Finite Group Databasebeta

← #26025832

Subgroups — #26025832

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×#15667970C211yesmaximal, characteristic
3#19151524C211yesmaximal, characteristic
4#19151518C211yesmaximal, characteristic, complemented
5#19151511C211yesmaximal, characteristic
6#19151487C212yesmaximal
7#19151484C212yesmaximal, complemented
8#19151480C212yesmaximal, complemented
9#19151469C212yesmaximal
10#19151465C211yesmaximal, characteristic, complemented
11#398×C89C211yesmaximal, characteristic, complemented
12C22×Dic178C2211yescharacteristic
13C22×C4×D89C2211yescharacteristic
14#15667977—24no—
15#15667970—24no—
16C2×C4⋊Dic89C2211yescharacteristic
17C2×#13083553C2212yes—
18C2×#13083553C2212yes—
19C2×#13083551C2212yes—
20C2×#13083551C2212yes—
21C2×#13083551C2211yescharacteristic
22C2×#13083551C2211yescharacteristic
23C2×C4×Dic89C2211yescharacteristic
24C2×C4×Dic89C2212yes—
25C2×C4×Dic89C2211yescharacteristic
26#15667919C2212yes—
27#15667919C2212yes—
28#15667919C2211yescharacteristic
29#15667919C2212yes—
30#15667919C2212yes—
31#15667919C2212yes—
32C2×C4⋊C4×C89C2212yes—
33C2×C4⋊C4×C89C2211yescharacteristic
34C2×C4⋊C4×C89C2211yescharacteristic
35#95×C89C2211yescharacteristic
36#95×C89C2212yes—
37C23×D89C2311yescharacteristic
38C2×Dic178—22no—
39C2×Dic178—24no—
40C22×Dic89C2312yes—
41C22×Dic89C2311yescharacteristic
42C22×Dic89C2311yescharacteristic
43C22×Dic89C2311yescharacteristic
44C22×Dic89C2312yes—
45C2×C4×D89—22no—
46C2×C4×D89—22no—
47C2×C4×D89—22no—
48C4⋊Dic89—22no—
49#13083553—24no—
50#13083553—24no—
51#13083551—24no—
52#13083551—22no—
53#13083551—22no—
54#13083551—24no—
55C4×Dic89—22no—
56C4×Dic89—24no—
57C4×Dic89D414yes—
58C22×C4×C89C2312yes—
59C22×C4×C89C2311yescharacteristic
60C22×C4×C89C2312yes—
61C22×C4×C89C2311yescharacteristic
62C22×C4×C89C2311yescharacteristic
63C4⋊C4×C89—22no—
64C4⋊C4×C89—22no—
65C4⋊C4×C89—24no—
66C23×C89C2411yescharacteristic
67C22×D89—21no—
68C22×D89—22no—
69C22×D89—21no—
70C22×D89—22no—
71C22×D89#4112yes—
72C2×C4×C89—21no—
73C2×C4×C89—21no—
74C2×C4×C89—22no—
75C2×C4×C89—21no—
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×C89—22no—
83C2×C4×C89C2×D412yes—
84C2×C4×C89#4112yes—
85C2×Dic89—22no—
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—
98C4×D89—28no—
99Dic178—28no—
100C22×C89C22×D411yescharacteristic
101C22×C89C2×#4111yescharacteristic
102C22×C89C2×#4112yes—
103C22×C89C2×#4111yescharacteristic
104C22×C892−1+412yes—
105C2×D89—22no—
106C2×D89—24no—
107C2×D89—41no—
108C2×D89—41no—
109C2×D89—42no—
110C4×C89—22no—
111C4×C89—22no—
112C4×C89—41no—
113C4×C89—42no—
114C4×C89—42no—
115Dic89—24no—
116Dic89—22no—
117Dic89—22no—
118Dic89—41no—
119Dic89—42no—
120C2×C89#52511yescharacteristic
121C2×C89#52511yescharacteristic
122C2×C89#53611yescharacteristic
123C2×C89#55212yes—
124C2×C89#55612yes—
125D89—42no—
126#2599—891nomaximal, Sylow
127C89#259911yescharacteristic, complemented, Sylow
128C2×C4×Q8—891no—
129C2×#117—891no—
130#398D8911yescharacteristic, complemented
131#397—891no—
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—892no—
145C2×C4⋊C4—892no—
146C2×C4⋊C4C2×D8911yescharacteristic
147C2×C4⋊C4C2×D8911yescharacteristic
148C2×C4⋊C4C2×D8912yes—
149C2×C22⋊C4—891no—
150C2×C22⋊C4—891no—
151C2×C22⋊C4—892no—
152C2×C22⋊C4—892no—
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—
164C24—891no—
165C2×Q8—1784no—
166C2×Q8—1782no—
167C22×C4—891no—
168C22×C4—891no—
169C22×C4—892no—
170C22×C4—892no—
171C22×C4—891no—
172C22×C4—1782no—
173C22×C4—1782no—
174C22×C4—1782no—
175C22×C4C22×D8912yes—
176C22×C4C22×D8912yes—
177C22×C4C22×D8911yescharacteristic
178C22×C4C22×D8911yescharacteristic
179C22×C4C22×D8911yescharacteristic
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—24no—
183C4⋊C4—1782no—
184C4⋊C4—1784no—
185C4⋊C4—1784no—
186C22⋊C4—1782no—
187C22⋊C4—1784no—
188C22⋊C4—1784no—
189C22⋊C4—1782no—
190C42—894no—
191C42—1782no—
192C42—1784no—
193C23—892no—
194C23—1781no—
195C23—1782no—
196C23—1781no—
197C23—1782no—
198C23C23×D8911yescharacteristic
199Q8—1788no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—892no—
212C2×C4—892no—
213C2×C4—894no—
214C2×C4—1788no—
215C2×C4—1781no—
216C2×C4—1782no—
217C2×C4—1782no—
218C2×C4—1782no—
219C2×C4—1782no—
220C2×C4—1782no—
221C2×C4—1781no—
222C2×C4—1782no—
223C2×C4—1781no—
224C2×C4—1782no—
225C2×C4D4×D8912yes—
226C2×C4#1308357312yes—
227C22—3561no—
228C22—3562no—
229C22—3561no—
230C22—1784no—
231C22—1782no—
232C22C2×D4×D8911yescharacteristic
233C22#41×D8911yescharacteristic
234C22#41×D8912yes—
235C22C2×#1308357311yescharacteristic
236C22#1566806012yes—
237C4—22no—
238C4—22no—
239C4—42no—
240C4—41no—
241C4—42no—
242C4—3561no—
243C4—3562no—
244C4—1782no—
245C4—1784no—
246C4—1782no—
247C2—3562no—
248C2#1915210611yescharacteristic
249C2#1915210811yescharacteristic
250C2#1915217311yescharacteristic
251C2#1915228012yes—
252C2#1915231912yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#398×C89C2
prime radicalC23×D89C23
hypercenter#398D89
hypocenterC89#2599
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#15667977C2semidirect
4. #19151518C2semidirect
7. #19151484C2semidirect
8. #19151480C2semidirect
10. #19151465C2semidirect
11. #398×C89C2semidirect
127. C89#2599semidirect
130. #398D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679772
C2×#156679702
#191515242
#191515182
#191515112
#191514872
#191514842
#191514802
#191514692
#191514652
#398×C892
#259989