Finite Group Databasebeta

← #26033395

Subgroups — #26033395

Order 11392.

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

normal subgroups only

This group has 360 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#19152412C211yesmaximal, characteristic, complemented
2#19152400C211yesmaximal, characteristic, complemented
3#19152040C212yesmaximal, complemented
4#19152038C211yesmaximal, characteristic, complemented
5#19152033C211yesmaximal, characteristic, complemented
6#19152032C212yesmaximal, complemented
7#19152029C212yesmaximal, complemented
8C2×#15667957C211yesmaximal, characteristic, complemented
9SD32×D89C212yesmaximal, complemented
10#19152014C211yesmaximal, characteristic, complemented
11#508×C89C211yesmaximal, characteristic, complemented
12#15668059—21no—
13#15668058—21no—
14#15668042—21no—
15#15668041—22no—
16#15668039—22no—
17#15668037—21no—
18#15668035C2212yes—
19#15668031C2212yescomplemented
20C2×Dic356C2211yescharacteristic, complemented
21Q16×D89C2212yescomplemented
22C2×D712C2211yescharacteristic
23D8×D89C2212yes—
24#15668018C2211yescharacteristic
25#15667958C2212yescomplemented
26#15667957C2212yescomplemented
27#15667957C2212yescomplemented
28#15667956C2212yescomplemented
29#15667955C2212yescomplemented
30#15667953C2212yescomplemented
31#15667952C2211yescharacteristic, complemented
32#15667951C2212yescomplemented
33C16×D89C2212yescomplemented
34#135×C89C2211yescharacteristic
35#135×C89C2211yescharacteristic, complemented
36Q32×C89C2211yescharacteristic, complemented
37SD32×C89C2211yescharacteristic, complemented
38SD32×C89C2211yescharacteristic, complemented
39D16×C89C2211yescharacteristic, complemented
40C2×C16×C89C2211yescharacteristic, complemented
41#13083575—22no—
42#13083574—41no—
43#13083574—41no—
44#13083574D411yescharacteristic
45#13083573—22no—
46#13083573—42no—
47C2×Dic178—21no—
48C2×Dic178—41no—
49Q8×D89—22no—
50C2×D356—21no—
51C2×D356—41no—
52D4×D89—22no—
53D4×D89—42no—
54Dic356—21no—
55Dic356C2312yes—
56#13083564—22no—
57#13083562—22no—
58#13083561—22no—
59D712—21no—
60D712C2312yes—
61#13083559—22no—
62#13083558D411yescharacteristic
63#13083557D412yes—
64C8×D89C2312yes—
65#13083549C2312yes—
66#41×C89—21no—
67#41×C89—21no—
68Q16×C89C2311yescharacteristic
69Q16×C89C2311yescharacteristic
70SD16×C89—21no—
71SD16×C89—21no—
72D8×C89C2311yescharacteristic
73D8×C89C2311yescharacteristic
74C2×C8×C89C2311yescharacteristic
75C16×C89C2311yescharacteristic
76C16×C89C2311yescharacteristic
77C22×D89—41no—
78C22×D89—42no—
79Q8×C89—21no—
80Q8×C89—21no—
81D4×C89—21no—
82D4×C89—21no—
83D4×C89—41no—
84D4×C89—41no—
85C2×C4×C89—41no—
86C2×C4×C89—41no—
87C2×C4×C89C2×D411yescharacteristic
88C22⋊D89—42no—
89C22⋊D89—42no—
90C22⋊D89D812yes—
91C2×Dic89—41no—
92C2×Dic89—42no—
93D356—22no—
94D356—42no—
95D356—41no—
96D356D811yescharacteristic
97C4×D89—42no—
98C4×D89—42no—
99C4×D89C2×D412yes—
100Dic178—22no—
101Dic178—41no—
102Dic178—42no—
103Dic178D811yescharacteristic
104C8×C89C2×D411yescharacteristic
105C8×C89C2411yescharacteristic
106#10623494C2×D412yes—
107C22×C89—41no—
108C22×C89—41no—
109C22×C89C2×D811yescharacteristic
110C2×D89—42no—
111C2×D89—162no—
112C2×D89—161no—
113C2×D89C2×D812yes—
114C4×C89—41no—
115C4×C89—41no—
116C4×C89C2×D811yescharacteristic
117C4×C89C22×D411yescharacteristic
118Dic89—42no—
119Dic89C2×D812yes—
120C2×C89—21no—
121C2×C89—81no—
122C2×C89—81no—
123C2×C89C22×D811yescharacteristic
124D89—22no—
125D89—82no—
126#3416—891nomaximal, Sylow
127C89#341611yescharacteristic, complemented, Sylow
128#578—891no—
129#576—891no—
130#510—891no—
131#510—892no—
132#509—891no—
133#509—892no—
134#508—892no—
135#508D8911yescharacteristic, complemented
136C2×SD32—892no—
137C2×SD32—891no—
138#504—891no—
1392−1+4—1781no—
140H(5,𝔽2)—1781no—
141#137—1782no—
142#137—1781no—
143AGL(1,ℤ/8)—1782no—
144AGL(1,ℤ/8)—1781no—
145#135—892no—
146#135—892no—
147#135C2×D8911yescharacteristic
148#135C2×D8911yescharacteristic, complemented
149C2×Q16—892no—
150C2×Q16—891no—
151C2×D8—892no—
152C2×D8—891no—
153#131—891no—
154Q32—892no—
155Q32C2×D8911yescharacteristic, complemented
156SD32—892no—
157SD32—892no—
158SD32—892no—
159SD32—892no—
160SD32C2×D8911yescharacteristic, complemented
161SD32C2×D8911yescharacteristic, complemented
162D16—892no—
163D16C2×D8911yescharacteristic, complemented
164M32—891no—
165M32—892no—
166C2×C16—892no—
167C2×C16C2×D8911yescharacteristic, complemented
168#41—21no—
169#41—21no—
170#41—891no—
171#41—3561no—
172#41—3561no—
173#41—3562no—
174#41—1782no—
175#41—1782no—
176C2×Q8—3561no—
177C2×Q8—1782no—
178C2×Q8—1781no—
179C2×D4—3561no—
180C2×D4—3562no—
181C2×D4—1782no—
182C2×D4—1781no—
183Q16—892no—
184Q16—1782no—
185Q16—1781no—
186Q16C22×D8911yescharacteristic
187Q16C22×D8911yescharacteristic
188SD16—21no—
189SD16—21no—
190SD16—1782no—
191SD16—1782no—
192D8—892no—
193D8—1782no—
194D8—1781no—
195D8C22×D8911yescharacteristic
196D8C22×D8911yescharacteristic
197M16—891no—
198M16—892no—
199C2×C8—892no—
200C2×C8C22×D8911yescharacteristic
201C16—892no—
202C16C22×D8911yescharacteristic
203C16C22×D8911yescharacteristic
204C23—3562no—
205C23—3561no—
206Q8—21no—
207Q8—21no—
208Q8—891no—
209Q8—3562no—
210Q8—3561no—
211Q8—1782no—
212D4—21no—
213D4—21no—
214D4—41no—
215D4—41no—
216D4—892no—
217D4—891no—
218D4—3562no—
219D4—3562no—
220D4—3562no—
221D4—3561no—
222D4—1782no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—892no—
226C2×C4—3562no—
227C2×C4—3562no—
228C2×C4—3562no—
229C2×C4—3561no—
230C2×C4D4×D8911yescharacteristic
231C8—892no—
232C8D4×D8911yescharacteristic
233C8C23×D8911yescharacteristic
234C22—41no—
235C22—41no—
236C22—892no—
237C22—3562no—
238C22—14241no—
239C22—14242no—
240C22D8×D8911yescharacteristic
241C4—41no—
242C4—41no—
243C4—892no—
244C4—3562no—
245C4D8×D8911yescharacteristic
246C4C2×D4×D8911yescharacteristic
247C2—21no—
248C2—81no—
249C2—81no—
250C2—1782no—
251C2—7122no—
252C2C2×D8×D8911yescharacteristic
subgroupG/H
centerC2C2×D8×D89
commutator, cosocleC8×C89C24
FrattiniC8C23×D89
Fitting#508×C89C2
socleC2×C89C22×D8
hypercenter#508D89
hypocenterC89#3416
LCSG ▷ C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #19152412C2semidirect
2. #19152400C2semidirect
3. #19152040C2semidirect
4. #19152038C2semidirect
5. #19152033C2semidirect
6. #19152032C2semidirect
7. #19152029C2semidirect
8. C2×#15667957C2semidirect
9. SD32×D89C2semidirect
10. #19152014C2semidirect
11. #508×C89C2semidirect
19. #15668031C22semidirect
20. C2×Dic356C22semidirect
21. Q16×D89C22semidirect
25. #15667958C22semidirect
26. #15667957C22semidirect
27. #15667957C22semidirect
28. #15667956C22semidirect
29. #15667955C22semidirect
30. #15667953C22semidirect
31. #15667952C22semidirect
32. #15667951C22semidirect
33. C16×D89C22semidirect
35. #135×C89C22semidirect
36. Q32×C89C22semidirect
37. SD32×C89C22semidirect
38. SD32×C89C22semidirect
39. D16×C89C22semidirect
40. C2×C16×C89C22semidirect
127. C89#3416semidirect
135. #508D89semidirect
148. #135C2×D89semidirect
155. Q32C2×D89semidirect
160. SD32C2×D89semidirect
161. SD32C2×D89semidirect
163. D16C2×D89semidirect
167. C2×C16C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191524122
#191524002
#191520402
#191520382
#191520332
#191520322
#191520292
C2×#156679572
SD32×D892
#191520142
#508×C892
#341689