Finite Group Databasebeta

← #26031095

Subgroups — #26031095

Order 11392.

418 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 109 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#19151937C212yesmaximal, complemented
3#19151924C212yesmaximal, complemented
4#19151851C211yesmaximal, characteristic, complemented
5#19151846C212yesmaximal, complemented
6#19151759C212yesmaximal, complemented
7#19151746C212yesmaximal, complemented
8#19151561C211yesmaximal, characteristic, complemented
9#470×C89C211yesmaximal, characteristic, complemented
10C2×#13083575C2212yes—
11C22×C4×D89C2211yescharacteristic
12C2×#13083561C2212yescomplemented
13C2×D712C2211yescharacteristic, complemented
14C2×#13083558C2211yescharacteristic
15#15667997—22no—
16#15667988C2212yes—
17#15667987C2212yes—
18#15667986C2212yes—
19#15667982—22no—
20#15667974—22no—
21#15667972—22no—
22#15667970C2212yes—
23#15667945C2212yescomplemented
24#15667944C2211yescharacteristic, complemented
25#15667936C2212yescomplemented
26#15667934C2212yescomplemented
27#15667932C2212yescomplemented
28#15667924C2212yes—
29#15667924C2212yes—
30C2×Q16×C89C2211yescharacteristic, complemented
31C2×M16×C89C2211yescharacteristic
32C22⋊Q8×C89C2212yes—
33#106×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—
50#13083558—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—
62M16×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—41no—
71C22×D89—42no—
72C22×D89C2×D412yes—
73Q8×C89—22no—
74Q8×C89—22no—
75C2×C4×C89—21no—
76C2×C4×C89—21no—
77C2×C4×C89—22no—
78C2×C4×C89—22no—
79C2×C4×C89C2×D411yescharacteristic
80C2×C4×C89C2411yescharacteristic
81C22⋊D89—44no—
82C2×Dic89—22no—
83C2×Dic89—41no—
84C2×Dic89C2×D412yes—
85D356—22no—
86D356—22no—
87D356—44no—
88D356—44no—
89C4×D89—22no—
90C4×D89—22no—
91C4×D89—42no—
92C4×D89—44no—
93C8×C89—21no—
94C8×C89—21no—
95#10623494—22no—
96C22×C89—21no—
97C22×C89—22no—
98C22×C89C22×D411yescharacteristic
99C2×D89—22no—
100C2×D89—22no—
101C2×D89—22no—
102C2×D89—44no—
103C2×D89—42no—
104C2×D89—42no—
105C2×D89—42no—
106C4×C89—21no—
107C4×C89—42no—
108C4×C89—42no—
109C4×C89H(5,𝔽2)11yescharacteristic
110C4×C89H(5,𝔽2)11yescharacteristic
111Dic89—22no—
112Dic89—42no—
113C2×C89—41no—
114C2×C89#53411yescharacteristic
115C2×C89#57512yes—
116D89—42no—
117D89—82no—
118#3197—891nomaximal, Sylow
119C89#319711yescharacteristic, complemented, Sylow
120#525—892no—
121#485—892no—
122#482—892no—
123#470D8911yescharacteristic, complemented
124#469—891no—
125#468—892no—
126#452—892no—
127#449—892no—
128#407—891no—
129C2×#41—892no—
130C23×C4—891no—
131C2×Q16C2×D8911yescharacteristic, complemented
132C2×SD16—892no—
133C2×D8—891no—
134C2×M16—891no—
135C2×M16C2×D8911yescharacteristic
136#123—1782no—
137C22⋊Q8—892no—
138C22⋊Q8C2×D8912yes—
139#121—892no—
140#121—892no—
141#120—1782no—
142C4×D4—1782no—
143C4×D4—1782no—
144#117—892no—
145#107—892no—
146#106—891no—
147#106C2×D8911yescharacteristic, complemented
148#103—892no—
149#103C2×D8912yescomplemented
150#102—892no—
151#102—892no—
152C22⋊C8—892no—
153C22⋊C8—892no—
154C24—891no—
155#41—3562no—
156#41—3562no—
157C2×Q8C22×D8912yes—
158C2×D4—892no—
159C2×D4—1782no—
160C2×D4—1782no—
161C2×D4—1782no—
162C22×C4—891no—
163C22×C4—892no—
164C22×C4—892no—
165C22×C4—3561no—
166C22×C4—3561no—
167C22×C4—1782no—
168C22×C4C22×D8911yescharacteristic
169Q16—41no—
170SD16—3562no—
171D8—3561no—
172M16—41no—
173M16—3561no—
174C2×C8—892no—
175C2×C8C22×D8911yescharacteristic
176C2×C8C22×D8911yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—892no—
179C4⋊C4—1782no—
180C4⋊C4C22×D8912yes—
181C22⋊C4—22no—
182C22⋊C4—1782no—
183C22⋊C4—1782no—
184C22⋊C4—1782no—
185C22⋊C4—1782no—
186C42—1782no—
187C23—892no—
188C23—3561no—
189C23—3562no—
190C23—1782no—
191C23D4×D8911yescharacteristic
192Q8—22no—
193Q8—22no—
194D4—3564no—
195D4—3564no—
196D4—3564no—
197D4—1782no—
198D4—1782no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—892no—
204C2×C4—3562no—
205C2×C4—3564no—
206C2×C4—3561no—
207C2×C4—1782no—
208C2×C4—1782no—
209C2×C4—1782no—
210C2×C4D4×D8911yescharacteristic
211C2×C4C23×D8911yescharacteristic
212C8—21no—
213C8—21no—
214C8—1782no—
215C22—22no—
216C22—21no—
217C22—3564no—
218C22—3562no—
219C22—3562no—
220C22—3562no—
221C22—1782no—
222C22—1782no—
223C22—1782no—
224C22C2×D4×D8911yescharacteristic
225C4—21no—
226C4—42no—
227C4—42no—
228C4—3562no—
229C4—1782no—
230C4#1566805711yescharacteristic
231C4#1566805811yescharacteristic
232C2—41no—
233C2—3562no—
234C2—7122no—
235C2#1915215611yescharacteristic
236C2#1915239712yes—
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#470×C89C2
socleC22×C89C22×D4
hypercenter#470D89
hypocenterC89#3197
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #19152111C2semidirect
2. #19151937C2semidirect
3. #19151924C2semidirect
4. #19151851C2semidirect
5. #19151846C2semidirect
6. #19151759C2semidirect
7. #19151746C2semidirect
8. #19151561C2semidirect
9. #470×C89C2semidirect
12. C2×#13083561C22semidirect
13. C2×D712C22semidirect
23. #15667945C22semidirect
24. #15667944C22semidirect
25. #15667936C22semidirect
26. #15667934C22semidirect
27. #15667932C22semidirect
30. C2×Q16×C89C22semidirect
33. #106×C89C22semidirect
34. #103×C89C22semidirect
119. C89#3197semidirect
123. #470D89semidirect
131. C2×Q16C2×D89semidirect
147. #106C2×D89semidirect
149. #103C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191521112
#191519372
#191519242
#191518512
#191518462
#191517592
#191517462
#191515612
#470×C892
#319789