Finite Group Databasebeta

← #26024540

Subgroups — #26024540

Order 11392.

512 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 139 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×#15667970C211yesmaximal, characteristic
2C2×C4⋊C4×D89C211yesmaximal, characteristic
3#19151536C211yesmaximal, characteristic, complemented
4#19151530C211yesmaximal, characteristic, complemented
5#19151528C211yesmaximal, characteristic, complemented
6#19151485C212yesmaximal, complemented
7#19151481C212yesmaximal, complemented
8#19151472C212yesmaximal
9#19151460C212yesmaximal
10#19151460C211yesmaximal, characteristic
11#400×C89C211yesmaximal, characteristic, complemented
12C22×C4×D89C2211yescharacteristic
13C22×C4×D89C2211yescharacteristic
14C22×C4×D89C2211yescharacteristic
15#15667970—24no—
16C2×C4⋊Dic89C2212yes—
17C2×C4⋊Dic89C2211yescharacteristic
18C2×C4⋊Dic89C2211yescharacteristic
19C2×#13083553C2212yes—
20C2×#13083553C2211yescharacteristic
21C2×#13083553C2211yescharacteristic
22C4⋊C4×D89—24no—
23C2×#13083551C2212yes—
24C2×#13083551C2212yes—
25C2×C4×Dic89C2212yes—
26#15667919C2212yes—
27#15667919C2212yes—
28#15667919C2212yes—
29#15667919C2212yes—
30#15667919C2211yescharacteristic
31#15667919C2212yes—
32C2×C4⋊C4×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2211yescharacteristic
34#95×C89C2212yes—
35#95×C89C2211yescharacteristic
36#95×C89C2212yes—
37C23×D89C2311yescharacteristic
38C22×Dic89C2311yescharacteristic
39C22×Dic89C2312yes—
40C22×Dic89C2312yes—
41C22×Dic89C2311yescharacteristic
42C22×Dic89C2311yescharacteristic
43C2×C4×D89—22no—
44C2×C4×D89—24no—
45C2×C4×D89—22no—
46C2×C4×D89—22no—
47C2×C4×D89—22no—
48C2×C4×D89—24no—
49C2×C4×D89D414yes—
50C4⋊Dic89—22no—
51C4⋊Dic89—22no—
52C4⋊Dic89—24no—
53#13083553—22no—
54#13083553—24no—
55#13083553—22no—
56#13083551—24no—
57#13083551—24no—
58C4×Dic89—24no—
59C22×C4×C89C2311yescharacteristic
60C22×C4×C89C2312yes—
61C22×C4×C89C2312yes—
62C22×C4×C89C2311yescharacteristic
63C22×C4×C89C2311yescharacteristic
64C4⋊C4×C89—22no—
65C4⋊C4×C89—22no—
66C23×C89C2411yescharacteristic
67C22×D89—21no—
68C22×D89—21no—
69C22×D89—22no—
70C22×D89C2×D412yes—
71C22×D89#4114yes—
72C2×C4×C89—21no—
73C2×C4×C89—22no—
74C2×C4×C89—21no—
75C2×C4×C89—22no—
76C2×C4×C89—21no—
77C2×C4×C89—22no—
78C2×C4×C89—22no—
79C2×C4×C89—22no—
80C2×C4×C89—24no—
81C2×C4×C89—22no—
82C2×C4×C89C2×D412yes—
83C2×C4×C89#4112yes—
84C2×Dic89—21no—
85C2×Dic89—22no—
86C2×Dic89—21no—
87C2×Dic89—22no—
88C2×Dic89—21no—
89C2×Dic89—22no—
90C2×Dic89—22no—
91C2×Dic89—22no—
92C2×Dic89—22no—
93C2×Dic89—22no—
94C2×Dic89—22no—
95C2×Dic89C2×D412yes—
96C2×Dic89#4112yes—
97C4×D89—28no—
98C4×D89—28no—
99C4×D89—44no—
100C22×C89C22×D411yescharacteristic
101C22×C89C2×#4112yes—
102C22×C89C2×#4111yescharacteristic
103C22×C89C2×#4111yescharacteristic
104C22×C892−1+412yes—
105C2×D89—22no—
106C2×D89—22no—
107C2×D89—24no—
108C2×D89—24no—
109C2×D89#12314yes—
110C4×C89—22no—
111C4×C89—22no—
112C4×C89—41no—
113C4×C89—42no—
114C4×C89—42no—
115Dic89—22no—
116Dic89—22no—
117Dic89—41no—
118Dic89—42no—
119Dic89—42no—
120C2×C89C2×#12311yescharacteristic
121C2×C89#52511yescharacteristic
122C2×C89#53611yescharacteristic
123C2×C89#55212yes—
124C2×C89#55212yes—
125D89—24no—
126#2484—891nomaximal, Sylow
127C89#248411yescharacteristic, complemented, Sylow
128C2×#117—891no—
129C22×C4⋊C4—891no—
130#400—891no—
131#400D8911yescharacteristic, complemented
132#398—891no—
133#398—891no—
134#387—892no—
135#387—892no—
136#385—892no—
137#381—891no—
138#381—892no—
139C23×C4—891no—
140C23×C4—891no—
141C23×C4—891no—
142#117—1784no—
143C2×C4⋊C4—891no—
144C2×C4⋊C4—891no—
145C2×C4⋊C4—891no—
146C2×C4⋊C4—891no—
147C2×C4⋊C4—892no—
148C2×C4⋊C4—892no—
149C2×C4⋊C4—1784no—
150C2×C4⋊C4C2×D8911yescharacteristic
151C2×C4⋊C4C2×D8911yescharacteristic
152C2×C22⋊C4—892no—
153C2×C22⋊C4—892no—
154C2×C42—892no—
155#95—892no—
156#95—892no—
157#95—892no—
158#95—892no—
159#95—891no—
160#95—892no—
161#95C2×D8912yes—
162#95C2×D8911yescharacteristic
163#95C2×D8912yes—
164C24—891no—
165C22×C4—891no—
166C22×C4—891no—
167C22×C4—894no—
168C22×C4—892no—
169C22×C4—891no—
170C22×C4—892no—
171C22×C4—1782no—
172C22×C4—1782no—
173C22×C4—1784no—
174C22×C4—1782no—
175C22×C4—1784no—
176C22×C4—1782no—
177C22×C4C22×D8912yes—
178C22×C4C22×D8912yes—
179C22×C4C22×D8911yescharacteristic
180C22×C4C22×D8911yescharacteristic
181C22×C4C22×D8911yescharacteristic
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—1782no—
185C4⋊C4—1782no—
186C4⋊C4—1784no—
187C4⋊C4—1782no—
188C4⋊C4—1782no—
189C4⋊C4—1784no—
190C22⋊C4—1784no—
191C22⋊C4—1784no—
192C42—1784no—
193C23—892no—
194C23—894no—
195C23—1781no—
196C23—1781no—
197C23—1782no—
198C23C23×D8911yescharacteristic
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—24no—
208C2×C4—22no—
209C2×C4—892no—
210C2×C4—892no—
211C2×C4—3564no—
212C2×C4—1788no—
213C2×C4—1788no—
214C2×C4—1782no—
215C2×C4—1781no—
216C2×C4—1782no—
217C2×C4—1782no—
218C2×C4—1782no—
219C2×C4—1782no—
220C2×C4—1782no—
221C2×C4—1782no—
222C2×C4—1781no—
223C2×C4—1782no—
224C2×C4—1781no—
225C2×C4D4×D8912yes—
226C2×C4#1308357512yes—
227C22—894no—
228C22—1782no—
229C22—1784no—
230C22—1784no—
231C22—1782no—
232C22C2×D4×D8911yescharacteristic
233C22#41×D8911yescharacteristic
234C22#41×D8912yes—
235C22C2×#1308357511yescharacteristic
236C22#1566805912yes—
237C4—22no—
238C4—22no—
239C4—42no—
240C4—42no—
241C4—41no—
242C4—3562no—
243C4—3561no—
244C4—3562no—
245C4—1782no—
246C4—1782no—
247C2—1784no—
248C2#123×D8911yescharacteristic
249C2#1915211111yescharacteristic
250C2#1915216811yescharacteristic
251C2#1915228412yes—
252C2#1915228612yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#400×C89C2
prime radicalC23×D89C23
hypercenter#400D89
hypocenterC89#2484
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
3. #19151536C2semidirect
4. #19151530C2semidirect
5. #19151528C2semidirect
6. #19151485C2semidirect
7. #19151481C2semidirect
11. #400×C89C2semidirect
127. C89#2484semidirect
131. #400D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679702
C2×C4⋊C4×D892
#191515362
#191515302
#191515282
#191514852
#191514812
#191514722
#191514602
#400×C892
#248489