Finite Group Databasebeta

← #26026020

Subgroups — #26026020

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×#15667990C212yesmaximal
3C2×#15667970C211yesmaximal, characteristic
4#19151531C212yesmaximal, complemented
5#19151528C211yesmaximal, characteristic, complemented
6#19151527C212yesmaximal
7#19151525C211yesmaximal, characteristic
8#19151524C211yesmaximal, characteristic
9#19151502C212yesmaximal, complemented
10#19151462C211yesmaximal, characteristic, complemented
11#398×C89C211yesmaximal, characteristic, complemented
12C22×Dic178C2212yes—
13C22×C4×D89C2211yescharacteristic
14#15668011—24no—
15#15667990—28no—
16#15667970—24no—
17C2×C4⋊Dic89C2211yescharacteristic
18C2×C4⋊Dic89C2211yescharacteristic
19C2×#13083553C2212yes—
20C2×#13083553C2212yes—
21C2×#13083553C2212yes—
22C2×#13083551C2211yescharacteristic
23C2×#13083551C2212yes—
24C2×#13083551C2212yes—
25C2×#13083551C2211yescharacteristic
26C2×C4×Dic89C2211yescharacteristic
27C2×C4×Dic89C2211yescharacteristic
28#15667919C2211yescharacteristic
29#15667919C2212yes—
30#15667919C2212yes—
31#15667919C2212yes—
32#15667919C2212yes—
33C2×C4⋊C4×C89C2211yescharacteristic
34C2×C4⋊C4×C89C2211yescharacteristic
35C2×C4⋊C4×C89C2212yes—
36#95×C89C2211yescharacteristic
37#95×C89C2212yes—
38C23×D89C2311yescharacteristic
39C2×Dic178—24no—
40C2×Dic178—24no—
41C2×Dic178—24no—
42C22×Dic89C2312yes—
43C22×Dic89C2311yescharacteristic
44C22×Dic89C2312yes—
45C22×Dic89C2311yescharacteristic
46C22×Dic89C2311yescharacteristic
47C2×C4×D89—22no—
48C2×C4×D89—22no—
49C2×C4×D89D414yes—
50C4⋊Dic89—22no—
51C4⋊Dic89—22no—
52#13083553—24no—
53#13083553—24no—
54#13083553—24no—
55#13083551—24no—
56#13083551—24no—
57#13083551—22no—
58#13083551—22no—
59C4×Dic89—22no—
60C4×Dic89D414yes—
61C22×C4×C89C2312yes—
62C22×C4×C89C2311yescharacteristic
63C22×C4×C89C2312yes—
64C22×C4×C89C2311yescharacteristic
65C22×C4×C89C2311yescharacteristic
66C4⋊C4×C89—22no—
67C4⋊C4×C89—24no—
68C4⋊C4×C89—22no—
69C23×C89C2411yescharacteristic
70C22×D89—21no—
71C22×D89—21no—
72C22×D89—22no—
73C22×D89—22no—
74C22×D89C2×D412yes—
75C2×C4×C89—21no—
76C2×C4×C89—21no—
77C2×C4×C89—22no—
78C2×C4×C89—21no—
79C2×C4×C89—22no—
80C2×C4×C89—22no—
81C2×C4×C89—22no—
82C2×C4×C89—22no—
83C2×C4×C89—22no—
84C2×C4×C89—22no—
85C2×C4×C89—22no—
86C2×C4×C89C2×D412yes—
87C2×C4×C89C2×D412yes—
88C2×Dic89—22no—
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×Dic89#4112yes—
101C4×D89—28no—
102Dic178—48no—
103C22×C89C22×D411yescharacteristic
104C22×C89C22×D411yescharacteristic
105C22×C89C2×#4111yescharacteristic
106C22×C892−1+412yes—
107C22×C892−1+412yes—
108C2×D89—22no—
109C2×D89—24no—
110C2×D89—41no—
111C2×D89—41no—
112C2×D89—42no—
113C4×C89—22no—
114C4×C89—22no—
115C4×C89—42no—
116C4×C89—41no—
117C4×C89—42no—
118Dic89—22no—
119Dic89—42no—
120Dic89—42no—
121Dic89—41no—
122Dic89#12114yes—
123C2×C89C2×#12111yescharacteristic
124C2×C89#53611yescharacteristic
125C2×C89#53612yes—
126C2×C89#53611yescharacteristic
127C2×C89#54112yes—
128D89—42no—
129#2621—891nomaximal, Sylow
130C89#262111yescharacteristic, complemented, Sylow
131C2×C4⋊Q8—891no—
132C2×C22⋊Q8—892no—
133C2×#117—891no—
134#398—891no—
135#398—892no—
136#398D8911yescharacteristic, complemented
137#397—891no—
138#397—891no—
139#397—892no—
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—892no—
149C2×C4⋊C4—892no—
150C2×C4⋊C4—892no—
151C2×C4⋊C4—891no—
152C2×C4⋊C4C2×D8911yescharacteristic
153C2×C4⋊C4C2×D8912yes—
154C2×C4⋊C4C2×D8911yescharacteristic
155C2×C22⋊C4—891no—
156C2×C22⋊C4—891no—
157C2×C22⋊C4—892no—
158C2×C22⋊C4—892no—
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—
168C24—891no—
169C2×Q8—1784no—
170C2×Q8—1784no—
171C2×Q8—1784no—
172C22×C4—891no—
173C22×C4—891no—
174C22×C4—894no—
175C22×C4—891no—
176C22×C4—892no—
177C22×C4—892no—
178C22×C4—1782no—
179C22×C4—1782no—
180C22×C4C22×D8911yescharacteristic
181C22×C4C22×D8912yes—
182C22×C4C22×D8912yes—
183C22×C4C22×D8911yescharacteristic
184C22×C4C22×D8911yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—24no—
187C4⋊C4—22no—
188C4⋊C4—1782no—
189C4⋊C4—1784no—
190C4⋊C4—1784no—
191C4⋊C4—1784no—
192C4⋊C4—1782no—
193C22⋊C4—1782no—
194C22⋊C4—1784no—
195C22⋊C4—1784no—
196C22⋊C4—1782no—
197C42—894no—
198C42—1782no—
199C23—892no—
200C23—1781no—
201C23—1781no—
202C23—1782no—
203C23—1782no—
204C23C23×D8911yescharacteristic
205Q8—3568no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—892no—
218C2×C4—892no—
219C2×C4—892no—
220C2×C4—892no—
221C2×C4—1788no—
222C2×C4—1781no—
223C2×C4—1782no—
224C2×C4—1782no—
225C2×C4—1782no—
226C2×C4—1782no—
227C2×C4—1782no—
228C2×C4—1782no—
229C2×C4—1782no—
230C2×C4—1782no—
231C2×C4D4×D8912yes—
232C2×C4D4×D8912yes—
233C22—3561no—
234C22—3561no—
235C22—3562no—
236C22—1784no—
237C22—1782no—
238C22C2×D4×D8911yescharacteristic
239C22C2×D4×D8911yescharacteristic
240C22#41×D8911yescharacteristic
241C22#1566805912yes—
242C22#1566806012yes—
243C4—22no—
244C4—22no—
245C4—41no—
246C4—42no—
247C4—42no—
248C4—894no—
249C4—3562no—
250C4—3561no—
251C4—3562no—
252C4—1782no—
253C2—3562no—
254C2#121×D8911yescharacteristic
255C2#1915217011yescharacteristic
256C2#1915217112yes—
257C2#1915217311yescharacteristic
258C2#1915220712yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#398×C89C2
prime radicalC23×D89C23
hypercenter#398D89
hypocenterC89#2621
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#15668011C2semidirect
4. #19151531C2semidirect
5. #19151528C2semidirect
9. #19151502C2semidirect
10. #19151462C2semidirect
11. #398×C89C2semidirect
130. C89#2621semidirect
136. #398D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156680112
C2×#156679902
C2×#156679702
#191515312
#191515282
#191515272
#191515252
#191515242
#191515022
#191514622
#398×C892
#262189