Finite Group Databasebeta

← #26023918

Subgroups — #26023918

Order 11392.

780 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 181 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×#15667989C212yesmaximal, complemented
2C22×C22⋊Dic89C212yesmaximal
3#19151534C211yesmaximal, characteristic, complemented
4#19151521C212yesmaximal, complemented
5#19151510C211yesmaximal, characteristic, complemented
6#19151473C212yesmaximal, complemented
7#19151470C212yesmaximal, complemented
8#19151456C212yesmaximal, complemented
9#379×C89C211yesmaximal, characteristic
10C22×Dic178C2211yescharacteristic, complemented
11C23×Dic89C2212yes—
12C23×Dic89C2212yes—
13#15667989—28no—
14C2×C4⋊Dic89C2212yescomplemented
15C2×C4⋊Dic89C2211yescharacteristic, complemented
16C2×#13083553C2212yescomplemented
17C2×#13083553C2212yescomplemented
18C2×#13083553C2212yescomplemented
19C2×C22⋊Dic89—28no—
20C2×C22⋊Dic89C2212yes—
21C2×C22⋊Dic89C2212yes—
22C2×C22⋊Dic89C2212yes—
23C2×C22⋊Dic89C2212yes—
24#15667919C2211yescharacteristic, complemented
25#15667919C2212yescomplemented
26#15667919C2211yescharacteristic, complemented
27#15667919C2212yescomplemented
28C25×C89C2211yescharacteristic
29C2×C22⋊C4×C89C2212yes—
30C2×C22⋊C4×C89C2212yes—
31C2×C22⋊C4×C89C2211yescharacteristic
32C2×C22⋊C4×C89C2211yescharacteristic
33C2×Dic178—24no—
34C2×Dic178—41no—
35C22×Dic89—24no—
36C22×Dic89—24no—
37C22×Dic89—24no—
38C22×Dic89—24no—
39C22×Dic89—42no—
40C22×Dic89—42no—
41C22×Dic89C2312yes—
42C22×Dic89C2312yes—
43C22×Dic89C2312yes—
44C22×Dic89C2312yes—
45C4⋊Dic89—24no—
46C4⋊Dic89—41no—
47#13083553—24no—
48#13083553—24no—
49#13083553—42no—
50C22⋊Dic89—24no—
51C22⋊Dic89—24no—
52C22⋊Dic89—24no—
53C22⋊Dic89D418yes—
54C24×C89—24no—
55C24×C89—24no—
56C24×C89—41no—
57C24×C89—41no—
58C24×C89Q814yescomplemented
59C24×C89C2311yescharacteristic
60C24×C89C2312yes—
61C22×C4×C89C2311yescharacteristic
62C22×C4×C89C2311yescharacteristic
63C22×C4×C89C2312yes—
64C22⋊C4×C89—24no—
65C22⋊C4×C89—24no—
66C22⋊C4×C89—41no—
67C22⋊C4×C89—41no—
68C23×C89—22no—
69C23×C89—22no—
70C23×C89—22no—
71C23×C89—22no—
72C23×C89—216no—
73C23×C89—22no—
74C23×C89—22no—
75C23×C89—21no—
76C23×C89—21no—
77C23×C89—44no—
78C23×C89—44no—
79C23×C89—48no—
80C23×C89—44no—
81C23×C89C2×D414yes—
82C23×C89C2×Q812yes—
83C23×C89C2×Q814yes—
84C23×C89#4114yes—
85C23×C89C2411yescharacteristic
86C2×C4×C89—22no—
87C2×C4×C89—22no—
88C2×C4×C89—22no—
89C2×C4×C89—22no—
90C2×C4×C89—22no—
91C2×C4×C89—21no—
92C2×C4×C89—21no—
93C2×Dic89—22no—
94C2×Dic89—22no—
95C2×Dic89—22no—
96C2×Dic89—22no—
97C2×Dic89—22no—
98C2×Dic89—22no—
99C2×Dic89—22no—
100C2×Dic89—22no—
101C2×Dic89—22no—
102C2×Dic89—22no—
103C2×Dic89—48no—
104C2×Dic89—48no—
105C2×Dic89C2×D414yes—
106C2×Dic89C2×D414yes—
107Dic178—44no—
108C22×C89—24no—
109C22×C89—24no—
110C22×C89—24no—
111C22×C89—24no—
112C22×C89—24no—
113C22×C89—24no—
114C22×C89—24no—
115C22×C89—22no—
116C22×C89—416no—
117C22×C89—41no—
118C22×C89—42no—
119C22×C89—41no—
120C22×C89C22⋊Q818yescomplemented
121C22×C89C22×D412yes—
122C22×C89C22×Q811yescharacteristic
123C22×C89C2×#4112yes—
124C22×C89H(5,𝔽2)11yescharacteristic
125C22×C89H(5,𝔽2)11yescharacteristic
126C4×C89—41no—
127C4×C89—42no—
128C4×C89—41no—
129Dic89—24no—
130Dic89—24no—
131Dic89—42no—
132Dic89—42no—
133C2×C89—28no—
134C2×C89—42no—
135C2×C89C2×C22⋊Q812yes—
136C2×C89#54311yescharacteristic
137C2×C89D4211yescharacteristic
138C2×C89#54612yes—
139C2×C89#55111yescharacteristic
140#2437—891nomaximal, Sylow
141C89#243711yescharacteristic, complemented, Sylow
142C2×C22⋊Q8—892no—
143C22×C22⋊C4—892no—
144#399—891no—
145#396—892no—
146#393—891no—
147#385—892no—
148#385—892no—
149#380—892no—
150#379D8911yescharacteristic
151C25C2×D8911yescharacteristic
152C22×Q8—891no—
153C23×C4—892no—
154C23×C4—892no—
155C22⋊Q8—1788no—
156C2×C4⋊C4—892no—
157C2×C4⋊C4—891no—
158C2×C4⋊C4—892no—
159C2×C4⋊C4—892no—
160C2×C4⋊C4—892no—
161C2×C22⋊C4—892no—
162C2×C22⋊C4—892no—
163C2×C22⋊C4—892no—
164C2×C22⋊C4—892no—
165C2×C22⋊C4—1788no—
166C2×C22⋊C4C2×D8912yes—
167C2×C22⋊C4C2×D8912yes—
168C2×C22⋊C4C2×D8911yescharacteristic
169C2×C22⋊C4C2×D8911yescharacteristic
170#95—891no—
171#95—892no—
172#95—892no—
173#95—891no—
174C24—24no—
175C24—24no—
176C24—41no—
177C24—41no—
178C24Dic17814yescomplemented
179C24C22×D8911yescharacteristic
180C24C22×D8912yes—
181C2×Q8—3561no—
182C2×Q8—1784no—
183C22×C4—892no—
184C22×C4—892no—
185C22×C4—892no—
186C22×C4—892no—
187C22×C4—3562no—
188C22×C4—3562no—
189C22×C4—1784no—
190C22×C4—1784no—
191C22×C4—1784no—
192C22×C4—1784no—
193C22×C4C22×D8911yescharacteristic
194C22×C4C22×D8912yes—
195C22×C4C22×D8911yescharacteristic
196C4⋊C4—3562no—
197C4⋊C4—3561no—
198C4⋊C4—1784no—
199C4⋊C4—1784no—
200C4⋊C4—1784no—
201C22⋊C4—24no—
202C22⋊C4—24no—
203C22⋊C4—41no—
204C22⋊C4—41no—
205C22⋊C4—898no—
206C22⋊C4—1784no—
207C22⋊C4—1784no—
208C22⋊C4—1784no—
209C23—22no—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—216no—
214C23—22no—
215C23—22no—
216C23—21no—
217C23—21no—
218C23—44no—
219C23—44no—
220C23—48no—
221C23—44no—
222C23D4×D8914yes—
223C23C2×Dic17812yes—
224C23C2×Dic17814yes—
225C23#1308357314yes—
226C23C23×D8911yescharacteristic
227Q8—3564no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—894no—
236C2×C4—894no—
237C2×C4—3568no—
238C2×C4—3568no—
239C2×C4—1782no—
240C2×C4—1782no—
241C2×C4—1782no—
242C2×C4—1782no—
243C2×C4—1782no—
244C2×C4—1782no—
245C2×C4—1782no—
246C2×C4—1782no—
247C2×C4—1782no—
248C2×C4—1782no—
249C22—24no—
250C22—24no—
251C22—24no—
252C22—24no—
253C22—24no—
254C22—24no—
255C22—22no—
256C22—24no—
257C22—416no—
258C22—41no—
259C22—42no—
260C22—41no—
261C22#1566798918yescomplemented
262C22C2×D4×D8912yes—
263C22C22×Dic17811yescharacteristic
264C22C2×#1308357312yes—
265C22#1566805711yescharacteristic
266C22#1566805711yescharacteristic
267C4—41no—
268C4—42no—
269C4—41no—
270C4—3562no—
271C4—3562no—
272C4—1784no—
273C4—1784no—
274C2—28no—
275C2—42no—
276C2C2×#1566798912yes—
277C2#1915222411yescharacteristic
278C2#1915223011yescharacteristic
279C2#1915223512yes—
280C2#1915227911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#379×C89C2
prime radicalC25×C89C22
hypercenter#379D89
hypocenterC89#2437
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#15667989C2semidirect
3. #19151534C2semidirect
4. #19151521C2semidirect
5. #19151510C2semidirect
6. #19151473C2semidirect
7. #19151470C2semidirect
8. #19151456C2semidirect
10. C22×Dic178C22semidirect
14. C2×C4⋊Dic89C22semidirect
15. C2×C4⋊Dic89C22semidirect
16. C2×#13083553C22semidirect
17. C2×#13083553C22semidirect
18. C2×#13083553C22semidirect
24. #15667919C22semidirect
25. #15667919C22semidirect
26. #15667919C22semidirect
27. #15667919C22semidirect
58. C24×C89Q8semidirect
120. C22×C89C22⋊Q8semidirect
141. C89#2437semidirect
178. C24Dic178semidirect
261. C22#15667989semidirect

Maximal subgroups

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

subgroupindex
C2×#156679892
C22×C22⋊Dic892
#191515342
#191515212
#191515102
#191514732
#191514702
#191514562
#379×C892
#243789