Finite Group Databasebeta

← #23752773

Subgroups — #23752773

Order 9664.

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×D604C211yesmaximal, characteristic, complemented
2C2×D4×D151C211yesmaximal, characteristic, complemented
3#18012724C212yesmaximal, complemented
4#18012722C211yesmaximal, characteristic, complemented
5#18012714C212yesmaximal, complemented
6#18012712C212yesmaximal, complemented
7#18012709C211yesmaximal, characteristic, complemented
8#18012709C212yesmaximal, complemented
9#18012707C211yesmaximal, characteristic, complemented
10C22⋊C4×D151C211yesmaximal, characteristic, complemented
11#123×C151C211yesmaximal, characteristic, complemented
12C23×D151C2211yescharacteristic
13C23×D151C2211yescharacteristic, complemented
14C23×D151C2211yescharacteristic, complemented
15C2×D604—24no—
16C2×D604C2212yes—
17C2×D604C2212yescomplemented
18C2×D604C2211yescharacteristic, complemented
19C2×D604C2212yescomplemented
20C2×C22⋊D151C2211yescharacteristic
21C2×C22⋊D151C2211yescharacteristic, complemented
22C2×C22⋊D151C2212yescomplemented
23D4×D151—24no—
24C2×C4×D151C2211yescharacteristic, complemented
25C2×C4×D151C2212yescomplemented
26Dic151⋊C4C2212yescomplemented
27C22⋊Dic151C2211yescharacteristic, complemented
28(C2×D151)⋊C4C2212yescomplemented
29(C2×D151)⋊C4C2212yescomplemented
30(C2×D151)⋊C4C2212yescomplemented
31(C2×D151)⋊C4C2212yescomplemented
32C2×D4×C151C2211yescharacteristic
33C22×C4×C151C2211yescharacteristic, complemented
34C4⋊C4×C151C2212yescomplemented
35C22⋊C4×C151C2211yescharacteristic, complemented
36C22⋊C4×C151C2212yescomplemented
37C22×D151—22no—
38C22×D151—22no—
39C22×D151—42no—
40C22×D151—42no—
41C22×D151—42no—
42C22×D151D414yescomplemented
43C22×D151C2311yescharacteristic
44C22×D151C2312yes—
45C22×D151C2311yescharacteristic
46C22×D151C2311yescharacteristic
47D604—22no—
48D604—24no—
49D604—24no—
50D604—42no—
51C22⋊D151—22no—
52C22⋊D151—22no—
53C22⋊D151—42no—
54C2×Dic151C2312yes—
55C2×Dic151C2311yescharacteristic
56C4×D151—22no—
57C4×D151—42no—
58C23×C151C2311yescharacteristic
59C23×C151C2311yescharacteristic
60D4×C151—22no—
61C2×C4×C151—22no—
62C2×C4×C151C2312yes—
63C2×C4×C151C2311yescharacteristic
64C2×C4×C151C2312yes—
65C22×C151—22no—
66C22×C151—21no—
67C22×C151—22no—
68C22×C151C2×D412yes—
69C22×C151C2411yescharacteristic
70C2×D151—22no—
71C2×D151—22no—
72C2×D151—21no—
73C2×D151—22no—
74C2×D151—22no—
75C2×D151—22no—
76C2×D151—22no—
77C2×D151—44no—
78C2×D151—44no—
79C2×D151—44no—
80C2×D151C2×D412yes—
81C2×D151C2×D412yes—
82C4×C151—22no—
83C4×C151—21no—
84C4×C151—22no—
85Dic151—21no—
86Dic151—22no—
87C2×C151—22no—
88C2×C151—41no—
89C2×C151C22×D411yescharacteristic
90C2×C151H(5,𝔽2)12yes—
91D151—22no—
92D151—22no—
93D151—41no—
94D151—42no—
95C151#53411yescharacteristic, complemented, Sylow
96#534—1511nomaximal, Sylow
97C22×D4—1511no—
98C22×D4—1511no—
99#123—1511no—
100#123—1512no—
101#123D15111yescharacteristic, complemented
102#121—1512no—
103#121—1512no—
104#120—1511no—
105#120—1512no—
106#120—1511no—
107C2×C22⋊C4—1511no—
108C24—1511no—
109C24—1511no—
110C24—1511no—
111C2×D4—3024no—
112C2×D4—3024no—
113C2×D4—1511no—
114C2×D4—1511no—
115C2×D4—1512no—
116C2×D4—1512no—
117C2×D4—1511no—
118C2×D4—1512no—
119C2×D4—1512no—
120C2×D4C2×D15111yescharacteristic
121C22×C4—1511no—
122C22×C4—1512no—
123C22×C4C2×D15111yescharacteristic, complemented
124C4⋊C4—1512no—
125C4⋊C4C2×D15112yescomplemented
126C22⋊C4—1511no—
127C22⋊C4—1512no—
128C22⋊C4—1512no—
129C22⋊C4—1512no—
130C22⋊C4—1512no—
131C22⋊C4C2×D15111yescharacteristic, complemented
132C22⋊C4C2×D15112yescomplemented
133C23—3022no—
134C23—3022no—
135C23—6042no—
136C23—6042no—
137C23—6042no—
138C23—1511no—
139C23—1512no—
140C23—1511no—
141C23—1511no—
142C23—1514no—
143C23C22×D15111yescharacteristic
144C23C22×D15111yescharacteristic
145D4—22no—
146D4—3024no—
147D4—3024no—
148D4—3022no—
149D4—3022no—
150D4—3022no—
151D4—6042no—
152D4—6042no—
153C2×C4—22no—
154C2×C4—3022no—
155C2×C4—6042no—
156C2×C4—1512no—
157C2×C4—1511no—
158C2×C4C22×D15112yes—
159C2×C4C22×D15111yescharacteristic
160C2×C4C22×D15112yes—
161C22—22no—
162C22—21no—
163C22—22no—
164C22—3022no—
165C22—3022no—
166C22—3022no—
167C22—3021no—
168C22—3022no—
169C22—3022no—
170C22—3022no—
171C22—6044no—
172C22—6044no—
173C22—6044no—
174C22—1512no—
175C22—1512no—
176C22D4×D15112yes—
177C22C23×D15111yescharacteristic
178C4—22no—
179C4—21no—
180C4—22no—
181C4—3021no—
182C4—3022no—
183C2—22no—
184C2—41no—
185C2—3022no—
186C2—3022no—
187C2—6042no—
188C2—6041no—
189C2C2×D4×D15111yescharacteristic
190C2#1801278512yes—
subgroupG/H
center, FrattiniC22C23×D151
commutator, socle, cosocleC22×C151C24
Fitting#123×C151C2
hypercenter#123D151
hypocenterC151#534
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C22×D604C2semidirect
2. C2×D4×D151C2semidirect
3. #18012724C2semidirect
4. #18012722C2semidirect
5. #18012714C2semidirect
6. #18012712C2semidirect
7. #18012709C2semidirect
8. #18012709C2semidirect
9. #18012707C2semidirect
10. C22⋊C4×D151C2semidirect
11. #123×C151C2semidirect
13. C23×D151C22semidirect
14. C23×D151C22semidirect
17. C2×D604C22semidirect
18. C2×D604C22semidirect
19. C2×D604C22semidirect
21. C2×C22⋊D151C22semidirect
22. C2×C22⋊D151C22semidirect
24. C2×C4×D151C22semidirect
25. C2×C4×D151C22semidirect
26. Dic151⋊C4C22semidirect
27. C22⋊Dic151C22semidirect
28. (C2×D151)⋊C4C22semidirect
29. (C2×D151)⋊C4C22semidirect
30. (C2×D151)⋊C4C22semidirect
31. (C2×D151)⋊C4C22semidirect
33. C22×C4×C151C22semidirect
34. C4⋊C4×C151C22semidirect
35. C22⋊C4×C151C22semidirect
36. C22⋊C4×C151C22semidirect
42. C22×D151D4semidirect
95. C151#534semidirect
101. #123D151semidirect
123. C22×C4C2×D151semidirect
125. C4⋊C4C2×D151semidirect
131. C22⋊C4C2×D151semidirect
132. C22⋊C4C2×D151semidirect