Finite Group Databasebeta

← #26025830

Subgroups — #26025830

Order 11392.

492 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 135 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×#15667968C211yesmaximal, characteristic
3#19151529C211yesmaximal, characteristic, complemented
4#19151519C211yesmaximal, characteristic, complemented
5#19151510C211yesmaximal, characteristic
6#19151491C212yesmaximal
7#19151481C212yesmaximal, complemented
8#19151480C212yesmaximal, complemented
9#19151470C212yesmaximal
10#19151465C211yesmaximal, characteristic, complemented
11#397×C89C211yesmaximal, characteristic
12C22×Dic178C2211yescharacteristic
13C23×Dic89C2211yescharacteristic
14#15667977—24no—
15#15667968—24no—
16C2×C4⋊Dic89C2212yes—
17C2×#13083553C2212yes—
18C2×#13083553C2212yes—
19C2×#13083553C2211yescharacteristic
20C2×#13083553C2211yescharacteristic
21C2×C22⋊Dic89C2212yes—
22C2×C22⋊Dic89C2211yescharacteristic
23C2×C4×Dic89C2212yes—
24C2×C4×Dic89C2211yescharacteristic
25C2×C4×Dic89C2211yescharacteristic
26#15667919C2212yes—
27#15667919C2212yes—
28#15667919C2211yescharacteristic
29#15667919C2212yes—
30#15667919C2212yes—
31#15667919C2212yes—
32C2×C4⋊C4×C89C2211yescharacteristic
33C2×C22⋊C4×C89C2212yes—
34C2×C22⋊C4×C89C2211yescharacteristic
35#95×C89C2211yescharacteristic
36#95×C89C2212yes—
37C2×Dic178—22no—
38C2×Dic178—24no—
39C22×Dic89—22no—
40C22×Dic89—22no—
41C22×Dic89—22no—
42C22×Dic89C2312yes—
43C22×Dic89C2311yescharacteristic
44C22×Dic89C2311yescharacteristic
45C22×Dic89C2311yescharacteristic
46C22×Dic89C2311yescharacteristic
47C22×Dic89C2312yes—
48C4⋊Dic89—24no—
49#13083553—22no—
50#13083553—22no—
51#13083553—24no—
52#13083553—24no—
53C22⋊Dic89—22no—
54C22⋊Dic89—24no—
55C4×Dic89—22no—
56C4×Dic89—24no—
57C4×Dic89D414yes—
58C24×C89C2311yescharacteristic
59C22×C4×C89C2312yes—
60C22×C4×C89C2311yescharacteristic
61C22×C4×C89C2312yes—
62C22×C4×C89C2311yescharacteristic
63C4⋊C4×C89—22no—
64C22⋊C4×C89—24no—
65C22⋊C4×C89—22no—
66C23×C89—21no—
67C23×C89—22no—
68C23×C89—21no—
69C23×C89—22no—
70C23×C89#4112yes—
71C23×C89C2411yescharacteristic
72C2×C4×C89—22no—
73C2×C4×C89—21no—
74C2×C4×C89—22no—
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×C89C2×D412yes—
82C2×Dic89—28no—
83C2×Dic89—22no—
84C2×Dic89—21no—
85C2×Dic89—21no—
86C2×Dic89—21no—
87C2×Dic89—21no—
88C2×Dic89—22no—
89C2×Dic89—22no—
90C2×Dic89—21no—
91C2×Dic89—22no—
92C2×Dic89—22no—
93C2×Dic89—22no—
94C2×Dic89—22no—
95C2×Dic89C2×D412yes—
96C2×Dic89C2×D412yes—
97C2×Dic89#4114yes—
98C2×Dic89#4112yes—
99Dic178—28no—
100C22×C89—22no—
101C22×C89—24no—
102C22×C89—41no—
103C22×C89—41no—
104C22×C89—42no—
105C22×C89C22×D411yescharacteristic
106C22×C89C2×#4111yescharacteristic
107C22×C89C2×#4112yes—
108C22×C89C2×#4111yescharacteristic
109C22×C892−1+412yes—
110C4×C89—22no—
111C4×C89—42no—
112C4×C89—41no—
113C4×C89—42no—
114Dic89—24no—
115Dic89—22no—
116Dic89—22no—
117Dic89—22no—
118Dic89—41no—
119Dic89—42no—
120C2×C89—42no—
121C2×C89#52511yescharacteristic
122C2×C89#52511yescharacteristic
123C2×C89#53611yescharacteristic
124C2×C89#55212yes—
125C2×C89#55612yes—
126#2599—891nomaximal, Sylow
127C89#259911yescharacteristic, complemented, Sylow
128C2×C4×Q8—891no—
129C2×#117—891no—
130#398—891no—
131#397D8911yescharacteristic
132#395—891no—
133#393—891no—
134#388—892no—
135#387—892no—
136#387—892no—
137#385—892no—
138#383—891no—
139C22×Q8—891no—
140C23×C4—891no—
141C4×Q8—1784no—
142#117—1784no—
143C2×C4⋊C4—891no—
144C2×C4⋊C4—891no—
145C2×C4⋊C4—892no—
146C2×C4⋊C4—892no—
147C2×C4⋊C4—892no—
148C2×C4⋊C4C2×D8911yescharacteristic
149C2×C22⋊C4—891no—
150C2×C22⋊C4—892no—
151C2×C22⋊C4C2×D8911yescharacteristic
152C2×C22⋊C4C2×D8912yes—
153C2×C42—891no—
154C2×C42—891no—
155C2×C42—892no—
156#95—892no—
157#95—892no—
158#95—891no—
159#95—892no—
160#95—892no—
161#95—892no—
162#95C2×D8911yescharacteristic
163#95C2×D8912yes—
164C24C22×D8911yescharacteristic
165C2×Q8—1784no—
166C2×Q8—1782no—
167C22×C4—891no—
168C22×C4—891no—
169C22×C4—892no—
170C22×C4—891no—
171C22×C4—892no—
172C22×C4—891no—
173C22×C4—1782no—
174C22×C4—1782no—
175C22×C4—1782no—
176C22×C4C22×D8912yes—
177C22×C4C22×D8911yescharacteristic
178C22×C4C22×D8912yes—
179C22×C4C22×D8911yescharacteristic
180C4⋊C4—22no—
181C4⋊C4—1782no—
182C4⋊C4—1784no—
183C4⋊C4—1784no—
184C4⋊C4—1784no—
185C4⋊C4—1782no—
186C22⋊C4—24no—
187C22⋊C4—22no—
188C22⋊C4—1782no—
189C22⋊C4—1784no—
190C42—894no—
191C42—1782no—
192C42—1784no—
193C23—21no—
194C23—22no—
195C23—21no—
196C23—22no—
197C23#1308357312yes—
198C23C23×D8911yescharacteristic
199Q8—1788no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—892no—
210C2×C4—892no—
211C2×C4—894no—
212C2×C4—892no—
213C2×C4—1781no—
214C2×C4—1782no—
215C2×C4—1782no—
216C2×C4—1782no—
217C2×C4—1782no—
218C2×C4—1788no—
219C2×C4—1782no—
220C2×C4—1781no—
221C2×C4—1781no—
222C2×C4—1782no—
223C2×C4—1781no—
224C2×C4—1781no—
225C2×C4—1782no—
226C2×C4D4×D8912yes—
227C22—24no—
228C22—22no—
229C22—41no—
230C22—42no—
231C22—41no—
232C22C2×D4×D8911yescharacteristic
233C22#41×D8912yes—
234C22#41×D8911yescharacteristic
235C22C2×#1308357311yescharacteristic
236C22#1566805912yes—
237C4—22no—
238C4—41no—
239C4—42no—
240C4—42no—
241C4—3562no—
242C4—3561no—
243C4—1782no—
244C4—1784no—
245C4—1782no—
246C4—1782no—
247C2—42no—
248C2#1915210611yescharacteristic
249C2#1915210811yescharacteristic
250C2#1915216811yescharacteristic
251C2#1915228512yes—
252C2#1915231512yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#397×C89C2
prime radicalC24×C89C23
hypercenter#397D89
hypocenterC89#2599
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#15667977C2semidirect
3. #19151529C2semidirect
4. #19151519C2semidirect
7. #19151481C2semidirect
8. #19151480C2semidirect
10. #19151465C2semidirect
127. C89#2599semidirect

Maximal subgroups

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

subgroupindex
C2×#156679772
C2×#156679682
#191515292
#191515192
#191515102
#191514912
#191514812
#191514802
#191514702
#191514652
#397×C892
#259989