Finite Group Databasebeta

← #26031046

Subgroups — #26031046

Order 11392.

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

normal subgroups only

This group has 424 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#19152111C212yesmaximal, complemented
2#19151938C212yesmaximal, complemented
3#19151925C212yesmaximal, complemented
4#19151834C211yesmaximal, characteristic, complemented
5#19151829C212yesmaximal, complemented
6#19151759C212yesmaximal, complemented
7#19151746C212yesmaximal, complemented
8C2×#15667924C211yesmaximal, characteristic, complemented
9#467×C89C211yesmaximal, characteristic, complemented
10C2×#13083575C2212yes—
11C22×C4×D89C2211yescharacteristic
12C2×#13083561C2212yescomplemented
13C2×D712C2211yescharacteristic, complemented
14C22×#10623494C2211yescharacteristic
15#15667997—22no—
16#15667988C2212yes—
17#15667987C2212yes—
18#15667986C2212yes—
19#15667982—22no—
20#15667974—22no—
21#15667972—22no—
22#15667970C2212yes—
23#15667946C2211yescharacteristic, complemented
24#15667943C2212yescomplemented
25#15667936C2212yescomplemented
26#15667934C2212yescomplemented
27#15667932C2212yescomplemented
28#15667924C2212yes—
29#15667924C2212yes—
30C2×Q16×C89C2211yescharacteristic, complemented
31C22×C8×C89C2211yescharacteristic
32C22⋊Q8×C89C2212yes—
33#107×C89C2211yescharacteristic, complemented
34#103×C89C2212yescomplemented
35C23×D89D411yescharacteristic
36#13083575—42no—
37#13083575—42no—
38C2×D356—22no—
39C2×D356—22no—
40C2×D356C2312yes—
41C2×C22⋊D89—22no—
42C22×Dic89D411yescharacteristic
43C2×C4×D89—22no—
44C2×C4×D89—41no—
45C2×C4×D89—41no—
46C2×C4×D89D412yes—
47C2×C4×D89C2312yes—
48#13083561—42no—
49D712—41no—
50C2×#10623494—41no—
51C2×#10623494C2312yes—
52C4⋊Dic89C2312yes—
53#13083553—22no—
54#13083551—22no—
55#13083551—22no—
56#13083551—22no—
57#13083551—22no—
58C4×Dic89—22no—
59C2×Q8×C89C2312yes—
60C22×C4×C89C2311yescharacteristic
61Q16×C89—41no—
62C2×C8×C89—41no—
63C2×C8×C89C2311yescharacteristic
64C2×C8×C89C2311yescharacteristic
65C4⋊C4×C89—22no—
66C4⋊C4×C89C2312yes—
67C22⋊C4×C89—22no—
68C23×C89C2×D411yescharacteristic
69C22×D89—22no—
70C22×D89—22no—
71C22×D89—41no—
72C22×D89—41no—
73C22×D89C2×D412yes—
74Q8×C89—22no—
75Q8×C89—22no—
76C2×C4×C89—21no—
77C2×C4×C89—21no—
78C2×C4×C89—22no—
79C2×C4×C89—22no—
80C2×C4×C89C2×D411yescharacteristic
81C2×C4×C89C2411yescharacteristic
82C22⋊D89—44no—
83C2×Dic89—22no—
84C2×Dic89—41no—
85C2×Dic89C2×D412yes—
86D356—22no—
87D356—22no—
88D356—44no—
89D356—44no—
90C4×D89—22no—
91C4×D89—22no—
92C4×D89—42no—
93C4×D89—44no—
94C8×C89—21no—
95C8×C89—21no—
96#10623494—22no—
97C22×C89—21no—
98C22×C89—21no—
99C22×C89#13512yes—
100C22×C89C22×D411yescharacteristic
101C2×D89—22no—
102C2×D89—22no—
103C2×D89—22no—
104C2×D89—44no—
105C2×D89—42no—
106C2×D89—42no—
107C2×D89—42no—
108C4×C89—21no—
109C4×C89—42no—
110C4×C89—42no—
111C4×C89H(5,𝔽2)11yescharacteristic
112C4×C89H(5,𝔽2)11yescharacteristic
113Dic89—22no—
114Dic89—42no—
115C2×C89—22no—
116C2×C89#53411yescharacteristic
117C2×C89C2×#13511yescharacteristic
118C2×C89#57511yescharacteristic
119D89—42no—
120D89—82no—
121#3191—891nomaximal, Sylow
122C89#319111yescharacteristic, complemented, Sylow
123#525—892no—
124#485—892no—
125#482—892no—
126#467D8911yescharacteristic, complemented
127#466—891no—
128#465—892no—
129#452—892no—
130#449—892no—
131C2×C22⋊C8—891no—
132C2×#41—892no—
133C23×C4—891no—
134C2×Q16C2×D8911yescharacteristic, complemented
135C2×SD16—892no—
136C2×D8—891no—
137C22×C8—891no—
138C22×C8C2×D8911yescharacteristic
139#123—1782no—
140C22⋊Q8—892no—
141C22⋊Q8C2×D8912yes—
142#121—892no—
143#121—892no—
144#120—1782no—
145C4×D4—1782no—
146C4×D4—1782no—
147#117—892no—
148#107—891no—
149#107C2×D8911yescharacteristic, complemented
150#106—892no—
151#103—892no—
152#103C2×D8912yescomplemented
153#102—892no—
154#102—892no—
155C22⋊C8—892no—
156C22⋊C8—892no—
157C24—891no—
158#41—3562no—
159#41—3562no—
160C2×Q8C22×D8912yes—
161C2×D4—892no—
162C2×D4—1782no—
163C2×D4—1782no—
164C2×D4—1782no—
165C22×C4—891no—
166C22×C4—892no—
167C22×C4—892no—
168C22×C4—3561no—
169C22×C4—3561no—
170C22×C4—1782no—
171C22×C4C22×D8911yescharacteristic
172Q16—41no—
173SD16—3562no—
174D8—3561no—
175C2×C8—41no—
176C2×C8—892no—
177C2×C8—3561no—
178C2×C8C22×D8911yescharacteristic
179C2×C8C22×D8911yescharacteristic
180C4⋊C4—22no—
181C4⋊C4—892no—
182C4⋊C4—1782no—
183C4⋊C4C22×D8912yes—
184C22⋊C4—22no—
185C22⋊C4—1782no—
186C22⋊C4—1782no—
187C22⋊C4—1782no—
188C22⋊C4—1782no—
189C42—1782no—
190C23—892no—
191C23—3561no—
192C23—3561no—
193C23—1782no—
194C23—1782no—
195C23D4×D8911yescharacteristic
196Q8—22no—
197Q8—22no—
198D4—3564no—
199D4—3564no—
200D4—3564no—
201D4—1782no—
202D4—1782no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—892no—
208C2×C4—3562no—
209C2×C4—3564no—
210C2×C4—3561no—
211C2×C4—1782no—
212C2×C4—1782no—
213C2×C4—1782no—
214C2×C4D4×D8911yescharacteristic
215C2×C4C23×D8911yescharacteristic
216C8—21no—
217C8—21no—
218C8—1782no—
219C22—21no—
220C22—21no—
221C22—3564no—
222C22—3562no—
223C22—3562no—
224C22—3562no—
225C22—1782no—
226C22—1782no—
227C22—1782no—
228C22#1566803512yes—
229C22C2×D4×D8911yescharacteristic
230C4—21no—
231C4—42no—
232C4—42no—
233C4—3562no—
234C4—1782no—
235C4#1566805711yescharacteristic
236C4#1566805811yescharacteristic
237C2—22no—
238C2—3562no—
239C2—7122no—
240C2#1915215611yescharacteristic
241C2C2×#1566803511yescharacteristic
242C2#1915239511yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#467×C89C2
socleC22×C89C22×D4
hypercenter#467D89
hypocenterC89#3191
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #19152111C2semidirect
2. #19151938C2semidirect
3. #19151925C2semidirect
4. #19151834C2semidirect
5. #19151829C2semidirect
6. #19151759C2semidirect
7. #19151746C2semidirect
8. C2×#15667924C2semidirect
9. #467×C89C2semidirect
12. C2×#13083561C22semidirect
13. C2×D712C22semidirect
23. #15667946C22semidirect
24. #15667943C22semidirect
25. #15667936C22semidirect
26. #15667934C22semidirect
27. #15667932C22semidirect
30. C2×Q16×C89C22semidirect
33. #107×C89C22semidirect
34. #103×C89C22semidirect
122. C89#3191semidirect
126. #467D89semidirect
134. C2×Q16C2×D89semidirect
149. #107C2×D89semidirect
152. #103C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191521112
#191519382
#191519252
#191518342
#191518292
#191517592
#191517462
C2×#156679242
#467×C892
#319189