Finite Group Databasebeta

← #26029494

Subgroups — #26029494

Order 11392.

758 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 165 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×#15668043C211yesmaximal, characteristic, complemented
2C2×#15668038C211yesmaximal, characteristic, complemented
3#19152109C211yesmaximal, characteristic, complemented
4#19151760C214yesmaximal, complemented
5#19151743C214yesmaximal, complemented
6#19151607C211yesmaximal, characteristic, complemented
7#19151603C211yesmaximal, characteristic, complemented
8#19151562C211yesmaximal, characteristic, complemented
9C22×#41×C89C211yesmaximal, characteristic, complemented
10C2×#13083574C2211yescharacteristic
11#15668043—24no—
12#15668038—24no—
13C2×#13083564C2212yescomplemented
14C2×#13083562C2212yescomplemented
15C2×#13083561C2212yescomplemented
16C2×#13083559C2212yescomplemented
17C2×#13083558C2211yescharacteristic
18C2×#13083558C2211yescharacteristic
19#15667995—21no—
20#15667991C2212yescomplemented
21#15667986C2212yescomplemented
22#15667981—21no—
23C4×C22⋊D89—22no—
24#15667971C2211yescharacteristic
25#15667936C2214yescomplemented
26#15667933C2214yescomplemented
27C22⋊#10623494C2214yescomplemented
28C2×#41×C89—24no—
29C2×#41×C89—24no—
30C2×#41×C89—22no—
31C2×#41×C89C2214yes—
32C22×Q8×C89C2211yescharacteristic
33C22×D4×C89—21no—
34C22×D4×C89C2211yescharacteristic
35C23×C4×C89—21no—
36C23×C4×C89C2211yescharacteristic
37#13083574—22no—
38#13083574—22no—
39C2×Dic178C2311yescharacteristic
40C2×D356C2311yescharacteristic
41C2×C22⋊D89—22no—
42C2×C22⋊D89—21no—
43C2×C4×D89—21no—
44#13083564—24no—
45#13083562—24no—
46#13083561—24no—
47#13083559—24no—
48#13083558—22no—
49#13083558—22no—
50C2×#10623494C2312yes—
51C2×#10623494C2312yes—
52C4⋊Dic89C2312yes—
53#13083553—22no—
54C22⋊Dic89—21no—
55C22⋊Dic89—22no—
56#13083551—22no—
57C4×Dic89—21no—
58C24×C89—21no—
59C24×C89D411yescharacteristic
60#41×C89—216no—
61#41×C89—28no—
62#41×C89—28no—
63C2×Q8×C89—22no—
64C2×Q8×C89—21no—
65C2×Q8×C89D414yescomplemented
66C2×Q8×C89C2312yes—
67C2×D4×C89—28no—
68C2×D4×C89—24no—
69C2×D4×C89—21no—
70C2×D4×C89—22no—
71C2×D4×C89D414yescomplemented
72C2×D4×C89C2312yes—
73C22×C4×C89—28no—
74C22×C4×C89—21no—
75C22×C4×C89—24no—
76C22×C4×C89—22no—
77C22×C4×C89—22no—
78C22×C4×C89D412yes—
79C22×C4×C89D411yescharacteristic
80C22×C4×C89C2312yes—
81C22×C4×C89C2311yescharacteristic
82C23×C89—22no—
83C23×C89—24no—
84C23×C89—22no—
85C23×C89—42no—
86C23×C89—44no—
87C23×C89C2×D412yes—
88C23×C89C2×D411yescharacteristic
89C22×D89—21no—
90Q8×C89—24no—
91Q8×C89—22no—
92Q8×C89C2×D414yes—
93D4×C89—216no—
94D4×C89—24no—
95D4×C89—22no—
96D4×C89C2×D414yes—
97C2×C4×C89—216no—
98C2×C4×C89—22no—
99C2×C4×C89—24no—
100C2×C4×C89—22no—
101C2×C4×C89—24no—
102C2×C4×C89—22no—
103C2×C4×C89—22no—
104C2×C4×C89C2×D412yes—
105C2×C4×C89C2×D411yescharacteristic
106C2×C4×C89C2×D412yes—
107C2×C4×C89C2×D412yes—
108C2×C4×C89C2411yescharacteristic
109C22⋊D89—44no—
110C22⋊D89—42no—
111C2×Dic89—22no—
112C2×Dic89—21no—
113D356—21no—
114D356—21no—
115C4×D89—42no—
116Dic178—21no—
117Dic178—21no—
118#10623494—22no—
119#10623494—22no—
120C22×C89—22no—
121C22×C89—22no—
122C22×C89—24no—
123C22×C89—22no—
124C22×C89—22no—
125C22×C89—44no—
126C22×C89—48no—
127C22×C89—44no—
128C22×C89#12012yes—
129C22×C89C22×D411yescharacteristic
130C2×D89—41no—
131C2×D89—42no—
132C4×C89—22no—
133C4×C89—24no—
134C4×C89#12012yes—
135C4×C89C22×D411yescharacteristic
136C4×C89C22×D411yescharacteristic
137Dic89—41no—
138Dic89—42no—
139C2×C89—22no—
140C2×C89—42no—
141C2×C89—44no—
142C2×C89C2×#12011yescharacteristic
143C2×C89#57512yes—
144D89—81no—
145#3005—891nomaximal, Sylow
146C89#300511yescharacteristic, complemented, Sylow
147C22×#41D8911yescharacteristic, complemented
148C2×#137—891no—
149C2×AGL(1,ℤ/8)—891no—
150#525—891no—
151#452—894no—
152#449—894no—
153#419—891no—
154#418—891no—
155#407—891no—
156C2×#41—24no—
157C2×#41—24no—
158C2×#41—22no—
159C2×#41—891no—
160C2×#41C2×D8914yes—
161C22×Q8C2×D8911yescharacteristic
162C22×D4—21no—
163C22×D4C2×D8911yescharacteristic
164C23×C4—21no—
165C23×C4C2×D8911yescharacteristic
166#137—1784no—
167AGL(1,ℤ/8)—1784no—
168C2×Q16—892no—
169C2×SD16—892no—
170C2×SD16—892no—
171C2×D8—892no—
172C2×M16—891no—
173C2×M16—891no—
174#123—1781no—
175C22⋊Q8—892no—
176#121—892no—
177#120—1781no—
178C4×D4—1782no—
179#117—891no—
180#103—894no—
181#102—894no—
182C22⋊C8—894no—
183C24—21no—
184C24C22⋊D8911yescharacteristic
185#41—216no—
186#41—28no—
187#41—28no—
188#41—1782no—
189#41—1782no—
190C2×Q8—22no—
191C2×Q8—21no—
192C2×Q8—891no—
193C2×Q8C22⋊D8914yescomplemented
194C2×Q8C22×D8912yes—
195C2×D4—28no—
196C2×D4—24no—
197C2×D4—21no—
198C2×D4—22no—
199C2×D4—891no—
200C2×D4—1782no—
201C2×D4—1781no—
202C2×D4C22⋊D8914yescomplemented
203C2×D4C22×D8912yes—
204C22×C4—28no—
205C22×C4—21no—
206C22×C4—24no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—1781no—
210C22×C4C22⋊D8912yes—
211C22×C4C22⋊D8911yescharacteristic
212C22×C4C22×D8912yes—
213C22×C4C22×D8911yescharacteristic
214Q16—1784no—
215SD16—1784no—
216SD16—1784no—
217D8—1784no—
218M16—1782no—
219M16—1782no—
220C2×C8—892no—
221C2×C8—892no—
222C4⋊C4—892no—
223C4⋊C4—1782no—
224C22⋊C4—1781no—
225C22⋊C4—1782no—
226C22⋊C4—1782no—
227C42—1781no—
228C23—22no—
229C23—24no—
230C23—22no—
231C23—42no—
232C23—44no—
233C23—1781no—
234C23C2×C22⋊D8912yes—
235C23C2×C22⋊D8911yescharacteristic
236Q8—24no—
237Q8—22no—
238Q8—1781no—
239Q8—1781no—
240Q8C2×C22⋊D8914yes—
241D4—216no—
242D4—24no—
243D4—22no—
244D4—3564no—
245D4—3562no—
246D4—1781no—
247D4—1781no—
248D4C2×C22⋊D8914yes—
249C2×C4—216no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—22no—
253C2×C4—24no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—3562no—
257C2×C4—1782no—
258C2×C4—1781no—
259C2×C4C2×C22⋊D8912yes—
260C2×C4C2×C22⋊D8911yescharacteristic
261C2×C4C2×C22⋊D8912yes—
262C2×C4C2×C22⋊D8912yes—
263C2×C4C23×D8911yescharacteristic
264C8—1782no—
265C8—1782no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—24no—
271C22—44no—
272C22—48no—
273C22—44no—
274C22—3562no—
275C22—3561no—
276C22#1566798112yes—
277C22C22×C22⋊D8911yescharacteristic
278C4—22no—
279C4—24no—
280C4—3562no—
281C4—3561no—
282C4#1566798112yes—
283C4C22×C22⋊D8911yescharacteristic
284C4C22×C22⋊D8911yescharacteristic
285C2—22no—
286C2—42no—
287C2—44no—
288C2—7121no—
289C2C2×#1566798111yescharacteristic
290C2#1915239612yes—
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingC22×#41×C89C2
socleC22×C89C22×D4
hypercenterC22×#41D89
hypocenterC89#3005
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#15668043C2semidirect
2. C2×#15668038C2semidirect
3. #19152109C2semidirect
4. #19151760C2semidirect
5. #19151743C2semidirect
6. #19151607C2semidirect
7. #19151603C2semidirect
8. #19151562C2semidirect
9. C22×#41×C89C2semidirect
13. C2×#13083564C22semidirect
14. C2×#13083562C22semidirect
15. C2×#13083561C22semidirect
16. C2×#13083559C22semidirect
20. #15667991C22semidirect
21. #15667986C22semidirect
25. #15667936C22semidirect
26. #15667933C22semidirect
27. C22⋊#10623494C22semidirect
65. C2×Q8×C89D4semidirect
71. C2×D4×C89D4semidirect
146. C89#3005semidirect
147. C22×#41D89semidirect
193. C2×Q8C22⋊D89semidirect
202. C2×D4C22⋊D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156680432
C2×#156680382
#191521092
#191517602
#191517432
#191516072
#191516032
#191515622
C22×#41×C892
#300589