Finite Group Databasebeta

← #26033394

Subgroups — #26033394

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#19152399C211yesmaximal, characteristic, complemented
3#19152039C211yesmaximal, characteristic, complemented
4#19152037C212yesmaximal, complemented
5#19152035C212yesmaximal, complemented
6#19152034C211yesmaximal, characteristic, complemented
7#19152030C211yesmaximal, characteristic, complemented
8#19152029C212yesmaximal, complemented
9SD32×D89C212yesmaximal, complemented
10#19152014C211yesmaximal, characteristic, complemented
11C2×SD32×C89C211yesmaximal, characteristic, complemented
12#15668060—21no—
13#15668057—21no—
14#15668044—22no—
15#15668043—21no—
16#15668038—21no—
17#15668036—22no—
18#15668035C2212yescomplemented
19#15668034C2211yescharacteristic
20#15668034C2211yescharacteristic, complemented
21#15668031C2212yes—
22Q16×D89C2212yescomplemented
23D8×D89C2212yes—
24#15668018C2211yescharacteristic
25Dic712C2211yescharacteristic, complemented
26#15667958C2212yescomplemented
27#15667957C2211yescharacteristic, complemented
28#15667957C2211yescharacteristic, complemented
29#15667956C2212yescomplemented
30#15667955C2212yescomplemented
31D1424C2211yescharacteristic, complemented
32#15667953C2212yescomplemented
33#15667952C2211yescharacteristic, complemented
34#15667951C2212yescomplemented
35C16×D89C2212yescomplemented
36C2×Q16×C89C2211yescharacteristic, complemented
37C2×D8×C89C2211yescharacteristic
38SD32×C89C2212yescomplemented
39SD32×C89C2212yescomplemented
40C2×C16×C89C2211yescharacteristic, complemented
41#13083575—22no—
42#13083575—41no—
43#13083574—21no—
44#13083574—21no—
45#13083574—42no—
46#13083574D411yescharacteristic
47#13083573—22no—
48#13083573—41no—
49Q8×D89—22no—
50Q8×D89—41no—
51C2×C22⋊D89—42no—
52D4×D89—22no—
53D4×D89—41no—
54Dic356C2311yescharacteristic
55Dic356C2311yescharacteristic
56#13083564—22no—
57#13083563—21no—
58#13083563—21no—
59#13083562—22no—
60#13083561—22no—
61D712C2311yescharacteristic
62D712C2311yescharacteristic
63#13083559—22no—
64#13083558D411yescharacteristic
65#13083557D412yes—
66C8×D89C2312yes—
67#13083549C2312yes—
68C2×Q8×C89—21no—
69C2×D4×C89—21no—
70Q16×C89—21no—
71Q16×C89C2312yes—
72D8×C89—21no—
73D8×C89C2312yes—
74C2×C8×C89C2311yescharacteristic
75C16×C89C2311yescharacteristic
76C16×C89C2311yescharacteristic
77C23×C89—41no—
78C22×D89—42no—
79Q8×C89—22no—
80Q8×C89—41no—
81D4×C89—22no—
82D4×C89—41no—
83C2×C4×C89—41no—
84C2×C4×C89C2×D411yescharacteristic
85C22⋊D89—41no—
86C22⋊D89—41no—
87C22⋊D89—42no—
88C22⋊D89—42no—
89C22⋊D89D812yes—
90C2×Dic89—42no—
91D356—21no—
92D356—21no—
93D356—42no—
94D356D811yescharacteristic
95C4×D89—42no—
96C4×D89—41no—
97C4×D89—41no—
98C4×D89—42no—
99C4×D89C2×D412yes—
100Dic178—21no—
101Dic178—21no—
102Dic178—42no—
103Dic178D811yescharacteristic
104C8×C89C2×D411yescharacteristic
105C8×C89C2411yescharacteristic
106#10623494C2×D412yes—
107C22×C89—42no—
108C22×C89—161no—
109C22×C89C2×D811yescharacteristic
110C2×D89—41no—
111C2×D89—41no—
112C2×D89—162no—
113C2×D89C2×D812yes—
114C4×C89—42no—
115C4×C89C2×D811yescharacteristic
116C4×C89C22×D411yescharacteristic
117Dic89—41no—
118Dic89—41no—
119Dic89C2×D812yes—
120C2×C89—21no—
121C2×C89—82no—
122C2×C89C22×D811yescharacteristic
123D89—22no—
124D89—81no—
125D89—81no—
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#508—891no—
136C2×SD32—892no—
137C2×SD32D8911yescharacteristic, complemented
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#135—891no—
149C2×Q16—892no—
150C2×Q16C2×D8911yescharacteristic, complemented
151C2×D8—892no—
152C2×D8C2×D8911yescharacteristic
153#131—891no—
154Q32—892no—
155Q32—891no—
156SD32—892no—
157SD32—892no—
158SD32—891no—
159SD32—891no—
160SD32C2×D8912yescomplemented
161SD32C2×D8912yescomplemented
162D16—892no—
163D16—891no—
164M32—891no—
165M32—892no—
166C2×C16—892no—
167C2×C16C2×D8911yescharacteristic, complemented
168#41—891no—
169#41—3562no—
170#41—3561no—
171#41—3561no—
172#41—1782no—
173#41—1782no—
174#41—1781no—
175#41—1781no—
176C2×Q8—21no—
177C2×Q8—3561no—
178C2×Q8—1782no—
179C2×D4—21no—
180C2×D4—3561no—
181C2×D4—3562no—
182C2×D4—1782no—
183Q16—21no—
184Q16—891no—
185Q16—891no—
186Q16—1782no—
187Q16C22×D8912yes—
188SD16—1782no—
189SD16—1782no—
190SD16—1781no—
191SD16—1781no—
192D8—21no—
193D8—891no—
194D8—891no—
195D8—1782no—
196D8C22×D8912yes—
197M16—891no—
198M16—892no—
199C2×C8—892no—
200C2×C8C22×D8911yescharacteristic
201C16—892no—
202C16C22×D8911yescharacteristic
203C16C22×D8911yescharacteristic
204C23—41no—
205C23—3562no—
206Q8—22no—
207Q8—41no—
208Q8—891no—
209Q8—3562no—
210Q8—1781no—
211Q8—1781no—
212D4—22no—
213D4—41no—
214D4—892no—
215D4—891no—
216D4—3562no—
217D4—3562no—
218D4—3562no—
219D4—3561no—
220D4—3561no—
221D4—1781no—
222D4—1781no—
223C2×C4—41no—
224C2×C4—892no—
225C2×C4—3562no—
226C2×C4—3562no—
227C2×C4—3562no—
228C2×C4—3561no—
229C2×C4—3561no—
230C2×C4D4×D8911yescharacteristic
231C8—892no—
232C8D4×D8911yescharacteristic
233C8C23×D8911yescharacteristic
234C22—42no—
235C22—161no—
236C22—892no—
237C22—3561no—
238C22—3561no—
239C22—14242no—
240C22D8×D8911yescharacteristic
241C4—42no—
242C4—892no—
243C4—3561no—
244C4—3561no—
245C4D8×D8911yescharacteristic
246C4C2×D4×D8911yescharacteristic
247C2—21no—
248C2—82no—
249C2—1782no—
250C2—7121no—
251C2—7121no—
252C2C2×D8×D8911yescharacteristic
subgroupG/H
centerC2C2×D8×D89
commutator, cosocleC8×C89C24
FrattiniC8C23×D89
FittingC2×SD32×C89C2
socleC2×C89C22×D8
hypercenterC2×SD32D89
hypocenterC89#3416
LCSG ▷ C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #19152411C2semidirect
2. #19152399C2semidirect
3. #19152039C2semidirect
4. #19152037C2semidirect
5. #19152035C2semidirect
6. #19152034C2semidirect
7. #19152030C2semidirect
8. #19152029C2semidirect
9. SD32×D89C2semidirect
10. #19152014C2semidirect
11. C2×SD32×C89C2semidirect
18. #15668035C22semidirect
20. #15668034C22semidirect
22. Q16×D89C22semidirect
25. Dic712C22semidirect
26. #15667958C22semidirect
27. #15667957C22semidirect
28. #15667957C22semidirect
29. #15667956C22semidirect
30. #15667955C22semidirect
31. D1424C22semidirect
32. #15667953C22semidirect
33. #15667952C22semidirect
34. #15667951C22semidirect
35. C16×D89C22semidirect
36. C2×Q16×C89C22semidirect
38. SD32×C89C22semidirect
39. SD32×C89C22semidirect
40. C2×C16×C89C22semidirect
127. C89#3416semidirect
137. C2×SD32D89semidirect
150. C2×Q16C2×D89semidirect
160. SD32C2×D89semidirect
161. SD32C2×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
#191524112
#191523992
#191520392
#191520372
#191520352
#191520342
#191520302
#191520292
SD32×D892
#191520142
C2×SD32×C892
#341689