Finite Group Databasebeta

← #509×D89 #26033372

Subgroups — #509×D89 #26033372

Order 11392.

400 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 115 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#135×D89C211yesmaximal, characteristic, complemented
2C2×D8×D89C211yesmaximal, characteristic, complemented
3#19152036C211yesmaximal, characteristic, complemented
4#19152035C212yesmaximal, complemented
5#19152034C211yesmaximal, characteristic, complemented
6#19152033C211yesmaximal, characteristic, complemented
7#19152032C212yesmaximal, complemented
8SD32×D89C212yesmaximal, complemented
9D16×D89C212yesmaximal, complemented
10M32×D89C211yesmaximal, characteristic, complemented
11#509×C89C211yesmaximal, characteristic, complemented
12#41×D89—21no—
13C2×D4×D89—21no—
14#15668035C2211yescharacteristic, complemented
15#15668034C2211yescharacteristic, complemented
16#15668033—21no—
17#15668032—21no—
18#15668031C2211yescharacteristic, complemented
19Q16×D89C2211yescharacteristic, complemented
20SD16×D89—21no—
21C2×D712C2211yescharacteristic, complemented
22C2×#13083559—21no—
23D8×D89—21no—
24D8×D89—21no—
25D8×D89C2212yes—
26D8×D89C2212yescomplemented
27D8×D89C2211yescharacteristic, complemented
28C2×C8×D89C2211yescharacteristic
29#15667957C2212yescomplemented
30#15667956C2212yescomplemented
31#15667955C2212yescomplemented
32D1424C2212yescomplemented
33#15667953C2212yescomplemented
34#15667953C2212yescomplemented
35#15667952C2211yescharacteristic, complemented
36#15667951C2212yescomplemented
37C16×D89C2212yescomplemented
38#135×C89C2211yescharacteristic, complemented
39C2×D8×C89C2211yescharacteristic, complemented
40SD32×C89C2212yescomplemented
41D16×C89C2212yescomplemented
42M32×C89C2211yescharacteristic, complemented
43C23×D89—41no—
44#13083575—21no—
45#13083574—21no—
46#13083574—41no—
47#13083573—21no—
48#13083573—41no—
49Q8×D89—21no—
50C2×D356—21no—
51C2×C22⋊D89—41no—
52D4×D89—22no—
53D4×D89—22no—
54D4×D89—21no—
55D4×D89—41no—
56D4×D89—41no—
57D4×D89—41no—
58C2×C4×D89—41no—
59C2×C4×D89D411yescharacteristic
60Dic356C2311yescharacteristic, complemented
61#13083564—21no—
62#13083563—21no—
63#13083562—21no—
64#13083561—21no—
65D712—21no—
66D712C2312yes—
67D712C2311yescharacteristic, complemented
68#13083559—22no—
69#13083559—22no—
70#13083559—21no—
71C2×#10623494D411yescharacteristic
72C8×D89D411yescharacteristic
73C8×D89D411yescharacteristic
74C8×D89C2311yescharacteristic
75C8×D89C2311yescharacteristic
76#13083549C2312yescomplemented
77#41×C89—21no—
78C2×D4×C89—21no—
79Q16×C89C2311yescharacteristic, complemented
80SD16×C89—21no—
81D8×C89—21no—
82D8×C89C2312yes—
83D8×C89C2311yescharacteristic, complemented
84C2×C8×C89C2311yescharacteristic
85C16×C89C2312yescomplemented
86C23×C89—41no—
87C22×D89—41no—
88C22×D89—41no—
89C22×D89—42no—
90C22×D89—42no—
91C22×D89—84no—
92C22×D89D811yescharacteristic
93Q8×C89—21no—
94D4×C89—22no—
95D4×C89—21no—
96D4×C89—41no—
97D4×C89—41no—
98C2×C4×C89—41no—
99C2×C4×C89C2×D411yescharacteristic
100C22⋊D89—41no—
101C22⋊D89—41no—
102C22⋊D89—42no—
103C22⋊D89—42no—
104C22⋊D89—41no—
105C2×Dic89—41no—
106C2×Dic89D811yescharacteristic
107D356—22no—
108D356—21no—
109D356—41no—
110D356—41no—
111C4×D89—41no—
112C4×D89—41no—
113C4×D89—41no—
114C4×D89D811yescharacteristic
115C4×D89D811yescharacteristic
116C4×D89C2×D411yescharacteristic
117C4×D89C2×D411yescharacteristic
118Dic178—21no—
119Dic178—41no—
120C8×C89C2×D411yescharacteristic
121C8×C89C2411yescharacteristic
122#10623494C2×D411yescharacteristic
123#10623494C2×D411yescharacteristic
124C22×C89—41no—
125C22×C89—42no—
126C22×C89—82no—
127C22×C89C2×D811yescharacteristic
128C2×D89—22no—
129C2×D89—41no—
130C2×D89—42no—
131C2×D89—84no—
132C2×D89—82no—
133C2×D89—82no—
134C2×D89—84no—
135C2×D89C2×D811yescharacteristic
136C2×D89C2×D811yescharacteristic
137C4×C89—41no—
138C4×C89C2×D811yescharacteristic
139C4×C89C22×D411yescharacteristic
140Dic89—41no—
141Dic89C2×D811yescharacteristic
142Dic89C2×D811yescharacteristic
143C2×C89—21no—
144C2×C89—82no—
145C2×C89—81no—
146C2×C89C22×D811yescharacteristic
147D89—21no—
148D89—81no—
149D89—82no—
150D89#50912yesdirect product factor
151C2×#509—891nomaximal, Sylow
152C89C2×#50911yescharacteristic, complemented, Sylow
153C2×#135—891no—
154C22×D8—891no—
155#509—891no—
156#509—891no—
157#509—892no—
158#509—892no—
159#509—891no—
160#509D8911yescharacteristic, direct product factor
161C2×SD32—892no—
162C2×D16—892no—
163C2×M32—891no—
164C2×#41—1781no—
165C22×D4—1781no—
166#135—891no—
167#135—891no—
168#135—891no—
169#135—1781no—
170#135—1781no—
171#135C2×D8911yescharacteristic, complemented
172C2×Q16—891no—
173C2×SD16—1781no—
174C2×D8—892no—
175C2×D8—892no—
176C2×D8—891no—
177C2×D8—891no—
178C2×D8—1781no—
179C2×D8—1781no—
180C2×D8—1781no—
181C2×D8C2×D8911yescharacteristic, complemented
182C22×C8—891no—
183SD32—892no—
184SD32—892no—
185SD32—892no—
186SD32C2×D8912yescomplemented
187D16—892no—
188D16—892no—
189D16—892no—
190D16C2×D8912yescomplemented
191M32—891no—
192M32—892no—
193M32C2×D8911yescharacteristic, complemented
194C2×C16—892no—
195C24—3561no—
196#41—21no—
197#41—3561no—
198#41—3561no—
199#41—1781no—
200#41—1781no—
201#41—1781no—
202C2×Q8—1781no—
203C2×D4—21no—
204C2×D4—3561no—
205C2×D4—3561no—
206C2×D4—3561no—
207C2×D4—3561no—
208C2×D4—1782no—
209C2×D4—1782no—
210C2×D4—1781no—
211C2×D4—1781no—
212C22×C4—891no—
213C22×C4—3561no—
214Q16—891no—
215Q16—1781no—
216Q16C22×D8911yescharacteristic, complemented
217SD16—21no—
218SD16—1781no—
219SD16—1781no—
220SD16—1781no—
221D8—21no—
222D8—891no—
223D8—892no—
224D8—1782no—
225D8—1782no—
226D8—1781no—
227D8—1781no—
228D8C22×D8912yes—
229D8C22×D8911yescharacteristic, complemented
230C2×C8—891no—
231C2×C8—891no—
232C2×C8—891no—
233C2×C8—891no—
234C2×C8—891no—
235C2×C8C22×D8911yescharacteristic
236C16—892no—
237C16C22×D8912yescomplemented
238C23—41no—
239C23—891no—
240C23—3561no—
241C23—3562no—
242C23—3562no—
243C23—3561no—
244C23—7124no—
245Q8—21no—
246Q8—3561no—
247Q8—1781no—
248D4—22no—
249D4—21no—
250D4—41no—
251D4—41no—
252D4—3561no—
253D4—3562no—
254D4—3562no—
255D4—3561no—
256D4—3561no—
257D4—3561no—
258D4—3561no—
259D4—1782no—
260D4—1781no—
261C2×C4—41no—
262C2×C4—891no—
263C2×C4—891no—
264C2×C4—891no—
265C2×C4—891no—
266C2×C4—891no—
267C2×C4—3561no—
268C2×C4—3561no—
269C2×C4—3561no—
270C2×C4—3561no—
271C2×C4D4×D8911yescharacteristic
272C8—891no—
273C8—891no—
274C8D4×D8911yescharacteristic
275C8C23×D8911yescharacteristic
276C22—41no—
277C22—42no—
278C22—82no—
279C22—891no—
280C22—891no—
281C22—3561no—
282C22—3562no—
283C22—1782no—
284C22—7122no—
285C22—7124no—
286C22—7122no—
287C22—7124no—
288C22D8×D8911yescharacteristic
289C4—41no—
290C4—891no—
291C4—891no—
292C4—3561no—
293C4D8×D8911yescharacteristic
294C4C2×D4×D8911yescharacteristic
295C2—21no—
296C2—82no—
297C2—81no—
298C2—892no—
299C2—1781no—
300C2—7121no—
301C2—7122no—
302C2C2×D8×D8911yescharacteristic
subgroupG/H
centerC2C2×D8×D89
commutator, cosocleC8×C89C24
FrattiniC8C23×D89
Fitting#509×C89C2
socleC2×C89C22×D8
hypercenter#509D89
hypocenterC89C2×#509
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. #135×D89C2semidirect
2. C2×D8×D89C2semidirect
3. #19152036C2semidirect
4. #19152035C2semidirect
5. #19152034C2semidirect
6. #19152033C2semidirect
7. #19152032C2semidirect
8. SD32×D89C2semidirect
9. D16×D89C2semidirect
10. M32×D89C2semidirect
11. #509×C89C2semidirect
14. #15668035C22semidirect
15. #15668034C22semidirect
18. #15668031C22semidirect
19. Q16×D89C22semidirect
21. C2×D712C22semidirect
26. D8×D89C22semidirect
27. D8×D89C22semidirect
29. #15667957C22semidirect
30. #15667956C22semidirect
31. #15667955C22semidirect
32. D1424C22semidirect
33. #15667953C22semidirect
34. #15667953C22semidirect
35. #15667952C22semidirect
36. #15667951C22semidirect
37. C16×D89C22semidirect
38. #135×C89C22semidirect
39. C2×D8×C89C22semidirect
40. SD32×C89C22semidirect
41. D16×C89C22semidirect
42. M32×C89C22semidirect
60. Dic356C23semidirect
67. D712C23semidirect
76. #13083549C23semidirect
79. Q16×C89C23semidirect
83. D8×C89C23semidirect
85. C16×C89C23semidirect
150. D89#509direct (N × H)
152. C89C2×#509semidirect
160. #509D89direct (N × H)
171. #135C2×D89semidirect
181. C2×D8C2×D89semidirect
186. SD32C2×D89semidirect
190. D16C2×D89semidirect
193. M32C2×D89semidirect
216. Q16C22×D89semidirect
229. D8C22×D89semidirect
237. C16C22×D89semidirect

Maximal subgroups

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

subgroupindex
#135×D892
C2×D8×D892
#191520362
#191520352
#191520342
#191520332
#191520322
SD32×D892
D16×D892
M32×D892
#509×C892
C2×#50989