Finite Group Databasebeta

← #20268352

Subgroups — #20268352

Order 6592.

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

normal subgroups only

This group has 346 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
1C22×D412C211yesmaximal, characteristic, complemented
2C2×D4×D103C211yesmaximal, characteristic, complemented
3#15693006C212yesmaximal, complemented
4#15693004C211yesmaximal, characteristic, complemented
5#15692996C212yesmaximal, complemented
6#15692994C212yesmaximal, complemented
7#15692991C211yesmaximal, characteristic, complemented
8#15692991C212yesmaximal, complemented
9#15692989C211yesmaximal, characteristic, complemented
10C22⋊C4×D103C211yesmaximal, characteristic, complemented
11#123×C103C211yesmaximal, characteristic, complemented
12C23×D103C2211yescharacteristic
13C23×D103C2211yescharacteristic, complemented
14C23×D103C2211yescharacteristic, complemented
15C2×D412—24no—
16C2×D412C2212yes—
17C2×D412C2211yescharacteristic, complemented
18C2×D412C2212yescomplemented
19C2×D412C2212yescomplemented
20C2×C22⋊D103C2211yescharacteristic
21C2×C22⋊D103C2211yescharacteristic, complemented
22C2×C22⋊D103C2212yescomplemented
23D4×D103—24no—
24C2×C4×D103C2211yescharacteristic, complemented
25C2×C4×D103C2212yescomplemented
26Dic103⋊C4C2212yescomplemented
27C22⋊Dic103C2211yescharacteristic, complemented
28(C2×D103)⋊C4C2212yescomplemented
29(C2×D103)⋊C4C2212yescomplemented
30(C2×D103)⋊C4C2212yescomplemented
31(C2×D103)⋊C4C2212yescomplemented
32C2×D4×C103C2211yescharacteristic
33C22×C4×C103C2211yescharacteristic, complemented
34C4⋊C4×C103C2212yescomplemented
35C22⋊C4×C103C2211yescharacteristic, complemented
36C22⋊C4×C103C2212yescomplemented
37C23×C103C2311yescharacteristic
38C23×C103C2311yescharacteristic
39C22×D103—22no—
40C22×D103—22no—
41C22×D103—42no—
42C22×D103—42no—
43C22×D103—42no—
44C22×D103D414yescomplemented
45C22×D103C2311yescharacteristic
46C22×D103C2312yes—
47C22×D103C2311yescharacteristic
48C22×D103C2311yescharacteristic
49D4×C103—22no—
50C2×C4×C103—22no—
51C2×C4×C103C2312yes—
52C2×C4×C103C2312yes—
53C2×C4×C103C2311yescharacteristic
54C22⋊D103—22no—
55C22⋊D103—22no—
56C22⋊D103—42no—
57C2×Dic103C2312yes—
58C2×Dic103C2311yescharacteristic
59D412—22no—
60D412—24no—
61D412—24no—
62D412—42no—
63C4×D103—22no—
64C4×D103—42no—
65C22×C103—22no—
66C22×C103—21no—
67C22×C103—22no—
68C22×C103C2×D412yes—
69C22×C103C2411yescharacteristic
70C2×D103—22no—
71C2×D103—22no—
72C2×D103—22no—
73C2×D103—21no—
74C2×D103—22no—
75C2×D103—22no—
76C2×D103—22no—
77C2×D103—44no—
78C2×D103—44no—
79C2×D103—44no—
80C2×D103C2×D412yes—
81C2×D103C2×D412yes—
82C4×C103—21no—
83C4×C103—22no—
84C4×C103—22no—
85Dic103—21no—
86Dic103—22no—
87C2×C103—22no—
88C2×C103—41no—
89C2×C103C22×D411yescharacteristic
90C2×C103H(5,𝔽2)12yes—
91D103—22no—
92D103—22no—
93D103—42no—
94D103—41no—
95C103#53411yescharacteristic, complemented, Sylow
96#534—1031nomaximal, Sylow
97C22×D4—1031no—
98C22×D4—1031no—
99#123—1031no—
100#123—1032no—
101#123D10311yescharacteristic, complemented
102#121—1032no—
103#121—1032no—
104#120—1031no—
105#120—1032no—
106#120—1031no—
107C2×C22⋊C4—1031no—
108C24—1031no—
109C24—1031no—
110C24—1031no—
111C2×D4—1032no—
112C2×D4—1031no—
113C2×D4—1031no—
114C2×D4—1032no—
115C2×D4—1032no—
116C2×D4—1031no—
117C2×D4—1032no—
118C2×D4—2064no—
119C2×D4—2064no—
120C2×D4C2×D10311yescharacteristic
121C22×C4—1032no—
122C22×C4—1031no—
123C22×C4C2×D10311yescharacteristic, complemented
124C4⋊C4—1032no—
125C4⋊C4C2×D10312yescomplemented
126C22⋊C4—1031no—
127C22⋊C4—1032no—
128C22⋊C4—1032no—
129C22⋊C4—1032no—
130C22⋊C4—1032no—
131C22⋊C4C2×D10311yescharacteristic, complemented
132C22⋊C4C2×D10312yescomplemented
133C23—1034no—
134C23—1031no—
135C23—1031no—
136C23—1032no—
137C23—1031no—
138C23—4122no—
139C23—4122no—
140C23—4122no—
141C23—2062no—
142C23—2062no—
143C23C22×D10311yescharacteristic
144C23C22×D10311yescharacteristic
145D4—22no—
146D4—4122no—
147D4—4122no—
148D4—2064no—
149D4—2064no—
150D4—2062no—
151D4—2062no—
152D4—2062no—
153C2×C4—22no—
154C2×C4—1032no—
155C2×C4—1031no—
156C2×C4—4122no—
157C2×C4—2062no—
158C2×C4C22×D10312yes—
159C2×C4C22×D10311yescharacteristic
160C2×C4C22×D10312yes—
161C22—22no—
162C22—21no—
163C22—22no—
164C22—1032no—
165C22—1032no—
166C22—4124no—
167C22—4124no—
168C22—4124no—
169C22—2062no—
170C22—2061no—
171C22—2062no—
172C22—2062no—
173C22—2062no—
174C22—2062no—
175C22—2062no—
176C22D4×D10312yes—
177C22C23×D10311yescharacteristic
178C4—22no—
179C4—21no—
180C4—22no—
181C4—2061no—
182C4—2062no—
183C2—22no—
184C2—41no—
185C2—4122no—
186C2—4121no—
187C2—2062no—
188C2—2062no—
189C2C2×D4×D10311yescharacteristic
190C2#1569306712yes—
subgroupG/H
center, FrattiniC22C23×D103
commutator, socleC22×C103C24
Fitting#123×C103C2
hypercenter#123D103
hypocenterC103#534
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C22×D412C2semidirect
2. C2×D4×D103C2semidirect
3. #15693006C2semidirect
4. #15693004C2semidirect
5. #15692996C2semidirect
6. #15692994C2semidirect
7. #15692991C2semidirect
8. #15692991C2semidirect
9. #15692989C2semidirect
10. C22⋊C4×D103C2semidirect
11. #123×C103C2semidirect
13. C23×D103C22semidirect
14. C23×D103C22semidirect
17. C2×D412C22semidirect
18. C2×D412C22semidirect
19. C2×D412C22semidirect
21. C2×C22⋊D103C22semidirect
22. C2×C22⋊D103C22semidirect
24. C2×C4×D103C22semidirect
25. C2×C4×D103C22semidirect
26. Dic103⋊C4C22semidirect
27. C22⋊Dic103C22semidirect
28. (C2×D103)⋊C4C22semidirect
29. (C2×D103)⋊C4C22semidirect
30. (C2×D103)⋊C4C22semidirect
31. (C2×D103)⋊C4C22semidirect
33. C22×C4×C103C22semidirect
34. C4⋊C4×C103C22semidirect
35. C22⋊C4×C103C22semidirect
36. C22⋊C4×C103C22semidirect
44. C22×D103D4semidirect
95. C103#534semidirect
101. #123D103semidirect
123. C22×C4C2×D103semidirect
125. C4⋊C4C2×D103semidirect
131. C22⋊C4C2×D103semidirect
132. C22⋊C4C2×D103semidirect