Finite Group Databasebeta

← #26026017

Subgroups — #26026017

Order 11392.

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

normal subgroups only

This group has 528 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×#15668011C211yesmaximal, characteristic, complemented
2C2×#15667989C212yesmaximal
3C2×#15667968C211yesmaximal, characteristic
4#19151532C212yesmaximal, complemented
5#19151530C211yesmaximal, characteristic, complemented
6#19151529C211yesmaximal, characteristic, complemented
7#19151526C212yesmaximal
8#19151523C211yesmaximal, characteristic
9#19151502C212yesmaximal, complemented
10#19151462C211yesmaximal, characteristic, complemented
11#397×C89C211yesmaximal, characteristic
12C22×Dic178C2212yes—
13C23×Dic89C2211yescharacteristic
14#15668011—24no—
15#15667989—28no—
16#15667968—24no—
17C2×C4⋊Dic89C2211yescharacteristic
18C2×C4⋊Dic89C2212yes—
19C2×#13083553C2212yes—
20C2×#13083553C2212yes—
21C2×#13083553C2211yescharacteristic
22C2×#13083553C2212yes—
23C2×#13083553C2211yescharacteristic
24C2×C22⋊Dic89C2212yes—
25C2×C22⋊Dic89C2211yescharacteristic
26C2×C4×Dic89C2211yescharacteristic
27C2×C4×Dic89C2211yescharacteristic
28#15667919C2211yescharacteristic
29#15667919C2212yes—
30#15667919C2212yes—
31#15667919C2212yes—
32#15667919C2212yes—
33C2×C4⋊C4×C89C2211yescharacteristic
34C2×C22⋊C4×C89C2211yescharacteristic
35C2×C22⋊C4×C89C2212yes—
36#95×C89C2211yescharacteristic
37#95×C89C2212yes—
38C2×Dic178—24no—
39C2×Dic178—24no—
40C2×Dic178—24no—
41C22×Dic89—22no—
42C22×Dic89—22no—
43C22×Dic89D414yes—
44C22×Dic89C2312yes—
45C22×Dic89C2311yescharacteristic
46C22×Dic89C2312yes—
47C22×Dic89C2311yescharacteristic
48C22×Dic89C2311yescharacteristic
49C22×Dic89C2311yescharacteristic
50C4⋊Dic89—22no—
51C4⋊Dic89—24no—
52#13083553—22no—
53#13083553—22no—
54#13083553—24no—
55#13083553—24no—
56#13083553—24no—
57C22⋊Dic89—24no—
58C22⋊Dic89—22no—
59C4×Dic89—22no—
60C4×Dic89D414yes—
61C24×C89C2311yescharacteristic
62C22×C4×C89C2312yes—
63C22×C4×C89C2311yescharacteristic
64C22×C4×C89C2312yes—
65C22×C4×C89C2311yescharacteristic
66C4⋊C4×C89—22no—
67C22⋊C4×C89—24no—
68C22⋊C4×C89—22no—
69C23×C89—21no—
70C23×C89—21no—
71C23×C89—22no—
72C23×C89—22no—
73C23×C89C2×D412yes—
74C23×C89C2411yescharacteristic
75C2×C4×C89—22no—
76C2×C4×C89—21no—
77C2×C4×C89—22no—
78C2×C4×C89—22no—
79C2×C4×C89—22no—
80C2×C4×C89—22no—
81C2×C4×C89—22no—
82C2×C4×C89—22no—
83C2×C4×C89—22no—
84C2×C4×C89C2×D412yes—
85C2×Dic89—21no—
86C2×Dic89—21no—
87C2×Dic89—22no—
88C2×Dic89—28no—
89C2×Dic89—21no—
90C2×Dic89—22no—
91C2×Dic89—22no—
92C2×Dic89—22no—
93C2×Dic89—22no—
94C2×Dic89—22no—
95C2×Dic89—22no—
96C2×Dic89—22no—
97C2×Dic89C2×D412yes—
98C2×Dic89C2×D412yes—
99C2×Dic89C2×D412yes—
100C2×Dic89C2×D412yes—
101C2×Dic89#4112yes—
102Dic178—48no—
103C22×C89—22no—
104C22×C89—24no—
105C22×C89—41no—
106C22×C89—41no—
107C22×C89—42no—
108C22×C89C22×D411yescharacteristic
109C22×C89C22×D411yescharacteristic
110C22×C89C2×#4111yescharacteristic
111C22×C892−1+412yes—
112C22×C892−1+412yes—
113C4×C89—22no—
114C4×C89—42no—
115C4×C89—41no—
116C4×C89—42no—
117Dic89—22no—
118Dic89—22no—
119Dic89—42no—
120Dic89—41no—
121Dic89—42no—
122Dic89#12114yes—
123C2×C89—42no—
124C2×C89C2×#12111yescharacteristic
125C2×C89#53611yescharacteristic
126C2×C89#53611yescharacteristic
127C2×C89#53612yes—
128C2×C89#54112yes—
129#2621—891nomaximal, Sylow
130C89#262111yescharacteristic, complemented, Sylow
131C2×C4⋊Q8—891no—
132C2×C22⋊Q8—892no—
133C2×#117—891no—
134#398—891no—
135#398—891no—
136#398—892no—
137#397—891no—
138#397—892no—
139#397D8911yescharacteristic
140#391—892no—
141#382—891no—
142C22×Q8—892no—
143C23×C4—891no—
144C4⋊Q8—1784no—
145C22⋊Q8—1788no—
146#117—1784no—
147C2×C4⋊C4—891no—
148C2×C4⋊C4—891no—
149C2×C4⋊C4—892no—
150C2×C4⋊C4—892no—
151C2×C4⋊C4—892no—
152C2×C4⋊C4—892no—
153C2×C4⋊C4—891no—
154C2×C4⋊C4C2×D8911yescharacteristic
155C2×C22⋊C4—891no—
156C2×C22⋊C4—892no—
157C2×C22⋊C4C2×D8911yescharacteristic
158C2×C22⋊C4C2×D8912yes—
159C2×C42—891no—
160C2×C42—891no—
161#95—892no—
162#95—891no—
163#95—892no—
164#95—892no—
165#95—892no—
166#95C2×D8911yescharacteristic
167#95C2×D8912yes—
168C24C22×D8911yescharacteristic
169C2×Q8—1784no—
170C2×Q8—1784no—
171C2×Q8—1784no—
172C22×C4—891no—
173C22×C4—894no—
174C22×C4—891no—
175C22×C4—891no—
176C22×C4—891no—
177C22×C4—892no—
178C22×C4—892no—
179C22×C4—1782no—
180C22×C4—1782no—
181C22×C4C22×D8911yescharacteristic
182C22×C4C22×D8912yes—
183C22×C4C22×D8912yes—
184C22×C4C22×D8911yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—1782no—
187C4⋊C4—1784no—
188C4⋊C4—1784no—
189C4⋊C4—1784no—
190C4⋊C4—1784no—
191C4⋊C4—1782no—
192C4⋊C4—1782no—
193C22⋊C4—24no—
194C22⋊C4—22no—
195C22⋊C4—1782no—
196C22⋊C4—1784no—
197C42—894no—
198C42—1782no—
199C23—21no—
200C23—21no—
201C23—22no—
202C23—22no—
203C23D4×D8912yes—
204C23C23×D8911yescharacteristic
205Q8—3568no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—892no—
216C2×C4—892no—
217C2×C4—892no—
218C2×C4—892no—
219C2×C4—892no—
220C2×C4—1788no—
221C2×C4—1781no—
222C2×C4—1782no—
223C2×C4—1782no—
224C2×C4—1782no—
225C2×C4—1782no—
226C2×C4—1782no—
227C2×C4—1782no—
228C2×C4—1782no—
229C2×C4—1781no—
230C2×C4—1781no—
231C2×C4—1782no—
232C2×C4D4×D8912yes—
233C22—24no—
234C22—22no—
235C22—41no—
236C22—41no—
237C22—42no—
238C22C2×D4×D8911yescharacteristic
239C22C2×D4×D8911yescharacteristic
240C22#41×D8911yescharacteristic
241C22#1566805912yes—
242C22#1566805912yes—
243C4—22no—
244C4—41no—
245C4—42no—
246C4—42no—
247C4—894no—
248C4—3561no—
249C4—3562no—
250C4—3562no—
251C4—1782no—
252C4—1782no—
253C2—42no—
254C2#121×D8911yescharacteristic
255C2#1915216811yescharacteristic
256C2#1915217011yescharacteristic
257C2#1915217012yes—
258C2#1915220512yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#397×C89C2
prime radicalC24×C89C23
hypercenter#397D89
hypocenterC89#2621
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#15668011C2semidirect
4. #19151532C2semidirect
5. #19151530C2semidirect
6. #19151529C2semidirect
9. #19151502C2semidirect
10. #19151462C2semidirect
130. C89#2621semidirect

Maximal subgroups

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

subgroupindex
C2×#156680112
C2×#156679892
C2×#156679682
#191515322
#191515302
#191515292
#191515262
#191515232
#191515022
#191514622
#397×C892
#262189