Finite Group Databasebeta

← #26031931

Subgroups — #26031931

Order 11392.

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

normal subgroups only

This group has 526 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×D8×D89C211yesmaximal, characteristic, complemented
2#19152236C212yesmaximal, complemented
3#19151983C211yesmaximal, characteristic, complemented
4#19151836C211yesmaximal, characteristic, complemented
5#19151834C211yesmaximal, characteristic, complemented
6#19151815C212yesmaximal, complemented
7#19151747C212yesmaximal, complemented
8#19151743C212yesmaximal, complemented
9D8×Dic89C211yesmaximal, characteristic, complemented
10C8×C22⋊D89C211yesmaximal, characteristic, complemented
11C2×#135×C89C211yesmaximal, characteristic, complemented
12C2×D4×D89C2212yes—
13C2×#13083561C2212yescomplemented
14C2×D712C2211yescharacteristic
15C2×#13083559C2212yes—
16D8×D89—24no—
17C2×C8×D89C2211yescharacteristic
18#15668001C2212yescomplemented
19#15667995—22no—
20#15667988C2212yes—
21#15667986C2212yescomplemented
22#15667984—22no—
23#15667980—22no—
24D4×Dic89C2212yescomplemented
25C4×C22⋊D89C2211yescharacteristic
26C2×#13083551—22no—
27#15667946C2211yescharacteristic, complemented
28#15667941C2211yescharacteristic, complemented
29#15667936C2212yescomplemented
30#15667934C2212yescomplemented
31#15667933C2212yescomplemented
32C22⋊#10623494C2211yescharacteristic, complemented
33#15667924C2211yescharacteristic
34C8×Dic89C2211yescharacteristic, complemented
35C2×#41×C89C2212yescomplemented
36#135×C89—24no—
37C2×Q16×C89C2211yescharacteristic, complemented
38C2×SD16×C89C2212yescomplemented
39C2×D8×C89C2211yescharacteristic
40C22×C8×C89C2211yescharacteristic, complemented
41C23×D89—22no—
42C2×D356C2312yes—
43C2×C22⋊D89—22no—
44C2×C22⋊D89—22no—
45C2×C22⋊D89D411yescharacteristic
46D4×D89—24no—
47D4×D89—42no—
48C22×Dic89—22no—
49C2×C4×D89C2311yescharacteristic
50#13083561—42no—
51D712—22no—
52#13083559—24no—
53C2×#10623494C2311yescharacteristic
54C2×#10623494C2311yescharacteristic
55C8×D89—22no—
56C4⋊Dic89C2312yes—
57#13083553—22no—
58#13083553D411yescharacteristic
59C22⋊Dic89—22no—
60C22⋊Dic89D411yescharacteristic
61#13083551—22no—
62#13083551—22no—
63#13083551—22no—
64#13083551—22no—
65#13083551D411yescharacteristic
66C4×Dic89C2311yescharacteristic
67#41×C89—24no—
68#41×C89—42no—
69C2×Q8×C89C2312yes—
70C2×D4×C89—22no—
71C2×D4×C89C2312yes—
72C22×C4×C89—22no—
73C22×C4×C89C2311yescharacteristic
74Q16×C89—22no—
75SD16×C89—24no—
76D8×C89D414yescomplemented
77C2×C8×C89—22no—
78C2×C8×C89C2311yescharacteristic
79C2×C8×C89C2311yescharacteristic
80C23×C89—22no—
81C23×C89C2×D411yescharacteristic
82C22×D89—22no—
83C22×D89—44no—
84C22×D89—44no—
85C22×D89—82no—
86C22×D89C2×D411yescharacteristic
87Q8×C89—22no—
88Q8×C89—22no—
89D4×C89—22no—
90D4×C89—44no—
91D4×C89C2×D414yes—
92C2×C4×C89—21no—
93C2×C4×C89—21no—
94C2×C4×C89—22no—
95C2×C4×C89—44no—
96C2×C4×C89C2×D411yescharacteristic
97C2×C4×C89C2411yescharacteristic
98C22⋊D89—22no—
99C22⋊D89—44no—
100C22⋊D89—82no—
101C2×Dic89—22no—
102C2×Dic89—82no—
103C2×Dic89C2×D411yescharacteristic
104C2×Dic89C2×D411yescharacteristic
105C2×Dic89C2×D411yescharacteristic
106D356—22no—
107D356—22no—
108C4×D89—21no—
109C4×D89—21no—
110C8×C89—21no—
111C8×C89C2×D412yes—
112#10623494—21no—
113#10623494—21no—
114C22×C89—24no—
115C22×C89—21no—
116C22×C89—21no—
117C22×C89—21no—
118C22×C89—42no—
119C22×C89—42no—
120C22×C89C22×D411yescharacteristic
121C2×D89—21no—
122C2×D89—21no—
123C2×D89—42no—
124C2×D89—42no—
125C2×D89—42no—
126C2×D89—88no—
127C2×D89#13512yescomplemented
128C4×C89—21no—
129C4×C89—42no—
130C4×C89C22×D411yescharacteristic
131C4×C89H(5,𝔽2)11yescharacteristic
132Dic89—21no—
133Dic89—21no—
134Dic89—21no—
135Dic89—42no—
136C2×C89—44no—
137C2×C89—41no—
138C2×C89D4211yescharacteristic
139C2×C89C2×#13511yescharacteristic
140C2×C89#57611yescharacteristic
141D89—22no—
142D89—82no—
143#3280—891nomaximal, Sylow
144C89#328011yescharacteristic, complemented, Sylow
145C2×#135D8911yescharacteristic, complemented
146C22×D8—891no—
147#546—892no—
148#495—891no—
149#467—891no—
150#466—891no—
151#463—892no—
152#450—892no—
153#449—892no—
154C4×D8—891no—
155C8×D4—891no—
156C2×#41C2×D8912yescomplemented
157C22×D4—892no—
158#135—24no—
159C2×Q16C2×D8911yescharacteristic, complemented
160C2×SD16—892no—
161C2×SD16C2×D8912yescomplemented
162C2×D8—892no—
163C2×D8—891no—
164C2×D8—1784no—
165C2×D8C2×D8911yescharacteristic
166C22×C8—891no—
167C22×C8C2×D8911yescharacteristic, complemented
168#124—892no—
169#123—1782no—
170C22⋊Q8—892no—
171#121—892no—
172#121—1782no—
173#120—1782no—
174C4×D4—891no—
175C4×D4—892no—
176C2×C22⋊C4—1782no—
177#107—891no—
178C4⋊C8—891no—
179#103—892no—
180#102—892no—
181#102—892no—
182C22⋊C8—891no—
183C22⋊C8—891no—
184C4×C8—891no—
185C24—1782no—
186#41—24no—
187#41—42no—
188C2×Q8C22×D8912yes—
189C2×D4—22no—
190C2×D4—891no—
191C2×D4—892no—
192C2×D4—3562no—
193C2×D4—1782no—
194C2×D4—1784no—
195C2×D4—1782no—
196C2×D4C22×D8912yes—
197C22×C4—22no—
198C22×C4—891no—
199C22×C4—1782no—
200C22×C4C22×D8911yescharacteristic
201Q16—22no—
202SD16—24no—
203SD16—3562no—
204D8—1784no—
205D8—1782no—
206D8C22⋊D8914yescomplemented
207C2×C8—22no—
208C2×C8—891no—
209C2×C8—891no—
210C2×C8—1782no—
211C2×C8C22×D8911yescharacteristic
212C2×C8C22×D8911yescharacteristic
213C4⋊C4—891no—
214C4⋊C4—892no—
215C4⋊C4—1782no—
216C22⋊C4—891no—
217C22⋊C4—891no—
218C22⋊C4—1782no—
219C22⋊C4—1782no—
220C22⋊C4—1782no—
221C22⋊C4—1782no—
222C22⋊C4—1782no—
223C42—891no—
224C23—22no—
225C23—891no—
226C23—3564no—
227C23—3564no—
228C23—1782no—
229C23—7122no—
230C23D4×D8911yescharacteristic
231Q8—22no—
232Q8—22no—
233D4—22no—
234D4—44no—
235D4—3564no—
236D4—1782no—
237D4—1782no—
238D4—1782no—
239D4—7122no—
240D4C2×C22⋊D8914yes—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—44no—
245C2×C4—891no—
246C2×C4—891no—
247C2×C4—891no—
248C2×C4—1782no—
249C2×C4—1781no—
250C2×C4—1781no—
251C2×C4—7122no—
252C2×C4D4×D8911yescharacteristic
253C2×C4C23×D8911yescharacteristic
254C8—21no—
255C8—1781no—
256C8—1781no—
257C8C2×C22⋊D8912yes—
258C22—21no—
259C22—21no—
260C22—24no—
261C22—21no—
262C22—42no—
263C22—42no—
264C22—892no—
265C22—3562no—
266C22—3562no—
267C22—3562no—
268C22—1781no—
269C22—1781no—
270C22—7128no—
271C22C2×D4×D8911yescharacteristic
272C4—21no—
273C4—42no—
274C4—3562no—
275C4—1781no—
276C4—1781no—
277C4—1781no—
278C4C22×C22⋊D8911yescharacteristic
279C4#1566805711yescharacteristic
280C2—41no—
281C2—44no—
282C2—1782no—
283C2—7122no—
284C2D4×C22⋊D8911yescharacteristic
285C2#135×D8911yescharacteristic
286C2#1915240011yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingC2×#135×C89C2
socleC22×C89C22×D4
hypercenterC2×#135D89
hypocenterC89#3280
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×D8×D89C2semidirect
2. #19152236C2semidirect
3. #19151983C2semidirect
4. #19151836C2semidirect
5. #19151834C2semidirect
6. #19151815C2semidirect
7. #19151747C2semidirect
8. #19151743C2semidirect
9. D8×Dic89C2semidirect
10. C8×C22⋊D89C2semidirect
11. C2×#135×C89C2semidirect
13. C2×#13083561C22semidirect
18. #15668001C22semidirect
21. #15667986C22semidirect
24. D4×Dic89C22semidirect
27. #15667946C22semidirect
28. #15667941C22semidirect
29. #15667936C22semidirect
30. #15667934C22semidirect
31. #15667933C22semidirect
32. C22⋊#10623494C22semidirect
34. C8×Dic89C22semidirect
35. C2×#41×C89C22semidirect
37. C2×Q16×C89C22semidirect
38. C2×SD16×C89C22semidirect
40. C22×C8×C89C22semidirect
76. D8×C89D4semidirect
127. C2×D89#135semidirect
144. C89#3280semidirect
145. C2×#135D89semidirect
156. C2×#41C2×D89semidirect
159. C2×Q16C2×D89semidirect
161. C2×SD16C2×D89semidirect
167. C22×C8C2×D89semidirect
206. D8C22⋊D89semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D892
#191522362
#191519832
#191518362
#191518342
#191518152
#191517472
#191517432
D8×Dic892
C8×C22⋊D892
C2×#135×C892
#328089