Finite Group Databasebeta

← #14583533

Subgroups — #14583533

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×D172C211yesmaximal, characteristic, complemented
2C2×D4×D43C211yesmaximal, characteristic, complemented
3C2×D4×D43C212yesmaximal, complemented
4#13063321C211yesmaximal, characteristic, complemented
5#13063300C211yesmaximal, characteristic, complemented
6#13063298C212yesmaximal, complemented
7#13063295C212yesmaximal, complemented
8#13063293C212yesmaximal, complemented
9#13063287C211yesmaximal, characteristic, complemented
10C4×C22⋊D43C211yesmaximal, characteristic, complemented
11#121×C43C211yesmaximal, characteristic, complemented
12C23×D43C2212yescomplemented
13C23×D43C2212yescomplemented
14C2×D4×C43C2212yescomplemented
15C2×D4×C43C2211yescharacteristic, complemented
16C22×C4×C43C2211yescharacteristic, complemented
17C2×C22⋊D43C2211yescharacteristic
18C2×C22⋊D43C2212yescomplemented
19C2×C22⋊D43C2212yescomplemented
20C2×C22⋊D43C2212yescomplemented
21D4×D43—28no—
22D4×D43—24no—
23C2×D172—24no—
24C2×D172C2211yescharacteristic
25C2×D172C2212yescomplemented
26C2×D172C2212yescomplemented
27C2×D172C2211yescharacteristic, complemented
28C2×C4×D43C2211yescharacteristic, complemented
29C2×C4×D43C2212yescomplemented
30C4⋊C4×C43C2211yescharacteristic, complemented
31C22⋊C4×C43C2212yescomplemented
32C22⋊Dic43C2211yescharacteristic, complemented
33(C2×D43)⋊C4C2211yescharacteristic, complemented
34(C2×D43)⋊C4C2212yescomplemented
35(C2×D43)⋊C4C2212yescomplemented
36Dic43⋊C4C2211yescharacteristic, complemented
37C4×Dic43C2211yescharacteristic, complemented
38C23×C43C2312yes—
39C23×C43C2311yescharacteristic
40C22×D43—24no—
41C22×D43—24no—
42C22×D43—24no—
43C22×D43—24no—
44C22×D43—42no—
45C22×D43—42no—
46C22×D43C2312yes—
47C22×D43C2312yes—
48C22×D43C2311yescharacteristic
49D4×C43—24no—
50D4×C43—22no—
51C2×C4×C43—22no—
52C2×C4×C43C2311yescharacteristic
53C2×C4×C43C2312yes—
54C2×C4×C43C2311yescharacteristic
55C22⋊D43—24no—
56C22⋊D43—24no—
57C22⋊D43—42no—
58C22⋊D43D414yescomplemented
59C2×Dic43C2311yescharacteristic
60C2×Dic43C2311yescharacteristic
61C2×Dic43C2311yescharacteristic
62D172—24no—
63D172—24no—
64D172—22no—
65D172D414yescomplemented
66C4×D43—22no—
67C4×D43—24no—
68C22×C43—21no—
69C22×C43—21no—
70C22×C43—22no—
71C22×C43—22no—
72C22×C43—22no—
73C22×C43C2×D412yescomplemented
74C22×C43C2411yescharacteristic
75C2×D43—21no—
76C2×D43—22no—
77C2×D43—22no—
78C2×D43—21no—
79C2×D43—22no—
80C2×D43—22no—
81C2×D43—22no—
82C2×D43—48no—
83C2×D43—48no—
84C2×D43C2×D412yescomplemented
85C2×D43C2×D414yescomplemented
86C4×C43—22no—
87C4×C43—21no—
88C4×C43C2×D412yescomplemented
89Dic43—21no—
90Dic43—21no—
91Dic43C2×D412yescomplemented
92C2×C43—22no—
93C2×C43—42no—
94C2×C43C22×D411yescharacteristic
95C2×C43C22×D411yescharacteristic
96C2×C43H(5,𝔽2)11yescharacteristic
97D43—22no—
98D43—24no—
99D43—42no—
100D42—431nomaximal, Sylow
101C43D4211yescharacteristic, complemented, Sylow
102C22×D4—432no—
103C22×D4—431no—
104C22×D4—431no—
105#127—431no—
106#121—431no—
107#121—432no—
108#121D4311yescharacteristic, complemented
109#120—432no—
110#120—432no—
111C4×D4—431no—
112C4×D4—431no—
113C24—432no—
114C24—432no—
115C2×D4—431no—
116C2×D4—432no—
117C2×D4—432no—
118C2×D4—432no—
119C2×D4—431no—
120C2×D4—432no—
121C2×D4—432no—
122C2×D4—431no—
123C2×D4—864no—
124C2×D4—868no—
125C2×D4—864no—
126C2×D4C2×D4312yescomplemented
127C2×D4C2×D4311yescharacteristic, complemented
128C22×C4—432no—
129C22×C4—431no—
130C22×C4C2×D4311yescharacteristic, complemented
131C4⋊C4—431no—
132C4⋊C4C2×D4311yescharacteristic, complemented
133C22⋊C4—431no—
134C22⋊C4—432no—
135C22⋊C4—431no—
136C22⋊C4—432no—
137C22⋊C4C2×D4312yescomplemented
138C42—431no—
139C23—432no—
140C23—431no—
141C23—432no—
142C23—864no—
143C23—864no—
144C23—864no—
145C23—864no—
146C23—1722no—
147C23—1722no—
148C23C22×D4312yes—
149C23C22×D4311yescharacteristic
150D4—24no—
151D4—22no—
152D4—434no—
153D4—434no—
154D4—864no—
155D4—864no—
156D4—864no—
157D4—864no—
158D4—862no—
159D4—1722no—
160C2×C4—22no—
161C2×C4—431no—
162C2×C4—431no—
163C2×C4—431no—
164C2×C4—864no—
165C2×C4—862no—
166C2×C4C22×D4312yes—
167C2×C4C22×D4311yescharacteristic
168C2×C4C22×D4311yescharacteristic
169C22—21no—
170C22—21no—
171C22—22no—
172C22—22no—
173C22—22no—
174C22—432no—
175C22—434no—
176C22—862no—
177C22—861no—
178C22—862no—
179C22—861no—
180C22—862no—
181C22—862no—
182C22—862no—
183C22—1728no—
184C22—1728no—
185C22D4×D4312yescomplemented
186C22C23×D4311yescharacteristic
187C4—21no—
188C4—22no—
189C4—432no—
190C4—861no—
191C4—861no—
192C4D4×D4312yescomplemented
193C2—22no—
194C2—42no—
195C2—864no—
196C2—862no—
197C2—1722no—
198C2C2×D4×D4311yescharacteristic
199C2C2×D4×D4311yescharacteristic
200C2#1306337111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D43
commutator, socle, cosocleC22×C43C24
Fitting#121×C43C2
hypercenter#121D43
hypocenterC43D42
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C22×D172C2semidirect
2. C2×D4×D43C2semidirect
3. C2×D4×D43C2semidirect
4. #13063321C2semidirect
5. #13063300C2semidirect
6. #13063298C2semidirect
7. #13063295C2semidirect
8. #13063293C2semidirect
9. #13063287C2semidirect
10. C4×C22⋊D43C2semidirect
11. #121×C43C2semidirect
12. C23×D43C22semidirect
13. C23×D43C22semidirect
14. C2×D4×C43C22semidirect
15. C2×D4×C43C22semidirect
16. C22×C4×C43C22semidirect
18. C2×C22⋊D43C22semidirect
19. C2×C22⋊D43C22semidirect
20. C2×C22⋊D43C22semidirect
25. C2×D172C22semidirect
26. C2×D172C22semidirect
27. C2×D172C22semidirect
28. C2×C4×D43C22semidirect
29. C2×C4×D43C22semidirect
30. C4⋊C4×C43C22semidirect
31. C22⋊C4×C43C22semidirect
32. C22⋊Dic43C22semidirect
33. (C2×D43)⋊C4C22semidirect
34. (C2×D43)⋊C4C22semidirect
35. (C2×D43)⋊C4C22semidirect
36. Dic43⋊C4C22semidirect
37. C4×Dic43C22semidirect
58. C22⋊D43D4semidirect
65. D172D4semidirect
73. C22×C43C2×D4semidirect
84. C2×D43C2×D4semidirect
85. C2×D43C2×D4semidirect
88. C4×C43C2×D4semidirect
91. Dic43C2×D4semidirect
101. C43D42semidirect
108. #121D43semidirect
126. C2×D4C2×D43semidirect
127. C2×D4C2×D43semidirect
130. C22×C4C2×D43semidirect
132. C4⋊C4C2×D43semidirect
137. C22⋊C4C2×D43semidirect
185. C22D4×D43semidirect
192. C4D4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×D1722
C2×D4×D432
#130633212
#130633002
#130632982
#130632952
#130632932
#130632872
C4×C22⋊D432
#121×C432
D4243