Finite Group Databasebeta

← #14583465

Subgroups — #14583465

Order 2752.

334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 334 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×#10621898C211yesmaximal, characteristic, complemented
2C2×D4×D43C211yesmaximal, characteristic, complemented
3#13063321C212yesmaximal, complemented
4#13063311C212yesmaximal, complemented
5#13063300C211yesmaximal, characteristic, complemented
6#13063299C211yesmaximal, characteristic, complemented
7#13063296C211yesmaximal, characteristic, complemented
8#13063295C212yesmaximal, complemented
9#13063293C212yesmaximal, complemented
10#13063283C211yesmaximal, characteristic, complemented
11#121×C43C211yesmaximal, characteristic, complemented
12C23×D43C2212yes—
13C2×D4×C43C2211yescharacteristic
14C2×D4×C43C2212yescomplemented
15C22×C4×C43C2211yescharacteristic, complemented
16C2×C22⋊D43C2211yescharacteristic
17C2×C22⋊D43C2212yes—
18C2×C22⋊D43C2211yescharacteristic, complemented
19C2×C22⋊D43C2212yescomplemented
20C2×C22⋊D43C2212yescomplemented
21D4×D43—24no—
22#10621898—24no—
23C2×D172C2211yescharacteristic
24C2×D172C2211yescharacteristic
25C2×D172C2212yescomplemented
26C2×C4×D43C2211yescharacteristic
27C2×C4×D43C2211yescharacteristic, complemented
28C2×Dic86C2211yescharacteristic, complemented
29C4⋊C4×C43C2211yescharacteristic, complemented
30C22⋊C4×C43C2212yescomplemented
31C22⋊Dic43C2212yescomplemented
32(C2×D43)⋊C4C2212yes—
33(C2×D43)⋊C4C2212yescomplemented
34(C2×D43)⋊C4C2212yescomplemented
35C4⋊Dic43C2211yescharacteristic, complemented
36C4×Dic43C2212yescomplemented
37C23×C43C2312yes—
38C23×C43C2311yescharacteristic
39C22×D43—24no—
40C22×D43—42no—
41C22×D43—42no—
42C22×D43C2312yes—
43C22×D43C2311yescharacteristic
44C22×D43C2311yescharacteristic
45D4×C43—22no—
46D4×C43—42no—
47C2×C4×C43—22no—
48C2×C4×C43C2312yes—
49C2×C4×C43C2311yescharacteristic
50C2×C4×C43C2311yescharacteristic
51C22⋊D43—22no—
52C22⋊D43—22no—
53C22⋊D43—24no—
54C22⋊D43—42no—
55C22⋊D43—42no—
56C2×Dic43C2312yes—
57C2×Dic43C2311yescharacteristic
58C2×Dic43C2311yescharacteristic
59D172—22no—
60D172—22no—
61D172—42no—
62C4×D43—22no—
63C4×D43D414yescomplemented
64Dic86—22no—
65C22×C43—22no—
66C22×C43—21no—
67C22×C43—22no—
68C22×C43—22no—
69C22×C43—21no—
70C22×C43—21no—
71C22×C43C2411yescharacteristic
72C2×D43—21no—
73C2×D43—21no—
74C2×D43—22no—
75C2×D43—21no—
76C2×D43—22no—
77C2×D43—22no—
78C2×D43—21no—
79C2×D43—21no—
80C2×D43—48no—
81C2×D43C2×D412yes—
82C4×C43—21no—
83C4×C43—22no—
84C4×C43C2×D412yes—
85Dic43—21no—
86Dic43—22no—
87Dic43C2×D412yes—
88C2×C43—42no—
89C2×C43—41no—
90C2×C43C22×D411yescharacteristic
91C2×C43H(5,𝔽2)11yescharacteristic
92C2×C43H(5,𝔽2)11yescharacteristic
93D43—22no—
94D43—41no—
95D43—42no—
96#535—431nomaximal, Sylow
97C43#53511yescharacteristic, complemented, Sylow
98C2×#41—431no—
99C22×D4—431no—
100#127—432no—
101#124—432no—
102#121—431no—
103#121—431no—
104#121—431no—
105#121D4311yescharacteristic, complemented
106#120—432no—
107#120—432no—
108#117—431no—
109C24—432no—
110#41—864no—
111C2×Q8—431no—
112C2×D4—431no—
113C2×D4—432no—
114C2×D4—431no—
115C2×D4—432no—
116C2×D4—432no—
117C2×D4—431no—
118C2×D4—431no—
119C2×D4—432no—
120C2×D4—864no—
121C2×D4C2×D4311yescharacteristic
122C2×D4C2×D4312yescomplemented
123C22×C4—431no—
124C22×C4—431no—
125C22×C4C2×D4311yescharacteristic, complemented
126C4⋊C4—431no—
127C4⋊C4C2×D4311yescharacteristic, complemented
128C22⋊C4—432no—
129C22⋊C4—432no—
130C22⋊C4—432no—
131C22⋊C4—432no—
132C22⋊C4C2×D4312yescomplemented
133C42—432no—
134C23—431no—
135C23—432no—
136C23—431no—
137C23—864no—
138C23—1722no—
139C23—1722no—
140C23C22×D4312yes—
141C23C22×D4311yescharacteristic
142Q8—862no—
143D4—22no—
144D4—42no—
145D4—862no—
146D4—864no—
147D4—862no—
148D4—862no—
149D4—862no—
150D4—1722no—
151D4—1722no—
152D4—1722no—
153C2×C4—22no—
154C2×C4—431no—
155C2×C4—434no—
156C2×C4—432no—
157C2×C4—431no—
158C2×C4—862no—
159C2×C4C22×D4312yes—
160C2×C4C22×D4311yescharacteristic
161C2×C4C22×D4311yescharacteristic
162C22—21no—
163C22—22no—
164C22—21no—
165C22—22no—
166C22—21no—
167C22—22no—
168C22—432no—
169C22—861no—
170C22—861no—
171C22—861no—
172C22—862no—
173C22—861no—
174C22—862no—
175C22—861no—
176C22—862no—
177C22—1728no—
178C22C23×D4311yescharacteristic
179C4—21no—
180C4—22no—
181C4—432no—
182C4—861no—
183C4—862no—
184C4D4×D4312yes—
185C2—42no—
186C2—41no—
187C2—862no—
188C2—1722no—
189C2—1721no—
190C2C2×D4×D4311yescharacteristic
191C2#1306337011yescharacteristic
192C2#1306337111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D43
commutator, socle, cosocleC22×C43C24
Fitting#121×C43C2
hypercenter#121D43
hypocenterC43#535
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#10621898C2semidirect
2. C2×D4×D43C2semidirect
3. #13063321C2semidirect
4. #13063311C2semidirect
5. #13063300C2semidirect
6. #13063299C2semidirect
7. #13063296C2semidirect
8. #13063295C2semidirect
9. #13063293C2semidirect
10. #13063283C2semidirect
11. #121×C43C2semidirect
14. C2×D4×C43C22semidirect
15. C22×C4×C43C22semidirect
18. C2×C22⋊D43C22semidirect
19. C2×C22⋊D43C22semidirect
20. C2×C22⋊D43C22semidirect
25. C2×D172C22semidirect
27. C2×C4×D43C22semidirect
28. C2×Dic86C22semidirect
29. C4⋊C4×C43C22semidirect
30. C22⋊C4×C43C22semidirect
31. C22⋊Dic43C22semidirect
33. (C2×D43)⋊C4C22semidirect
34. (C2×D43)⋊C4C22semidirect
35. C4⋊Dic43C22semidirect
36. C4×Dic43C22semidirect
63. C4×D43D4semidirect
97. C43#535semidirect
105. #121D43semidirect
122. C2×D4C2×D43semidirect
125. C22×C4C2×D43semidirect
127. C4⋊C4C2×D43semidirect
132. C22⋊C4C2×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#106218982
C2×D4×D432
#130633212
#130633112
#130633002
#130632992
#130632962
#130632952
#130632932
#130632832
#121×C432
#53543