Finite Group Databasebeta

← #26024529

Subgroups — #26024529

Order 11392.

700 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 141 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×C22⋊C4×D89C212yesmaximal
2#19151526C212yesmaximal, complemented
3#19151523C211yesmaximal, characteristic, complemented
4#19151472C212yesmaximal, complemented
5#19151469C212yesmaximal, complemented
6#19151460C212yesmaximal, complemented
7#19151460C212yesmaximal, complemented
8#19151453C211yesmaximal, characteristic
9#397×C89C211yesmaximal, characteristic, complemented
10C24×D89C2211yescharacteristic
11C22×C4×D89C2212yes—
12C22×C4×D89C2212yes—
13C2×C4⋊Dic89C2211yescharacteristic, complemented
14C2×#13083553C2212yescomplemented
15C2×C22⋊Dic89C2212yes—
16C2×C22⋊Dic89C2211yescharacteristic
17C2×#13083551C2212yes—
18C2×#13083551C2212yes—
19C2×#13083551C2212yes—
20C2×#13083551C2212yes—
21C22⋊C4×D89—28no—
22#15667919C2211yescharacteristic, complemented
23#15667919C2212yescomplemented
24#15667919C2212yescomplemented
25#15667919C2212yescomplemented
26#15667919C2212yescomplemented
27C2×C4⋊C4×C89C2211yescharacteristic, complemented
28C2×C22⋊C4×C89C2212yes—
29C2×C22⋊C4×C89C2211yescharacteristic
30#95×C89C2211yescharacteristic, complemented
31#95×C89C2212yescomplemented
32C23×D89—24no—
33C23×D89—24no—
34C23×D89—41no—
35C23×D89—41no—
36C23×D89D414yes—
37C23×D89C2312yes—
38C22×Dic89C2312yes—
39C22×Dic89C2312yes—
40C22×Dic89C2312yes—
41C2×C4×D89—24no—
42C2×C4×D89—24no—
43C2×C4×D89—24no—
44C2×C4×D89—24no—
45C2×C4×D89—42no—
46C2×C4×D89—42no—
47C4⋊Dic89—41no—
48#13083553—42no—
49C22⋊Dic89—24no—
50C22⋊Dic89—41no—
51#13083551—24no—
52#13083551—24no—
53#13083551—24no—
54#13083551—24no—
55C24×C89C2311yescharacteristic
56C22×C4×C89C2312yes—
57C22×C4×C89C2312yes—
58C22×C4×C89C2311yescharacteristic
59C22×C4×C89C2311yescharacteristic
60C4⋊C4×C89—41no—
61C22⋊C4×C89—24no—
62C22⋊C4×C89—41no—
63C23×C89—22no—
64C23×C89—22no—
65C23×C89—21no—
66C23×C89—21no—
67C23×C89C2×D412yes—
68C23×C89C2411yescharacteristic
69C22×D89—22no—
70C22×D89—22no—
71C22×D89—22no—
72C22×D89—22no—
73C22×D89—216no—
74C22×D89—44no—
75C22×D89—48no—
76C22×D89—44no—
77C22×D89—44no—
78C22×D89C2×D414yes—
79C22×D89#4114yes—
80C22×D89#4114yes—
81C2×C4×C89—22no—
82C2×C4×C89—22no—
83C2×C4×C89—22no—
84C2×C4×C89—22no—
85C2×C4×C89—22no—
86C2×C4×C89—22no—
87C2×C4×C89—21no—
88C2×C4×C89—21no—
89C2×C4×C89—22no—
90C2×C4×C89—22no—
91C2×Dic89—22no—
92C2×Dic89—22no—
93C2×Dic89—22no—
94C2×Dic89—22no—
95C2×Dic89—22no—
96C2×Dic89—22no—
97C2×Dic89—22no—
98C2×Dic89—22no—
99C2×Dic89—22no—
100C4×D89—48no—
101C4×D89—48no—
102C22×C89—24no—
103C22×C89—22no—
104C22×C89—42no—
105C22×C89—41no—
106C22×C89—41no—
107C22×C89C22×D411yescharacteristic
108C22×C89C2×#4112yes—
109C22×C89C2×#4112yes—
110C22×C89H(5,𝔽2)11yescharacteristic
111C22×C89H(5,𝔽2)11yescharacteristic
112C2×D89—24no—
113C2×D89—24no—
114C2×D89—24no—
115C2×D89—24no—
116C2×D89—24no—
117C2×D89—24no—
118C2×D89—416no—
119C2×D89#12318yes—
120C4×C89—42no—
121C4×C89—42no—
122C4×C89—41no—
123C4×C89—41no—
124Dic89—42no—
125Dic89—42no—
126Dic89—42no—
127C2×C89—42no—
128C2×C89C2×#12312yes—
129C2×C89#53411yescharacteristic
130C2×C89#55112yes—
131C2×C89#55111yescharacteristic
132C2×C89#55111yescharacteristic
133D89—28no—
134#2483—891nomaximal, Sylow
135C89#248311yescharacteristic, complemented, Sylow
136C22×C22⋊C4—892no—
137#397—891no—
138#397—892no—
139#397D8911yescharacteristic, complemented
140#385—892no—
141#385—892no—
142#381—892no—
143#381—892no—
144#379—891no—
145C25—891no—
146C23×C4—892no—
147C23×C4—892no—
148C2×C4⋊C4—892no—
149C2×C4⋊C4—891no—
150C2×C4⋊C4C2×D8911yescharacteristic, complemented
151C2×C22⋊C4—891no—
152C2×C22⋊C4—892no—
153C2×C22⋊C4—892no—
154C2×C22⋊C4—892no—
155C2×C22⋊C4—892no—
156C2×C22⋊C4—892no—
157C2×C22⋊C4—1788no—
158C2×C22⋊C4C2×D8912yes—
159C2×C22⋊C4C2×D8911yescharacteristic
160#95—891no—
161#95—892no—
162#95—892no—
163#95—892no—
164#95—892no—
165#95C2×D8911yescharacteristic, complemented
166#95C2×D8912yescomplemented
167C24—892no—
168C24—894no—
169C24—3561no—
170C24—3561no—
171C24—1784no—
172C24—1784no—
173C24C22×D8911yescharacteristic
174C22×C4—892no—
175C22×C4—892no—
176C22×C4—892no—
177C22×C4—3562no—
178C22×C4—3562no—
179C22×C4—1784no—
180C22×C4—1784no—
181C22×C4—1784no—
182C22×C4—1784no—
183C22×C4C22×D8912yes—
184C22×C4C22×D8911yescharacteristic
185C22×C4C22×D8911yescharacteristic
186C22×C4C22×D8912yes—
187C4⋊C4—41no—
188C4⋊C4—3562no—
189C4⋊C4—3561no—
190C22⋊C4—24no—
191C22⋊C4—41no—
192C22⋊C4—3561no—
193C22⋊C4—1784no—
194C22⋊C4—1784no—
195C22⋊C4—1784no—
196C22⋊C4—1784no—
197C22⋊C4—1784no—
198C23—22no—
199C23—22no—
200C23—21no—
201C23—21no—
202C23—894no—
203C23—894no—
204C23—894no—
205C23—3564no—
206C23—3568no—
207C23—3564no—
208C23—3564no—
209C23—17816no—
210C23—1782no—
211C23—1782no—
212C23—1782no—
213C23—1782no—
214C23D4×D8912yes—
215C23C23×D8911yescharacteristic
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—3568no—
227C2×C4—3568no—
228C2×C4—1782no—
229C2×C4—1782no—
230C2×C4—1782no—
231C2×C4—1782no—
232C2×C4—1782no—
233C2×C4—1782no—
234C2×C4—1782no—
235C2×C4—1782no—
236C2×C4—1782no—
237C22—22no—
238C22—24no—
239C22—42no—
240C22—41no—
241C22—41no—
242C22—898no—
243C22—35616no—
244C22—1784no—
245C22—1784no—
246C22—1784no—
247C22—1784no—
248C22—1784no—
249C22—1784no—
250C22C2×D4×D8911yescharacteristic
251C22#41×D8912yes—
252C22#41×D8912yes—
253C22#1566805711yescharacteristic
254C22#1566805811yescharacteristic
255C4—42no—
256C4—41no—
257C4—41no—
258C4—42no—
259C4—3562no—
260C4—3562no—
261C4—3562no—
262C2—42no—
263C2—1788no—
264C2#123×D8912yes—
265C2#1915215611yescharacteristic
266C2#1915227312yes—
267C2#1915227611yescharacteristic
268C2#1915227811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#397×C89C2
prime radicalC24×D89C22
hypercenter#397D89
hypocenterC89#2483
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #19151526C2semidirect
3. #19151523C2semidirect
4. #19151472C2semidirect
5. #19151469C2semidirect
6. #19151460C2semidirect
7. #19151460C2semidirect
9. #397×C89C2semidirect
13. C2×C4⋊Dic89C22semidirect
14. C2×#13083553C22semidirect
22. #15667919C22semidirect
23. #15667919C22semidirect
24. #15667919C22semidirect
25. #15667919C22semidirect
26. #15667919C22semidirect
27. C2×C4⋊C4×C89C22semidirect
30. #95×C89C22semidirect
31. #95×C89C22semidirect
135. C89#2483semidirect
139. #397D89semidirect
150. C2×C4⋊C4C2×D89semidirect
165. #95C2×D89semidirect
166. #95C2×D89semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D892
#191515262
#191515232
#191514722
#191514692
#191514602
#191514532
#397×C892
#248389