Finite Group Databasebeta

← #26024568

Subgroups — #26024568

Order 11392.

584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 157 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×#15667972C211yesmaximal, characteristic
2C22×#13083553C211yesmaximal, characteristic, complemented
3#19151539C212yesmaximal, complemented
4#19151533C212yesmaximal, complemented
5#19151493C212yesmaximal, complemented
6#19151477C211yesmaximal, characteristic
7#19151475C211yesmaximal, characteristic
8#19151470C211yesmaximal, characteristic, complemented
9#19151457C212yesmaximal, complemented
10#19151456C211yesmaximal, characteristic, complemented
11#385×C89C211yesmaximal, characteristic, complemented
12C22×C22⋊D89C2211yescharacteristic
13C23×Dic89C2211yescharacteristic
14C23×Dic89C2211yescharacteristic
15C22×C4×D89C2211yescharacteristic
16#15667972—24no—
17C2×#13083553—24no—
18C2×#13083553C2212yes—
19C2×#13083553C2212yes—
20C2×#13083553C2212yes—
21C2×#13083553C2211yescharacteristic
22C2×#13083553C2212yes—
23C2×C22⋊Dic89C2211yescharacteristic
24C2×#13083551C2211yescharacteristic
25C2×#13083551C2212yes—
26C2×#13083551C2212yes—
27C2×C4×Dic89C2211yescharacteristic
28#15667919C2212yes—
29#15667919C2212yes—
30#15667919C2212yes—
31#15667919C2212yes—
32C23×C4×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2212yes—
34C2×C22⋊C4×C89C2211yescharacteristic
35C2×C22⋊C4×C89C2211yescharacteristic
36#95×C89C2212yes—
37C23×D89C2311yescharacteristic
38C2×C22⋊D89—22no—
39C2×C22⋊D89—22no—
40C2×C22⋊D89Q814yes—
41C22×Dic89—24no—
42C22×Dic89—22no—
43C22×Dic89—42no—
44C22×Dic89D414yes—
45C22×Dic89C2312yes—
46C22×Dic89C2312yes—
47C22×Dic89C2311yescharacteristic
48C22×Dic89C2311yescharacteristic
49C22×Dic89C2311yescharacteristic
50C2×C4×D89—22no—
51C2×C4×D89—24no—
52#13083553—22no—
53#13083553—24no—
54#13083553—24no—
55#13083553—24no—
56#13083553—42no—
57C22⋊Dic89—22no—
58#13083551—22no—
59#13083551—42no—
60#13083551—42no—
61C4×Dic89—22no—
62C24×C89C2311yescharacteristic
63C22×C4×C89—22no—
64C22×C4×C89—42no—
65C22×C4×C89C2311yescharacteristic
66C22×C4×C89C2312yes—
67C22×C4×C89C2312yes—
68C22×C4×C89C2311yescharacteristic
69C4⋊C4×C89—42no—
70C22⋊C4×C89—22no—
71C22⋊C4×C89—22no—
72C23×C89—22no—
73C23×C89—22no—
74C23×C89C2×D412yes—
75C23×C89C2×Q812yes—
76C23×C89#4112yes—
77C23×C89C2411yescharacteristic
78C22×D89—21no—
79C22×D89—22no—
80C22×D89—21no—
81C22×D89—22no—
82C22×D89C2×Q812yes—
83C2×C4×C89—21no—
84C2×C4×C89—21no—
85C2×C4×C89—22no—
86C2×C4×C89—22no—
87C2×C4×C89—22no—
88C2×C4×C89—22no—
89C2×C4×C89—22no—
90C2×C4×C89—22no—
91C2×C4×C89—22no—
92C2×C4×C89—22no—
93C2×C4×C89—44no—
94C22⋊D89—28no—
95C2×Dic89—21no—
96C2×Dic89—22no—
97C2×Dic89—21no—
98C2×Dic89—28no—
99C2×Dic89—22no—
100C2×Dic89—22no—
101C2×Dic89—22no—
102C2×Dic89—22no—
103C2×Dic89—22no—
104C2×Dic89—22no—
105C2×Dic89—44no—
106C2×Dic89C2×D412yes—
107C2×Dic89C2×D412yes—
108C2×Dic89C2×Q812yes—
109C2×Dic89#4114yes—
110C4×D89—44no—
111C22×C89—22no—
112C22×C89—22no—
113C22×C89—24no—
114C22×C89—24no—
115C22×C89C22⋊Q814yes—
116C22×C89C22×D411yescharacteristic
117C22×C89C22×Q811yescharacteristic
118C22×C89C2×#4111yescharacteristic
119C22×C89C2×#4112yes—
120C22×C89H(5,𝔽2)12yes—
121C2×D89—22no—
122C2×D89—24no—
123C2×D89—41no—
124C2×D89—41no—
125C2×D89—42no—
126C4×C89—41no—
127C4×C89—41no—
128C4×C89—42no—
129C4×C89—42no—
130Dic89—22no—
131Dic89—22no—
132Dic89—42no—
133Dic89—42no—
134Dic89#12314yes—
135C2×C89—24no—
136C2×C89C2×C22⋊Q811yescharacteristic
137C2×C89C2×#12311yescharacteristic
138C2×C89#53511yescharacteristic
139C2×C89#55312yes—
140C2×C89#55412yes—
141D89—42no—
142#2487—891nomaximal, Sylow
143C89#248711yescharacteristic, complemented, Sylow
144C2×C4×D4—891no—
145C22×C4⋊C4—891no—
146#400—892no—
147#399—892no—
148#389—892no—
149#386—891no—
150#386—891no—
151#385—891no—
152#385D8911yescharacteristic, complemented
153#380—891no—
154#380—892no—
155C22×D4—891no—
156C23×C4—891no—
157C23×C4—891no—
158C23×C4—891no—
159C23×C4C2×D8911yescharacteristic
160C4×D4—1784no—
161C2×C4⋊C4—892no—
162C2×C4⋊C4—892no—
163C2×C4⋊C4—892no—
164C2×C4⋊C4—891no—
165C2×C4⋊C4—892no—
166C2×C4⋊C4—1784no—
167C2×C4⋊C4C2×D8912yes—
168C2×C22⋊C4—892no—
169C2×C22⋊C4—892no—
170C2×C22⋊C4—891no—
171C2×C22⋊C4—891no—
172C2×C22⋊C4C2×D8911yescharacteristic
173C2×C22⋊C4C2×D8911yescharacteristic
174C2×C42—891no—
175#95—892no—
176#95—892no—
177#95—892no—
178#95—892no—
179#95C2×D8912yes—
180C24—891no—
181C24C22×D8911yescharacteristic
182C2×D4—894no—
183C2×D4—1782no—
184C2×D4—1782no—
185C22×C4—22no—
186C22×C4—42no—
187C22×C4—891no—
188C22×C4—894no—
189C22×C4—891no—
190C22×C4—891no—
191C22×C4—892no—
192C22×C4—892no—
193C22×C4—3562no—
194C22×C4—1782no—
195C22×C4—1784no—
196C22×C4—1784no—
197C22×C4—1782no—
198C22×C4C22×D8911yescharacteristic
199C22×C4C22×D8912yes—
200C22×C4C22×D8912yes—
201C22×C4C22×D8911yescharacteristic
202C4⋊C4—42no—
203C4⋊C4—3562no—
204C4⋊C4—1784no—
205C4⋊C4—1784no—
206C4⋊C4—1782no—
207C4⋊C4—1784no—
208C22⋊C4—22no—
209C22⋊C4—22no—
210C22⋊C4—3562no—
211C22⋊C4—3562no—
212C22⋊C4—1782no—
213C22⋊C4—1782no—
214C42—1782no—
215C23—22no—
216C23—22no—
217C23—892no—
218C23—1781no—
219C23—1782no—
220C23—1781no—
221C23—1782no—
222C23D4×D8912yes—
223C23Q8×D8912yes—
224C23#1308357412yes—
225C23C23×D8911yescharacteristic
226D4—1788no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—44no—
238C2×C4—892no—
239C2×C4—894no—
240C2×C4—892no—
241C2×C4—892no—
242C2×C4—3564no—
243C2×C4—3564no—
244C2×C4—1788no—
245C2×C4—1782no—
246C2×C4—1782no—
247C2×C4—1782no—
248C2×C4—1782no—
249C2×C4—1782no—
250C2×C4—1782no—
251C2×C4—1781no—
252C2×C4—1782no—
253C2×C4—1781no—
254C22—22no—
255C22—24no—
256C22—24no—
257C22—22no—
258C22—3561no—
259C22—3562no—
260C22—3561no—
261C22—1784no—
262C22—1782no—
263C22#1566799014yes—
264C22C2×D4×D8911yescharacteristic
265C22C2×Q8×D8911yescharacteristic
266C22#41×D8912yes—
267C22C2×#1308357411yescharacteristic
268C22#1566805712yes—
269C4—42no—
270C4—41no—
271C4—42no—
272C4—41no—
273C4—894no—
274C4—3562no—
275C4—3562no—
276C4—1782no—
277C4—1782no—
278C2—24no—
279C2—3562no—
280C2C2×#1566799011yescharacteristic
281C2#123×D8911yescharacteristic
282C2#1915216311yescharacteristic
283C2#1915229712yes—
284C2#1915230212yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#385×C89C2
prime radicalC22×C22⋊D89C22
hypercenter#385D89
hypocenterC89#2487
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C22×#13083553C2semidirect
3. #19151539C2semidirect
4. #19151533C2semidirect
5. #19151493C2semidirect
8. #19151470C2semidirect
9. #19151457C2semidirect
10. #19151456C2semidirect
11. #385×C89C2semidirect
143. C89#2487semidirect
152. #385D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679722
C22×#130835532
#191515392
#191515332
#191514932
#191514772
#191514752
#191514702
#191514572
#191514562
#385×C892
#248789