Finite Group Databasebeta

← #26026595

Subgroups — #26026595

Order 11392.

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

normal subgroups only

This group has 568 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×#15667993C212yesmaximal
2C2×#15667989C212yesmaximal, complemented
3#19151532C212yesmaximal, complemented
4#19151526C212yesmaximal, complemented
5#19151518C211yesmaximal, characteristic, complemented
6#19151486C212yesmaximal, complemented
7#19151473C212yesmaximal, complemented
8#19151467C211yesmaximal, characteristic, complemented
9#394×C89C211yesmaximal, characteristic
10C22×Dic178C2211yescharacteristic
11C23×Dic89C2212yes—
12#15667993—28no—
13#15667989—28no—
14C2×C4⋊Dic89C2212yes—
15C2×C4⋊Dic89C2211yescharacteristic
16C2×#13083553C2212yes—
17C2×#13083553C2212yes—
18C2×#13083553C2212yes—
19C2×#13083553C2212yes—
20C2×C22⋊Dic89C2212yes—
21C2×C22⋊Dic89C2212yes—
22C2×C22⋊Dic89C2212yes—
23C2×C4×Dic89C2211yescharacteristic
24#15667919C2212yes—
25#15667919C2212yes—
26#15667919C2212yes—
27#15667919C2211yescharacteristic
28C22×D4×C89C2211yescharacteristic
29C2×C4⋊C4×C89C2211yescharacteristic
30C2×C22⋊C4×C89C2212yes—
31C2×C22⋊C4×C89C2212yes—
32#95×C89C2211yescharacteristic
33C2×Dic178—24no—
34C2×Dic178—41no—
35C22×Dic89—24no—
36C22×Dic89—24no—
37C22×Dic89—42no—
38C22×Dic89C2312yes—
39C22×Dic89C2312yes—
40C22×Dic89C2312yes—
41C22×Dic89C2312yes—
42C4⋊Dic89—24no—
43C4⋊Dic89—41no—
44#13083553—24no—
45#13083553—24no—
46#13083553—24no—
47#13083553—24no—
48C22⋊Dic89—24no—
49C22⋊Dic89—24no—
50C22⋊Dic89D418yes—
51C4×Dic89—22no—
52C24×C89C2312yes—
53C2×D4×C89—24no—
54C2×D4×C89—41no—
55C22×C4×C89C2311yescharacteristic
56C22×C4×C89C2312yes—
57C22×C4×C89C2311yescharacteristic
58C22×C4×C89C2311yescharacteristic
59C4⋊C4×C89—41no—
60C22⋊C4×C89—24no—
61C22⋊C4×C89—24no—
62C23×C89—22no—
63C23×C89—22no—
64C23×C89—22no—
65C23×C89—22no—
66C23×C89—22no—
67C23×C89—22no—
68C23×C89C2×D414yes—
69C23×C89C2411yescharacteristic
70D4×C89—44no—
71C2×C4×C89—21no—
72C2×C4×C89—21no—
73C2×C4×C89—22no—
74C2×C4×C89—22no—
75C2×C4×C89—22no—
76C2×C4×C89—22no—
77C2×C4×C89—21no—
78C2×C4×C89—21no—
79C2×C4×C89—22no—
80C2×C4×C89#4112yes—
81C2×Dic89—22no—
82C2×Dic89—22no—
83C2×Dic89—22no—
84C2×Dic89—22no—
85C2×Dic89—22no—
86C2×Dic89—22no—
87C2×Dic89—22no—
88C2×Dic89—22no—
89C2×Dic89—22no—
90C2×Dic89—22no—
91C2×Dic89—48no—
92C2×Dic89C2×D414yes—
93C2×Dic89C2×D414yes—
94Dic178—44no—
95C22×C89—24no—
96C22×C89—24no—
97C22×C89—24no—
98C22×C89—42no—
99C22×C89—42no—
100C22×C89—42no—
101C22×C89—42no—
102C22×C89C22×D412yes—
103C22×C89C2×#4111yescharacteristic
104C22×C89H(5,𝔽2)11yescharacteristic
105C22×C892−1+411yescharacteristic
106C22×C892−1+412yes—
107C4×C89—22no—
108C4×C89—41no—
109C4×C89—41no—
110C4×C89—42no—
111Dic89—24no—
112Dic89—24no—
113Dic89—42no—
114Dic89—42no—
115C2×C89—44no—
116C2×C89#53612yes—
117C2×C89#53911yescharacteristic
118C2×C89D4211yescharacteristic
119C2×C89#54712yes—
120C2×C89#56311yescharacteristic
121#2680—891nomaximal, Sylow
122C89#268011yescharacteristic, complemented, Sylow
123C2×#123—892no—
124C2×C22⋊Q8—892no—
125#398—892no—
126#397—892no—
127#395—891no—
128#394D8911yescharacteristic
129#388—892no—
130#385—892no—
131#384—891no—
132C22×Q8—891no—
133C22×D4C2×D8911yescharacteristic
134C23×C4—892no—
135#123—1788no—
136C22⋊Q8—1788no—
137C2×C4⋊C4—891no—
138C2×C4⋊C4—892no—
139C2×C4⋊C4—892no—
140C2×C4⋊C4—892no—
141C2×C4⋊C4—892no—
142C2×C4⋊C4—892no—
143C2×C4⋊C4C2×D8911yescharacteristic
144C2×C22⋊C4—892no—
145C2×C22⋊C4—892no—
146C2×C22⋊C4—892no—
147C2×C22⋊C4C2×D8912yes—
148C2×C22⋊C4C2×D8912yes—
149C2×C42—891no—
150#95—892no—
151#95—892no—
152#95—892no—
153#95—891no—
154#95C2×D8911yescharacteristic
155C24C22×D8912yes—
156C2×Q8—3561no—
157C2×Q8—1784no—
158C2×D4—24no—
159C2×D4—41no—
160C22×C4—892no—
161C22×C4—892no—
162C22×C4—892no—
163C22×C4—892no—
164C22×C4—3562no—
165C22×C4—1784no—
166C22×C4—1784no—
167C22×C4C22×D8912yes—
168C22×C4C22×D8911yescharacteristic
169C22×C4C22×D8911yescharacteristic
170C22×C4C22×D8911yescharacteristic
171C4⋊C4—41no—
172C4⋊C4—3561no—
173C4⋊C4—1784no—
174C4⋊C4—1784no—
175C4⋊C4—1784no—
176C4⋊C4—1784no—
177C4⋊C4—1784no—
178C22⋊C4—24no—
179C22⋊C4—24no—
180C22⋊C4—898no—
181C22⋊C4—1784no—
182C22⋊C4—1784no—
183C42—1782no—
184C23—22no—
185C23—22no—
186C23—22no—
187C23—22no—
188C23—22no—
189C23—22no—
190C23D4×D8914yes—
191C23C23×D8911yescharacteristic
192Q8—3564no—
193D4—44no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—894no—
204C2×C4—894no—
205C2×C4—3568no—
206C2×C4—1782no—
207C2×C4—1782no—
208C2×C4—1782no—
209C2×C4—1782no—
210C2×C4—1782no—
211C2×C4—1782no—
212C2×C4—1782no—
213C2×C4—1782no—
214C2×C4—1782no—
215C2×C4—1782no—
216C2×C4#1308357312yes—
217C22—24no—
218C22—24no—
219C22—24no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22C2×D4×D8912yes—
225C22C2×#1308357311yescharacteristic
226C22#1566805711yescharacteristic
227C22#1566805911yescharacteristic
228C22#1566805912yes—
229C4—22no—
230C4—41no—
231C4—41no—
232C4—42no—
233C4—3562no—
234C4—3562no—
235C4—1784no—
236C4—1784no—
237C2—44no—
238C2#1915217012yes—
239C2#1915219311yescharacteristic
240C2#1915223011yescharacteristic
241C2#1915224812yes—
242C2#1915234811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#394×C89C2
prime radicalC22×D4×C89C22
hypercenter#394D89
hypocenterC89#2680
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#15667989C2semidirect
3. #19151532C2semidirect
4. #19151526C2semidirect
5. #19151518C2semidirect
6. #19151486C2semidirect
7. #19151473C2semidirect
8. #19151467C2semidirect
122. C89#2680semidirect

Maximal subgroups

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

subgroupindex
C2×#156679932
C2×#156679892
#191515322
#191515262
#191515182
#191514862
#191514732
#191514672
#394×C892
#268089