Finite Group Databasebeta

← #121×D43 #14583387

Subgroups — #121×D43 #14583387

Order 2752.

426 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 121 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×D43C212yesmaximal, complemented
2C2×D4×D43C211yesmaximal, characteristic, complemented
3C22×C4×D43C211yesmaximal, characteristic, complemented
4#13063300C211yesmaximal, characteristic, complemented
5#13063299C211yesmaximal, characteristic, complemented
6#13063298C212yesmaximal, complemented
7#13063297C212yesmaximal, complemented
8#13063296C211yesmaximal, characteristic, complemented
9C4⋊C4×D43C211yesmaximal, characteristic, complemented
10C22⋊C4×D43C212yesmaximal, complemented
11#121×C43C211yesmaximal, characteristic, complemented
12C23×D43C2212yes—
13C23×D43C2211yescharacteristic
14C2×D4×C43C2211yescharacteristic, complemented
15C2×D4×C43C2212yescomplemented
16C22×C4×C43C2211yescharacteristic, complemented
17C2×C22⋊D43C2212yescomplemented
18C2×C22⋊D43C2212yescomplemented
19C2×C22⋊D43C2212yescomplemented
20C22×Dic43C2211yescharacteristic, complemented
21D4×D43—24no—
22D4×D43—28no—
23C2×D172C2212yescomplemented
24C2×D172C2211yescharacteristic, complemented
25C2×C4×D43—24no—
26C2×C4×D43C2211yescharacteristic
27C2×C4×D43C2212yes—
28C2×C4×D43C2211yescharacteristic
29C2×C4×D43C2211yescharacteristic, complemented
30C2×C4×D43C2211yescharacteristic, complemented
31C4⋊C4×C43C2211yescharacteristic, complemented
32C22⋊C4×C43C2212yescomplemented
33C22⋊Dic43C2212yescomplemented
34(C2×D43)⋊C4C2212yescomplemented
35(C2×D43)⋊C4C2212yescomplemented
36C4⋊Dic43C2211yescharacteristic, complemented
37Dic43⋊C4C2212yescomplemented
38C23×C43C2312yes—
39C23×C43C2311yescharacteristic
40C22×D43—22no—
41C22×D43—22no—
42C22×D43—24no—
43C22×D43—24no—
44C22×D43—24no—
45C22×D43D414yescomplemented
46C22×D43C2312yes—
47C22×D43C2311yescharacteristic
48C22×D43C2311yescharacteristic
49D4×C43—24no—
50D4×C43—22no—
51C2×C4×C43—22no—
52C2×C4×C43C2312yes—
53C2×C4×C43C2311yescharacteristic
54C2×C4×C43C2311yescharacteristic
55C22⋊D43—24no—
56C22⋊D43—24no—
57C22⋊D43—24no—
58C2×Dic43—22no—
59C2×Dic43C2312yes—
60C2×Dic43C2311yescharacteristic
61C2×Dic43C2311yescharacteristic
62D172—24no—
63D172—22no—
64C4×D43—22no—
65C4×D43—24no—
66C4×D43—22no—
67C4×D43—22no—
68C4×D43D414yescomplemented
69C22×C43—21no—
70C22×C43—21no—
71C22×C43—22no—
72C22×C43—22no—
73C22×C43—22no—
74C22×C43C2×D412yescomplemented
75C22×C43C2411yescharacteristic
76C2×D43—21no—
77C2×D43—21no—
78C2×D43—28no—
79C2×D43—22no—
80C2×D43—22no—
81C2×D43—22no—
82C2×D43—48no—
83C2×D43C2×D412yes—
84C2×D43C2×D412yes—
85C2×D43C2×D412yescomplemented
86C2×D43#4112yes—
87C4×C43—21no—
88C4×C43—22no—
89C4×C43C2×D412yescomplemented
90Dic43—21no—
91Dic43—22no—
92Dic43C2×D412yescomplemented
93C2×C43—22no—
94C2×C43—42no—
95C2×C43C22×D411yescharacteristic
96C2×C43C22×D411yescharacteristic
97C2×C43C2×#4111yescharacteristic
98D43—22no—
99D43—42no—
100D43#12114yesdirect product factor
101C2×#121—431nomaximal, Sylow
102C43C2×#12111yescharacteristic, complemented, Sylow
103C22×D4—431no—
104C22×D4—432no—
105C23×C4—431no—
106#121—431no—
107#121—432no—
108#121—431no—
109#121—431no—
110#121—432no—
111#121D4311yescharacteristic, direct product factor
112C2×C4⋊C4—431no—
113C2×C22⋊C4—432no—
114C24—431no—
115C24—432no—
116C2×D4—432no—
117C2×D4—432no—
118C2×D4—432no—
119C2×D4—432no—
120C2×D4—431no—
121C2×D4—864no—
122C2×D4—868no—
123C2×D4C2×D4312yescomplemented
124C2×D4C2×D4311yescharacteristic, complemented
125C22×C4—431no—
126C22×C4—431no—
127C22×C4—431no—
128C22×C4—432no—
129C22×C4—431no—
130C22×C4—431no—
131C22×C4—864no—
132C22×C4C2×D4311yescharacteristic, complemented
133C4⋊C4—432no—
134C4⋊C4—431no—
135C4⋊C4C2×D4311yescharacteristic, complemented
136C22⋊C4—432no—
137C22⋊C4—432no—
138C22⋊C4—432no—
139C22⋊C4C2×D4312yescomplemented
140C23—431no—
141C23—434no—
142C23—431no—
143C23—432no—
144C23—862no—
145C23—862no—
146C23—864no—
147C23—864no—
148C23—864no—
149C23C22×D4312yes—
150C23C22×D4311yescharacteristic
151D4—24no—
152D4—22no—
153D4—864no—
154D4—864no—
155D4—864no—
156D4—864no—
157D4—862no—
158C2×C4—22no—
159C2×C4—431no—
160C2×C4—434no—
161C2×C4—431no—
162C2×C4—432no—
163C2×C4—862no—
164C2×C4—862no—
165C2×C4—864no—
166C2×C4—862no—
167C2×C4—862no—
168C2×C4C22×D4311yescharacteristic
169C2×C4C22×D4312yes—
170C2×C4C22×D4311yescharacteristic
171C22—21no—
172C22—21no—
173C22—22no—
174C22—22no—
175C22—22no—
176C22—432no—
177C22—432no—
178C22—432no—
179C22—432no—
180C22—868no—
181C22—861no—
182C22—861no—
183C22—862no—
184C22—862no—
185C22—862no—
186C22—1728no—
187C22D4×D4312yescomplemented
188C22C23×D4311yescharacteristic
189C4—21no—
190C4—22no—
191C4—432no—
192C4—861no—
193C4—862no—
194C4D4×D4312yescomplemented
195C2—22no—
196C2—42no—
197C2—434no—
198C2—862no—
199C2—1722no—
200C2C2×D4×D4311yescharacteristic
201C2C2×D4×D4311yescharacteristic
202C2#41×D4311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D43
commutator, socle, cosocleC22×C43C24
Fitting#121×C43C2
hypercenter#121D43
hypocenterC43C2×#121
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D4×D43C2semidirect
2. C2×D4×D43C2semidirect
3. C22×C4×D43C2semidirect
4. #13063300C2semidirect
5. #13063299C2semidirect
6. #13063298C2semidirect
7. #13063297C2semidirect
8. #13063296C2semidirect
9. C4⋊C4×D43C2semidirect
10. C22⋊C4×D43C2semidirect
11. #121×C43C2semidirect
14. C2×D4×C43C22semidirect
15. C2×D4×C43C22semidirect
16. C22×C4×C43C22semidirect
17. C2×C22⋊D43C22semidirect
18. C2×C22⋊D43C22semidirect
19. C2×C22⋊D43C22semidirect
20. C22×Dic43C22semidirect
23. C2×D172C22semidirect
24. C2×D172C22semidirect
29. C2×C4×D43C22semidirect
30. C2×C4×D43C22semidirect
31. C4⋊C4×C43C22semidirect
32. C22⋊C4×C43C22semidirect
33. C22⋊Dic43C22semidirect
34. (C2×D43)⋊C4C22semidirect
35. (C2×D43)⋊C4C22semidirect
36. C4⋊Dic43C22semidirect
37. Dic43⋊C4C22semidirect
45. C22×D43D4semidirect
68. C4×D43D4semidirect
74. C22×C43C2×D4semidirect
85. C2×D43C2×D4semidirect
89. C4×C43C2×D4semidirect
92. Dic43C2×D4semidirect
100. D43#121direct (N × H)
102. C43C2×#121semidirect
111. #121D43direct (N × H)
123. C2×D4C2×D43semidirect
124. C2×D4C2×D43semidirect
132. C22×C4C2×D43semidirect
135. C4⋊C4C2×D43semidirect
139. C22⋊C4C2×D43semidirect
187. C22D4×D43semidirect
194. C4D4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D432
C22×C4×D432
#130633002
#130632992
#130632982
#130632972
#130632962
C4⋊C4×D432
C22⋊C4×D432
#121×C432
C2×#12143