Finite Group Databasebeta

← #20268425

Subgroups — #20268425

Order 6592.

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×D412C211yesmaximal, characteristic, complemented
2C2×D4×D103C212yesmaximal, complemented
3C2×D4×D103C211yesmaximal, characteristic, complemented
4#15693017C211yesmaximal, characteristic, complemented
5#15692996C211yesmaximal, characteristic, complemented
6#15692994C212yesmaximal, complemented
7#15692991C212yesmaximal, complemented
8#15692989C212yesmaximal, complemented
9#15692983C211yesmaximal, characteristic, complemented
10C4×C22⋊D103C211yesmaximal, characteristic, complemented
11#121×C103C211yesmaximal, characteristic, complemented
12C23×D103C2212yescomplemented
13C23×D103C2212yescomplemented
14C2×D412—24no—
15C2×D412C2211yescharacteristic
16C2×D412C2212yescomplemented
17C2×D412C2212yescomplemented
18C2×D412C2211yescharacteristic, complemented
19C2×C22⋊D103C2211yescharacteristic
20C2×C22⋊D103C2212yescomplemented
21C2×C22⋊D103C2212yescomplemented
22C2×C22⋊D103C2212yescomplemented
23D4×D103—28no—
24D4×D103—24no—
25C2×C4×D103C2211yescharacteristic, complemented
26C2×C4×D103C2212yescomplemented
27Dic103⋊C4C2211yescharacteristic, complemented
28C22⋊Dic103C2211yescharacteristic, complemented
29(C2×D103)⋊C4C2211yescharacteristic, complemented
30(C2×D103)⋊C4C2212yescomplemented
31(C2×D103)⋊C4C2212yescomplemented
32C4×Dic103C2211yescharacteristic, complemented
33C2×D4×C103C2212yescomplemented
34C2×D4×C103C2211yescharacteristic, complemented
35C22×C4×C103C2211yescharacteristic, complemented
36C4⋊C4×C103C2211yescharacteristic, complemented
37C22⋊C4×C103C2212yescomplemented
38C23×C103C2312yes—
39C23×C103C2311yescharacteristic
40C22×D103—24no—
41C22×D103—24no—
42C22×D103—24no—
43C22×D103—24no—
44C22×D103—42no—
45C22×D103—42no—
46C22×D103C2312yes—
47C22×D103C2311yescharacteristic
48C22×D103C2312yes—
49D4×C103—24no—
50D4×C103—22no—
51C2×C4×C103—22no—
52C2×C4×C103C2311yescharacteristic
53C2×C4×C103C2312yes—
54C2×C4×C103C2311yescharacteristic
55C22⋊D103—24no—
56C22⋊D103—24no—
57C22⋊D103—42no—
58C22⋊D103D414yescomplemented
59C2×Dic103C2311yescharacteristic
60C2×Dic103C2311yescharacteristic
61C2×Dic103C2311yescharacteristic
62D412—24no—
63D412—24no—
64D412—22no—
65D412D414yescomplemented
66C4×D103—22no—
67C4×D103—24no—
68C22×C103—21no—
69C22×C103—21no—
70C22×C103—22no—
71C22×C103—22no—
72C22×C103—22no—
73C22×C103C2×D412yescomplemented
74C22×C103C2411yescharacteristic
75C2×D103—21no—
76C2×D103—22no—
77C2×D103—21no—
78C2×D103—22no—
79C2×D103—22no—
80C2×D103—22no—
81C2×D103—22no—
82C2×D103—48no—
83C2×D103—48no—
84C2×D103C2×D412yescomplemented
85C2×D103C2×D414yescomplemented
86C4×C103—22no—
87C4×C103—21no—
88C4×C103C2×D412yescomplemented
89Dic103—21no—
90Dic103—21no—
91Dic103C2×D412yescomplemented
92C2×C103—22no—
93C2×C103—42no—
94C2×C103C22×D411yescharacteristic
95C2×C103C22×D411yescharacteristic
96C2×C103H(5,𝔽2)11yescharacteristic
97D103—22no—
98D103—24no—
99D103—42no—
100C103D4211yescharacteristic, complemented, Sylow
101D42—1031nomaximal, Sylow
102C22×D4—1032no—
103C22×D4—1031no—
104C22×D4—1031no—
105#127—1031no—
106#121—1031no—
107#121—1032no—
108#121D10311yescharacteristic, complemented
109#120—1032no—
110#120—1032no—
111C4×D4—1031no—
112C4×D4—1031no—
113C24—1032no—
114C24—1032no—
115C2×D4—1031no—
116C2×D4—1032no—
117C2×D4—1032no—
118C2×D4—1032no—
119C2×D4—1031no—
120C2×D4—1032no—
121C2×D4—1032no—
122C2×D4—1031no—
123C2×D4—2064no—
124C2×D4—2068no—
125C2×D4—2064no—
126C2×D4C2×D10312yescomplemented
127C2×D4C2×D10311yescharacteristic, complemented
128C22×C4—1032no—
129C22×C4—1031no—
130C22×C4C2×D10311yescharacteristic, complemented
131C4⋊C4—1031no—
132C4⋊C4C2×D10311yescharacteristic, complemented
133C22⋊C4—1031no—
134C22⋊C4—1032no—
135C22⋊C4—1031no—
136C22⋊C4—1032no—
137C22⋊C4C2×D10312yescomplemented
138C42—1031no—
139C23—1031no—
140C23—1032no—
141C23—1032no—
142C23—4122no—
143C23—4122no—
144C23—2064no—
145C23—2064no—
146C23—2064no—
147C23—2064no—
148C23C22×D10312yes—
149C23C22×D10311yescharacteristic
150D4—24no—
151D4—22no—
152D4—1034no—
153D4—1034no—
154D4—4122no—
155D4—2064no—
156D4—2064no—
157D4—2064no—
158D4—2064no—
159D4—2062no—
160C2×C4—22no—
161C2×C4—1031no—
162C2×C4—1031no—
163C2×C4—1031no—
164C2×C4—2064no—
165C2×C4—2062no—
166C2×C4C22×D10312yes—
167C2×C4C22×D10311yescharacteristic
168C2×C4C22×D10311yescharacteristic
169C22—21no—
170C22—21no—
171C22—22no—
172C22—22no—
173C22—22no—
174C22—1032no—
175C22—1034no—
176C22—4128no—
177C22—4128no—
178C22—2062no—
179C22—2062no—
180C22—2062no—
181C22—2062no—
182C22—2061no—
183C22—2062no—
184C22—2061no—
185C22D4×D10312yescomplemented
186C22C23×D10311yescharacteristic
187C4—21no—
188C4—22no—
189C4—1032no—
190C4—2061no—
191C4—2061no—
192C4D4×D10312yescomplemented
193C2—22no—
194C2—42no—
195C2—4122no—
196C2—2064no—
197C2—2062no—
198C2C2×D4×D10311yescharacteristic
199C2C2×D4×D10311yescharacteristic
200C2#1569306711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D103
commutator, socleC22×C103C24
Fitting#121×C103C2
hypercenter#121D103
hypocenterC103D42
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C22×D412C2semidirect
2. C2×D4×D103C2semidirect
3. C2×D4×D103C2semidirect
4. #15693017C2semidirect
5. #15692996C2semidirect
6. #15692994C2semidirect
7. #15692991C2semidirect
8. #15692989C2semidirect
9. #15692983C2semidirect
10. C4×C22⋊D103C2semidirect
11. #121×C103C2semidirect
12. C23×D103C22semidirect
13. C23×D103C22semidirect
16. C2×D412C22semidirect
17. C2×D412C22semidirect
18. C2×D412C22semidirect
20. C2×C22⋊D103C22semidirect
21. C2×C22⋊D103C22semidirect
22. C2×C22⋊D103C22semidirect
25. C2×C4×D103C22semidirect
26. C2×C4×D103C22semidirect
27. Dic103⋊C4C22semidirect
28. C22⋊Dic103C22semidirect
29. (C2×D103)⋊C4C22semidirect
30. (C2×D103)⋊C4C22semidirect
31. (C2×D103)⋊C4C22semidirect
32. C4×Dic103C22semidirect
33. C2×D4×C103C22semidirect
34. C2×D4×C103C22semidirect
35. C22×C4×C103C22semidirect
36. C4⋊C4×C103C22semidirect
37. C22⋊C4×C103C22semidirect
58. C22⋊D103D4semidirect
65. D412D4semidirect
73. C22×C103C2×D4semidirect
84. C2×D103C2×D4semidirect
85. C2×D103C2×D4semidirect
88. C4×C103C2×D4semidirect
91. Dic103C2×D4semidirect
100. C103D42semidirect
108. #121D103semidirect
126. C2×D4C2×D103semidirect
127. C2×D4C2×D103semidirect
130. C22×C4C2×D103semidirect
132. C4⋊C4C2×D103semidirect
137. C22⋊C4C2×D103semidirect
185. C22D4×D103semidirect
192. C4D4×D103semidirect