Finite Group Databasebeta

← #26031938

Subgroups — #26031938

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×#15668031C211yesmaximal, characteristic, complemented
2C2×D8×D89C211yesmaximal, characteristic, complemented
3#19152243C212yesmaximal, complemented
4#19151982C211yesmaximal, characteristic, complemented
5#19151840C211yesmaximal, characteristic, complemented
6#19151835C211yesmaximal, characteristic, complemented
7#19151813C212yesmaximal, complemented
8#19151750C212yesmaximal, complemented
9#19151744C212yesmaximal, complemented
10C8×D356C211yesmaximal, characteristic, complemented
11C4×D8×C89C211yesmaximal, characteristic, complemented
12C2×#13083573C2212yescomplemented
13C2×D4×D89C2212yes—
14#15668031—24no—
15C2×Dic356C2211yescharacteristic, complemented
16C2×#13083563C2212yescomplemented
17C2×#13083562C2212yescomplemented
18C2×D712C2211yescharacteristic
19C2×#13083559C2212yes—
20D8×D89—24no—
21C2×C8×D89C2211yescharacteristic
22C2×C8×D89C2211yescharacteristic, complemented
23#15668000C2212yescomplemented
24#15667996—22no—
25#15667992C2212yes—
26#15667987C2212yescomplemented
27#15667986—22no—
28#15667982—22no—
29C4×D356C2211yescharacteristic
30C2×#13083551—22no—
31C4⋊#10623494C2211yescharacteristic, complemented
32#15667935C2212yescomplemented
33#15667932C2212yescomplemented
34#15667924C2211yescharacteristic
35#15667924C2211yescharacteristic, complemented
36C2×D8×C89C2211yescharacteristic
37C4×D4×C89C2212yescomplemented
38#107×C89C2211yescharacteristic, complemented
39#102×C89C2212yescomplemented
40C4×C8×C89C2211yescharacteristic, complemented
41C23×D89—22no—
42#13083573—24no—
43#13083573—42no—
44C2×Dic178C2312yes—
45C2×D356—22no—
46C2×D356D411yescharacteristic
47C2×D356C2312yes—
48C2×C22⋊D89—22no—
49C2×C22⋊D89—22no—
50D4×D89—24no—
51D4×D89—42no—
52C22×Dic89—22no—
53C2×C4×D89C2311yescharacteristic
54C2×C4×D89C2311yescharacteristic
55Dic356—22no—
56#13083563—42no—
57#13083562—24no—
58D712—22no—
59#13083559—24no—
60C2×#10623494C2311yescharacteristic
61C2×#10623494C2311yescharacteristic
62C8×D89—22no—
63C8×D89—22no—
64C4⋊Dic89—22no—
65C4⋊Dic89D411yescharacteristic
66#13083551—22no—
67#13083551—22no—
68#13083551—22no—
69#13083551—22no—
70#13083551D411yescharacteristic
71#13083551D411yescharacteristic
72C2×D4×C89C2312yes—
73C22×C4×C89—22no—
74D8×C89D414yescomplemented
75C2×C8×C89C2311yescharacteristic
76C2×C8×C89C2311yescharacteristic
77C4⋊C4×C89C2312yes—
78C22⋊C4×C89—22no—
79C42×C89C2311yescharacteristic
80C23×C89—22no—
81C22×D89—22no—
82C22×D89—44no—
83C22×D89—44no—
84C22×D89—82no—
85C22×D89C2×D411yescharacteristic
86C22×D89C2×D411yescharacteristic
87D4×C89—22no—
88D4×C89C2×D414yes—
89C2×C4×C89—22no—
90C2×C4×C89—82no—
91C2×C4×C89C2×D411yescharacteristic
92C2×C4×C89C2×D411yescharacteristic
93C2×C4×C89C2411yescharacteristic
94C22⋊D89—44no—
95C22⋊D89—44no—
96C2×Dic89—22no—
97C2×Dic89—44no—
98C2×Dic89C2×D411yescharacteristic
99C2×Dic89C2×D411yescharacteristic
100D356—22no—
101D356—22no—
102D356—22no—
103D356—82no—
104C4×D89—21no—
105C4×D89—21no—
106C4×D89—21no—
107C4×D89—21no—
108Dic178—22no—
109Dic178—22no—
110C8×C89—21no—
111C8×C89C2×D412yes—
112#10623494—21no—
113#10623494—21no—
114C22×C89—24no—
115C22×C89—42no—
116C22×C89—42no—
117C22×C89C22×D411yescharacteristic
118C2×D89—21no—
119C2×D89—21no—
120C2×D89—21no—
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—21no—
130C4×C89—42no—
131C4×C89C22×D411yescharacteristic
132C4×C89H(5,𝔽2)11yescharacteristic
133Dic89—21no—
134Dic89—21no—
135Dic89—42no—
136C2×C89—44no—
137C2×C89D4211yescharacteristic
138C2×C89C2×#13511yescharacteristic
139C2×C89#57611yescharacteristic
140D89—22no—
141D89—41no—
142D89—82no—
143#3280—891nomaximal, Sylow
144C89#328011yescharacteristic, complemented, Sylow
145C2×#135—891no—
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×D8D8911yescharacteristic, complemented
155C8×D4—891no—
156C2×#41—892no—
157C22×D4—892no—
158#135—1784no—
159C2×Q16—891no—
160C2×SD16—892no—
161C2×SD16—892no—
162C2×D8—892no—
163C2×D8—891no—
164C2×D8—1784no—
165C2×D8C2×D8911yescharacteristic
166C22×C8—891no—
167C22×C8—891no—
168#124—892no—
169#123—1782no—
170C22⋊Q8—892no—
171#121—892no—
172#121—1782no—
173#120—1782no—
174C4×D4—891no—
175C4×D4C2×D8912yescomplemented
176C2×C22⋊C4—1782no—
177#107C2×D8911yescharacteristic, complemented
178C4⋊C8—891no—
179#103—892no—
180#102—892no—
181#102C2×D8912yescomplemented
182C22⋊C8—891no—
183C22⋊C8—891no—
184C4×C8C2×D8911yescharacteristic, complemented
185C24—1782no—
186#41—3562no—
187#41—1784no—
188C2×Q8—892no—
189C2×D4—891no—
190C2×D4—892no—
191C2×D4—3562no—
192C2×D4—1782no—
193C2×D4—1782no—
194C2×D4—1782no—
195C2×D4—1784no—
196C2×D4C22×D8912yes—
197C22×C4—22no—
198C22×C4—891no—
199C22×C4—891no—
200C22×C4—1782no—
201Q16—1782no—
202SD16—3562no—
203SD16—1784no—
204D8—1784no—
205D8—1782no—
206D8D35614yescomplemented
207C2×C8—891no—
208C2×C8—891no—
209C2×C8—1782no—
210C2×C8—1782no—
211C2×C8C22×D8911yescharacteristic
212C2×C8C22×D8911yescharacteristic
213C4⋊C4—891no—
214C4⋊C4—1782no—
215C4⋊C4C22×D8912yes—
216C22⋊C4—22no—
217C22⋊C4—891no—
218C22⋊C4—891no—
219C22⋊C4—1782no—
220C22⋊C4—1782no—
221C22⋊C4—1782no—
222C22⋊C4—1782no—
223C42C22×D8911yescharacteristic
224C23—22no—
225C23—891no—
226C23—891no—
227C23—3564no—
228C23—3564no—
229C23—1782no—
230C23—7122no—
231Q8—1782no—
232Q8—1782no—
233D4—22no—
234D4—3564no—
235D4—3564no—
236D4—1782no—
237D4—1782no—
238D4—1782no—
239D4—7122no—
240D4C2×D35614yes—
241C2×C4—22no—
242C2×C4—82no—
243C2×C4—891no—
244C2×C4—891no—
245C2×C4—3564no—
246C2×C4—1782no—
247C2×C4—1781no—
248C2×C4—1781no—
249C2×C4—1781no—
250C2×C4—1781no—
251C2×C4D4×D8911yescharacteristic
252C2×C4D4×D8911yescharacteristic
253C2×C4C23×D8911yescharacteristic
254C8—21no—
255C8—1781no—
256C8—1781no—
257C8C2×D35612yes—
258C22—24no—
259C22—42no—
260C22—42no—
261C22—892no—
262C22—3562no—
263C22—3562no—
264C22—3562no—
265C22—1781no—
266C22—1781no—
267C22—1781no—
268C22—1781no—
269C22—1781no—
270C22—7128no—
271C22C2×D4×D8911yescharacteristic
272C4—21no—
273C4—21no—
274C4—42no—
275C4—3562no—
276C4—1781no—
277C4—1781no—
278C4C22×D35611yescharacteristic
279C4#1566805811yescharacteristic
280C2—44no—
281C2—3561no—
282C2—1782no—
283C2—7122no—
284C2D4×D35611yescharacteristic
285C2#135×D8911yescharacteristic
286C2#1915239911yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingC4×D8×C89C2
socleC22×C89C22×D4
hypercenterC4×D8D89
hypocenterC89#3280
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#15668031C2semidirect
2. C2×D8×D89C2semidirect
3. #19152243C2semidirect
4. #19151982C2semidirect
5. #19151840C2semidirect
6. #19151835C2semidirect
7. #19151813C2semidirect
8. #19151750C2semidirect
9. #19151744C2semidirect
10. C8×D356C2semidirect
11. C4×D8×C89C2semidirect
12. C2×#13083573C22semidirect
15. C2×Dic356C22semidirect
16. C2×#13083563C22semidirect
17. C2×#13083562C22semidirect
22. C2×C8×D89C22semidirect
23. #15668000C22semidirect
26. #15667987C22semidirect
31. C4⋊#10623494C22semidirect
32. #15667935C22semidirect
33. #15667932C22semidirect
35. #15667924C22semidirect
37. C4×D4×C89C22semidirect
38. #107×C89C22semidirect
39. #102×C89C22semidirect
40. C4×C8×C89C22semidirect
74. D8×C89D4semidirect
127. C2×D89#135semidirect
144. C89#3280semidirect
154. C4×D8D89semidirect
175. C4×D4C2×D89semidirect
177. #107C2×D89semidirect
181. #102C2×D89semidirect
184. C4×C8C2×D89semidirect
206. D8D356semidirect

Maximal subgroups

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

subgroupindex
C2×#156680312
C2×D8×D892
#191522432
#191519822
#191518402
#191518352
#191518132
#191517502
#191517442
C8×D3562
C4×D8×C892
#328089