Finite Group Databasebeta

← #26028267

Subgroups — #26028267

Order 11392.

478 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 133 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×#15667995C211yesmaximal, characteristic
2C2×#15667991C211yesmaximal, characteristic, complemented
3#19151530C211yesmaximal, characteristic, complemented
4#19151528C212yesmaximal, complemented
5#19151525C211yesmaximal, characteristic, complemented
6#19151523C212yesmaximal, complemented
7#19151520C212yesmaximal, complemented
8#19151519C211yesmaximal, characteristic, complemented
9#19151514C212yesmaximal
10#19151511C211yesmaximal, characteristic, complemented
11#380×C89C211yesmaximal, characteristic, complemented
12C22×Dic178C2211yescharacteristic
13C22×C22⋊D89C2211yescharacteristic
14#15667995—24no—
15#15667991—24no—
16C2×C4⋊Dic89C2211yescharacteristic
17C2×C4⋊Dic89C2212yes—
18C2×C4⋊Dic89C2212yes—
19C2×#13083553C2211yescharacteristic
20C2×#13083553C2212yes—
21C2×#13083553C2211yescharacteristic
22C2×C22⋊Dic89C2212yes—
23C2×C22⋊Dic89C2211yescharacteristic
24C2×#13083551C2211yescharacteristic
25C2×#13083551C2211yescharacteristic
26C2×#13083551C2212yes—
27C2×#13083551C2212yes—
28#15667919C2212yes—
29#15667919C2212yes—
30#15667919C2212yes—
31#15667919C2212yes—
32C23×C4×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2212yes—
34C2×C22⋊C4×C89C2212yes—
35#95×C89C2211yescharacteristic
36#95×C89C2211yescharacteristic
37C23×D89C2311yescharacteristic
38C2×Dic178—22no—
39C2×Dic178—42no—
40C2×C22⋊D89—22no—
41C2×C22⋊D89—42no—
42C22×Dic89C2311yescharacteristic
43C22×Dic89C2312yes—
44C22×Dic89C2311yescharacteristic
45C22×Dic89C2311yescharacteristic
46C22×Dic89C2312yes—
47C4⋊Dic89—22no—
48C4⋊Dic89—42no—
49C4⋊Dic89—42no—
50#13083553—24no—
51#13083553—22no—
52#13083553—22no—
53C22⋊Dic89—24no—
54C22⋊Dic89—22no—
55#13083551—22no—
56#13083551—22no—
57#13083551—42no—
58#13083551—42no—
59C24×C89C2311yescharacteristic
60C22×C4×C89—42no—
61C22×C4×C89D414yes—
62C22×C4×C89C2312yes—
63C22×C4×C89C2312yes—
64C22×C4×C89C2311yescharacteristic
65C22×C4×C89C2311yescharacteristic
66C4⋊C4×C89—42no—
67C22⋊C4×C89—42no—
68C23×C89—21no—
69C23×C89—22no—
70C23×C89—22no—
71C23×C89—21no—
72C23×C89C2×D412yes—
73C23×C89C2411yescharacteristic
74C22×D89—21no—
75C22×D89—21no—
76C22×D89—22no—
77C22×D89—22no—
78C22×D89—21no—
79C2×C4×C89—22no—
80C2×C4×C89—22no—
81C2×C4×C89—22no—
82C2×C4×C89—22no—
83C2×C4×C89—22no—
84C2×C4×C89—22no—
85C2×C4×C89—22no—
86C2×C4×C89—22no—
87C2×C4×C89—44no—
88C2×C4×C89C2×D412yes—
89C2×C4×C89C2×D412yes—
90C22⋊D89—44no—
91C2×Dic89—21no—
92C2×Dic89—21no—
93C2×Dic89—22no—
94C2×Dic89—22no—
95C2×Dic89—21no—
96C2×Dic89—22no—
97C2×Dic89—22no—
98C2×Dic89—21no—
99C2×Dic89—22no—
100C2×Dic89—22no—
101C2×Dic89—22no—
102C2×Dic89—21no—
103C2×Dic89—22no—
104Dic178—44no—
105C22×C89—22no—
106C22×C89—22no—
107C22×C89—22no—
108C22×C89—42no—
109C22×C89—42no—
110C22×C89C22×D411yescharacteristic
111C22×C89H(5,𝔽2)12yes—
112C22×C89H(5,𝔽2)11yescharacteristic
113C22×C892−1+412yes—
114C22×C892−1+411yescharacteristic
115C2×D89—41no—
116C2×D89—41no—
117C2×D89—41no—
118C2×D89—42no—
119C2×D89—42no—
120C4×C89—22no—
121C4×C89—22no—
122C4×C89—42no—
123C4×C89—42no—
124Dic89—42no—
125Dic89—41no—
126Dic89—41no—
127Dic89—41no—
128Dic89—42no—
129C2×C89—42no—
130C2×C89#53411yescharacteristic
131C2×C89#53611yescharacteristic
132C2×C89#53711yescharacteristic
133C2×C89#56212yes—
134C2×C89#56312yes—
135D89—81no—
136#2814—891nomaximal, Sylow
137C89#281411yescharacteristic, complemented, Sylow
138C2×#123—891no—
139C2×C22⋊Q8—891no—
140#398—892no—
141#398—891no—
142#397—892no—
143#397—891no—
144#396—892no—
145#395—891no—
146#394—892no—
147#393—891no—
148#380D8911yescharacteristic, complemented
149C22×Q8—891no—
150C22×D4—891no—
151C23×C4C2×D8911yescharacteristic
152#123—1784no—
153C22⋊Q8—1784no—
154C2×C4⋊C4—892no—
155C2×C4⋊C4—892no—
156C2×C4⋊C4—892no—
157C2×C4⋊C4—891no—
158C2×C4⋊C4—891no—
159C2×C4⋊C4—891no—
160C2×C4⋊C4C2×D8912yes—
161C2×C22⋊C4—892no—
162C2×C22⋊C4—892no—
163C2×C22⋊C4—892no—
164C2×C22⋊C4—891no—
165C2×C22⋊C4—891no—
166C2×C22⋊C4—891no—
167C2×C22⋊C4C2×D8912yes—
168#95—892no—
169#95—892no—
170#95—892no—
171#95—892no—
172#95C2×D8911yescharacteristic
173#95C2×D8911yescharacteristic
174C24—891no—
175C24C22×D8911yescharacteristic
176C2×Q8—3562no—
177C2×Q8—1782no—
178C2×D4—3562no—
179C2×D4—1782no—
180C22×C4—42no—
181C22×C4—891no—
182C22×C4—891no—
183C22×C4—892no—
184C22×C4—892no—
185C22×C4—891no—
186C22×C4D35614yes—
187C22×C4C22×D8912yes—
188C22×C4C22×D8912yes—
189C22×C4C22×D8911yescharacteristic
190C22×C4C22×D8911yescharacteristic
191C4⋊C4—42no—
192C4⋊C4—3562no—
193C4⋊C4—3562no—
194C4⋊C4—1784no—
195C4⋊C4—1782no—
196C4⋊C4—1782no—
197C4⋊C4—1782no—
198C22⋊C4—42no—
199C22⋊C4—3562no—
200C22⋊C4—3562no—
201C22⋊C4—1784no—
202C22⋊C4—1782no—
203C22⋊C4—1782no—
204C22⋊C4—1782no—
205C23—21no—
206C23—22no—
207C23—22no—
208C23—21no—
209C23—1781no—
210C23—1781no—
211C23—1782no—
212C23—1782no—
213C23—1781no—
214C23C2×D35612yes—
215C23C23×D8911yescharacteristic
216Q8—3564no—
217D4—3564no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—44no—
227C2×C4—1781no—
228C2×C4—1781no—
229C2×C4—1782no—
230C2×C4—1782no—
231C2×C4—1781no—
232C2×C4—1782no—
233C2×C4—1782no—
234C2×C4—1781no—
235C2×C4—1782no—
236C2×C4—1782no—
237C2×C4—1782no—
238C2×C4—1781no—
239C2×C4—1782no—
240C2×C4C2×D35612yes—
241C2×C4C2×D35612yes—
242C22—22no—
243C22—22no—
244C22—22no—
245C22—42no—
246C22—42no—
247C22—3561no—
248C22—3561no—
249C22—3561no—
250C22—3562no—
251C22—3562no—
252C22C22×D35611yescharacteristic
253C22#1566805712yes—
254C22#1566805711yescharacteristic
255C22#1566805912yes—
256C22#1566806011yescharacteristic
257C4—22no—
258C4—22no—
259C4—42no—
260C4—42no—
261C4—3561no—
262C4—3562no—
263C4—3561no—
264C4—3561no—
265C4—3562no—
266C2—42no—
267C2—7121no—
268C2#1915216011yescharacteristic
269C2#1915217411yescharacteristic
270C2#1915217911yescharacteristic
271C2#1915234312yes—
272C2#1915234912yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#380×C89C2
prime radicalC22×C22⋊D89C22
hypercenter#380D89
hypocenterC89#2814
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#15667991C2semidirect
3. #19151530C2semidirect
4. #19151528C2semidirect
5. #19151525C2semidirect
6. #19151523C2semidirect
7. #19151520C2semidirect
8. #19151519C2semidirect
10. #19151511C2semidirect
11. #380×C89C2semidirect
137. C89#2814semidirect
148. #380D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679952
C2×#156679912
#191515302
#191515282
#191515252
#191515232
#191515202
#191515192
#191515142
#191515112
#380×C892
#281489