Finite Group Databasebeta

← C2×SD64×D89 #36712545

Subgroups — C2×SD64×D89 #36712545

Order 22784.

502 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C2×Q32×D89C211yesmaximal, characteristic, complemented
2C2×D16×D89C211yesmaximal, characteristic
3C2×#19151437C211yesmaximal, characteristic, complemented
4C2×#19151436C211yesmaximal, characteristic, complemented
5C2×#19151435C211yesmaximal, characteristic, complemented
6SD64×D89C218yesmaximal, direct product factor
7C2×C32×D89C211yesmaximal, characteristic, complemented
8C2×SD64×C89C211yesmaximal, characteristic, complemented
9C2×Q16×D89—21no—
10C2×D8×D89—21no—
11C2×Dic712C2211yescharacteristic, complemented
12C2×#15667958—21no—
13Q32×D89—22no—
14Q32×D89C2214yescomplemented
15C2×D1424C2211yescharacteristic
16C2×#15667953—21no—
17D16×D89—22no—
18D16×D89C2214yes—
19C2×C16×D89C2211yescharacteristic
20#19151437C2214yescomplemented
21#19151436C2214yescomplemented
22#19151435C2214yescomplemented
23C2×#15667918C2211yescharacteristic, complemented
24C32×D89C2214yescomplemented
25C2×Q32×C89C2211yescharacteristic, complemented
26C2×D16×C89C2211yescharacteristic
27SD64×C89C2214yescomplemented
28C2×C32×C89C2211yescharacteristic, complemented
29C2×Q8×D89—41no—
30C2×D4×D89—41no—
31C2×Dic356—21no—
32C2×#13083564—41no—
33Q16×D89—24no—
34Q16×D89—42no—
35C2×D712—21no—
36C2×#13083559—41no—
37D8×D89—24no—
38D8×D89—42no—
39C2×C8×D89D411yescharacteristic
40Dic712—21no—
41Dic712C2312yescomplemented
42#15667958—24no—
43D1424—21no—
44D1424C2312yes—
45#15667953—24no—
46C2×#13083549D411yescharacteristic
47C16×D89D412yes—
48C16×D89C2312yes—
49#15667918C2312yescomplemented
50C2×Q16×C89—21no—
51C2×D8×C89—21no—
52Q32×C89—21no—
53Q32×C89C2312yescomplemented
54D16×C89—21no—
55D16×C89C2312yes—
56C2×C16×C89C2311yescharacteristic
57C32×C89C2312yescomplemented
58C23×D89—81no—
59C2×Dic178—41no—
60C2×Dic178—81no—
61Q8×D89—44no—
62Q8×D89—82no—
63C2×D356—41no—
64C2×C22⋊D89—81no—
65D4×D89—44no—
66D4×D89—82no—
67C2×C4×D89—81no—
68C2×C4×D89D811yescharacteristic
69Dic356—22no—
70Dic356—41no—
71#13083564—44no—
72D712—22no—
73D712—41no—
74#13083559—44no—
75C2×#10623494D811yescharacteristic
76C8×D89D812yes—
77C8×D89C2×D412yes—
78#13083549C2×D412yes—
79C2×Q8×C89—41no—
80C2×D4×C89—41no—
81Q16×C89—22no—
82Q16×C89—41no—
83D8×C89—22no—
84D8×C89—41no—
85C2×C8×C89C2×D411yescharacteristic
86C16×C89C2×D411yescharacteristic
87C16×C89C2411yescharacteristic
88C23×C89—81no—
89C22×D89—81no—
90C22×D89—84no—
91C22×D89—164no—
92C22×D89D1611yescharacteristic
93Q8×C89—42no—
94Q8×C89—81no—
95D4×C89—42no—
96D4×C89—81no—
97C2×C4×C89—81no—
98C2×C4×C89C2×D811yescharacteristic
99C22⋊D89—84no—
100C2×Dic89—81no—
101C2×Dic89D1611yescharacteristic
102D356—42no—
103D356—81no—
104C4×D89—84no—
105C4×D89D1612yes—
106C4×D89C2×D812yes—
107Dic178—42no—
108Dic178—81no—
109Dic178—84no—
110C8×C89C2×D811yescharacteristic
111C8×C89C22×D411yescharacteristic
112#10623494C2×D812yes—
113C22×C89—82no—
114C22×C89—162no—
115C22×C89C2×D1611yescharacteristic
116C2×D89—82no—
117C2×D89—162no—
118C2×D89—168no—
119C2×D89SD6414yesdirect product factor
120C2×D89C2×D1612yes—
121C4×C89—82no—
122C4×C89C2×D1611yescharacteristic
123C4×C89C22×D811yescharacteristic
124Dic89—82no—
125Dic89C2×D1612yes—
126C22×SD64—891nomaximal, Sylow
127C2×C89—162no—
128C2×C89C2×SD6412yescomplemented
129C2×C89C22×D1611yescharacteristic
130D89—162no—
131D89C2×SD6414yesdirect product factor
132C22×Q32—891no—
133C22×D16—891no—
134C2×SD64—891no—
135C2×SD64—891no—
136C2×SD64—898no—
137C2×SD64—891no—
138C2×SD64D8911yescharacteristic, direct product factor
139C22×C32—891no—
140C89C22×SD6411yescharacteristic, complemented, Sylow
141C22×Q16—1781no—
142C22×D8—1781no—
143C2×Q32—894no—
144C2×Q32—891no—
145C2×Q32—1782no—
146C2×Q32—1781no—
147C2×Q32C2×D8911yescharacteristic, complemented
148C2×D16—894no—
149C2×D16—891no—
150C2×D16—1782no—
151C2×D16—1781no—
152C2×D16C2×D8911yescharacteristic
153C22×C16—891no—
154SD64—894no—
155SD64—894no—
156SD64—894no—
157SD64C2×D8914yesdirect product factor
158C2×C32—891no—
159C2×C32—894no—
160C2×C32C2×D8911yescharacteristic, complemented
161C22×Q8—3561no—
162C22×D4—3561no—
163C2×Q16—21no—
164C2×Q16—3562no—
165C2×Q16—3561no—
166C2×Q16—1784no—
167C2×Q16—1781no—
168C2×D8—21no—
169C2×D8—3562no—
170C2×D8—3561no—
171C2×D8—1784no—
172C2×D8—1781no—
173C22×C8—891no—
174Q32—21no—
175Q32—892no—
176Q32—1784no—
177Q32—1781no—
178Q32C22×D8912yescomplemented
179D16—21no—
180D16—892no—
181D16—1784no—
182D16—1781no—
183D16C22×D8912yes—
184C2×C16—891no—
185C2×C16—892no—
186C2×C16—892no—
187C2×C16C22×D8911yescharacteristic
188C32—892no—
189C32C22×D8912yescomplemented
190C24—7121no—
191C2×Q8—41no—
192C2×Q8—3564no—
193C2×Q8—3561no—
194C2×Q8—7121no—
195C2×Q8—7122no—
196C2×D4—41no—
197C2×D4—3564no—
198C2×D4—3561no—
199C2×D4—7122no—
200C2×D4—7121no—
201C22×C4—891no—
202C22×C4—7121no—
203Q16—22no—
204Q16—41no—
205Q16—3564no—
206Q16—3561no—
207Q16—1782no—
208D8—22no—
209D8—41no—
210D8—3564no—
211D8—3561no—
212D8—1782no—
213C2×C8—891no—
214C2×C8—892no—
215C2×C8—892no—
216C2×C8D4×D8911yescharacteristic
217C16—892no—
218C16D4×D8911yescharacteristic
219C16C23×D8911yescharacteristic
220C23—81no—
221C23—891no—
222C23—14244no—
223C23—7124no—
224C23—7121no—
225Q8—42no—
226Q8—81no—
227Q8—3562no—
228Q8—7124no—
229Q8—7121no—
230D4—42no—
231D4—81no—
232D4—3562no—
233D4—7124no—
234D4—7121no—
235C2×C4—81no—
236C2×C4—891no—
237C2×C4—892no—
238C2×C4—892no—
239C2×C4—7124no—
240C2×C4—7121no—
241C2×C4D8×D8911yescharacteristic
242C8—892no—
243C8D8×D8911yescharacteristic
244C8C2×D4×D8911yescharacteristic
245C22—82no—
246C22—162no—
247C22—894no—
248C22—892no—
249C22—14248no—
250C22—14242no—
251C22—7122no—
252C22D16×D8911yescharacteristic
253C4—82no—
254C4—892no—
255C4—7122no—
256C4D16×D8911yescharacteristic
257C4C2×D8×D8911yescharacteristic
258C2—162no—
259C2—894no—
260C2—14242no—
261C2SD64×D8912yesdirect product factor
262C2C2×D16×D8911yescharacteristic
subgroupG/H
centerC22D16×D89
commutator, cosocleC16×C89C24
FrattiniC16C23×D89
FittingC2×SD64×C89C2
socleC22×C89C2×D16
prime radicalC2×D16×D89C2
hypercenterC2×SD64D89
hypocenterC89C22×SD64
LCSG ▷ C16×C89 ▷ C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×SD64

Complements

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

NH ≅ G/Ntype
1. C2×Q32×D89C2semidirect
3. C2×#19151437C2semidirect
4. C2×#19151436C2semidirect
5. C2×#19151435C2semidirect
6. SD64×D89C2direct (N × H)
7. C2×C32×D89C2semidirect
8. C2×SD64×C89C2semidirect
11. C2×Dic712C22semidirect
14. Q32×D89C22semidirect
20. #19151437C22semidirect
21. #19151436C22semidirect
22. #19151435C22semidirect
23. C2×#15667918C22semidirect
24. C32×D89C22semidirect
25. C2×Q32×C89C22semidirect
27. SD64×C89C22semidirect
28. C2×C32×C89C22semidirect
41. Dic712C23semidirect
49. #15667918C23semidirect
53. Q32×C89C23semidirect
57. C32×C89C23semidirect
119. C2×D89SD64direct (N × H)
128. C2×C89C2×SD64semidirect
131. D89C2×SD64direct (N × H)
138. C2×SD64D89direct (N × H)
140. C89C22×SD64semidirect
147. C2×Q32C2×D89semidirect
157. SD64C2×D89direct (N × H)
160. C2×C32C2×D89semidirect
178. Q32C22×D89semidirect
189. C32C22×D89semidirect
261. C2SD64×D89direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q32×D892
C2×D16×D892
C2×#191514372
C2×#191514362
C2×#191514352
SD64×D892
C2×C32×D892
C2×SD64×C892
C22×SD6489