Finite Group Databasebeta

← #26025952

Subgroups — #26025952

Order 11392.

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

normal subgroups only

This group has 476 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×#15667969C211yesmaximal, characteristic
2#19151536C211yesmaximal, characteristic, complemented
3#19151533C211yesmaximal, characteristic
4#19151529C211yesmaximal, characteristic, complemented
5#19151524C211yesmaximal, characteristic
6#19151493C212yesmaximal, complemented
7#19151488C212yesmaximal
8#19151479C212yesmaximal, complemented
9#19151469C212yesmaximal
10#19151444C211yesmaximal, characteristic, complemented
11C2×#125×C89C211yesmaximal, characteristic, complemented
12C22×C4×D89C2211yescharacteristic
13#15667969—24no—
14C2×#13083553C2212yes—
15C2×#13083553C2212yes—
16C2×#13083553C2211yescharacteristic
17C2×#13083553C2211yescharacteristic
18C2×#13083551C2212yes—
19C2×#13083551C2212yes—
20C2×#13083551C2211yescharacteristic
21C2×#13083551C2211yescharacteristic
22C2×C4×Dic89C2212yes—
23C2×C4×Dic89C2211yescharacteristic
24#15667919C2212yes—
25#15667919C2211yescharacteristic
26#15667919C2211yescharacteristic
27#15667919C2212yes—
28#15667919C2212yes—
29#15667919C2212yes—
30#15667919C2212yes—
31#125×C89—24no—
32C2×C4⋊C4×C89C2212yes—
33C2×C4⋊C4×C89C2212yes—
34C2×C4⋊C4×C89C2211yescharacteristic
35C2×C4⋊C4×C89C2211yescharacteristic
36C2×C42×C89C2211yescharacteristic
37C23×D89C2311yescharacteristic
38C22×Dic89C2312yes—
39C22×Dic89C2311yescharacteristic
40C22×Dic89C2311yescharacteristic
41C22×Dic89C2311yescharacteristic
42C22×Dic89C2312yes—
43C2×C4×D89—22no—
44C2×C4×D89—22no—
45C2×C4×D89—22no—
46#13083553—22no—
47#13083553—22no—
48#13083553—24no—
49#13083553—24no—
50#13083551—24no—
51#13083551—22no—
52#13083551—22no—
53#13083551—24no—
54C4×Dic89—22no—
55C4×Dic89—24no—
56C22×C4×C89C2312yes—
57C22×C4×C89C2312yes—
58C22×C4×C89C2311yescharacteristic
59C22×C4×C89C2311yescharacteristic
60C22×C4×C89C2311yescharacteristic
61C4⋊C4×C89—24no—
62C4⋊C4×C89—24no—
63C4⋊C4×C89—22no—
64C4⋊C4×C89—22no—
65C42×C89D414yes—
66C23×C89C2411yescharacteristic
67C22×D89—21no—
68C22×D89—22no—
69C22×D89—21no—
70C22×D89—22no—
71C22×D89#4112yes—
72C2×C4×C89—22no—
73C2×C4×C89—21no—
74C2×C4×C89—21no—
75C2×C4×C89—22no—
76C2×C4×C89—22no—
77C2×C4×C89—22no—
78C2×C4×C89—22no—
79C2×C4×C89—22no—
80C2×C4×C89—22no—
81C2×C4×C89—22no—
82C2×C4×C89C2×D412yes—
83C2×C4×C89C2×D412yes—
84C2×C4×C89C2×D412yes—
85C2×Dic89—21no—
86C2×Dic89—22no—
87C2×Dic89—21no—
88C2×Dic89—22no—
89C2×Dic89—21no—
90C2×Dic89—21no—
91C2×Dic89—22no—
92C2×Dic89—22no—
93C2×Dic89—22no—
94C2×Dic89—22no—
95C2×Dic89—22no—
96C2×Dic89#4114yes—
97C2×Dic89#4112yes—
98C4×D89—28no—
99C22×C89C22×D411yescharacteristic
100C22×C89C2×#4111yescharacteristic
101C22×C89C2×#4111yescharacteristic
102C22×C89C2×#4112yes—
103C22×C892−1+412yes—
104C2×D89—22no—
105C2×D89—24no—
106C2×D89—41no—
107C2×D89—41no—
108C2×D89—42no—
109C4×C89—22no—
110C4×C89—22no—
111C4×C89—22no—
112C4×C89—42no—
113C4×C89—42no—
114Dic89—22no—
115Dic89—24no—
116Dic89—41no—
117Dic89—41no—
118Dic89—42no—
119C2×C89#52511yescharacteristic
120C2×C89#53211yescharacteristic
121C2×C89#53611yescharacteristic
122C2×C89#55212yes—
123C2×C89#55212yes—
124D89—42no—
125#2611—891nomaximal, Sylow
126C89#261111yescharacteristic, complemented, Sylow
127C2×#125D8911yescharacteristic, complemented
128C2×#117—891no—
129#400—891no—
130#399—891no—
131#398—891no—
132#397—891no—
133#389—892no—
134#388—892no—
135#387—892no—
136#385—892no—
137#376—891no—
138C23×C4—891no—
139#125—24no—
140#117—1784no—
141C2×C4⋊C4—891no—
142C2×C4⋊C4—891no—
143C2×C4⋊C4—892no—
144C2×C4⋊C4—892no—
145C2×C4⋊C4C2×D8912yes—
146C2×C4⋊C4C2×D8912yes—
147C2×C4⋊C4C2×D8911yescharacteristic
148C2×C4⋊C4C2×D8911yescharacteristic
149C2×C22⋊C4—891no—
150C2×C22⋊C4—891no—
151C2×C22⋊C4—892no—
152C2×C22⋊C4—892no—
153C2×C42—891no—
154C2×C42—892no—
155C2×C42C2×D8911yescharacteristic
156#95—892no—
157#95—891no—
158#95—891no—
159#95—892no—
160#95—892no—
161#95—892no—
162#95—892no—
163C24—891no—
164C22×C4—892no—
165C22×C4—891no—
166C22×C4—892no—
167C22×C4—891no—
168C22×C4—891no—
169C22×C4—1782no—
170C22×C4—1782no—
171C22×C4—1782no—
172C22×C4C22×D8912yes—
173C22×C4C22×D8912yes—
174C22×C4C22×D8911yescharacteristic
175C22×C4C22×D8911yescharacteristic
176C22×C4C22×D8911yescharacteristic
177C4⋊C4—24no—
178C4⋊C4—24no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—1784no—
182C4⋊C4—1784no—
183C4⋊C4—1782no—
184C4⋊C4—1782no—
185C22⋊C4—1784no—
186C22⋊C4—1784no—
187C22⋊C4—1782no—
188C22⋊C4—1782no—
189C42—1784no—
190C42—1782no—
191C42C22⋊D8914yes—
192C23—892no—
193C23—1781no—
194C23—1782no—
195C23—1781no—
196C23—1782no—
197C23C23×D8911yescharacteristic
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—894no—
209C2×C4—892no—
210C2×C4—1788no—
211C2×C4—1781no—
212C2×C4—1781no—
213C2×C4—1782no—
214C2×C4—1782no—
215C2×C4—1782no—
216C2×C4—1782no—
217C2×C4—1782no—
218C2×C4—1781no—
219C2×C4—1782no—
220C2×C4—1781no—
221C2×C4—1782no—
222C2×C4C2×C22⋊D8912yes—
223C2×C4C2×C22⋊D8912yes—
224C2×C4C2×C22⋊D8912yes—
225C22—3561no—
226C22—3561no—
227C22—3562no—
228C22—1784no—
229C22—1782no—
230C22C22×C22⋊D8911yescharacteristic
231C22#41×D8912yes—
232C22#41×D8911yescharacteristic
233C22#41×D8911yescharacteristic
234C22#1566806012yes—
235C4—22no—
236C4—22no—
237C4—22no—
238C4—42no—
239C4—42no—
240C4—3561no—
241C4—3561no—
242C4—3562no—
243C4—1784no—
244C4—1782no—
245C2—3562no—
246C2#1915210511yescharacteristic
247C2#1915214411yescharacteristic
248C2#1915217211yescharacteristic
249C2#1915228012yes—
250C2#1915228012yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
FittingC2×#125×C89C2
prime radicalC23×D89C23
hypercenterC2×#125D89
hypocenterC89#2611
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #19151536C2semidirect
4. #19151529C2semidirect
6. #19151493C2semidirect
8. #19151479C2semidirect
10. #19151444C2semidirect
11. C2×#125×C89C2semidirect
126. C89#2611semidirect
127. C2×#125D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679692
#191515362
#191515332
#191515292
#191515242
#191514932
#191514882
#191514792
#191514692
#191514442
C2×#125×C892
#261189