Finite Group Databasebeta

← #26027287

Subgroups — #26027287

Order 11392.

552 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#19151534C211yesmaximal, characteristic, complemented
2#19151525C212yesmaximal, complemented
3#19151520C212yesmaximal, complemented
4#19151491C212yesmaximal, complemented
5#19151490C212yesmaximal, complemented
6#19151487C212yesmaximal, complemented
7#19151453C212yesmaximal
8#19151453C211yesmaximal, characteristic
9#397×C89C211yesmaximal, characteristic, complemented
10C24×D89C2211yescharacteristic
11C2×C4⋊Dic89C2211yescharacteristic, complemented
12C2×C4⋊Dic89C2212yescomplemented
13C2×#13083553C2212yescomplemented
14C2×C22⋊Dic89C2211yescharacteristic
15C2×C22⋊Dic89C2212yes—
16C2×#13083551C2212yes—
17C2×#13083551C2212yes—
18C2×#13083551C2212yes—
19C2×#13083551C2212yes—
20C2×#13083551C2212yes—
21C2×#13083551C2212yes—
22C2×C4×Dic89C2212yescomplemented
23#15667919C2212yescomplemented
24#15667919C2212yescomplemented
25#15667919C2211yescharacteristic, complemented
26C2×C4⋊C4×C89C2211yescharacteristic, complemented
27C2×C22⋊C4×C89C2212yes—
28C2×C22⋊C4×C89C2211yescharacteristic
29#95×C89C2211yescharacteristic, complemented
30#95×C89C2212yescomplemented
31C23×D89—22no—
32C23×D89—24no—
33C23×D89—41no—
34C23×D89—42no—
35C23×D89—41no—
36C23×D89C2312yes—
37C22×Dic89C2312yes—
38C22×Dic89C2312yes—
39C22×Dic89C2312yes—
40C4⋊Dic89—41no—
41C4⋊Dic89—42no—
42#13083553—42no—
43C22⋊Dic89—42no—
44C22⋊Dic89—41no—
45#13083551—24no—
46#13083551—24no—
47#13083551—42no—
48#13083551—42no—
49#13083551—42no—
50#13083551—42no—
51C4×Dic89—42no—
52C24×C89C2311yescharacteristic
53C22×C4×C89C2312yes—
54C22×C4×C89C2311yescharacteristic
55C22×C4×C89C2312yes—
56C22×C4×C89C2311yescharacteristic
57C4⋊C4×C89—41no—
58C22⋊C4×C89—24no—
59C22⋊C4×C89—41no—
60C23×C89—22no—
61C23×C89—21no—
62C23×C89—21no—
63C23×C89—22no—
64C23×C89#4112yes—
65C23×C89C2411yescharacteristic
66C22×D89—22no—
67C22×D89—22no—
68C22×D89—22no—
69C22×D89—22no—
70C22×D89—22no—
71C22×D89—22no—
72C22×D89—44no—
73C22×D89—48no—
74C22×D89—48no—
75C22×D89—44no—
76C22×D89—44no—
77C22×D89#4114yes—
78C2×C4×C89—22no—
79C2×C4×C89—22no—
80C2×C4×C89—22no—
81C2×C4×C89—22no—
82C2×C4×C89—21no—
83C2×C4×C89—21no—
84C2×C4×C89—22no—
85C2×C4×C89—22no—
86C2×C4×C89—22no—
87C2×C4×C89—22no—
88C2×Dic89—22no—
89C2×Dic89—22no—
90C2×Dic89—22no—
91C2×Dic89—22no—
92C2×Dic89—22no—
93C2×Dic89—22no—
94C2×Dic89—22no—
95C2×Dic89—22no—
96C2×Dic89—22no—
97C22×C89—22no—
98C22×C89—24no—
99C22×C89—42no—
100C22×C89—41no—
101C22×C89—41no—
102C22×C89C2×#4112yes—
103C22×C89C2×#4111yescharacteristic
104C22×C89H(5,𝔽2)11yescharacteristic
105C22×C89H(5,𝔽2)11yescharacteristic
106C22×C89H(5,𝔽2)12yes—
107C2×D89—24no—
108C2×D89—24no—
109C2×D89—24no—
110C2×D89—416no—
111C2×D89—42no—
112C2×D89—42no—
113C2×D89—42no—
114C2×D89—42no—
115C4×C89—42no—
116C4×C89—42no—
117C4×C89—41no—
118C4×C89—41no—
119Dic89—42no—
120Dic89—42no—
121Dic89—42no—
122C2×C89—42no—
123C2×C89#53811yescharacteristic
124C2×C89#53812yes—
125C2×C89#55112yes—
126C2×C89#55111yescharacteristic
127C2×C89#56011yescharacteristic
128D89—44no—
129#2735—891nomaximal, Sylow
130C89#273511yescharacteristic, complemented, Sylow
131#399—891no—
132#397—892no—
133#397D8911yescharacteristic, complemented
134#396—892no—
135#388—892no—
136#388—892no—
137#388—892no—
138#379—891no—
139#379—892no—
140C25—891no—
141C2×C4⋊C4—891no—
142C2×C4⋊C4—892no—
143C2×C4⋊C4—892no—
144C2×C4⋊C4C2×D8911yescharacteristic, complemented
145C2×C22⋊C4—891no—
146C2×C22⋊C4—892no—
147C2×C22⋊C4—892no—
148C2×C22⋊C4—892no—
149C2×C22⋊C4—892no—
150C2×C22⋊C4—892no—
151C2×C22⋊C4—892no—
152C2×C22⋊C4—892no—
153C2×C22⋊C4C2×D8912yes—
154C2×C22⋊C4C2×D8911yescharacteristic
155C2×C42—892no—
156#95—892no—
157#95—892no—
158#95—891no—
159#95C2×D8911yescharacteristic, complemented
160#95C2×D8912yescomplemented
161C24—892no—
162C24—3561no—
163C24—3561no—
164C24—3562no—
165C24—1784no—
166C24—1782no—
167C24C22×D8911yescharacteristic
168C22×C4—892no—
169C22×C4—892no—
170C22×C4—892no—
171C22×C4C22×D8912yes—
172C22×C4C22×D8911yescharacteristic
173C22×C4C22×D8912yes—
174C22×C4C22×D8911yescharacteristic
175C4⋊C4—41no—
176C4⋊C4—3562no—
177C4⋊C4—3561no—
178C4⋊C4—3562no—
179C22⋊C4—24no—
180C22⋊C4—41no—
181C22⋊C4—3562no—
182C22⋊C4—3562no—
183C22⋊C4—3562no—
184C22⋊C4—3562no—
185C22⋊C4—3562no—
186C22⋊C4—3561no—
187C22⋊C4—1784no—
188C22⋊C4—1784no—
189C42—3562no—
190C23—22no—
191C23—21no—
192C23—21no—
193C23—22no—
194C23—894no—
195C23—3564no—
196C23—3568no—
197C23—3564no—
198C23—3568no—
199C23—3564no—
200C23—1782no—
201C23—1782no—
202C23—1782no—
203C23—1782no—
204C23—1782no—
205C23—1782no—
206C23#1308357312yes—
207C23C23×D8911yescharacteristic
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—1782no—
219C2×C4—1782no—
220C2×C4—1782no—
221C2×C4—1782no—
222C2×C4—1782no—
223C2×C4—1782no—
224C2×C4—1782no—
225C2×C4—1782no—
226C2×C4—1782no—
227C22—22no—
228C22—24no—
229C22—42no—
230C22—41no—
231C22—41no—
232C22—35616no—
233C22—3562no—
234C22—3562no—
235C22—3562no—
236C22—3562no—
237C22—1784no—
238C22—1784no—
239C22—1784no—
240C22#41×D8912yes—
241C22C2×#1308357311yescharacteristic
242C22#1566805711yescharacteristic
243C22#1566805811yescharacteristic
244C22#1566805812yes—
245C4—42no—
246C4—42no—
247C4—41no—
248C4—41no—
249C4—3562no—
250C4—3562no—
251C4—3562no—
252C2—42no—
253C2—3564no—
254C2#1915218511yescharacteristic
255C2#1915218712yes—
256C2#1915227112yes—
257C2#1915227811yescharacteristic
258C2#1915233811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#397×C89C2
prime radicalC24×D89C22
hypercenter#397D89
hypocenterC89#2735
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #19151534C2semidirect
2. #19151525C2semidirect
3. #19151520C2semidirect
4. #19151491C2semidirect
5. #19151490C2semidirect
6. #19151487C2semidirect
9. #397×C89C2semidirect
11. C2×C4⋊Dic89C22semidirect
12. C2×C4⋊Dic89C22semidirect
13. C2×#13083553C22semidirect
22. C2×C4×Dic89C22semidirect
23. #15667919C22semidirect
24. #15667919C22semidirect
25. #15667919C22semidirect
26. C2×C4⋊C4×C89C22semidirect
29. #95×C89C22semidirect
30. #95×C89C22semidirect
130. C89#2735semidirect
133. #397D89semidirect
144. C2×C4⋊C4C2×D89semidirect
159. #95C2×D89semidirect
160. #95C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191515342
#191515252
#191515202
#191514912
#191514902
#191514872
#191514532
#397×C892
#273589