Finite Group Databasebeta

← #13093051

Subgroups — #13093051

Order 1472.

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
1C2×D4×D23C211yesmaximal, characteristic, complemented
2C2×D4×D23C212yesmaximal, complemented
3C22×D92C211yesmaximal, characteristic, complemented
4C23×#121C211yesmaximal, characteristic, complemented
5#10625111C211yesmaximal, characteristic, complemented
6#10625108C212yesmaximal, complemented
7C4×C22⋊D23C211yesmaximal, characteristic, complemented
8#10625066C211yesmaximal, characteristic, complemented
9#10625064C211yesmaximal, characteristic, complemented
10#10625055C212yesmaximal, complemented
11#10625053C212yesmaximal, complemented
12C23×D23C2212yescomplemented
13C23×D23C2212yescomplemented
14C2×D4×C23C2212yescomplemented
15C2×D4×C23C2211yescharacteristic, complemented
16C22×C4×C23C2211yescharacteristic, complemented
17C2×C22⋊D23C2211yescharacteristic
18C2×C22⋊D23C2212yescomplemented
19C2×C22⋊D23C2212yescomplemented
20C2×C22⋊D23C2212yescomplemented
21D4×D23—28no—
22D4×D23—24no—
23C2×D92—24no—
24C2×D92C2211yescharacteristic
25C2×D92C2212yescomplemented
26C2×D92C2212yescomplemented
27C2×D92C2211yescharacteristic, complemented
28C2×C4×D23C2212yescomplemented
29C2×C4×D23C2211yescharacteristic, complemented
30C4⋊C4×C23C2211yescharacteristic, complemented
31C22⋊C4×C23C2212yescomplemented
32C22⋊Dic23C2211yescharacteristic, complemented
33(C2×D23)⋊C4C2211yescharacteristic, complemented
34(C2×D23)⋊C4C2212yescomplemented
35(C2×D23)⋊C4C2212yescomplemented
36Dic23⋊C4C2211yescharacteristic, complemented
37C4×Dic23C2211yescharacteristic, complemented
38C23×C23C2312yes—
39C23×C23C2311yescharacteristic
40C22×D23—24no—
41C22×D23—24no—
42C22×D23—24no—
43C22×D23—24no—
44C22×D23—42no—
45C22×D23—42no—
46C22×D23C2312yes—
47C22×D23C2312yes—
48C22×D23C2311yescharacteristic
49D4×C23—24no—
50D4×C23—22no—
51C2×C4×C23—22no—
52C2×C4×C23C2311yescharacteristic
53C2×C4×C23C2312yes—
54C2×C4×C23C2311yescharacteristic
55C22⋊D23—24no—
56C22⋊D23—24no—
57C22⋊D23—42no—
58C22⋊D23D414yescomplemented
59C2×Dic23C2311yescharacteristic
60C2×Dic23C2311yescharacteristic
61C2×Dic23C2311yescharacteristic
62D92—24no—
63D92—24no—
64D92—22no—
65D92D414yescomplemented
66C4×D23—22no—
67C4×D23—24no—
68C22×C23—21no—
69C22×C23—21no—
70C22×C23—22no—
71C22×C23—22no—
72C22×C23—22no—
73C22×C23C2×D412yescomplemented
74C22×C23C2411yescharacteristic
75C2×D23—21no—
76C2×D23—22no—
77C2×D23—22no—
78C2×D23—21no—
79C2×D23—22no—
80C2×D23—22no—
81C2×D23—22no—
82C2×D23—48no—
83C2×D23—48no—
84C2×D23C2×D412yescomplemented
85C2×D23C2×D414yescomplemented
86C4×C23—22no—
87C4×C23—21no—
88C4×C23C2×D412yescomplemented
89Dic23—21no—
90Dic23—21no—
91Dic23C2×D412yescomplemented
92D42—231nomaximal, Sylow
93C2×C23—22no—
94C2×C23—42no—
95C2×C23C22×D411yescharacteristic
96C2×C23C22×D411yescharacteristic
97C2×C23H(5,𝔽2)11yescharacteristic
98D23—22no—
99D23—24no—
100D23—42no—
101C22×D4—232no—
102C22×D4—231no—
103C22×D4—231no—
104#127—231no—
105#121—231no—
106#121—232no—
107#121D2311yescharacteristic, complemented
108#120—232no—
109#120—232no—
110C4×D4—231no—
111C4×D4—231no—
112C23D4211yescharacteristic, complemented, Sylow
113C24—232no—
114C24—232no—
115C2×D4—231no—
116C2×D4—232no—
117C2×D4—232no—
118C2×D4—232no—
119C2×D4—231no—
120C2×D4—232no—
121C2×D4—232no—
122C2×D4—231no—
123C2×D4—464no—
124C2×D4—468no—
125C2×D4—464no—
126C2×D4C2×D2312yescomplemented
127C2×D4C2×D2311yescharacteristic, complemented
128C22×C4—232no—
129C22×C4—231no—
130C22×C4C2×D2311yescharacteristic, complemented
131C4⋊C4—231no—
132C4⋊C4C2×D2311yescharacteristic, complemented
133C22⋊C4—231no—
134C22⋊C4—232no—
135C22⋊C4—231no—
136C22⋊C4—232no—
137C22⋊C4C2×D2312yescomplemented
138C42—231no—
139C23—231no—
140C23—232no—
141C23—232no—
142C23—464no—
143C23—464no—
144C23—464no—
145C23—464no—
146C23—922no—
147C23—922no—
148C23C22×D2312yes—
149C23C22×D2311yescharacteristic
150D4—24no—
151D4—22no—
152D4—234no—
153D4—234no—
154D4—464no—
155D4—464no—
156D4—464no—
157D4—464no—
158D4—462no—
159D4—922no—
160C2×C4—22no—
161C2×C4—231no—
162C2×C4—231no—
163C2×C4—231no—
164C2×C4—464no—
165C2×C4—462no—
166C2×C4C22×D2312yes—
167C2×C4C22×D2311yescharacteristic
168C2×C4C22×D2311yescharacteristic
169C22—21no—
170C22—21no—
171C22—22no—
172C22—22no—
173C22—22no—
174C22—232no—
175C22—234no—
176C22—462no—
177C22—461no—
178C22—462no—
179C22—461no—
180C22—462no—
181C22—462no—
182C22—462no—
183C22—928no—
184C22—928no—
185C22D4×D2312yescomplemented
186C22C23×D2311yescharacteristic
187C4—21no—
188C4—22no—
189C4—232no—
190C4—461no—
191C4—461no—
192C4D4×D2312yescomplemented
193C2—22no—
194C2—42no—
195C2—464no—
196C2—462no—
197C2—922no—
198C2C2×D4×D2311yescharacteristic
199C2C2×D4×D2311yescharacteristic
200C2#1062516011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D23
commutator, socle, cosocleC22×C23C24
FittingC23×#121C2
hypercenter#121D23
hypocenterC23D42
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D4×D23C2semidirect
2. C2×D4×D23C2semidirect
3. C22×D92C2semidirect
4. C23×#121C2semidirect
5. #10625111C2semidirect
6. #10625108C2semidirect
7. C4×C22⋊D23C2semidirect
8. #10625066C2semidirect
9. #10625064C2semidirect
10. #10625055C2semidirect
11. #10625053C2semidirect
12. C23×D23C22semidirect
13. C23×D23C22semidirect
14. C2×D4×C23C22semidirect
15. C2×D4×C23C22semidirect
16. C22×C4×C23C22semidirect
18. C2×C22⋊D23C22semidirect
19. C2×C22⋊D23C22semidirect
20. C2×C22⋊D23C22semidirect
25. C2×D92C22semidirect
26. C2×D92C22semidirect
27. C2×D92C22semidirect
28. C2×C4×D23C22semidirect
29. C2×C4×D23C22semidirect
30. C4⋊C4×C23C22semidirect
31. C22⋊C4×C23C22semidirect
32. C22⋊Dic23C22semidirect
33. (C2×D23)⋊C4C22semidirect
34. (C2×D23)⋊C4C22semidirect
35. (C2×D23)⋊C4C22semidirect
36. Dic23⋊C4C22semidirect
37. C4×Dic23C22semidirect
58. C22⋊D23D4semidirect
65. D92D4semidirect
73. C22×C23C2×D4semidirect
84. C2×D23C2×D4semidirect
85. C2×D23C2×D4semidirect
88. C4×C23C2×D4semidirect
91. Dic23C2×D4semidirect
107. #121D23semidirect
112. C23D42semidirect
126. C2×D4C2×D23semidirect
127. C2×D4C2×D23semidirect
130. C22×C4C2×D23semidirect
132. C4⋊C4C2×D23semidirect
137. C22⋊C4C2×D23semidirect
185. C22D4×D23semidirect
192. C4D4×D23semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D232
C22×D922
C23×#1212
#106251112
#106251082
C4×C22⋊D232
#106250662
#106250642
#106250552
#106250532
D4223