Finite Group Databasebeta

← C2×#26022563 #36712559

Subgroups — C2×#26022563 #36712559

Order 22784.

502 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 131 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×#19152027C211yesmaximal, characteristic, complemented
2C2×D16×D89C211yesmaximal, characteristic, complemented
3#26022563C218yesmaximal, direct product factor
4C2×#19151437C211yesmaximal, characteristic, complemented
5C2×#19151436C211yesmaximal, characteristic, complemented
6C2×#19151433C211yesmaximal, characteristic, complemented
7C2×#19151431C211yesmaximal, characteristic, complemented
8C2×D32×C89C211yesmaximal, characteristic, complemented
9C2×#15668031—21no—
10C2×D8×D89—21no—
11#19152027—22no—
12#19152027C2214yescomplemented
13C2×Dic712C2211yescharacteristic, complemented
14C2×#15667956—21no—
15C2×D1424C2211yescharacteristic
16C2×#15667953—21no—
17D16×D89—22no—
18D16×D89C2214yescomplemented
19C2×C16×D89C2211yescharacteristic
20#19151437C2214yescomplemented
21#19151436C2214yescomplemented
22#19151433C2214yescomplemented
23#19151431C2214yescomplemented
24C2×#15667918C2211yescharacteristic, complemented
25C2×D16×C89C2211yescharacteristic
26C2×D16×C89C2211yescharacteristic, complemented
27D32×C89C2214yescomplemented
28C2×C32×C89C2211yescharacteristic, complemented
29C2×#13083573—41no—
30C2×D4×D89—41no—
31#15668031—24no—
32#15668031—42no—
33C2×Dic356—21no—
34C2×#13083562—41no—
35C2×D712—21no—
36C2×#13083559—41no—
37D8×D89—24no—
38D8×D89—42no—
39C2×C8×D89D411yescharacteristic
40Dic712—21no—
41Dic712C2312yescomplemented
42#15667956—24no—
43D1424—21no—
44D1424C2312yes—
45#15667953—24no—
46C2×#13083549D411yescharacteristic
47C16×D89D412yes—
48C16×D89C2312yes—
49#15667918C2312yescomplemented
50C2×D8×C89—21no—
51C2×D8×C89—21no—
52D16×C89—21no—
53D16×C89—21no—
54D16×C89C2312yes—
55D16×C89C2312yescomplemented
56C2×C16×C89C2311yescharacteristic
57C32×C89C2312yescomplemented
58C23×D89—81no—
59#13083573—44no—
60#13083573—82no—
61C2×Dic178—41no—
62C2×D356—41no—
63C2×C22⋊D89—81no—
64C2×C22⋊D89—81no—
65D4×D89—44no—
66D4×D89—82no—
67C22×Dic89—81no—
68C2×C4×D89D811yescharacteristic
69Dic356—22no—
70Dic356—41no—
71#13083562—44no—
72D712—22no—
73D712—41no—
74#13083559—44no—
75C2×#10623494D811yescharacteristic
76C8×D89D812yes—
77C8×D89C2×D412yes—
78#13083549C2×D412yes—
79C2×D4×C89—41no—
80C2×D4×C89—41no—
81D8×C89—22no—
82D8×C89—22no—
83D8×C89—41no—
84D8×C89—41no—
85C2×C8×C89C2×D411yescharacteristic
86C16×C89C2×D411yescharacteristic
87C16×C89C2411yescharacteristic
88C23×C89—81no—
89C23×C89—81no—
90C22×D89—81no—
91C22×D89—84no—
92C22×D89—164no—
93C22×D89D1611yescharacteristic
94D4×C89—42no—
95D4×C89—42no—
96D4×C89—81no—
97D4×C89—81no—
98C2×C4×C89C2×D811yescharacteristic
99C22⋊D89—84no—
100C22⋊D89—84no—
101C2×Dic89—81no—
102C2×Dic89—84no—
103C2×Dic89D1611yescharacteristic
104D356—42no—
105D356—81no—
106C4×D89D1612yes—
107C4×D89C2×D812yes—
108Dic178—42no—
109Dic178—81no—
110C8×C89C2×D811yescharacteristic
111C8×C89C22×D411yescharacteristic
112#10623494C2×D812yes—
113C22×C89—82no—
114C22×C89—82no—
115C22×C89—162no—
116C22×C89—162no—
117C22×C89C2×D1611yescharacteristic
118C2×D89—22no—
119C2×D89—82no—
120C2×D89—168no—
121C2×D89—162no—
122C2×D89C2×D1612yes—
123C4×C89C2×D1611yescharacteristic
124C4×C89C22×D811yescharacteristic
125Dic89—82no—
126Dic89C2×D1612yes—
127C2×#2263—891nomaximal, Sylow
128C2×C89—162no—
129C2×C89—162no—
130C2×C89#226312yescomplemented
131C2×C89C22×D1611yescharacteristic
132D89—22no—
133D89—162no—
134C2×#508—891no—
135C22×D16—891no—
136#2263—898no—
137C2×SD64—891no—
138C2×SD64—891no—
139C2×D32—891no—
140C2×D32D8911yescharacteristic, complemented
141C2×M64—891no—
142C89C2×#226311yescharacteristic, complemented, Sylow
143C2×#135—1781no—
144C22×D8—1781no—
145#508—894no—
146#508—1782no—
147C2×Q32—891no—
148C2×SD32—1781no—
149C2×D16—894no—
150C2×D16—891no—
151C2×D16—1782no—
152C2×D16—1781no—
153C2×D16C2×D8911yescharacteristic
154C2×D16C2×D8911yescharacteristic, complemented
155C22×C16—891no—
156SD64—894no—
157SD64—894no—
158D32—894no—
159D32C2×D8914yescomplemented
160M64—894no—
161C2×C32—891no—
162C2×C32C2×D8911yescharacteristic, complemented
163C2×#41—3561no—
164C22×D4—3561no—
165#135—3562no—
166#135—1784no—
167C2×Q16—1781no—
168C2×SD16—3561no—
169C2×D8—21no—
170C2×D8—21no—
171C2×D8—3562no—
172C2×D8—3561no—
173C2×D8—1784no—
174C2×D8—1781no—
175C22×C8—891no—
176Q32—892no—
177Q32—1781no—
178SD32—1784no—
179D16—21no—
180D16—21no—
181D16—892no—
182D16—1784no—
183D16—1781no—
184D16C22×D8912yes—
185D16C22×D8912yescomplemented
186C2×C16—891no—
187C2×C16—892no—
188C2×C16—892no—
189C2×C16C22×D8911yescharacteristic
190C32—892no—
191C32C22×D8912yescomplemented
192C24—7121no—
193#41—3564no—
194#41—7122no—
195C2×Q8—3561no—
196C2×D4—41no—
197C2×D4—41no—
198C2×D4—3564no—
199C2×D4—3561no—
200C2×D4—7122no—
201C2×D4—7121no—
202C2×D4—7121no—
203C22×C4—891no—
204C22×C4—7121no—
205Q16—3561no—
206Q16—1782no—
207SD16—3564no—
208D8—22no—
209D8—22no—
210D8—41no—
211D8—41no—
212D8—3564no—
213D8—3561no—
214D8—1782no—
215C2×C8—891no—
216C2×C8—892no—
217C2×C8—892no—
218C2×C8D4×D8911yescharacteristic
219C16—892no—
220C16D4×D8911yescharacteristic
221C16C23×D8911yescharacteristic
222C23—81no—
223C23—81no—
224C23—891no—
225C23—14244no—
226C23—7124no—
227C23—7121no—
228Q8—3562no—
229Q8—7121no—
230D4—42no—
231D4—42no—
232D4—81no—
233D4—81no—
234D4—3562no—
235D4—7124no—
236D4—7124no—
237D4—7121no—
238C2×C4—891no—
239C2×C4—892no—
240C2×C4—892no—
241C2×C4—7124no—
242C2×C4—7121no—
243C2×C4D8×D8911yescharacteristic
244C8—892no—
245C8D8×D8911yescharacteristic
246C8C2×D4×D8911yescharacteristic
247C22—82no—
248C22—82no—
249C22—162no—
250C22—162no—
251C22—892no—
252C22—14248no—
253C22—14242no—
254C22—1782no—
255C22—7122no—
256C22D16×D8911yescharacteristic
257C4—892no—
258C4—7122no—
259C4D16×D8911yescharacteristic
260C4C2×D8×D8911yescharacteristic
261C2—162no—
262C2—162no—
263C2—14242no—
264C2—1782no—
265C2#2602256312yesdirect product factor
266C2C2×D16×D8911yescharacteristic
subgroupG/H
centerC22D16×D89
commutator, cosocleC16×C89C24
FrattiniC16C23×D89
FittingC2×D32×C89C2
socleC22×C89C2×D16
hypercenterC2×D32D89
hypocenterC89C2×#2263
LCSG ▷ C16×C89 ▷ C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×D32

Complements

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

NH ≅ G/Ntype
1. C2×#19152027C2semidirect
2. C2×D16×D89C2semidirect
3. #26022563C2direct (N × H)
4. C2×#19151437C2semidirect
5. C2×#19151436C2semidirect
6. C2×#19151433C2semidirect
7. C2×#19151431C2semidirect
8. C2×D32×C89C2semidirect
12. #19152027C22semidirect
13. C2×Dic712C22semidirect
18. D16×D89C22semidirect
20. #19151437C22semidirect
21. #19151436C22semidirect
22. #19151433C22semidirect
23. #19151431C22semidirect
24. C2×#15667918C22semidirect
26. C2×D16×C89C22semidirect
27. D32×C89C22semidirect
28. C2×C32×C89C22semidirect
41. Dic712C23semidirect
49. #15667918C23semidirect
55. D16×C89C23semidirect
57. C32×C89C23semidirect
130. C2×C89#2263semidirect
140. C2×D32D89semidirect
142. C89C2×#2263semidirect
154. C2×D16C2×D89semidirect
159. D32C2×D89semidirect
162. C2×C32C2×D89semidirect
185. D16C22×D89semidirect
191. C32C22×D89semidirect
265. C2#26022563direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191520272
C2×D16×D892
#260225632
C2×#191514372
C2×#191514362
C2×#191514332
C2×#191514312
C2×D32×C892
C2×#226389