Finite Group Databasebeta

← #26023657

Subgroups — #26023657

Order 11392.

610 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 165 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×#15667996C211yesmaximal, characteristic
2C2×#15667996C211yesmaximal, characteristic
3C2×#15667968C211yesmaximal, characteristic, complemented
4C22×C4⋊Dic89C211yesmaximal, characteristic, complemented
5#19151530C212yesmaximal, complemented
6#19151520C212yesmaximal, complemented
7#19151497C212yesmaximal, complemented
8#19151490C212yesmaximal, complemented
9#19151477C211yesmaximal, characteristic
10#19151459C211yesmaximal, characteristic, complemented
11#385×C89C211yesmaximal, characteristic, complemented
12C22×C22⋊D89C2211yescharacteristic
13C23×Dic89C2211yescharacteristic
14C23×Dic89C2211yescharacteristic
15#15667996—24no—
16#15667996—24no—
17#15667968—24no—
18C2×C4⋊Dic89—24no—
19C2×C4⋊Dic89C2212yes—
20C2×C4⋊Dic89C2211yescharacteristic
21C2×C4⋊Dic89C2212yes—
22C2×C4⋊Dic89C2212yes—
23C2×C4⋊Dic89C2211yescharacteristic
24C2×#13083553C2212yes—
25C2×C22⋊Dic89C2211yescharacteristic
26C2×#13083551C2212yes—
27C2×#13083551C2211yescharacteristic
28C2×#13083551C2212yes—
29C2×#13083551C2211yescharacteristic
30C2×C4×Dic89C2212yes—
31#15667919C2212yes—
32#15667919C2212yes—
33#15667919C2212yes—
34C23×C4×C89C2211yescharacteristic
35C2×C4⋊C4×C89C2212yes—
36C2×C22⋊C4×C89C2211yescharacteristic
37C2×C22⋊C4×C89C2211yescharacteristic
38#95×C89C2212yes—
39C23×D89C2311yescharacteristic
40C2×C22⋊D89—22no—
41C2×C22⋊D89—22no—
42C2×C22⋊D89—22no—
43C22×Dic89—22no—
44C22×Dic89—22no—
45C22×Dic89—22no—
46C22×Dic89—22no—
47C22×Dic89—22no—
48C22×Dic89D414yes—
49C22×Dic89C2312yes—
50C22×Dic89C2311yescharacteristic
51C22×Dic89C2312yes—
52C22×Dic89C2311yescharacteristic
53C22×Dic89C2311yescharacteristic
54C4⋊Dic89—24no—
55C4⋊Dic89—22no—
56C4⋊Dic89—22no—
57C4⋊Dic89—24no—
58C4⋊Dic89—24no—
59#13083553—24no—
60C22⋊Dic89—22no—
61#13083551—24no—
62#13083551—24no—
63#13083551—22no—
64#13083551—22no—
65C4×Dic89—24no—
66C24×C89C2311yescharacteristic
67C22×C4×C89—22no—
68C22×C4×C89—24no—
69C22×C4×C89C2311yescharacteristic
70C22×C4×C89C2311yescharacteristic
71C22×C4×C89C2312yes—
72C22×C4×C89C2312yes—
73C4⋊C4×C89—24no—
74C22⋊C4×C89—22no—
75C22⋊C4×C89D414yes—
76C23×C89—22no—
77C23×C89—22no—
78C23×C89C2×D412yes—
79C23×C89C2×D412yes—
80C23×C89#4112yes—
81C23×C89C2411yescharacteristic
82C22×D89—21no—
83C22×D89—21no—
84C22×D89—22no—
85C22×D89—21no—
86C22×D89—22no—
87C2×C4×C89—28no—
88C2×C4×C89—22no—
89C2×C4×C89—22no—
90C2×C4×C89—22no—
91C2×C4×C89—22no—
92C2×C4×C89—21no—
93C2×C4×C89—21no—
94C2×C4×C89—22no—
95C2×C4×C89—22no—
96C2×C4×C89C2×D414yes—
97C2×C4×C89#4114yes—
98C22⋊D89—44no—
99C2×Dic89—28no—
100C2×Dic89—21no—
101C2×Dic89—21no—
102C2×Dic89—21no—
103C2×Dic89—21no—
104C2×Dic89—22no—
105C2×Dic89—22no—
106C2×Dic89—22no—
107C2×Dic89—21no—
108C2×Dic89—21no—
109C2×Dic89—22no—
110C2×Dic89—22no—
111C2×Dic89—21no—
112C2×Dic89—22no—
113C2×Dic89—44no—
114C2×Dic89C2×D412yes—
115C2×Dic89C2×D412yes—
116C22×C89—22no—
117C22×C89—22no—
118C22×C89—24no—
119C22×C89—24no—
120C22×C89#12114yes—
121C22×C89C22×D411yescharacteristic
122C22×C89C22×D411yescharacteristic
123C22×C89C2×#4111yescharacteristic
124C22×C89C2×#4112yes—
125C22×C892−1+412yes—
126C2×D89—41no—
127C2×D89—41no—
128C2×D89—41no—
129C2×D89—42no—
130C2×D89—42no—
131C4×C89—24no—
132C4×C89—24no—
133C4×C89—41no—
134C4×C89—41no—
135Dic89—22no—
136Dic89—22no—
137Dic89—42no—
138Dic89—41no—
139Dic89—42no—
140C2×C89—24no—
141C2×C89C2×#12111yescharacteristic
142C2×C89#52511yescharacteristic
143C2×C89#53611yescharacteristic
144C2×C89#54712yes—
145C2×C89#55212yes—
146D89—81no—
147#2413—891nomaximal, Sylow
148C89#241311yescharacteristic, complemented, Sylow
149C2×#123—891no—
150C2×#123—891no—
151C2×#117—891no—
152C22×C4⋊C4—891no—
153#398—892no—
154#396—892no—
155#389—892no—
156#388—892no—
157#386—891no—
158#385D8911yescharacteristic, complemented
159#381—891no—
160C22×D4—891no—
161C23×C4—891no—
162C23×C4—891no—
163C23×C4C2×D8911yescharacteristic
164#123—1784no—
165#123—1784no—
166#117—1784no—
167C2×C4⋊C4—892no—
168C2×C4⋊C4—892no—
169C2×C4⋊C4—892no—
170C2×C4⋊C4—891no—
171C2×C4⋊C4—892no—
172C2×C4⋊C4—891no—
173C2×C4⋊C4—1784no—
174C2×C4⋊C4C2×D8912yes—
175C2×C22⋊C4—891no—
176C2×C22⋊C4—891no—
177C2×C22⋊C4—892no—
178C2×C22⋊C4—891no—
179C2×C22⋊C4—892no—
180C2×C22⋊C4C2×D8911yescharacteristic
181C2×C22⋊C4C2×D8911yescharacteristic
182C2×C42—892no—
183#95—892no—
184#95—892no—
185#95—892no—
186#95C2×D8912yes—
187C24—891no—
188C24C22×D8911yescharacteristic
189C2×D4—1782no—
190C2×D4—1782no—
191C2×D4—1782no—
192C22×C4—22no—
193C22×C4—24no—
194C22×C4—894no—
195C22×C4—891no—
196C22×C4—891no—
197C22×C4—892no—
198C22×C4—892no—
199C22×C4—891no—
200C22×C4—1782no—
201C22×C4—1782no—
202C22×C4—1782no—
203C22×C4—1782no—
204C22×C4—1782no—
205C22×C4C22×D8911yescharacteristic
206C22×C4C22×D8911yescharacteristic
207C22×C4C22×D8912yes—
208C22×C4C22×D8912yes—
209C4⋊C4—24no—
210C4⋊C4—1784no—
211C4⋊C4—1784no—
212C4⋊C4—1782no—
213C4⋊C4—1782no—
214C4⋊C4—1784no—
215C4⋊C4—1784no—
216C22⋊C4—22no—
217C22⋊C4—1782no—
218C22⋊C4—1782no—
219C22⋊C4—1782no—
220C22⋊C4—1784no—
221C22⋊C4—1784no—
222C22⋊C4D35614yes—
223C42—1784no—
224C23—22no—
225C23—22no—
226C23—1781no—
227C23—1781no—
228C23—1782no—
229C23—1781no—
230C23—1782no—
231C23D4×D8912yes—
232C23C2×D35612yes—
233C23#1308357512yes—
234C23C23×D8911yescharacteristic
235D4—3564no—
236C2×C4—28no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—892no—
246C2×C4—892no—
247C2×C4—3564no—
248C2×C4—1782no—
249C2×C4—1781no—
250C2×C4—1782no—
251C2×C4—1782no—
252C2×C4—1781no—
253C2×C4—1782no—
254C2×C4—1782no—
255C2×C4—1781no—
256C2×C4—1782no—
257C2×C4—1788no—
258C2×C4—1781no—
259C2×C4—1781no—
260C2×C4—1781no—
261C2×C4—1781no—
262C2×C4C2×D35614yes—
263C2×C4#1308357314yes—
264C22—22no—
265C22—24no—
266C22—24no—
267C22—22no—
268C22—3561no—
269C22—3562no—
270C22—3562no—
271C22—3561no—
272C22—3561no—
273C22#1566798714yes—
274C22C2×D4×D8911yescharacteristic
275C22C22×D35611yescharacteristic
276C22C2×#1308357312yes—
277C22C2×#1308357511yescharacteristic
278C22#1566805912yes—
279C4—24no—
280C4—24no—
281C4—41no—
282C4—41no—
283C4—3562no—
284C4—3562no—
285C4—3561no—
286C4—1782no—
287C4—1782no—
288C2—24no—
289C2—7121no—
290C2C2×#1566798711yescharacteristic
291C2#1915210411yescharacteristic
292C2#1915217011yescharacteristic
293C2#1915225212yes—
294C2#1915229012yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#385×C89C2
prime radicalC22×C22⋊D89C22
hypercenter#385D89
hypocenterC89#2413
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. C2×#15667968C2semidirect
4. C22×C4⋊Dic89C2semidirect
5. #19151530C2semidirect
6. #19151520C2semidirect
7. #19151497C2semidirect
8. #19151490C2semidirect
10. #19151459C2semidirect
11. #385×C89C2semidirect
148. C89#2413semidirect
158. #385D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679962
C2×#156679682
C22×C4⋊Dic892
#191515302
#191515202
#191514972
#191514902
#191514772
#191514592
#385×C892
#241389