Finite Group Databasebeta

← #26033392

Subgroups — #26033392

Order 11392.

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

normal subgroups only

This group has 370 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#19152400C211yesmaximal, characteristic, complemented
2#19152399C211yesmaximal, characteristic, complemented
3#19152036C211yesmaximal, characteristic, complemented
4#19152035C212yesmaximal, complemented
5#19152032C212yesmaximal, complemented
6#19152029C212yesmaximal, complemented
7#19152028C211yesmaximal, characteristic, complemented
8C2×#15667953C211yesmaximal, characteristic, complemented
9D16×D89C212yesmaximal, complemented
10#19152016C211yesmaximal, characteristic, complemented
11#509×C89C211yesmaximal, characteristic, complemented
12#15668058—21no—
13#15668057—21no—
14#15668039—22no—
15#15668038—21no—
16#15668037—21no—
17#15668036—22no—
18#15668035C2212yescomplemented
19#15668034C2211yescharacteristic, complemented
20#15668031C2212yescomplemented
21C2×D712C2211yescharacteristic, complemented
22D8×D89C2212yescomplemented
23D8×D89C2212yescomplemented
24#15668018C2211yescharacteristic
25#15667958C2211yescharacteristic, complemented
26#15667957C2212yescomplemented
27#15667956C2211yescharacteristic, complemented
28#15667955C2211yescharacteristic, complemented
29D1424C2212yescomplemented
30#15667953C2211yescharacteristic, complemented
31#15667953C2212yescomplemented
32#15667953C2212yescomplemented
33#15667951C2212yescomplemented
34C2×#13083549C2211yescharacteristic, complemented
35C16×D89C2212yescomplemented
36#135×C89C2211yescharacteristic, complemented
37C2×D8×C89C2211yescharacteristic, complemented
38SD32×C89C2212yescomplemented
39D16×C89C2212yescomplemented
40M32×C89C2211yescharacteristic, complemented
41#13083575—22no—
42#13083574—21no—
43#13083574—41no—
44#13083574D411yescharacteristic
45#13083573—22no—
46#13083573—41no—
47C2×D356—21no—
48C2×D356—41no—
49C2×C22⋊D89—42no—
50D4×D89—22no—
51D4×D89—22no—
52D4×D89—42no—
53D4×D89—41no—
54Dic356C2311yescharacteristic
55#13083563—21no—
56#13083562—22no—
57#13083561—22no—
58D712—21no—
59D712C2311yescharacteristic
60D712C2312yes—
61#13083559—22no—
62#13083559—22no—
63#13083558D411yescharacteristic
64#13083557D412yes—
65C8×D89C2312yes—
66#13083549C2311yescharacteristic
67#13083549C2311yescharacteristic
68#41×C89—21no—
69C2×D4×C89—21no—
70Q16×C89C2311yescharacteristic
71SD16×C89—21no—
72D8×C89—21no—
73D8×C89C2311yescharacteristic
74D8×C89C2312yes—
75C2×C8×C89C2311yescharacteristic
76C16×C89C2312yes—
77C23×C89—41no—
78C22×D89—41no—
79C22×D89—42no—
80C22×D89—42no—
81Q8×C89—21no—
82D4×C89—22no—
83D4×C89—21no—
84D4×C89—41no—
85D4×C89—41no—
86C2×C4×C89—41no—
87C2×C4×C89C2×D411yescharacteristic
88C22⋊D89—41no—
89C22⋊D89—42no—
90C22⋊D89—42no—
91C22⋊D89—42no—
92C22⋊D89D812yes—
93C2×Dic89—42no—
94D356—21no—
95D356—22no—
96D356—42no—
97D356—41no—
98D356D811yescharacteristic
99C4×D89—41no—
100C4×D89—42no—
101C4×D89C2×D412yes—
102Dic178—21no—
103Dic178D811yescharacteristic
104C8×C89C2×D411yescharacteristic
105C8×C89C2411yescharacteristic
106#10623494C2×D412yes—
107C22×C89—42no—
108C22×C89—41no—
109C22×C89—161no—
110C22×C89C2×D811yescharacteristic
111C2×D89—42no—
112C2×D89—41no—
113C2×D89—162no—
114C2×D89—162no—
115C2×D89—161no—
116C2×D89C2×D812yes—
117C4×C89—41no—
118C4×C89C2×D811yescharacteristic
119C4×C89C22×D411yescharacteristic
120Dic89—41no—
121Dic89C2×D812yes—
122C2×C89—21no—
123C2×C89—81no—
124C2×C89—82no—
125C2×C89C22×D811yescharacteristic
126D89—22no—
127D89—82no—
128D89—81no—
129#3415—891nomaximal, Sylow
130C89#341511yescharacteristic, complemented, Sylow
131#576—891no—
132#576—891no—
133#509—892no—
134#509—892no—
135#509—891no—
136#509D8911yescharacteristic, complemented
137#508—891no—
138#508—892no—
139C2×D16—891no—
140C2×D16—892no—
141#504—891no—
142H(5,𝔽2)—1781no—
143H(5,𝔽2)—1781no—
144AGL(1,ℤ/8)—1782no—
145AGL(1,ℤ/8)—1782no—
146AGL(1,ℤ/8)—1781no—
147AGL(1,ℤ/8)—1781no—
148#135—892no—
149#135—892no—
150#135—891no—
151#135C2×D8911yescharacteristic, complemented
152C2×D8—892no—
153C2×D8—892no—
154C2×D8—891no—
155C2×D8C2×D8911yescharacteristic, complemented
156#131—891no—
157Q32—891no—
158SD32—891no—
159SD32—891no—
160SD32—892no—
161SD32C2×D8912yescomplemented
162D16—892no—
163D16—891no—
164D16—892no—
165D16—892no—
166D16C2×D8912yescomplemented
167M32—892no—
168M32C2×D8911yescharacteristic, complemented
169C2×C16—891no—
170C2×C16—892no—
171#41—21no—
172#41—891no—
173#41—3561no—
174#41—3561no—
175#41—1782no—
176#41—1782no—
177#41—1781no—
178C2×D4—21no—
179C2×D4—3561no—
180C2×D4—3562no—
181C2×D4—3561no—
182C2×D4—3562no—
183C2×D4—1782no—
184C2×D4—1782no—
185C2×D4—1781no—
186Q16—891no—
187Q16C22×D8911yescharacteristic
188SD16—21no—
189SD16—1782no—
190SD16—1782no—
191SD16—1781no—
192D8—21no—
193D8—892no—
194D8—891no—
195D8—1782no—
196D8—1782no—
197D8—1781no—
198D8C22×D8912yes—
199D8C22×D8911yescharacteristic
200M16—891no—
201M16—892no—
202C2×C8—892no—
203C2×C8C22×D8911yescharacteristic
204C16—891no—
205C16—891no—
206C16C22×D8912yes—
207C23—41no—
208C23—3562no—
209C23—3562no—
210C23—3561no—
211Q8—21no—
212Q8—891no—
213Q8—1781no—
214D4—22no—
215D4—21no—
216D4—41no—
217D4—41no—
218D4—892no—
219D4—891no—
220D4—3562no—
221D4—3562no—
222D4—3562no—
223D4—3562no—
224D4—3561no—
225D4—3561no—
226D4—1781no—
227D4—1782no—
228C2×C4—41no—
229C2×C4—892no—
230C2×C4—3562no—
231C2×C4—3562no—
232C2×C4—3561no—
233C2×C4D4×D8911yescharacteristic
234C8—892no—
235C8D4×D8911yescharacteristic
236C8C23×D8911yescharacteristic
237C22—41no—
238C22—42no—
239C22—161no—
240C22—892no—
241C22—3562no—
242C22—3561no—
243C22—14241no—
244C22—14242no—
245C22—14242no—
246C22D8×D8911yescharacteristic
247C4—41no—
248C4—892no—
249C4—3561no—
250C4D8×D8911yescharacteristic
251C4C2×D4×D8911yescharacteristic
252C2—21no—
253C2—82no—
254C2—81no—
255C2—1782no—
256C2—7122no—
257C2—7121no—
258C2C2×D8×D8911yescharacteristic
subgroupG/H
centerC2C2×D8×D89
commutator, cosocleC8×C89C24
FrattiniC8C23×D89
Fitting#509×C89C2
socleC2×C89C22×D8
hypercenter#509D89
hypocenterC89#3415
LCSG ▷ C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #19152400C2semidirect
2. #19152399C2semidirect
3. #19152036C2semidirect
4. #19152035C2semidirect
5. #19152032C2semidirect
6. #19152029C2semidirect
7. #19152028C2semidirect
8. C2×#15667953C2semidirect
9. D16×D89C2semidirect
10. #19152016C2semidirect
11. #509×C89C2semidirect
18. #15668035C22semidirect
19. #15668034C22semidirect
20. #15668031C22semidirect
21. C2×D712C22semidirect
22. D8×D89C22semidirect
23. D8×D89C22semidirect
25. #15667958C22semidirect
26. #15667957C22semidirect
27. #15667956C22semidirect
28. #15667955C22semidirect
29. D1424C22semidirect
30. #15667953C22semidirect
31. #15667953C22semidirect
32. #15667953C22semidirect
33. #15667951C22semidirect
34. C2×#13083549C22semidirect
35. C16×D89C22semidirect
36. #135×C89C22semidirect
37. C2×D8×C89C22semidirect
38. SD32×C89C22semidirect
39. D16×C89C22semidirect
40. M32×C89C22semidirect
130. C89#3415semidirect
136. #509D89semidirect
151. #135C2×D89semidirect
155. C2×D8C2×D89semidirect
161. SD32C2×D89semidirect
166. D16C2×D89semidirect
168. M32C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191524002
#191523992
#191520362
#191520352
#191520322
#191520292
#191520282
C2×#156679532
D16×D892
#191520162
#509×C892
#341589