Finite Group Databasebeta

← #26023541

Subgroups — #26023541

Order 11392.

568 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 143 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×#15667977C211yesmaximal, characteristic, complemented
2C2×#15667974C211yesmaximal, characteristic
3#19151536C211yesmaximal, characteristic, complemented
4#19151527C212yesmaximal, complemented
5#19151516C211yesmaximal, characteristic
6#19151515C211yesmaximal, characteristic
7#19151511C212yesmaximal, complemented
8#19151445C212yesmaximal, complemented
9#19151445C212yesmaximal, complemented
10#19151443C211yesmaximal, characteristic, complemented
11#400×C89C211yesmaximal, characteristic, complemented
12C22×Dic178C2211yescharacteristic
13C22×D356C2211yescharacteristic
14C22×C4×D89C2212yes—
15#15667977—24no—
16#15667974—24no—
17C2×#13083553C2211yescharacteristic
18C2×#13083553C2211yescharacteristic
19C2×#13083551C2212yes—
20C2×#13083551C2212yes—
21C2×#13083551C2212yes—
22C2×#13083551C2212yes—
23C2×#13083551C2212yes—
24C2×C4×Dic89C2212yes—
25C2×C4×Dic89C2211yescharacteristic
26C2×C4×Dic89C2211yescharacteristic
27C2×C4×Dic89C2211yescharacteristic
28#15667919C2212yes—
29#15667919C2211yescharacteristic
30#15667919C2212yes—
31#15667919C2212yes—
32C2×C4⋊C4×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2211yescharacteristic
34#95×C89C2211yescharacteristic
35#95×C89C2212yes—
36#95×C89C2212yes—
37C23×D89C2312yes—
38C2×Dic178—22no—
39C2×Dic178—22no—
40C2×Dic178—22no—
41C2×D356—24no—
42C2×D356—22no—
43C22×Dic89C2312yes—
44C22×Dic89C2311yescharacteristic
45C22×Dic89C2311yescharacteristic
46C22×Dic89C2311yescharacteristic
47C22×Dic89C2311yescharacteristic
48C2×C4×D89—24no—
49C2×C4×D89—24no—
50C2×C4×D89—24no—
51#13083553—22no—
52#13083553—22no—
53#13083551—24no—
54#13083551—24no—
55#13083551—24no—
56#13083551—24no—
57#13083551—24no—
58C4×Dic89—22no—
59C4×Dic89—22no—
60C4×Dic89—24no—
61C4×Dic89D414yes—
62C22×C4×C89C2312yes—
63C22×C4×C89C2312yes—
64C22×C4×C89C2311yescharacteristic
65C22×C4×C89C2311yescharacteristic
66C22×C4×C89C2311yescharacteristic
67C4⋊C4×C89—22no—
68C4⋊C4×C89—22no—
69C23×C89C2411yescharacteristic
70C22×D89—22no—
71C22×D89—22no—
72C22×D89—22no—
73C22×D89—22no—
74C22×D89—22no—
75C22×D89—22no—
76C22×D89#4114yes—
77C2×C4×C89—21no—
78C2×C4×C89—22no—
79C2×C4×C89—21no—
80C2×C4×C89—21no—
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—22no—
88C2×C4×C89C2×D412yes—
89C2×C4×C89#4112yes—
90C2×Dic89—21no—
91C2×Dic89—21no—
92C2×Dic89—21no—
93C2×Dic89—21no—
94C2×Dic89—21no—
95C2×Dic89—22no—
96C2×Dic89—22no—
97C2×Dic89—22no—
98C2×Dic89—22no—
99C2×Dic89C2×D412yes—
100C2×Dic89C2×D412yes—
101C2×Dic89#4112yes—
102C2×Dic89#4114yes—
103D356—28no—
104C4×D89—48no—
105Dic178—28no—
106C22×C89C22×D411yescharacteristic
107C22×C89C2×#4112yes—
108C22×C89C2×#4111yescharacteristic
109C22×C89C2×#4111yescharacteristic
110C22×C89C2×#4112yes—
111C2×D89—24no—
112C2×D89—24no—
113C2×D89—24no—
114C2×D89—42no—
115C2×D89—42no—
116C2×D89—42no—
117C2×D89—42no—
118C4×C89—22no—
119C4×C89—22no—
120C4×C89—41no—
121C4×C89—42no—
122C4×C89—42no—
123Dic89—22no—
124Dic89—22no—
125Dic89—41no—
126Dic89—42no—
127Dic89#12414yes—
128C2×C89#52511yescharacteristic
129C2×C89#52511yescharacteristic
130C2×C89C2×#12411yescharacteristic
131C2×C89#52912yes—
132C2×C89#52912yes—
133D89—44no—
134#2398—891nomaximal, Sylow
135C89#239811yescharacteristic, complemented, Sylow
136C2×C4×Q8—891no—
137C2×C4×D4—891no—
138#400—891no—
139#400D8911yescharacteristic, complemented
140#397—892no—
141#394—891no—
142#394—891no—
143#393—892no—
144C4×C22⋊C4—892no—
145C4×C22⋊C4—892no—
146#376—891no—
147C22×Q8—891no—
148C22×D4—891no—
149C23×C4—892no—
150C4×Q8—1784no—
151C4×D4—1784no—
152C2×C4⋊C4—891no—
153C2×C4⋊C4—891no—
154C2×C4⋊C4C2×D8911yescharacteristic
155C2×C4⋊C4C2×D8911yescharacteristic
156C2×C22⋊C4—892no—
157C2×C22⋊C4—892no—
158C2×C22⋊C4—892no—
159C2×C22⋊C4—892no—
160C2×C22⋊C4—892no—
161C2×C42—891no—
162C2×C42—891no—
163C2×C42—891no—
164C2×C42—892no—
165#95—892no—
166#95—891no—
167#95—892no—
168#95—892no—
169#95C2×D8911yescharacteristic
170#95C2×D8912yes—
171#95C2×D8912yes—
172C24—892no—
173C2×Q8—1782no—
174C2×Q8—1782no—
175C2×Q8—1782no—
176C2×D4—1784no—
177C2×D4—1782no—
178C22×C4—891no—
179C22×C4—891no—
180C22×C4—891no—
181C22×C4—892no—
182C22×C4—891no—
183C22×C4—1784no—
184C22×C4—1784no—
185C22×C4—1784no—
186C22×C4C22×D8912yes—
187C22×C4C22×D8912yes—
188C22×C4C22×D8911yescharacteristic
189C22×C4C22×D8911yescharacteristic
190C22×C4C22×D8911yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—1782no—
194C4⋊C4—1782no—
195C22⋊C4—1784no—
196C22⋊C4—1784no—
197C22⋊C4—1784no—
198C22⋊C4—1784no—
199C22⋊C4—1784no—
200C42—894no—
201C42—1782no—
202C42—1782no—
203C42—1784no—
204C23—894no—
205C23—1782no—
206C23—1782no—
207C23—1782no—
208C23—1782no—
209C23—1782no—
210C23—1782no—
211C23C23×D8911yescharacteristic
212Q8—1788no—
213D4—1788no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—892no—
226C2×C4—894no—
227C2×C4—892no—
228C2×C4—892no—
229C2×C4—3568no—
230C2×C4—1781no—
231C2×C4—1782no—
232C2×C4—1782no—
233C2×C4—1782no—
234C2×C4—1782no—
235C2×C4—1781no—
236C2×C4—1781no—
237C2×C4—1781no—
238C2×C4—1781no—
239C2×C4D4×D8912yes—
240C2×C4#1308357512yes—
241C22—3562no—
242C22—3562no—
243C22—3562no—
244C22—3562no—
245C22—1784no—
246C22—1784no—
247C22—1784no—
248C22C2×D4×D8911yescharacteristic
249C22#41×D8911yescharacteristic
250C22#41×D8912yes—
251C22#41×D8912yes—
252C22C2×#1308357511yescharacteristic
253C4—22no—
254C4—22no—
255C4—42no—
256C4—41no—
257C4—42no—
258C4—894no—
259C4—3562no—
260C4—3561no—
261C4—1782no—
262C4—1782no—
263C2—3564no—
264C2#1915210611yescharacteristic
265C2#1915211111yescharacteristic
266C2#124×D8911yescharacteristic
267C2#1915213112yes—
268C2#1915213312yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#400×C89C2
prime radicalC22×D356C22
hypercenter#400D89
hypocenterC89#2398
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#15667977C2semidirect
3. #19151536C2semidirect
4. #19151527C2semidirect
7. #19151511C2semidirect
8. #19151445C2semidirect
9. #19151445C2semidirect
10. #19151443C2semidirect
11. #400×C89C2semidirect
135. C89#2398semidirect
139. #400D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679772
C2×#156679742
#191515362
#191515272
#191515162
#191515152
#191515112
#191514452
#191514432
#400×C892
#239889