Finite Group Databasebeta

← #23752772

Subgroups — #23752772

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×C22⋊D151C211yesmaximal, characteristic, complemented
2C2×D4×D151C211yesmaximal, characteristic, complemented
3#18012723C211yesmaximal, characteristic, complemented
4#18012721C212yesmaximal, complemented
5#18012720C211yesmaximal, characteristic, complemented
6#18012712C212yesmaximal, complemented
7#18012710C212yesmaximal, complemented
8#18012708C211yesmaximal, characteristic, complemented
9#18012707C212yesmaximal, complemented
10C22⋊C4×D151C211yesmaximal, characteristic, complemented
11#120×C151C211yesmaximal, characteristic, complemented
12C23×D151C2211yescharacteristic
13C23×D151C2211yescharacteristic, complemented
14C2×D604C2211yescharacteristic, complemented
15C2×C22⋊D151—24no—
16C2×C22⋊D151C2212yes—
17C2×C22⋊D151C2211yescharacteristic
18C2×C22⋊D151C2211yescharacteristic, complemented
19C2×C22⋊D151C2212yescomplemented
20C2×C22⋊D151C2212yescomplemented
21D4×D151—24no—
22C22×Dic151C2211yescharacteristic, complemented
23C2×C4×D151C2211yescharacteristic, complemented
24C2×C4×D151C2212yescomplemented
25C4⋊Dic151C2212yescomplemented
26Dic151⋊C4C2212yescomplemented
27C22⋊Dic151C2211yescharacteristic, complemented
28C22⋊Dic151C2212yescomplemented
29C22⋊Dic151C2212yescomplemented
30(C2×D151)⋊C4C2212yescomplemented
31(C2×D151)⋊C4C2212yescomplemented
32C24×C151C2211yescharacteristic, complemented
33C2×D4×C151C2211yescharacteristic
34C2×D4×C151C2212yescomplemented
35C22⋊C4×C151C2211yescharacteristic, complemented
36C22⋊C4×C151C2212yescomplemented
37C22×D151—22no—
38C22×D151—42no—
39C22×D151—42no—
40C22×D151D414yescomplemented
41C22×D151C2311yescharacteristic
42C22×D151C2311yescharacteristic
43C22×D151C2311yescharacteristic
44D604—22no—
45C22⋊D151—22no—
46C22⋊D151—22no—
47C22⋊D151—24no—
48C22⋊D151—24no—
49C22⋊D151—42no—
50C2×Dic151—22no—
51C2×Dic151C2312yes—
52C2×Dic151C2312yes—
53C2×Dic151C2311yescharacteristic
54C4×D151—22no—
55C4×D151—42no—
56C23×C151—22no—
57C23×C151—42no—
58C23×C151C2312yes—
59C23×C151C2311yescharacteristic
60C23×C151C2311yescharacteristic
61D4×C151—22no—
62D4×C151—42no—
63C2×C4×C151C2312yes—
64C2×C4×C151C2311yescharacteristic
65C22×C151—22no—
66C22×C151—21no—
67C22×C151—22no—
68C22×C151—22no—
69C22×C151—22no—
70C22×C151—22no—
71C22×C151—44no—
72C22×C151C2×D412yes—
73C22×C151C2411yescharacteristic
74C2×D151—22no—
75C2×D151—22no—
76C2×D151—21no—
77C2×D151—22no—
78C2×D151—44no—
79C2×D151—44no—
80C2×D151C2×D412yes—
81C2×D151C2×D412yes—
82C4×C151—21no—
83C4×C151—22no—
84Dic151—21no—
85Dic151—22no—
86Dic151—22no—
87C2×C151—22no—
88C2×C151—41no—
89C2×C151—42no—
90C2×C151C22×D411yescharacteristic
91C2×C151H(5,𝔽2)12yes—
92D151—22no—
93D151—22no—
94D151—41no—
95C151#53411yescharacteristic, complemented, Sylow
96#534—1511nomaximal, Sylow
97C22×D4—1511no—
98C22×D4—1511no—
99#123—1511no—
100#123—1512no—
101#123—1511no—
102#121—1512no—
103#121—1512no—
104#120—1511no—
105#120—1512no—
106#120D15111yescharacteristic, complemented
107C2×C22⋊C4—1511no—
108C24—1511no—
109C24—1511no—
110C24C2×D15111yescharacteristic, complemented
111C2×D4—3024no—
112C2×D4—3024no—
113C2×D4—1512no—
114C2×D4—1511no—
115C2×D4—1511no—
116C2×D4—1512no—
117C2×D4—1512no—
118C2×D4—1511no—
119C2×D4C2×D15111yescharacteristic
120C2×D4C2×D15112yescomplemented
121C22×C4—1511no—
122C22×C4—1511no—
123C22×C4—1512no—
124C4⋊C4—1512no—
125C4⋊C4—1512no—
126C22⋊C4—1511no—
127C22⋊C4—1512no—
128C22⋊C4—1512no—
129C22⋊C4—1512no—
130C22⋊C4—1512no—
131C22⋊C4C2×D15111yescharacteristic, complemented
132C22⋊C4C2×D15112yescomplemented
133C23—22no—
134C23—42no—
135C23—3022no—
136C23—6042no—
137C23—6042no—
138C23—1511no—
139C23—1511no—
140C23—1511no—
141C23—1514no—
142C23C22×D15111yescharacteristic
143C23C22×D15112yes—
144C23C22×D15111yescharacteristic
145D4—22no—
146D4—42no—
147D4—3022no—
148D4—3022no—
149D4—3024no—
150D4—3024no—
151D4—3022no—
152D4—6042no—
153C2×C4—3022no—
154C2×C4—3022no—
155C2×C4—6042no—
156C2×C4—1512no—
157C2×C4—1511no—
158C2×C4—1512no—
159C2×C4C22×D15112yes—
160C2×C4C22×D15111yescharacteristic
161C22—22no—
162C22—21no—
163C22—22no—
164C22—22no—
165C22—22no—
166C22—22no—
167C22—44no—
168C22—3022no—
169C22—3022no—
170C22—3021no—
171C22—3022no—
172C22—6044no—
173C22—6044no—
174C22—1512no—
175C22—1512no—
176C22D4×D15112yes—
177C22C23×D15111yescharacteristic
178C4—21no—
179C4—22no—
180C4—3021no—
181C4—3022no—
182C4—3022no—
183C2—22no—
184C2—42no—
185C2—41no—
186C2—3022no—
187C2—3022no—
188C2—6041no—
189C2C2×D4×D15111yescharacteristic
190C2#1801278412yes—
subgroupG/H
center, FrattiniC22C23×D151
commutator, socle, cosocleC22×C151C24
Fitting#120×C151C2
hypercenter#120D151
hypocenterC151#534
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D151C2semidirect
2. C2×D4×D151C2semidirect
3. #18012723C2semidirect
4. #18012721C2semidirect
5. #18012720C2semidirect
6. #18012712C2semidirect
7. #18012710C2semidirect
8. #18012708C2semidirect
9. #18012707C2semidirect
10. C22⋊C4×D151C2semidirect
11. #120×C151C2semidirect
13. C23×D151C22semidirect
14. C2×D604C22semidirect
18. C2×C22⋊D151C22semidirect
19. C2×C22⋊D151C22semidirect
20. C2×C22⋊D151C22semidirect
22. C22×Dic151C22semidirect
23. C2×C4×D151C22semidirect
24. C2×C4×D151C22semidirect
25. C4⋊Dic151C22semidirect
26. Dic151⋊C4C22semidirect
27. C22⋊Dic151C22semidirect
28. C22⋊Dic151C22semidirect
29. C22⋊Dic151C22semidirect
30. (C2×D151)⋊C4C22semidirect
31. (C2×D151)⋊C4C22semidirect
32. C24×C151C22semidirect
34. C2×D4×C151C22semidirect
35. C22⋊C4×C151C22semidirect
36. C22⋊C4×C151C22semidirect
40. C22×D151D4semidirect
95. C151#534semidirect
106. #120D151semidirect
110. C24C2×D151semidirect
120. C2×D4C2×D151semidirect
131. C22⋊C4C2×D151semidirect
132. C22⋊C4C2×D151semidirect