Finite Group Databasebeta

← #44566915

Subgroups — #44566915

Order 32192.

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
1C22×D2012C211yesmaximal, characteristic, complemented
2C2×D4×D503C212yesmaximal, complemented
3C2×D4×D503C211yesmaximal, characteristic, complemented
4#30632860C211yesmaximal, characteristic, complemented
5#30632839C211yesmaximal, characteristic, complemented
6#30632837C212yesmaximal, complemented
7#30632834C212yesmaximal, complemented
8#30632832C212yesmaximal, complemented
9#30632826C211yesmaximal, characteristic, complemented
10C4×C22⋊D503C211yesmaximal, characteristic, complemented
11#121×C503C211yesmaximal, characteristic, complemented
12C23×D503C2212yescomplemented
13C23×D503C2212yescomplemented
14C2×D2012—24no—
15C2×D2012C2211yescharacteristic
16C2×D2012C2212yescomplemented
17C2×D2012C2212yescomplemented
18C2×D2012C2211yescharacteristic, complemented
19C2×C22⋊D503C2211yescharacteristic
20C2×C22⋊D503C2212yescomplemented
21C2×C22⋊D503C2212yescomplemented
22C2×C22⋊D503C2212yescomplemented
23D4×D503—24no—
24D4×D503—28no—
25C2×C4×D503C2211yescharacteristic, complemented
26C2×C4×D503C2212yescomplemented
27Dic503⋊C4C2211yescharacteristic, complemented
28C22⋊Dic503C2211yescharacteristic, complemented
29(C2×D503)⋊C4C2211yescharacteristic, complemented
30(C2×D503)⋊C4C2212yescomplemented
31(C2×D503)⋊C4C2212yescomplemented
32C4×Dic503C2211yescharacteristic, complemented
33C2×D4×C503C2212yescomplemented
34C2×D4×C503C2211yescharacteristic, complemented
35C22×C4×C503C2211yescharacteristic, complemented
36C4⋊C4×C503C2211yescharacteristic, complemented
37C22⋊C4×C503C2212yescomplemented
38C22×D503—24no—
39C22×D503—24no—
40C22×D503—24no—
41C22×D503—24no—
42C22×D503—42no—
43C22×D503—42no—
44C22×D503C2312yes—
45C22×D503C2311yescharacteristic
46C22×D503C2312yes—
47D2012—24no—
48D2012—24no—
49D2012—22no—
50D2012D414yescomplemented
51C22⋊D503—24no—
52C22⋊D503—24no—
53C22⋊D503—42no—
54C22⋊D503D414yescomplemented
55C2×Dic503C2311yescharacteristic
56C2×Dic503C2311yescharacteristic
57C2×Dic503C2311yescharacteristic
58C4×D503—22no—
59C4×D503—24no—
60C23×C503C2312yes—
61C23×C503C2311yescharacteristic
62D4×C503—24no—
63D4×C503—22no—
64C2×C4×C503—22no—
65C2×C4×C503C2311yescharacteristic
66C2×C4×C503C2312yes—
67C2×C4×C503C2311yescharacteristic
68C22×C503—21no—
69C22×C503—21no—
70C22×C503—22no—
71C22×C503—22no—
72C22×C503—22no—
73C22×C503C2×D412yescomplemented
74C22×C503C2411yescharacteristic
75C2×D503—21no—
76C2×D503—22no—
77C2×D503—21no—
78C2×D503—22no—
79C2×D503—22no—
80C2×D503—22no—
81C2×D503—22no—
82C2×D503—48no—
83C2×D503—48no—
84C2×D503C2×D414yescomplemented
85C2×D503C2×D412yescomplemented
86C4×C503—21no—
87C4×C503—22no—
88C4×C503C2×D412yescomplemented
89Dic503—21no—
90Dic503—21no—
91Dic503C2×D412yescomplemented
92C2×C503—22no—
93C2×C503—42no—
94C2×C503C22×D411yescharacteristic
95C2×C503C22×D411yescharacteristic
96C2×C503H(5,𝔽2)11yescharacteristic
97D503—22no—
98D503—24no—
99D503—42no—
100C503D4211yescharacteristic, complemented, Sylow
101D42—5031nomaximal, Sylow
102C22×D4—5031no—
103C22×D4—5032no—
104C22×D4—5031no—
105#127—5031no—
106#121—5031no—
107#121—5032no—
108#121D50311yescharacteristic, complemented
109#120—5032no—
110#120—5032no—
111C4×D4—5031no—
112C4×D4—5031no—
113C24—5032no—
114C24—5032no—
115C2×D4—10064no—
116C2×D4—10068no—
117C2×D4—10064no—
118C2×D4—5032no—
119C2×D4—5032no—
120C2×D4—5032no—
121C2×D4—5031no—
122C2×D4—5032no—
123C2×D4—5032no—
124C2×D4—5031no—
125C2×D4—5031no—
126C2×D4C2×D50312yescomplemented
127C2×D4C2×D50311yescharacteristic, complemented
128C22×C4—5032no—
129C22×C4—5031no—
130C22×C4C2×D50311yescharacteristic, complemented
131C4⋊C4—5031no—
132C4⋊C4C2×D50311yescharacteristic, complemented
133C22⋊C4—5031no—
134C22⋊C4—5032no—
135C22⋊C4—5031no—
136C22⋊C4—5032no—
137C22⋊C4C2×D50312yescomplemented
138C42—5031no—
139C23—20122no—
140C23—20122no—
141C23—10064no—
142C23—10064no—
143C23—10064no—
144C23—10064no—
145C23—5032no—
146C23—5032no—
147C23—5031no—
148C23C22×D50312yes—
149C23C22×D50311yescharacteristic
150D4—24no—
151D4—22no—
152D4—20122no—
153D4—10064no—
154D4—10064no—
155D4—10064no—
156D4—10064no—
157D4—10062no—
158D4—5034no—
159D4—5034no—
160C2×C4—22no—
161C2×C4—10064no—
162C2×C4—10062no—
163C2×C4—5031no—
164C2×C4—5031no—
165C2×C4—5031no—
166C2×C4C22×D50312yes—
167C2×C4C22×D50311yescharacteristic
168C2×C4C22×D50311yescharacteristic
169C22—21no—
170C22—21no—
171C22—22no—
172C22—22no—
173C22—22no—
174C22—20128no—
175C22—20128no—
176C22—10062no—
177C22—10062no—
178C22—10062no—
179C22—10062no—
180C22—10061no—
181C22—10062no—
182C22—10061no—
183C22—5032no—
184C22—5034no—
185C22D4×D50312yescomplemented
186C22C23×D50311yescharacteristic
187C4—21no—
188C4—22no—
189C4—10061no—
190C4—10061no—
191C4—5032no—
192C4D4×D50312yescomplemented
193C2—22no—
194C2—42no—
195C2—20122no—
196C2—10064no—
197C2—10062no—
198C2C2×D4×D50311yescharacteristic
199C2C2×D4×D50311yescharacteristic
200C2#3063291011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D503
commutator, socle, cosocleC22×C503C24
Fitting#121×C503C2
hypercenter#121D503
hypocenterC503D42
LCSG ▷ C22×C503 ▷ C503
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C22×D2012C2semidirect
2. C2×D4×D503C2semidirect
3. C2×D4×D503C2semidirect
4. #30632860C2semidirect
5. #30632839C2semidirect
6. #30632837C2semidirect
7. #30632834C2semidirect
8. #30632832C2semidirect
9. #30632826C2semidirect
10. C4×C22⋊D503C2semidirect
11. #121×C503C2semidirect
12. C23×D503C22semidirect
13. C23×D503C22semidirect
16. C2×D2012C22semidirect
17. C2×D2012C22semidirect
18. C2×D2012C22semidirect
20. C2×C22⋊D503C22semidirect
21. C2×C22⋊D503C22semidirect
22. C2×C22⋊D503C22semidirect
25. C2×C4×D503C22semidirect
26. C2×C4×D503C22semidirect
27. Dic503⋊C4C22semidirect
28. C22⋊Dic503C22semidirect
29. (C2×D503)⋊C4C22semidirect
30. (C2×D503)⋊C4C22semidirect
31. (C2×D503)⋊C4C22semidirect
32. C4×Dic503C22semidirect
33. C2×D4×C503C22semidirect
34. C2×D4×C503C22semidirect
35. C22×C4×C503C22semidirect
36. C4⋊C4×C503C22semidirect
37. C22⋊C4×C503C22semidirect
50. D2012D4semidirect
54. C22⋊D503D4semidirect
73. C22×C503C2×D4semidirect
84. C2×D503C2×D4semidirect
85. C2×D503C2×D4semidirect
88. C4×C503C2×D4semidirect
91. Dic503C2×D4semidirect
100. C503D42semidirect
108. #121D503semidirect
126. C2×D4C2×D503semidirect
127. C2×D4C2×D503semidirect
130. C22×C4C2×D503semidirect
132. C4⋊C4C2×D503semidirect
137. C22⋊C4C2×D503semidirect
185. C22D4×D503semidirect
192. C4D4×D503semidirect

Maximal subgroups

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

subgroupindex
C22×D20122
C2×D4×D5032
#306328602
#306328392
#306328372
#306328342
#306328322
#306328262
C4×C22⋊D5032
#121×C5032
D42503