Finite Group Databasebeta

← #26025435

Subgroups — #26025435

Order 11392.

584 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 147 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×#15667992C211yesmaximal, characteristic, complemented
2C2×#15667974C211yesmaximal, characteristic
3#19151533C211yesmaximal, characteristic, complemented
4#19151518C211yesmaximal, characteristic, complemented
5#19151511C211yesmaximal, characteristic, complemented
6#19151485C212yesmaximal, complemented
7#19151476C212yesmaximal
8#19151472C212yesmaximal, complemented
9#19151457C212yesmaximal, complemented
10#95×D89C211yesmaximal, characteristic, complemented
11#400×C89C211yesmaximal, characteristic, complemented
12C22×Dic178C2211yescharacteristic
13C22×D356C2211yescharacteristic
14C22×C4×D89C2212yes—
15C22×C4×D89C2211yescharacteristic
16C22×C4×D89C2211yescharacteristic
17#15667992—24no—
18#15667974—24no—
19C2×C4⋊Dic89C2212yes—
20C2×#13083553C2212yes—
21C2×#13083553C2212yes—
22C2×#13083551C2211yescharacteristic
23C2×#13083551C2212yes—
24C2×#13083551C2212yes—
25C2×#13083551C2211yescharacteristic
26C2×#13083551C2212yes—
27C2×C4×Dic89C2211yescharacteristic
28#15667919C2212yes—
29#15667919C2211yescharacteristic
30#15667919C2212yes—
31#15667919C2212yes—
32C2×C4⋊C4×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2211yescharacteristic
34#95×C89C2211yescharacteristic
35#95×C89C2212yes—
36#95×C89C2212yes—
37C23×D89C2311yescharacteristic
38C23×D89C2311yescharacteristic
39C2×Dic178—22no—
40C2×Dic178—42no—
41C2×D356—22no—
42C2×D356—22no—
43C2×D356Q814yescomplemented
44C22×Dic89C2312yes—
45C22×Dic89C2311yescharacteristic
46C22×Dic89C2311yescharacteristic
47C22×Dic89C2312yes—
48C2×C4×D89—24no—
49C2×C4×D89—22no—
50C2×C4×D89—24no—
51C2×C4×D89—42no—
52C2×C4×D89—42no—
53C2×C4×D89—42no—
54C2×C4×D89D414yes—
55C4⋊Dic89—24no—
56#13083553—24no—
57#13083553—42no—
58#13083551—22no—
59#13083551—24no—
60#13083551—22no—
61#13083551—24no—
62#13083551—42no—
63C4×Dic89—22no—
64C22×C4×C89C2312yes—
65C22×C4×C89C2311yescharacteristic
66C22×C4×C89C2312yes—
67C22×C4×C89C2311yescharacteristic
68C22×C4×C89C2311yescharacteristic
69C4⋊C4×C89—22no—
70C4⋊C4×C89—22no—
71C23×C89C2411yescharacteristic
72C22×D89—22no—
73C22×D89—22no—
74C22×D89—21no—
75C22×D89—22no—
76C22×D89—21no—
77C22×D89—22no—
78C22×D89C2×D412yes—
79C22×D89C2×Q812yes—
80C22×D89C2×Q812yes—
81C22×D89#4112yes—
82C2×C4×C89—21no—
83C2×C4×C89—21no—
84C2×C4×C89—22no—
85C2×C4×C89—22no—
86C2×C4×C89—21no—
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×C89C2×D412yes—
94C2×C4×C89C2×Q812yes—
95C2×Dic89—22no—
96C2×Dic89—22no—
97C2×Dic89—22no—
98C2×Dic89—21no—
99C2×Dic89—22no—
100C2×Dic89—22no—
101C2×Dic89—22no—
102C2×Dic89—22no—
103C2×Dic89C2×D412yes—
104C2×Dic89#4114yes—
105D356—28no—
106C4×D89—44no—
107C4×D89—48no—
108C4×D89—44no—
109Dic178—44no—
110C22×C89C22×D411yescharacteristic
111C22×C89C22×Q811yescharacteristic
112C22×C89C2×#4111yescharacteristic
113C22×C89C2×#4112yes—
114C22×C89H(5,𝔽2)12yes—
115C2×D89—22no—
116C2×D89—22no—
117C2×D89—24no—
118C2×D89—24no—
119C2×D89—22no—
120C2×D89—24no—
121C2×D89—41no—
122C2×D89—41no—
123C2×D89—42no—
124C2×D89C22⋊Q814yes—
125C4×C89—22no—
126C4×C89—22no—
127C4×C89—42no—
128C4×C89—41no—
129C4×C89—42no—
130Dic89—22no—
131Dic89—24no—
132Dic89—41no—
133Dic89—42no—
134C2×C89C2×C22⋊Q811yescharacteristic
135C2×C89#53211yescharacteristic
136C2×C89#53411yescharacteristic
137C2×C89#55112yes—
138C2×C89#55412yes—
139D89—24no—
140D89—42no—
141#2564—891nomaximal, Sylow
142C89#256411yescharacteristic, complemented, Sylow
143C2×C22⋊Q8—891no—
144C2×C4×D4—891no—
145#400D8911yescharacteristic, complemented
146#399—891no—
147#395—891no—
148#393—891no—
149#387—892no—
150#386—892no—
151#385—892no—
152#380—892no—
153C2×#95—891no—
154C22×Q8—891no—
155C22×D4—891no—
156C23×C4—891no—
157C23×C4—891no—
158C23×C4—892no—
159C22⋊Q8—1784no—
160C4×D4—1784no—
161C2×C4⋊C4—892no—
162C2×C4⋊C4—892no—
163C2×C4⋊C4—892no—
164C2×C4⋊C4C2×D8911yescharacteristic
165C2×C4⋊C4C2×D8911yescharacteristic
166C2×C22⋊C4—892no—
167C2×C22⋊C4—891no—
168C2×C22⋊C4—891no—
169C2×C22⋊C4—892no—
170C2×C22⋊C4—892no—
171C2×C42—891no—
172#95—892no—
173#95—891no—
174#95—892no—
175#95—892no—
176#95C2×D8911yescharacteristic
177#95C2×D8912yes—
178#95C2×D8912yes—
179C24—891no—
180C24—891no—
181C2×Q8—3562no—
182C2×Q8—1782no—
183C2×D4—894no—
184C2×D4—1782no—
185C2×D4—1782no—
186C22×C4—892no—
187C22×C4—891no—
188C22×C4—894no—
189C22×C4—891no—
190C22×C4—892no—
191C22×C4—3562no—
192C22×C4—3562no—
193C22×C4—3562no—
194C22×C4—1782no—
195C22×C4—1784no—
196C22×C4—1784no—
197C22×C4C22×D8912yes—
198C22×C4C22×D8912yes—
199C22×C4C22×D8911yescharacteristic
200C22×C4C22×D8911yescharacteristic
201C22×C4C22×D8911yescharacteristic
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—3562no—
205C4⋊C4—1784no—
206C4⋊C4—1784no—
207C22⋊C4—3562no—
208C22⋊C4—1784no—
209C22⋊C4—1782no—
210C22⋊C4—1784no—
211C22⋊C4—1782no—
212C42—1782no—
213C23—892no—
214C23—892no—
215C23—892no—
216C23—892no—
217C23—1781no—
218C23—1782no—
219C23—1781no—
220C23—1782no—
221C23—1782no—
222C23—1782no—
223C23C23×D8911yescharacteristic
224Q8—3564no—
225D4—1788no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—892no—
238C2×C4—894no—
239C2×C4—3564no—
240C2×C4—3564no—
241C2×C4—3568no—
242C2×C4—1781no—
243C2×C4—1782no—
244C2×C4—1782no—
245C2×C4—1782no—
246C2×C4—1782no—
247C2×C4—1782no—
248C2×C4—1782no—
249C2×C4—1782no—
250C2×C4D4×D8912yes—
251C2×C4Q8×D8912yes—
252C22—894no—
253C22—3561no—
254C22—3561no—
255C22—3562no—
256C22—1784no—
257C22—1782no—
258C22—1782no—
259C22—1782no—
260C22—1784no—
261C22—1784no—
262C22C2×D4×D8911yescharacteristic
263C22C2×Q8×D8911yescharacteristic
264C22#41×D8912yes—
265C22#41×D8911yescharacteristic
266C22#1566805812yes—
267C4—22no—
268C4—22no—
269C4—42no—
270C4—41no—
271C4—42no—
272C4—3561no—
273C4—3562no—
274C4—1782no—
275C4—1784no—
276C2—3562no—
277C2—1784no—
278C2C22⋊Q8×D8911yescharacteristic
279C2#1915214711yescharacteristic
280C2#1915215911yescharacteristic
281C2#1915227312yes—
282C2#1915230412yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#400×C89C2
prime radicalC22×D356C22
hypercenter#400D89
hypocenterC89#2564
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#15667992C2semidirect
3. #19151533C2semidirect
4. #19151518C2semidirect
5. #19151511C2semidirect
6. #19151485C2semidirect
8. #19151472C2semidirect
9. #19151457C2semidirect
10. #95×D89C2semidirect
11. #400×C89C2semidirect
43. C2×D356Q8semidirect
142. C89#2564semidirect
145. #400D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679922
C2×#156679742
#191515332
#191515182
#191515112
#191514852
#191514762
#191514722
#191514572
#95×D892
#400×C892
#256489