Finite Group Databasebeta

← #26033397

Subgroups — #26033397

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#19152411C211yesmaximal, characteristic, complemented
2#19152400C211yesmaximal, characteristic, complemented
3#19152040C212yesmaximal, complemented
4#19152036C211yesmaximal, characteristic, complemented
5#19152035C212yesmaximal, complemented
6#19152031C212yesmaximal, complemented
7#19152028C211yesmaximal, characteristic, complemented
8C2×#15667955C211yesmaximal, characteristic, complemented
9SD32×D89C212yesmaximal, complemented
10#19152016C211yesmaximal, characteristic, complemented
11#510×C89C211yesmaximal, characteristic, complemented
12#15668060—21no—
13#15668058—21no—
14#15668044—22no—
15#15668043—21no—
16#15668039—22no—
17#15668037—21no—
18#15668035C2212yes—
19#15668035C2212yescomplemented
20#15668034C2211yescharacteristic, complemented
21Q16×D89C2212yescomplemented
22C2×D712C2211yescharacteristic
23D8×D89C2212yes—
24#15668018C2211yescharacteristic
25#15667958C2211yescharacteristic, complemented
26#15667957C2212yescomplemented
27#15667956C2211yescharacteristic, complemented
28#15667955C2212yescomplemented
29#15667955C2212yescomplemented
30#15667955C2211yescharacteristic, complemented
31D1424C2212yescomplemented
32#15667953C2211yescharacteristic, complemented
33#15667951C2212yescomplemented
34C2×#13083549C2211yescharacteristic, complemented
35C16×D89C2212yescomplemented
36#135×C89C2211yescharacteristic
37C2×Q16×C89C2211yescharacteristic, complemented
38Q32×C89C2212yescomplemented
39SD32×C89C2212yescomplemented
40M32×C89C2211yescharacteristic, complemented
41#13083575—22no—
42#13083575—22no—
43#13083575—41no—
44#13083574—21no—
45#13083574—42no—
46#13083574—41no—
47#13083574D411yescharacteristic
48Q8×D89—22no—
49Q8×D89—41no—
50C2×D356—21no—
51C2×D356—41no—
52D4×D89—22no—
53D4×D89—42no—
54Dic356C2311yescharacteristic
55#13083564—22no—
56#13083563—21no—
57#13083561—22no—
58#13083561—22no—
59D712—21no—
60D712C2312yes—
61D712C2311yescharacteristic
62#13083559—22no—
63#13083558D411yescharacteristic
64#13083557D412yes—
65C8×D89C2312yes—
66#13083549C2311yescharacteristic
67#13083549C2311yescharacteristic
68#41×C89—21no—
69C2×Q8×C89—21no—
70Q16×C89—21no—
71Q16×C89C2312yes—
72Q16×C89C2311yescharacteristic
73SD16×C89—21no—
74D8×C89C2311yescharacteristic
75C2×C8×C89C2311yescharacteristic
76C16×C89C2312yes—
77C22×D89—41no—
78C22×D89—42no—
79Q8×C89—21no—
80Q8×C89—22no—
81Q8×C89—41no—
82D4×C89—21no—
83D4×C89—41no—
84C2×C4×C89—41no—
85C2×C4×C89—41no—
86C2×C4×C89C2×D411yescharacteristic
87C22⋊D89—41no—
88C22⋊D89—42no—
89C22⋊D89D812yes—
90D356—22no—
91D356—21no—
92D356—42no—
93D356—42no—
94D356—41no—
95D356D811yescharacteristic
96C4×D89—42no—
97C4×D89—41no—
98C4×D89—42no—
99C4×D89—42no—
100C4×D89C2×D412yes—
101Dic178—21no—
102Dic178—42no—
103Dic178D811yescharacteristic
104C8×C89C2×D411yescharacteristic
105C8×C89C2411yescharacteristic
106#10623494C2×D412yes—
107C22×C89—41no—
108C22×C89C2×D811yescharacteristic
109C2×D89—41no—
110C2×D89—42no—
111C2×D89—162no—
112C2×D89—161no—
113C2×D89C2×D812yes—
114C4×C89—42no—
115C4×C89—41no—
116C4×C89C2×D811yescharacteristic
117C4×C89C22×D411yescharacteristic
118Dic89—41no—
119Dic89C2×D812yes—
120C2×C89—21no—
121C2×C89—81no—
122C2×C89C22×D811yescharacteristic
123D89—22no—
124D89—81no—
125D89—82no—
126#3416—891nomaximal, Sylow
127C89#341611yescharacteristic, complemented, Sylow
128#578—891no—
129#576—891no—
130#510—892no—
131#510D8911yescharacteristic, complemented
132#509—892no—
133#509—891no—
134#508—891no—
135#508—892no—
136C2×SD32—891no—
137C2×SD32—892no—
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#135—891no—
148#135C2×D8911yescharacteristic
149C2×Q16—892no—
150C2×Q16C2×D8911yescharacteristic, complemented
151C2×D8—892no—
152C2×D8—891no—
153#131—891no—
154Q32—891no—
155Q32C2×D8912yescomplemented
156SD32—892no—
157SD32—892no—
158SD32—891no—
159SD32—891no—
160SD32—892no—
161SD32C2×D8912yescomplemented
162D16—891no—
163D16—892no—
164M32—892no—
165M32C2×D8911yescharacteristic, complemented
166C2×C16—891no—
167C2×C16—892no—
168#41—21no—
169#41—891no—
170#41—3562no—
171#41—3561no—
172#41—3561no—
173#41—1782no—
174#41—1782no—
175#41—1781no—
176C2×Q8—21no—
177C2×Q8—3561no—
178C2×Q8—1782no—
179C2×D4—3561no—
180C2×D4—3562no—
181C2×D4—1782no—
182C2×D4—1781no—
183Q16—21no—
184Q16—891no—
185Q16—1782no—
186Q16C22×D8912yes—
187Q16C22×D8911yescharacteristic
188SD16—21no—
189SD16—1782no—
190SD16—1782no—
191SD16—1781no—
192D8—891no—
193D8—892no—
194D8—1782no—
195D8—1781no—
196D8C22×D8911yescharacteristic
197M16—891no—
198M16—892no—
199C2×C8—892no—
200C2×C8C22×D8911yescharacteristic
201C16—891no—
202C16—891no—
203C16C22×D8912yes—
204C23—3562no—
205C23—3561no—
206Q8—21no—
207Q8—22no—
208Q8—41no—
209Q8—891no—
210Q8—3562no—
211Q8—1781no—
212D4—21no—
213D4—41no—
214D4—892no—
215D4—891no—
216D4—3562no—
217D4—3562no—
218D4—3562no—
219D4—3561no—
220D4—3561no—
221D4—1782no—
222D4—1781no—
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—892no—
236C22—3561no—
237C22—3562no—
238C22—14241no—
239C22—14242no—
240C22D8×D8911yescharacteristic
241C4—41no—
242C4—42no—
243C4—892no—
244C4—3561no—
245C4D8×D8911yescharacteristic
246C4C2×D4×D8911yescharacteristic
247C2—21no—
248C2—81no—
249C2—1782no—
250C2—7121no—
251C2—7122no—
252C2C2×D8×D8911yescharacteristic
subgroupG/H
centerC2C2×D8×D89
commutator, cosocleC8×C89C24
FrattiniC8C23×D89
Fitting#510×C89C2
socleC2×C89C22×D8
hypercenter#510D89
hypocenterC89#3416
LCSG ▷ C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
1. #19152411C2semidirect
2. #19152400C2semidirect
3. #19152040C2semidirect
4. #19152036C2semidirect
5. #19152035C2semidirect
6. #19152031C2semidirect
7. #19152028C2semidirect
8. C2×#15667955C2semidirect
9. SD32×D89C2semidirect
10. #19152016C2semidirect
11. #510×C89C2semidirect
19. #15668035C22semidirect
20. #15668034C22semidirect
21. Q16×D89C22semidirect
25. #15667958C22semidirect
26. #15667957C22semidirect
27. #15667956C22semidirect
28. #15667955C22semidirect
29. #15667955C22semidirect
30. #15667955C22semidirect
31. D1424C22semidirect
32. #15667953C22semidirect
33. #15667951C22semidirect
34. C2×#13083549C22semidirect
35. C16×D89C22semidirect
37. C2×Q16×C89C22semidirect
38. Q32×C89C22semidirect
39. SD32×C89C22semidirect
40. M32×C89C22semidirect
127. C89#3416semidirect
131. #510D89semidirect
150. C2×Q16C2×D89semidirect
155. Q32C2×D89semidirect
161. SD32C2×D89semidirect
165. M32C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191524112
#191524002
#191520402
#191520362
#191520352
#191520312
#191520282
C2×#156679552
SD32×D892
#191520162
#510×C892
#341689