Finite Group Databasebeta

← #28403707

Subgroups — #28403707

Order 14464.

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

normal subgroups only

This group has 364 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#135×D113C212yesmaximal, complemented
2#20299040C212yesmaximal, complemented
3#20299037C212yesmaximal, complemented
4#20299035C212yesmaximal, complemented
5#20299032C212yesmaximal, complemented
6#20299030C211yesmaximal, characteristic, complemented
7#20299028C212yesmaximal, complemented
8C2×#16813561C211yesmaximal, characteristic, complemented
9#508×C113C211yesmaximal, characteristic, complemented
10#41×D113—22no—
11#16813645C2212yes—
12#16813644C2212yescomplemented
13#16813643—22no—
14#16813642—22no—
15#16813641C2212yes—
16Q16×D113C2212yescomplemented
17SD16×D113—22no—
18D8×D113C2212yescomplemented
19C2×C8×D113C2211yescharacteristic
20Dic904C2211yescharacteristic, complemented
21#16813568C2212yescomplemented
22#16813567C2212yescomplemented
23#16813566C2212yescomplemented
24#16813565C2212yescomplemented
25D1808C2211yescharacteristic, complemented
26#16813563C2212yescomplemented
27#16813561C2212yescomplemented
28#16813561C2212yescomplemented
29C2×#14268622C2211yescharacteristic, complemented
30#135×C113C2212yescomplemented
31Q32×C113C2211yescharacteristic, complemented
32SD32×C113C2212yescomplemented
33D16×C113C2211yescharacteristic, complemented
34C2×C16×C113C2211yescharacteristic, complemented
35#14268648—22no—
36#14268647—22no—
37#14268647—42no—
38#14268646—22no—
39#14268646—42no—
40Q8×D113—22no—
41D4×D113—22no—
42D4×D113—42no—
43C2×C4×D113—42no—
44C2×C4×D113D411yescharacteristic
45Dic452C2312yes—
46#14268637—22no—
47#14268636—22no—
48#14268635—22no—
49#14268634—22no—
50D904C2312yes—
51#14268632—22no—
52C2×#11744751D411yescharacteristic
53C8×D113D412yes—
54C8×D113C2312yes—
55#14268622C2312yes—
56#41×C113—22no—
57Q16×C113C2312yes—
58SD16×C113—22no—
59D8×C113C2312yes—
60C2×C8×C113C2311yescharacteristic
61C16×C113C2311yescharacteristic
62C16×C113C2311yescharacteristic
63C22×D113—42no—
64C22×D113D811yescharacteristic
65Q8×C113—22no—
66D4×C113—22no—
67D4×C113—42no—
68C2×C4×C113—42no—
69C2×C4×C113C2×D411yescharacteristic
70C22⋊D113—42no—
71C22⋊D113—42no—
72C22⋊D113—42no—
73C2×Dic113—42no—
74C2×Dic113D811yescharacteristic
75D452—22no—
76D452—42no—
77C4×D113—42no—
78C4×D113—42no—
79C4×D113—42no—
80C4×D113D812yes—
81C4×D113C2×D412yes—
82Dic226—22no—
83Dic226—42no—
84C8×C113C2×D411yescharacteristic
85C8×C113C2411yescharacteristic
86#11744751C2×D412yes—
87C22×C113—42no—
88C22×C113C2×D811yescharacteristic
89C2×D113—41no—
90C2×D113—42no—
91C2×D113—84no—
92C2×D113C2×D812yes—
93C4×C113—42no—
94C4×C113C2×D811yescharacteristic
95C4×C113C22×D411yescharacteristic
96Dic113—42no—
97Dic113C2×D812yes—
98C2×C113—21no—
99C2×C113—82no—
100C2×C113C22×D811yescharacteristic
101D113—22no—
102D113—82no—
103#3414—1131nomaximal, Sylow
104C113#341411yescharacteristic, complemented, Sylow
105C2×#135—1132no—
106#510—1132no—
107#510—1132no—
108#509—1132no—
109#509—1132no—
110#508—1132no—
111#508—1131no—
112#508D11311yescharacteristic, complemented
113C2×M32—1131no—
114C2×#41—2262no—
115#135—1132no—
116#135—1132no—
117#135—1132no—
118#135—2262no—
119#135—2262no—
120#135C2×D11312yescomplemented
121C2×Q16—1132no—
122C2×SD16—2262no—
123C2×D8—1132no—
124C22×C8—1131no—
125Q32—1132no—
126Q32—1131no—
127Q32C2×D11311yescharacteristic, complemented
128SD32—1132no—
129SD32—1132no—
130SD32—1132no—
131SD32C2×D11312yescomplemented
132D16—1132no—
133D16—1131no—
134D16C2×D11311yescharacteristic, complemented
135M32—1132no—
136M32—1132no—
137C2×C16—1131no—
138C2×C16C2×D11311yescharacteristic, complemented
139#41—22no—
140#41—4522no—
141#41—4522no—
142#41—2262no—
143#41—2262no—
144#41—2262no—
145C2×Q8—2262no—
146C2×D4—4522no—
147C2×D4—2262no—
148C22×C4—1131no—
149C22×C4—4522no—
150Q16—1132no—
151Q16—2262no—
152Q16C22×D11312yes—
153SD16—22no—
154SD16—2262no—
155SD16—2262no—
156SD16—2262no—
157D8—1132no—
158D8—2262no—
159D8C22×D11312yes—
160C2×C8—1131no—
161C2×C8—1132no—
162C2×C8—1132no—
163C2×C8C22×D11311yescharacteristic
164C16—1132no—
165C16C22×D11311yescharacteristic
166C16C22×D11311yescharacteristic
167C23—1131no—
168C23—4522no—
169Q8—22no—
170Q8—4522no—
171Q8—2262no—
172D4—22no—
173D4—42no—
174D4—4522no—
175D4—4522no—
176D4—4522no—
177D4—4522no—
178D4—2262no—
179C2×C4—42no—
180C2×C4—1131no—
181C2×C4—1132no—
182C2×C4—1132no—
183C2×C4—4522no—
184C2×C4—4522no—
185C2×C4—4522no—
186C2×C4—4522no—
187C2×C4D4×D11311yescharacteristic
188C8—1132no—
189C8D4×D11311yescharacteristic
190C8C23×D11311yescharacteristic
191C22—42no—
192C22—1132no—
193C22—9044no—
194C22—4521no—
195C22—4522no—
196C22D8×D11311yescharacteristic
197C4—42no—
198C4—1132no—
199C4—4522no—
200C4D8×D11311yescharacteristic
201C4C2×D4×D11311yescharacteristic
202C2—21no—
203C2—82no—
204C2—9042no—
205C2—2262no—
206C2C2×D8×D11311yescharacteristic
subgroupG/H
centerC4D8×D113
commutator, cosocleC8×C113C24
FrattiniC8C23×D113
Fitting#508×C113C2
socleC2×C113C22×D8
hypercenter#508D113
hypocenterC113#3414
LCSG ▷ C8×C113 ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #135×D113C2semidirect
2. #20299040C2semidirect
3. #20299037C2semidirect
4. #20299035C2semidirect
5. #20299032C2semidirect
6. #20299030C2semidirect
7. #20299028C2semidirect
8. C2×#16813561C2semidirect
9. #508×C113C2semidirect
12. #16813644C22semidirect
16. Q16×D113C22semidirect
18. D8×D113C22semidirect
20. Dic904C22semidirect
21. #16813568C22semidirect
22. #16813567C22semidirect
23. #16813566C22semidirect
24. #16813565C22semidirect
25. D1808C22semidirect
26. #16813563C22semidirect
27. #16813561C22semidirect
28. #16813561C22semidirect
29. C2×#14268622C22semidirect
30. #135×C113C22semidirect
31. Q32×C113C22semidirect
32. SD32×C113C22semidirect
33. D16×C113C22semidirect
34. C2×C16×C113C22semidirect
104. C113#3414semidirect
112. #508D113semidirect
120. #135C2×D113semidirect
127. Q32C2×D113semidirect
131. SD32C2×D113semidirect
134. D16C2×D113semidirect
138. C2×C16C2×D113semidirect

Maximal subgroups

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

subgroupindex
#135×D1132
#202990402
#202990372
#202990352
#202990322
#202990302
#202990282
C2×#168135612
#508×C1132
#3414113