Finite Group Databasebeta

← #14583457

Subgroups — #14583457

Order 2752.

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×D43C212yesmaximal, complemented
2#13063310C212yesmaximal, complemented
3#13063307C212yesmaximal, complemented
4#13063299C211yesmaximal, characteristic, complemented
5#13063297C212yesmaximal, complemented
6#13063295C212yesmaximal, complemented
7#13063293C212yesmaximal, complemented
8C2×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
9#121×C43C211yesmaximal, characteristic, complemented
10C23×D43C2211yescharacteristic
11C23×D43C2212yescomplemented
12C2×D4×C43C2212yescomplemented
13C2×D4×C43C2211yescharacteristic, complemented
14C22×C4×C43C2211yescharacteristic, complemented
15C2×C22⋊D43C2212yes—
16C2×C22⋊D43C2212yescomplemented
17C2×C22⋊D43C2212yescomplemented
18C22×Dic43C2211yescharacteristic, complemented
19D4×D43—28no—
20C2×D172C2212yes—
21C2×D172C2211yescharacteristic, complemented
22C2×C4×D43C2212yescomplemented
23C4⋊C4×C43C2211yescharacteristic, complemented
24C22⋊C4×C43C2212yescomplemented
25C22⋊Dic43C2212yescomplemented
26(C2×D43)⋊C4C2212yescomplemented
27(C2×D43)⋊C4C2212yescomplemented
28(C2×D43)⋊C4C2212yescomplemented
29(C2×D43)⋊C4C2212yescomplemented
30C4⋊Dic43C2211yescharacteristic, complemented
31Dic43⋊C4C2212yescomplemented
32C23×C43C2312yes—
33C23×C43C2311yescharacteristic
34C22×D43—24no—
35C22×D43—41no—
36C22×D43—41no—
37C22×D43—42no—
38C22×D43—42no—
39C22×D43D414yescomplemented
40C22×D43C2312yes—
41C22×D43C2312yes—
42D4×C43—24no—
43D4×C43—41no—
44C2×C4×C43—41no—
45C2×C4×C43C2312yes—
46C2×C4×C43C2311yescharacteristic
47C2×C4×C43C2311yescharacteristic
48C22⋊D43—24no—
49C22⋊D43—24no—
50C22⋊D43—42no—
51C2×Dic43—41no—
52C2×Dic43C2312yes—
53C2×Dic43C2312yes—
54D172—24no—
55D172—41no—
56C4×D43—24no—
57C22×C43—21no—
58C22×C43—21no—
59C22×C43—22no—
60C22×C43—22no—
61C22×C43—22no—
62C22×C43C2×D412yes—
63C22×C43C2411yescharacteristic
64C2×D43—22no—
65C2×D43—22no—
66C2×D43—22no—
67C2×D43—22no—
68C2×D43—22no—
69C2×D43—44no—
70C2×D43—48no—
71C2×D43C2×D414yes—
72C4×C43—22no—
73C4×C43—21no—
74C4×C43—21no—
75Dic43—22no—
76Dic43—22no—
77C2×C43—22no—
78C2×C43—42no—
79C2×C43C22×D411yescharacteristic
80C2×C43H(5,𝔽2)11yescharacteristic
81C2×C43H(5,𝔽2)11yescharacteristic
82D43—24no—
83D43—42no—
84#534—431nomaximal, Sylow
85C43#53411yescharacteristic, complemented, Sylow
86C22×D4—432no—
87#123—432no—
88#123—432no—
89#121—432no—
90#121—431no—
91#121D4311yescharacteristic, complemented
92#120—432no—
93#120—432no—
94C2×C22⋊C4—431no—
95C24—431no—
96C24—432no—
97C2×D4—432no—
98C2×D4—432no—
99C2×D4—432no—
100C2×D4—432no—
101C2×D4—431no—
102C2×D4—868no—
103C2×D4C2×D4312yescomplemented
104C2×D4C2×D4311yescharacteristic, complemented
105C22×C4—431no—
106C22×C4—432no—
107C22×C4C2×D4311yescharacteristic, complemented
108C4⋊C4—432no—
109C4⋊C4—431no—
110C4⋊C4C2×D4311yescharacteristic, complemented
111C22⋊C4—432no—
112C22⋊C4—432no—
113C22⋊C4—432no—
114C22⋊C4—432no—
115C22⋊C4—432no—
116C22⋊C4C2×D4312yescomplemented
117C23—432no—
118C23—434no—
119C23—432no—
120C23—864no—
121C23—1721no—
122C23—1721no—
123C23—1722no—
124C23—1722no—
125C23C22×D4312yes—
126C23C22×D4311yescharacteristic
127D4—24no—
128D4—41no—
129D4—864no—
130D4—864no—
131D4—864no—
132D4—1721no—
133D4—1722no—
134C2×C4—41no—
135C2×C4—432no—
136C2×C4—432no—
137C2×C4—864no—
138C2×C4—1721no—
139C2×C4C22×D4311yescharacteristic
140C2×C4C22×D4311yescharacteristic
141C2×C4C22×D4312yes—
142C22—21no—
143C22—21no—
144C22—22no—
145C22—22no—
146C22—22no—
147C22—434no—
148C22—862no—
149C22—862no—
150C22—862no—
151C22—862no—
152C22—862no—
153C22—1724no—
154C22—1728no—
155C22D4×D4312yes—
156C22C23×D4311yescharacteristic
157C4—22no—
158C4—21no—
159C4—21no—
160C4—862no—
161C4—862no—
162C2—22no—
163C2—42no—
164C2—864no—
165C2—1722no—
166C2C2×D4×D4311yescharacteristic
167C2#1306337011yescharacteristic
168C2#1306337111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D43
commutator, socle, cosocleC22×C43C24
Fitting#121×C43C2
hypercenter#121D43
hypocenterC43#534
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. #13063310C2semidirect
3. #13063307C2semidirect
4. #13063299C2semidirect
5. #13063297C2semidirect
6. #13063295C2semidirect
7. #13063293C2semidirect
8. C2×(C2×D43)⋊C4C2semidirect
9. #121×C43C2semidirect
11. C23×D43C22semidirect
12. C2×D4×C43C22semidirect
13. C2×D4×C43C22semidirect
14. C22×C4×C43C22semidirect
16. C2×C22⋊D43C22semidirect
17. C2×C22⋊D43C22semidirect
18. C22×Dic43C22semidirect
21. C2×D172C22semidirect
22. C2×C4×D43C22semidirect
23. C4⋊C4×C43C22semidirect
24. C22⋊C4×C43C22semidirect
25. C22⋊Dic43C22semidirect
26. (C2×D43)⋊C4C22semidirect
27. (C2×D43)⋊C4C22semidirect
28. (C2×D43)⋊C4C22semidirect
29. (C2×D43)⋊C4C22semidirect
30. C4⋊Dic43C22semidirect
31. Dic43⋊C4C22semidirect
39. C22×D43D4semidirect
85. C43#534semidirect
91. #121D43semidirect
103. C2×D4C2×D43semidirect
104. C2×D4C2×D43semidirect
107. C22×C4C2×D43semidirect
110. C4⋊C4C2×D43semidirect
116. C22⋊C4C2×D43semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D432
#130633102
#130633072
#130632992
#130632972
#130632952
#130632932
C2×(C2×D43)⋊C42
#121×C432
#53443