Finite Group Databasebeta

← #26030197

Subgroups — #26030197

Order 11392.

410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C22⋊Q8×D89C211yesmaximal, characteristic
2C2×#15667970C211yesmaximal, characteristic
3#19151941C212yesmaximal, complemented
4#19151937C212yesmaximal, complemented
5#19151933C211yesmaximal, characteristic, complemented
6#19151929C211yesmaximal, characteristic, complemented
7#19151926C211yesmaximal, characteristic, complemented
8#19151639C212yesmaximal, complemented
9#19151605C212yesmaximal, complemented
10#19151560C211yesmaximal, characteristic
11#484×C89C211yesmaximal, characteristic, complemented
12C2×Q8×D89C2211yescharacteristic
13C22×C4×D89C2211yescharacteristic
14C2×#13083557C2212yes—
15#15667992C2211yescharacteristic
16#15667991C2211yescharacteristic
17#15667990—21no—
18#15667989—21no—
19#15667988C2211yescharacteristic
20#15667970—21no—
21#15667970—21no—
22#15667970C2212yes—
23#15667970C2212yes—
24C2×C4⋊Dic89C2211yescharacteristic
25C4⋊C4×D89—21no—
26C4⋊C4×D89C2211yescharacteristic
27C2×#13083551—21no—
28C22⋊C4×D89—21no—
29C2×C4×Dic89—21no—
30#15667945C2212yescomplemented
31#15667944C2212yescomplemented
32#15667943C2212yescomplemented
33#15667937C2212yescomplemented
34#15667936C2212yescomplemented
35#15667935C2212yescomplemented
36C22⋊#10623494C2211yescharacteristic
37#15667924C2212yes—
38C22⋊Q8×C89C2211yescharacteristic
39C2×C4⋊C4×C89C2211yescharacteristic
40#107×C89C2212yescomplemented
41#103×C89C2212yescomplemented
42C22⋊C8×C89C2211yescharacteristic
43C23×D89D411yescharacteristic
44C2×Dic178—21no—
45C2×Dic178C2311yescharacteristic
46Q8×D89—24no—
47C22×Dic89—21no—
48C22×Dic89D411yescharacteristic
49C2×C4×D89—24no—
50C2×C4×D89—21no—
51C2×C4×D89—21no—
52C2×C4×D89D411yescharacteristic
53C2×C4×D89D411yescharacteristic
54C2×C4×D89C2311yescharacteristic
55C2×C4×D89C2311yescharacteristic
56#13083557—24no—
57C2×#10623494C2312yes—
58C4⋊Dic89—21no—
59C4⋊Dic89—21no—
60C4⋊Dic89C2312yes—
61C4⋊Dic89C2311yescharacteristic
62#13083553—21no—
63#13083553—21no—
64#13083553—21no—
65C22⋊Dic89—21no—
66#13083551—22no—
67#13083551—22no—
68#13083551—21no—
69#13083551—21no—
70C4×Dic89—22no—
71C4×Dic89—22no—
72C2×Q8×C89C2311yescharacteristic
73C22×C4×C89—21no—
74C22×C4×C89C2311yescharacteristic
75C2×C8×C89C2312yes—
76C4⋊C4×C89—21no—
77C4⋊C4×C89—21no—
78C4⋊C4×C89C2312yes—
79C4⋊C4×C89C2311yescharacteristic
80C22⋊C4×C89—21no—
81C23×C89C2×D411yescharacteristic
82C22×D89—22no—
83C22×D89—22no—
84C22×D89—41no—
85C22×D89C2×D411yescharacteristic
86C22×D89C2×D411yescharacteristic
87Q8×C89—22no—
88C2×C4×C89—22no—
89C2×C4×C89—21no—
90C2×C4×C89—21no—
91C2×C4×C89—22no—
92C2×C4×C89—42no—
93C2×C4×C89C2×D411yescharacteristic
94C2×C4×C89C2411yescharacteristic
95C2×Dic89—22no—
96C2×Dic89—22no—
97C2×Dic89—21no—
98C2×Dic89—21no—
99C2×Dic89—42no—
100C2×Dic89C2×D411yescharacteristic
101C2×Dic89C2×D411yescharacteristic
102C4×D89—22no—
103C4×D89—22no—
104C4×D89—22no—
105C4×D89—42no—
106C4×D89—42no—
107C4×D89#4114yes—
108Dic178—22no—
109Dic178—42no—
110C8×C89—22no—
111#10623494—22no—
112C22×C89—21no—
113C22×C89—21no—
114C22×C89#13712yes—
115C22×C89C22×D411yescharacteristic
116C2×D89—21no—
117C2×D89—21no—
118C2×D89—21no—
119C2×D89—21no—
120C2×D89—21no—
121C2×D89—44no—
122C2×D89#12312yes—
123C4×C89—21no—
124C4×C89—41no—
125C4×C89—41no—
126C4×C89—42no—
127C4×C89C2×#4112yes—
128Dic89—21no—
129Dic89—41no—
130Dic89—42no—
131Dic89—41no—
132Dic89#12312yes—
133C2×C89—22no—
134C2×C89C2×#12311yescharacteristic
135C2×C89C2×#13711yescharacteristic
136C2×C89#57511yescharacteristic
137D89—22no—
138D89—41no—
139#3095—891nomaximal, Sylow
140C89#309511yescharacteristic, complemented, Sylow
141C2×C22⋊Q8—891no—
142C2×#117—891no—
143#485—892no—
144#485—892no—
145#484—891no—
146#484D8911yescharacteristic, complemented
147#483—891no—
148#483—891no—
149#428—892no—
150#419—892no—
151#407—891no—
152C22×Q8—891no—
153C23×C4—891no—
154C2×M16—892no—
155C22⋊Q8—891no—
156C22⋊Q8—891no—
157C22⋊Q8—891no—
158C22⋊Q8—1781no—
159C22⋊Q8—1781no—
160C22⋊Q8C2×D8911yescharacteristic
161#117—892no—
162#117—892no—
163#117—1781no—
164#117—1781no—
165C2×C4⋊C4—891no—
166C2×C4⋊C4—891no—
167C2×C4⋊C4—1781no—
168C2×C4⋊C4C2×D8911yescharacteristic
169C2×C22⋊C4—1781no—
170C2×C22⋊C4—1781no—
171C2×C42—1781no—
172#107—892no—
173#107C2×D8912yescomplemented
174#106—892no—
175#106—892no—
176#103—892no—
177#103—892no—
178#103—892no—
179#103C2×D8912yescomplemented
180C22⋊C8—891no—
181C22⋊C8—892no—
182C22⋊C8C2×D8911yescharacteristic
183C24—891no—
184C2×Q8—891no—
185C2×Q8—1781no—
186C2×Q8—1784no—
187C2×Q8C22×D8911yescharacteristic
188C22×C4—21no—
189C22×C4—891no—
190C22×C4—891no—
191C22×C4—891no—
192C22×C4—891no—
193C22×C4—891no—
194C22×C4—1784no—
195C22×C4—1781no—
196C22×C4—1781no—
197C22×C4—1781no—
198C22×C4C22×D8911yescharacteristic
199M16—1784no—
200C2×C8—892no—
201C2×C8C22×D8912yes—
202C4⋊C4—21no—
203C4⋊C4—21no—
204C4⋊C4—892no—
205C4⋊C4—891no—
206C4⋊C4—1781no—
207C4⋊C4—1781no—
208C4⋊C4—1781no—
209C4⋊C4—1781no—
210C4⋊C4—1781no—
211C4⋊C4C22×D8912yes—
212C4⋊C4C22×D8911yescharacteristic
213C22⋊C4—21no—
214C22⋊C4—1782no—
215C22⋊C4—1782no—
216C22⋊C4—1781no—
217C22⋊C4—1781no—
218C22⋊C4—1781no—
219C42—1782no—
220C42—1782no—
221C23—891no—
222C23—891no—
223C23—3561no—
224C23—1782no—
225C23—1782no—
226C23D4×D8911yescharacteristic
227Q8—22no—
228Q8—3562no—
229Q8—1782no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—891no—
236C2×C4—894no—
237C2×C4—891no—
238C2×C4—3562no—
239C2×C4—3562no—
240C2×C4—3562no—
241C2×C4—1782no—
242C2×C4—1782no—
243C2×C4—1782no—
244C2×C4—1782no—
245C2×C4—1781no—
246C2×C4—1781no—
247C2×C4—1782no—
248C2×C4D4×D8911yescharacteristic
249C2×C4C23×D8911yescharacteristic
250C8—22no—
251C8—1782no—
252C22—21no—
253C22—21no—
254C22—892no—
255C22—3564no—
256C22—1781no—
257C22—1781no—
258C22—1781no—
259C22—1781no—
260C22—1781no—
261C22#1566804412yes—
262C22C2×D4×D8911yescharacteristic
263C4—21no—
264C4—42no—
265C4—41no—
266C4—41no—
267C4—892no—
268C4—3562no—
269C4—3561no—
270C4—3561no—
271C4—1781no—
272C4#41×D8912yes—
273C2—22no—
274C2—3561no—
275C2—1782no—
276C2#123×D8911yescharacteristic
277C2C2×#1566804411yescharacteristic
278C2#1915239411yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#484×C89C2
socleC22×C89C22×D4
prime radicalC23×D89D4
hypercenter#484D89
hypocenterC89#3095
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #19151941C2semidirect
4. #19151937C2semidirect
5. #19151933C2semidirect
6. #19151929C2semidirect
7. #19151926C2semidirect
8. #19151639C2semidirect
9. #19151605C2semidirect
11. #484×C89C2semidirect
30. #15667945C22semidirect
31. #15667944C22semidirect
32. #15667943C22semidirect
33. #15667937C22semidirect
34. #15667936C22semidirect
35. #15667935C22semidirect
40. #107×C89C22semidirect
41. #103×C89C22semidirect
140. C89#3095semidirect
146. #484D89semidirect
173. #107C2×D89semidirect
179. #103C2×D89semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D892
C2×#156679702
#191519412
#191519372
#191519332
#191519292
#191519262
#191516392
#191516052
#191515602
#484×C892
#309589