Finite Group Databasebeta

← #28403712

Subgroups — #28403712

Order 14464.

370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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
1#20299400C212yesmaximal, complemented
2#20299035C214yesmaximal, complemented
3#20299033C212yesmaximal, complemented
4#20299031C212yesmaximal, complemented
5C2×D1808C211yesmaximal, characteristic, complemented
6D16×D113C212yesmaximal, complemented
7#20299014C211yesmaximal, characteristic, complemented
8#508×C113C211yesmaximal, characteristic, complemented
9#16813668—22no—
10#16813649—24no—
11#16813647—22no—
12#16813645C2214yescomplemented
13C2×D904C2212yescomplemented
14D8×D113C2214yescomplemented
15#16813628C2211yescharacteristic
16#16813565C2214yescomplemented
17D1808C2212yescomplemented
18D1808C2212yescomplemented
19#16813563C2214yescomplemented
20#16813562C2211yescharacteristic, complemented
21#16813561C2212yescomplemented
22C16×D113C2212yescomplemented
23#135×C113C2212yescomplemented
24Q32×C113C2211yescharacteristic, complemented
25SD32×C113C2212yescomplemented
26D16×C113C2211yescharacteristic, complemented
27C2×C16×C113C2211yescharacteristic, complemented
28#14268648—24no—
29#14268647—42no—
30#14268647D411yescharacteristic
31C2×D452—22no—
32C2×D452—42no—
33D4×D113—24no—
34D4×D113—44no—
35#14268634—24no—
36D904—22no—
37D904C2314yes—
38#14268632—24no—
39#14268631D411yescharacteristic
40#14268630D412yes—
41C8×D113C2312yes—
42#14268622C2312yes—
43#41×C113—22no—
44Q16×C113C2312yes—
45SD16×C113—22no—
46D8×C113C2312yes—
47C2×C8×C113C2311yescharacteristic
48C16×C113C2311yescharacteristic
49C16×C113C2311yescharacteristic
50C22×D113—42no—
51C22×D113—44no—
52Q8×C113—22no—
53D4×C113—22no—
54D4×C113—42no—
55C2×C4×C113—42no—
56C2×C4×C113C2×D411yescharacteristic
57C22⋊D113—44no—
58C22⋊D113D812yes—
59D452—24no—
60D452—44no—
61D452—42no—
62D452D811yescharacteristic
63C4×D113—44no—
64C4×D113C2×D412yes—
65Dic226D811yescharacteristic
66C8×C113C2×D411yescharacteristic
67C8×C113C2411yescharacteristic
68#11744751C2×D412yes—
69C22×C113—42no—
70C22×C113C2×D811yescharacteristic
71C2×D113—44no—
72C2×D113—164no—
73C2×D113—162no—
74C2×D113C2×D812yes—
75C4×C113—42no—
76C4×C113C2×D811yescharacteristic
77C4×C113C22×D411yescharacteristic
78Dic113C2×D812yes—
79C2×C113—21no—
80C2×C113—82no—
81C2×C113C22×D811yescharacteristic
82D113—22no—
83D113—84no—
84#3415—1131nomaximal, Sylow
85C113#341511yescharacteristic, complemented, Sylow
86#576—1132no—
87#509—1132no—
88#509—1134no—
89#508—1132no—
90#508D11311yescharacteristic, complemented
91C2×D16—1132no—
92C2×D16—1131no—
93#504—1131no—
94H(5,𝔽2)—2262no—
95AGL(1,ℤ/8)—2264no—
96AGL(1,ℤ/8)—2262no—
97#135—1134no—
98#135C2×D11312yescomplemented
99C2×D8—1134no—
100C2×D8—1132no—
101#131—1131no—
102Q32C2×D11311yescharacteristic, complemented
103SD32—1134no—
104SD32C2×D11312yescomplemented
105D16—1134no—
106D16—1132no—
107D16—1132no—
108D16C2×D11311yescharacteristic, complemented
109M32—1131no—
110M32—1132no—
111C2×C16—1132no—
112C2×C16C2×D11311yescharacteristic, complemented
113#41—22no—
114#41—1131no—
115#41—4522no—
116#41—2264no—
117C2×D4—4522no—
118C2×D4—4524no—
119C2×D4—2264no—
120C2×D4—2262no—
121Q16C22×D11312yes—
122SD16—22no—
123SD16—2264no—
124D8—1134no—
125D8—2264no—
126D8—2262no—
127D8C22×D11312yes—
128M16—1131no—
129M16—1132no—
130C2×C8—1132no—
131C2×C8C22×D11311yescharacteristic
132C16—1132no—
133C16C22×D11311yescharacteristic
134C16C22×D11311yescharacteristic
135C23—4524no—
136C23—4522no—
137Q8—22no—
138Q8—1131no—
139D4—22no—
140D4—42no—
141D4—1132no—
142D4—1131no—
143D4—4524no—
144D4—4524no—
145D4—4522no—
146D4—2264no—
147C2×C4—42no—
148C2×C4—1132no—
149C2×C4—4524no—
150C2×C4D4×D11311yescharacteristic
151C8—1132no—
152C8D4×D11311yescharacteristic
153C8C23×D11311yescharacteristic
154C22—42no—
155C22—18082no—
156C22—18084no—
157C22—1132no—
158C22—4524no—
159C22D8×D11311yescharacteristic
160C4—42no—
161C4—1132no—
162C4D8×D11311yescharacteristic
163C4C2×D4×D11311yescharacteristic
164C2—21no—
165C2—82no—
166C2—9044no—
167C2—2262no—
168C2C2×D8×D11311yescharacteristic
subgroupG/H
centerC2C2×D8×D113
commutator, cosocleC8×C113C24
FrattiniC8C23×D113
Fitting#508×C113C2
socleC2×C113C22×D8
hypercenter#508D113
hypocenterC113#3415
LCSG ▷ C8×C113 ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #20299400C2semidirect
2. #20299035C2semidirect
3. #20299033C2semidirect
4. #20299031C2semidirect
5. C2×D1808C2semidirect
6. D16×D113C2semidirect
7. #20299014C2semidirect
8. #508×C113C2semidirect
12. #16813645C22semidirect
13. C2×D904C22semidirect
14. D8×D113C22semidirect
16. #16813565C22semidirect
17. D1808C22semidirect
18. D1808C22semidirect
19. #16813563C22semidirect
20. #16813562C22semidirect
21. #16813561C22semidirect
22. C16×D113C22semidirect
23. #135×C113C22semidirect
24. Q32×C113C22semidirect
25. SD32×C113C22semidirect
26. D16×C113C22semidirect
27. C2×C16×C113C22semidirect
85. C113#3415semidirect
90. #508D113semidirect
98. #135C2×D113semidirect
102. Q32C2×D113semidirect
104. SD32C2×D113semidirect
108. D16C2×D113semidirect
112. C2×C16C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202994002
#202990352
#202990332
#202990312
C2×D18082
D16×D1132
#202990142
#508×C1132
#3415113