Finite Group Databasebeta

← #14583464

Subgroups — #14583464

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×#10621900C211yesmaximal, characteristic, complemented
2C22×C22⋊D43C211yesmaximal, characteristic, complemented
3#13063321C212yesmaximal, complemented
4#13063311C212yesmaximal, complemented
5#13063298C212yesmaximal, complemented
6#13063297C212yesmaximal, complemented
7#13063295C211yesmaximal, characteristic, complemented
8#13063294C211yesmaximal, characteristic, complemented
9#13063293C211yesmaximal, characteristic, complemented
10#13063281C211yesmaximal, characteristic, complemented
11#120×C43C211yesmaximal, characteristic, complemented
12C24×C43C2211yescharacteristic
13C23×D43C2211yescharacteristic
14C2×D4×C43C2211yescharacteristic
15C2×D4×C43C2212yescomplemented
16C2×C22⋊D43—24no—
17C2×C22⋊D43C2211yescharacteristic
18C2×C22⋊D43C2212yes—
19C2×C22⋊D43C2212yes—
20C2×C22⋊D43C2211yescharacteristic, complemented
21C2×C22⋊D43C2212yescomplemented
22C2×C22⋊D43C2212yescomplemented
23C22×Dic43C2211yescharacteristic
24C22×Dic43C2211yescharacteristic, complemented
25#10621900—24no—
26C2×D172C2212yescomplemented
27C2×C4×D43C2211yescharacteristic, complemented
28C2×Dic86C2211yescharacteristic, complemented
29C22⋊C4×C43C2211yescharacteristic
30C22⋊C4×C43C2212yescomplemented
31C22⋊Dic43C2211yescharacteristic
32C22⋊Dic43C2212yescomplemented
33(C2×D43)⋊C4C2212yescomplemented
34(C2×D43)⋊C4C2212yescomplemented
35Dic43⋊C4C2212yescomplemented
36C4×Dic43C2212yescomplemented
37C23×C43—22no—
38C23×C43—42no—
39C23×C43C2312yes—
40C23×C43C2311yescharacteristic
41C23×C43C2311yescharacteristic
42C22×D43—22no—
43C22×D43—42no—
44C22×D43C2312yes—
45C22×D43C2311yescharacteristic
46D4×C43—22no—
47D4×C43—42no—
48C2×C4×C43C2312yes—
49C2×C4×C43C2311yescharacteristic
50C22⋊D43—22no—
51C22⋊D43—22no—
52C22⋊D43—24no—
53C22⋊D43—24no—
54C22⋊D43—42no—
55C22⋊D43—42no—
56C2×Dic43—22no—
57C2×Dic43D414yescomplemented
58C2×Dic43C2312yes—
59C2×Dic43C2311yescharacteristic
60C2×Dic43C2311yescharacteristic
61C2×Dic43C2311yescharacteristic
62D172—42no—
63C4×D43—22no—
64Dic86—22no—
65C22×C43—22no—
66C22×C43—22no—
67C22×C43—21no—
68C22×C43—22no—
69C22×C43—22no—
70C22×C43—22no—
71C22×C43—44no—
72C22×C43C2×D412yes—
73C22×C43C2411yescharacteristic
74C2×D43—22no—
75C2×D43—21no—
76C2×D43—22no—
77C2×D43—22no—
78C2×D43—22no—
79C2×D43—44no—
80C4×C43—21no—
81C4×C43—22no—
82Dic43—21no—
83Dic43—22no—
84Dic43C2×D412yes—
85Dic43C2×D412yes—
86C2×C43—22no—
87C2×C43—41no—
88C2×C43—42no—
89C2×C43C22×D411yescharacteristic
90C2×C43H(5,𝔽2)12yes—
91D43—41no—
92D43—42no—
93#535—431nomaximal, Sylow
94C43#53511yescharacteristic, complemented, Sylow
95C2×#41—431no—
96C22×D4—431no—
97#127—432no—
98#124—432no—
99#121—432no—
100#121—432no—
101#120—431no—
102#120—431no—
103#120—431no—
104#120D4311yescharacteristic, complemented
105#117—431no—
106C24—431no—
107C24C2×D4311yescharacteristic
108#41—864no—
109C2×Q8—431no—
110C2×D4—431no—
111C2×D4—432no—
112C2×D4—432no—
113C2×D4—431no—
114C2×D4—432no—
115C2×D4—432no—
116C2×D4—432no—
117C2×D4—864no—
118C2×D4C2×D4311yescharacteristic
119C2×D4C2×D4312yescomplemented
120C22×C4—431no—
121C22×C4—431no—
122C22×C4—431no—
123C4⋊C4—432no—
124C22⋊C4—431no—
125C22⋊C4—432no—
126C22⋊C4—432no—
127C22⋊C4—432no—
128C22⋊C4C2×D4311yescharacteristic
129C22⋊C4C2×D4312yescomplemented
130C42—432no—
131C23—22no—
132C23—42no—
133C23—432no—
134C23—431no—
135C23—862no—
136C23—1722no—
137C23C22×D4312yes—
138C23C22×D4311yescharacteristic
139C23C22×D4311yescharacteristic
140Q8—862no—
141D4—22no—
142D4—42no—
143D4—864no—
144D4—864no—
145D4—862no—
146D4—862no—
147D4—1722no—
148D4—1722no—
149D4—1722no—
150C2×C4—434no—
151C2×C4—431no—
152C2×C4—431no—
153C2×C4—432no—
154C2×C4—431no—
155C2×C4—862no—
156C2×C4—862no—
157C2×C4C22×D4312yes—
158C2×C4C22×D4311yescharacteristic
159C22—22no—
160C22—21no—
161C22—22no—
162C22—22no—
163C22—22no—
164C22—22no—
165C22—44no—
166C22—861no—
167C22—862no—
168C22—862no—
169C22—862no—
170C22—862no—
171C22—1724no—
172C22D4×D4312yes—
173C22C23×D4311yescharacteristic
174C4—21no—
175C4—22no—
176C4—432no—
177C4—432no—
178C4—861no—
179C4—862no—
180C2—22no—
181C2—42no—
182C2—41no—
183C2—1722no—
184C2—1721no—
185C2C2×D4×D4311yescharacteristic
186C2#1306337012yes—
subgroupG/H
center, FrattiniC22C23×D43
commutator, socle, cosocleC22×C43C24
Fitting#120×C43C2
hypercenter#120D43
hypocenterC43#535
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C2×#10621900C2semidirect
2. C22×C22⋊D43C2semidirect
3. #13063321C2semidirect
4. #13063311C2semidirect
5. #13063298C2semidirect
6. #13063297C2semidirect
7. #13063295C2semidirect
8. #13063294C2semidirect
9. #13063293C2semidirect
10. #13063281C2semidirect
11. #120×C43C2semidirect
15. C2×D4×C43C22semidirect
20. C2×C22⋊D43C22semidirect
21. C2×C22⋊D43C22semidirect
22. C2×C22⋊D43C22semidirect
24. C22×Dic43C22semidirect
26. C2×D172C22semidirect
27. C2×C4×D43C22semidirect
28. C2×Dic86C22semidirect
30. C22⋊C4×C43C22semidirect
32. C22⋊Dic43C22semidirect
33. (C2×D43)⋊C4C22semidirect
34. (C2×D43)⋊C4C22semidirect
35. Dic43⋊C4C22semidirect
36. C4×Dic43C22semidirect
57. C2×Dic43D4semidirect
94. C43#535semidirect
104. #120D43semidirect
119. C2×D4C2×D43semidirect
129. C22⋊C4C2×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#106219002
C22×C22⋊D432
#130633212
#130633112
#130632982
#130632972
#130632952
#130632942
#130632932
#130632812
#120×C432
#53543