Finite Group Databasebeta

← #28402374

Subgroups — #28402374

Order 14464.

476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 125 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#20299403C212yesmaximal, complemented
2#20299400C212yesmaximal, complemented
3#20298975C211yesmaximal, characteristic, complemented
4#20298869C212yesmaximal, complemented
5#20298868C212yesmaximal, complemented
6#20298767C214yesmaximal, complemented
7#20298716C211yesmaximal, characteristic, complemented
8#443×C113C211yesmaximal, characteristic, complemented
9#16813668C2214yescomplemented
10#16813650—24no—
11#16813650C2214yescomplemented
12#16813649—24no—
13#16813647C2214yescomplemented
14#16813645—22no—
15#16813644—22no—
16#16813644C2211yescharacteristic
17C2×D904—22no—
18C2×D904C2212yescomplemented
19C2×D904C2212yescomplemented
20D8×D113—22no—
21#16813628C2212yescomplemented
22#16813619C2212yescomplemented
23#16813558C2211yescharacteristic, complemented
24#16813550C2212yescomplemented
25#16813538C2214yescomplemented
26#135×C113C2211yescharacteristic
27#131×C113C2212yescomplemented
28#108×C113C2211yescharacteristic, complemented
29#104×C113C2212yescomplemented
30C4×C8×C113C2211yescharacteristic, complemented
31#14268648—24no—
32#14268647—24no—
33#14268647C2312yes—
34C2×D452—24no—
35C2×D452—42no—
36C2×D452C2314yes—
37D4×D113—24no—
38D4×D113—44no—
39Dic452D411yescharacteristic, complemented
40#14268636—24no—
41#14268636D412yescomplemented
42#14268634—24no—
43D904—24no—
44D904—22no—
45D904—22no—
46D904—22no—
47D904—22no—
48D904D411yescharacteristic, complemented
49#14268632—24no—
50#14268631C2312yes—
51#14268630—22no—
52C8×D113—22no—
53#41×C113C2312yes—
54Q16×C113D411yescharacteristic, complemented
55SD16×C113D412yescomplemented
56D8×C113D411yescharacteristic, complemented
57M16×C113—22no—
58M16×C113C2312yes—
59C2×C8×C113—22no—
60C2×C8×C113C2311yescharacteristic
61C2×C8×C113C2311yescharacteristic
62C42×C113C2311yescharacteristic
63C22×D113—24no—
64C22×D113—44no—
65Q8×C113C2×D412yes—
66D4×C113—22no—
67D4×C113C2×D412yes—
68C2×C4×C113—21no—
69C2×C4×C113—22no—
70C2×C4×C113C2411yescharacteristic
71C22⋊D113—22no—
72C22⋊D113—44no—
73D452—24no—
74D452—24no—
75D452—44no—
76D452—84no—
77D452C2×D412yes—
78C4×D113—22no—
79C4×D113—44no—
80Dic226C2×D412yes—
81C8×C113—22no—
82C8×C113C2×D411yescharacteristic
83C8×C113C2×D411yescharacteristic
84C8×C113C2×D411yescharacteristic
85C8×C113C2×D411yescharacteristic
86#11744751—22no—
87C22×C113—22no—
88C22×C113H(5,𝔽2)11yescharacteristic
89C2×D113—22no—
90C2×D113—44no—
91C2×D113—84no—
92C2×D113—164no—
93C4×C113—22no—
94C4×C113—22no—
95C4×C113C22×D411yescharacteristic
96C4×C113C22×D411yescharacteristic
97Dic113—22no—
98C2×C113—21no—
99C2×C113—42no—
100C2×C113D4211yescharacteristic
101D113—42no—
102D113—84no—
103#3292—1131nomaximal, Sylow
104C113#329211yescharacteristic, complemented, Sylow
105#576—1132no—
106#576—1132no—
107#493—1131no—
108#472—1132no—
109#472—1132no—
110#453—1134no—
111#443—1131no—
112#443D11311yescharacteristic, complemented
113H(5,𝔽2)—1134no—
114AGL(1,ℤ/8)—1134no—
115AGL(1,ℤ/8)—1134no—
116AGL(1,ℤ/8)—2264no—
117AGL(1,ℤ/8)—2264no—
118#135—1131no—
119#135—2262no—
120#135—2262no—
121#135C2×D11311yescharacteristic
122C2×D8—1132no—
123C2×D8—1132no—
124C2×D8—2262no—
125C2×D8—2262no—
126#131—1132no—
127#131C2×D11312yescomplemented
128#127—1132no—
129#108—1131no—
130#108C2×D11311yescharacteristic, complemented
131#104—1132no—
132#104C2×D11312yescomplemented
133#100—1134no—
134C4×C8C2×D11311yescharacteristic, complemented
135#41—1132no—
136#41—2264no—
137#41—2264no—
138#41C22×D11312yes—
139C2×D4—1134no—
140C2×D4—4522no—
141C2×D4—4524no—
142C2×D4—2264no—
143C2×D4—2264no—
144Q16—1131no—
145Q16D45211yescharacteristic, complemented
146SD16—1132no—
147SD16—2264no—
148SD16—2264no—
149SD16D45212yescomplemented
150D8—1131no—
151D8—2264no—
152D8—2264no—
153D8—2262no—
154D8—2262no—
155D8—2262no—
156D8—2262no—
157D8D45211yescharacteristic, complemented
158M16—22no—
159M16—1132no—
160M16—2262no—
161M16C22×D11312yes—
162C2×C8—22no—
163C2×C8—2262no—
164C2×C8C22×D11311yescharacteristic
165C2×C8C22×D11311yescharacteristic
166C42C22×D11311yescharacteristic
167C23—4524no—
168C23—2264no—
169Q8—1132no—
170Q8C2×D45212yes—
171D4—22no—
172D4—1132no—
173D4—9044no—
174D4—4524no—
175D4—4524no—
176D4—2262no—
177D4—2264no—
178D4—2264no—
179D4C2×D45212yes—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—4524no—
183C2×C4—2262no—
184C2×C4C23×D11311yescharacteristic
185C8—22no—
186C8—2262no—
187C8D4×D11311yescharacteristic
188C8D4×D11311yescharacteristic
189C8C2×D45211yescharacteristic
190C8C2×D45211yescharacteristic
191C22—22no—
192C22—18084no—
193C22—9044no—
194C22—4524no—
195C22—2262no—
196C22#1681366811yescharacteristic
197C4—22no—
198C4—22no—
199C4—2262no—
200C4C2×D4×D11311yescharacteristic
201C4C22×D45211yescharacteristic
202C2—21no—
203C2—42no—
204C2—9044no—
205C2—4522no—
206C2D4×D45211yescharacteristic
subgroupG/H
centerC2D4×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#443×C113C2
socleC2×C113D42
hypercenter#443D113
hypocenterC113#3292
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #20299403C2semidirect
2. #20299400C2semidirect
3. #20298975C2semidirect
4. #20298869C2semidirect
5. #20298868C2semidirect
6. #20298767C2semidirect
7. #20298716C2semidirect
8. #443×C113C2semidirect
9. #16813668C22semidirect
11. #16813650C22semidirect
13. #16813647C22semidirect
18. C2×D904C22semidirect
19. C2×D904C22semidirect
21. #16813628C22semidirect
22. #16813619C22semidirect
23. #16813558C22semidirect
24. #16813550C22semidirect
25. #16813538C22semidirect
27. #131×C113C22semidirect
28. #108×C113C22semidirect
29. #104×C113C22semidirect
30. C4×C8×C113C22semidirect
39. Dic452D4semidirect
41. #14268636D4semidirect
48. D904D4semidirect
54. Q16×C113D4semidirect
55. SD16×C113D4semidirect
56. D8×C113D4semidirect
104. C113#3292semidirect
112. #443D113semidirect
127. #131C2×D113semidirect
130. #108C2×D113semidirect
132. #104C2×D113semidirect
134. C4×C8C2×D113semidirect
145. Q16D452semidirect
149. SD16D452semidirect
157. D8D452semidirect

Maximal subgroups

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

subgroupindex
#202994032
#202994002
#202989752
#202988692
#202988682
#202987672
#202987162
#443×C1132
#3292113