—432no—
95#120—431no—
96#120—432no—
97#120D4311yescharacteristic, complemented
98C4×D4—432no—
99C24—431no—
100C24—432no—
101C24C2×D4311yescharacteristic, complemented
102C2×D4—432no—
103C2×D4—432no—
104C2×D4—432no—
105C2×D4—432no—
106C2×D4—432no—
107C2×D4—432no—
108C2×D4—431no—
109C2×D4—868no—
110C2×D4—868no—
111C2×D4C2×D4312yescomplemented
112C2×D4C2×D4311yescharacteristic, complemented
113C22×C4—432no—
114C22×C4—432no—
115C4⋊C4—432no—
116C22⋊C4—431no—
117C22⋊C4—432no—
118C22⋊C4—432no—
119C22⋊C4C2×D4312yescomplemented
120C22⋊C4C2×D4311yescharacteristic, complemented
121C42—431no—
122C23—24no—
123C23—41no—
124C23—432no—
125C23—432no—
126C23—864no—
127C23—864no—
128C23—864no—
129C23—1722no—
130C23—1721no—
131C23C22×D4311yescharacteristic
132C23C22×D4311yescharacteristic
133C23C22×D4312yes—
134D4—24no—
135D4—41no—
136D4—438no—
137D4—864no—
138D4—864no—
139D4—864no—
140D4—864no—
141D4—864no—
142D4—1721no—
143C2×C4—432no—
144C2×C4—432no—
145C2×C4—864no—
146C2×C4—864no—
147C2×C4C22×D4311yescharacteristic
148C2×C4C22×D4312yes—
149C22—22no—
150C22—22no—
151C22—22no—
152C22—22no—
153C22—21no—
154C22—21no—
155C22—44no—
156C22—434no—
157C22—862no—
158C22—862no—
159C22—862no—
160C22—862no—
161C22—862no—
162C22—1728no—
163C22—1724no—
164C22D4×D4314yescomplemented
165C22C23×D4311yescharacteristic
166C4—22no—
167C4—21no—
168C4—434no—
169C4—862no—
170C2—24no—
171C2—41no—
172C2—41no—
173C2—864no—
174C2—1722no—
175C2C2×D4×D4312yes—
176C2#1306337011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D43
commutator, socle, cosocleC22×C43C24
Fitting#120×C43C2
hypercenter#120D43
hypocenterC43D42
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D43C2semidirect
2. C2×D4×D43C2semidirect
3. #13063321C2semidirect
4. #13063298C2semidirect
5. #13063297C2semidirect
6. #13063295C2semidirect
7. #13063293C2semidirect
8. (C22⋊D43)⋊C4C2semidirect
9. #120×C43C2semidirect
10. C24×C43C22semidirect
11. C23×D43C22semidirect
12. C23×D43C22semidirect
13. C2×D4×C43C22semidirect
14. C2×D4×C43C22semidirect
17. C2×C22⋊D43C22semidirect
18. C2×C22⋊D43C22semidirect
19. C2×C22⋊D43C22semidirect
20. C2×C22⋊D43C22semidirect
21. C22×Dic43C22semidirect
23. C2×D172C22semidirect
24. C2×D172C22semidirect
25. C2×C4×D43C22semidirect
26. C22⋊C4×C43C22semidirect
27. C22⋊C4×C43C22semidirect
28. C22⋊Dic43C22semidirect
29. (C2×D43)⋊C4C22semidirect
30. (C2×D43)⋊C4C22semidirect
31. Dic43⋊C4C22semidirect
32. C4×Dic43C22semidirect
53. C22⋊D43D4semidirect
67. C22×C43C2×D4semidirect
76. C2×D43C2×D4semidirect
80. Dic43C2×D4semidirect
89. C43D42semidirect
97. #120D43semidirect
101. C24C2×D43semidirect
111. C2×D4C2×D43semidirect
112. C2×D4C2×D43semidirect
119. C22⋊C4C2×D43semidirect
120. C22⋊C4C2×D43semidirect
164. C22D4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D432
C2×D4×D432
#130633212
#130632982
#130632972
#130632952
#130632932
(C22⋊D43)⋊C42
#120×C432
D4243