Finite Group Databasebeta

← #26033385

Subgroups — #26033385

Order 11392.

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×D89C212yesmaximal, complemented
2#19152040C212yesmaximal, complemented
3#19152037C212yesmaximal, complemented
4#19152035C212yesmaximal, complemented
5#19152032C212yesmaximal, complemented
6#19152030C211yesmaximal, characteristic, complemented
7#19152028C212yesmaximal, complemented
8C2×#15667951C211yesmaximal, characteristic, complemented
9#508×C89C211yesmaximal, characteristic, complemented
10#41×D89—22no—
11#15668035C2212yes—
12#15668034C2212yescomplemented
13#15668033—22no—
14#15668032—22no—
15#15668031C2212yes—
16Q16×D89C2212yescomplemented
17SD16×D89—22no—
18D8×D89C2212yescomplemented
19C2×C8×D89C2211yescharacteristic
20Dic712C2211yescharacteristic, complemented
21#15667958C2212yescomplemented
22#15667957C2212yescomplemented
23#15667956C2212yescomplemented
24#15667955C2212yescomplemented
25D1424C2211yescharacteristic, complemented
26#15667953C2212yescomplemented
27#15667951C2212yescomplemented
28#15667951C2212yescomplemented
29C2×#13083549C2211yescharacteristic, complemented
30#135×C89C2212yescomplemented
31Q32×C89C2211yescharacteristic, complemented
32SD32×C89C2212yescomplemented
33D16×C89C2211yescharacteristic, complemented
34C2×C16×C89C2211yescharacteristic, complemented
35#13083575—22no—
36#13083574—22no—
37#13083574—42no—
38#13083573—22no—
39#13083573—42no—
40Q8×D89—22no—
41D4×D89—22no—
42D4×D89—42no—
43C2×C4×D89—42no—
44C2×C4×D89D411yescharacteristic
45Dic356C2312yes—
46#13083564—22no—
47#13083563—22no—
48#13083562—22no—
49#13083561—22no—
50D712C2312yes—
51#13083559—22no—
52C2×#10623494D411yescharacteristic
53C8×D89D412yes—
54C8×D89C2312yes—
55#13083549C2312yes—
56#41×C89—22no—
57Q16×C89C2312yes—
58SD16×C89—22no—
59D8×C89C2312yes—
60C2×C8×C89C2311yescharacteristic
61C16×C89C2311yescharacteristic
62C16×C89C2311yescharacteristic
63C22×D89—42no—
64C22×D89D811yescharacteristic
65Q8×C89—22no—
66D4×C89—22no—
67D4×C89—42no—
68C2×C4×C89—42no—
69C2×C4×C89C2×D411yescharacteristic
70C22⋊D89—42no—
71C22⋊D89—42no—
72C22⋊D89—42no—
73C2×Dic89—42no—
74C2×Dic89D811yescharacteristic
75D356—22no—
76D356—42no—
77C4×D89—42no—
78C4×D89—42no—
79C4×D89—42no—
80C4×D89D812yes—
81C4×D89C2×D412yes—
82Dic178—22no—
83Dic178—42no—
84C8×C89C2×D411yescharacteristic
85C8×C89C2411yescharacteristic
86#10623494C2×D412yes—
87C22×C89—42no—
88C22×C89C2×D811yescharacteristic
89C2×D89—41no—
90C2×D89—42no—
91C2×D89—84no—
92C2×D89C2×D812yes—
93C4×C89—42no—
94C4×C89C2×D811yescharacteristic
95C4×C89C22×D411yescharacteristic
96Dic89—42no—
97Dic89C2×D812yes—
98C2×C89—21no—
99C2×C89—82no—
100C2×C89C22×D811yescharacteristic
101D89—22no—
102D89—82no—
103#3414—891nomaximal, Sylow
104C89#341411yescharacteristic, complemented, Sylow
105C2×#135—892no—
106#510—892no—
107#510—892no—
108#509—892no—
109#509—892no—
110#508—892no—
111#508—891no—
112#508D8911yescharacteristic, complemented
113C2×M32—891no—
114C2×#41—1782no—
115#135—892no—
116#135—892no—
117#135—892no—
118#135—1782no—
119#135—1782no—
120#135C2×D8912yescomplemented
121C2×Q16—892no—
122C2×SD16—1782no—
123C2×D8—892no—
124C22×C8—891no—
125Q32—892no—
126Q32—891no—
127Q32C2×D8911yescharacteristic, complemented
128SD32—892no—
129SD32—892no—
130SD32—892no—
131SD32C2×D8912yescomplemented
132D16—892no—
133D16—891no—
134D16C2×D8911yescharacteristic, complemented
135M32—892no—
136M32—892no—
137C2×C16—891no—
138C2×C16C2×D8911yescharacteristic, complemented
139#41—22no—
140#41—3562no—
141#41—3562no—
142#41—1782no—
143#41—1782no—
144#41—1782no—
145C2×Q8—1782no—
146C2×D4—3562no—
147C2×D4—1782no—
148C22×C4—891no—
149C22×C4—3562no—
150Q16—892no—
151Q16—1782no—
152Q16C22×D8912yes—
153SD16—22no—
154SD16—1782no—
155SD16—1782no—
156SD16—1782no—
157D8—892no—
158D8—1782no—
159D8C22×D8912yes—
160C2×C8—891no—
161C2×C8—892no—
162C2×C8—892no—
163C2×C8C22×D8911yescharacteristic
164C16—892no—
165C16C22×D8911yescharacteristic
166C16C22×D8911yescharacteristic
167C23—891no—
168C23—3562no—
169Q8—22no—
170Q8—3562no—
171Q8—1782no—
172D4—22no—
173D4—42no—
174D4—3562no—
175D4—3562no—
176D4—3562no—
177D4—3562no—
178D4—1782no—
179C2×C4—42no—
180C2×C4—891no—
181C2×C4—892no—
182C2×C4—892no—
183C2×C4—3562no—
184C2×C4—3562no—
185C2×C4—3562no—
186C2×C4—3562no—
187C2×C4D4×D8911yescharacteristic
188C8—892no—
189C8D4×D8911yescharacteristic
190C8C23×D8911yescharacteristic
191C22—42no—
192C22—892no—
193C22—3561no—
194C22—3562no—
195C22—7124no—
196C22D8×D8911yescharacteristic
197C4—42no—
198C4—892no—
199C4—3562no—
200C4D8×D8911yescharacteristic
201C4C2×D4×D8911yescharacteristic
202C2—21no—
203C2—82no—
204C2—1782no—
205C2—7122no—
206C2C2×D8×D8911yescharacteristic
subgroupG/H
centerC4D8×D89
commutator, cosocleC8×C89C24
FrattiniC8C23×D89
Fitting#508×C89C2
socleC2×C89C22×D8
hypercenter#508D89
hypocenterC89#3414
LCSG ▷ C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #135×D89C2semidirect
2. #19152040C2semidirect
3. #19152037C2semidirect
4. #19152035C2semidirect
5. #19152032C2semidirect
6. #19152030C2semidirect
7. #19152028C2semidirect
8. C2×#15667951C2semidirect
9. #508×C89C2semidirect
12. #15668034C22semidirect
16. Q16×D89C22semidirect
18. D8×D89C22semidirect
20. Dic712C22semidirect
21. #15667958C22semidirect
22. #15667957C22semidirect
23. #15667956C22semidirect
24. #15667955C22semidirect
25. D1424C22semidirect
26. #15667953C22semidirect
27. #15667951C22semidirect
28. #15667951C22semidirect
29. C2×#13083549C22semidirect
30. #135×C89C22semidirect
31. Q32×C89C22semidirect
32. SD32×C89C22semidirect
33. D16×C89C22semidirect
34. C2×C16×C89C22semidirect
104. C89#3414semidirect
112. #508D89semidirect
120. #135C2×D89semidirect
127. Q32C2×D89semidirect
131. SD32C2×D89semidirect
134. D16C2×D89semidirect
138. C2×C16C2×D89semidirect

Maximal subgroups

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

subgroupindex
#135×D892
#191520402
#191520372
#191520352
#191520322
#191520302
#191520282
C2×#156679512
#508×C892
#341489