Finite Group Databasebeta

← #26026056

Subgroups — #26026056

Order 11392.

668 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 143 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×#15667988C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D89C211yesmaximal, characteristic
3#19151535C211yesmaximal, characteristic, complemented
4#19151534C211yesmaximal, characteristic, complemented
5#19151522C212yesmaximal, complemented
6#19151521C212yesmaximal, complemented
7#19151509C211yesmaximal, characteristic, complemented
8#19151472C212yesmaximal, complemented
9#19151457C211yesmaximal, characteristic, complemented
10#19151453C212yesmaximal
11#393×C89C211yesmaximal, characteristic, complemented
12C24×D89C2211yescharacteristic
13C22×C4×D89C2211yescharacteristic
14C22×C4×D89C2211yescharacteristic
15#15667988—24no—
16C2×C4⋊Dic89C2211yescharacteristic, complemented
17C2×C4⋊Dic89C2212yescomplemented
18C2×#13083553C2212yescomplemented
19C2×#13083553C2212yescomplemented
20C2×#13083553C2212yescomplemented
21C2×C22⋊Dic89C2211yescharacteristic
22C2×C22⋊Dic89C2212yes—
23C2×#13083551C2212yes—
24C2×#13083551C2212yes—
25C2×#13083551C2211yescharacteristic
26C2×#13083551C2211yescharacteristic
27C2×#13083551C2212yes—
28C2×#13083551C2212yes—
29C22⋊C4×D89—24no—
30#15667919C2211yescharacteristic, complemented
31#15667919C2212yescomplemented
32C22×Q8×C89C2211yescharacteristic, complemented
33C2×C22⋊C4×C89C2211yescharacteristic
34C2×C22⋊C4×C89C2212yes—
35#95×C89C2211yescharacteristic, complemented
36#95×C89C2212yescomplemented
37C23×D89—22no—
38C23×D89—22no—
39C23×D89—42no—
40C23×D89—42no—
41C23×D89Q814yescomplemented
42C23×D89C2311yescharacteristic
43C23×D89C2311yescharacteristic
44C22×Dic89C2311yescharacteristic
45C22×Dic89C2312yes—
46C22×Dic89C2312yes—
47C22×Dic89C2311yescharacteristic
48C2×C4×D89—22no—
49C2×C4×D89—42no—
50C2×C4×D89—42no—
51C2×C4×D89D414yes—
52C4⋊Dic89—22no—
53C4⋊Dic89—42no—
54#13083553—24no—
55#13083553—42no—
56#13083553—42no—
57C22⋊Dic89—22no—
58C22⋊Dic89—42no—
59#13083551—24no—
60#13083551—24no—
61#13083551—22no—
62#13083551—22no—
63#13083551—42no—
64#13083551—42no—
65C24×C89C2311yescharacteristic
66C2×Q8×C89—22no—
67C2×Q8×C89—42no—
68C22×C4×C89C2311yescharacteristic
69C22×C4×C89C2312yes—
70C22×C4×C89C2312yes—
71C22×C4×C89C2311yescharacteristic
72C22⋊C4×C89—22no—
73C22⋊C4×C89—42no—
74C23×C89—21no—
75C23×C89—21no—
76C23×C89—22no—
77C23×C89—22no—
78C23×C89C2×Q812yes—
79C23×C89C2411yescharacteristic
80C22×D89—22no—
81C22×D89—22no—
82C22×D89—21no—
83C22×D89—21no—
84C22×D89—22no—
85C22×D89—22no—
86C22×D89—28no—
87C22×D89—48no—
88C22×D89—44no—
89C22×D89—44no—
90C22×D89—48no—
91C22×D89C2×D412yes—
92C22×D89C2×Q812yes—
93C22×D89C2×Q812yes—
94C22×D89#4112yes—
95Q8×C89—44no—
96C2×C4×C89—22no—
97C2×C4×C89—21no—
98C2×C4×C89—22no—
99C2×C4×C89—22no—
100C2×C4×C89—22no—
101C2×C4×C89—22no—
102C2×C4×C89—22no—
103C2×C4×C89—22no—
104C2×C4×C89—22no—
105C2×C4×C89C2×D412yes—
106C2×Dic89—22no—
107C2×Dic89—21no—
108C2×Dic89—22no—
109C2×Dic89—22no—
110C2×Dic89—22no—
111C2×Dic89—22no—
112C2×Dic89—22no—
113C2×Dic89—22no—
114C2×Dic89—22no—
115C2×Dic89C2×D412yes—
116C4×D89—44no—
117C4×D89—44no—
118C22×C89—22no—
119C22×C89—24no—
120C22×C89—41no—
121C22×C89—41no—
122C22×C89—42no—
123C22×C89C22×D411yescharacteristic
124C22×C89C22×Q811yescharacteristic
125C22×C89C2×#4111yescharacteristic
126C22×C89H(5,𝔽2)12yes—
127C22×C89H(5,𝔽2)12yes—
128C2×D89—22no—
129C2×D89—22no—
130C2×D89—24no—
131C2×D89—24no—
132C2×D89—22no—
133C2×D89—24no—
134C2×D89—416no—
135C2×D89—41no—
136C2×D89—41no—
137C2×D89—42no—
138C2×D89C22⋊Q814yes—
139C4×C89—22no—
140C4×C89—42no—
141C4×C89—41no—
142C4×C89—42no—
143Dic89—22no—
144Dic89—41no—
145Dic89—42no—
146Dic89—42no—
147C2×C89—42no—
148C2×C89C2×C22⋊Q811yescharacteristic
149C2×C89#53411yescharacteristic
150C2×C89#53511yescharacteristic
151C2×C89#53812yes—
152C2×C89#54312yes—
153D89—24no—
154D89—42no—
155#2626—891nomaximal, Sylow
156C89#262611yescharacteristic, complemented, Sylow
157C2×C22⋊Q8—891no—
158C22×C22⋊C4—891no—
159#399—891no—
160#399—891no—
161#396—892no—
162#396—892no—
163#393—891no—
164#393D8911yescharacteristic, complemented
165#385—892no—
166#380—891no—
167#379—892no—
168C25—891no—
169C22×Q8C2×D8911yescharacteristic, complemented
170C23×C4—891no—
171C23×C4—891no—
172C22⋊Q8—1784no—
173C2×C4⋊C4—892no—
174C2×C4⋊C4—892no—
175C2×C4⋊C4—892no—
176C2×C4⋊C4—892no—
177C2×C4⋊C4—891no—
178C2×C22⋊C4—892no—
179C2×C22⋊C4—892no—
180C2×C22⋊C4—892no—
181C2×C22⋊C4—891no—
182C2×C22⋊C4—891no—
183C2×C22⋊C4—891no—
184C2×C22⋊C4—892no—
185C2×C22⋊C4—892no—
186C2×C22⋊C4—1784no—
187C2×C22⋊C4C2×D8911yescharacteristic
188C2×C22⋊C4C2×D8912yes—
189#95—891no—
190#95—892no—
191#95C2×D8911yescharacteristic, complemented
192#95C2×D8912yescomplemented
193C24—891no—
194C24—894no—
195C24—891no—
196C24—3562no—
197C24—3562no—
198C24—1782no—
199C24—1782no—
200C24C22×D8911yescharacteristic
201C2×Q8—22no—
202C2×Q8—42no—
203C22×C4—891no—
204C22×C4—894no—
205C22×C4—892no—
206C22×C4—891no—
207C22×C4—892no—
208C22×C4—3562no—
209C22×C4—3562no—
210C22×C4—1782no—
211C22×C4C22×D8912yes—
212C22×C4C22×D8912yes—
213C22×C4C22×D8911yescharacteristic
214C22×C4C22×D8911yescharacteristic
215C4⋊C4—3562no—
216C4⋊C4—3562no—
217C4⋊C4—3562no—
218C4⋊C4—1784no—
219C4⋊C4—1782no—
220C22⋊C4—22no—
221C22⋊C4—42no—
222C22⋊C4—3562no—
223C22⋊C4—3562no—
224C22⋊C4—3562no—
225C22⋊C4—1782no—
226C22⋊C4—1784no—
227C22⋊C4—1784no—
228C22⋊C4—1782no—
229C22⋊C4—1782no—
230C23—21no—
231C23—21no—
232C23—22no—
233C23—22no—
234C23—892no—
235C23—892no—
236C23—892no—
237C23—892no—
238C23—3568no—
239C23—3564no—
240C23—3564no—
241C23—3568no—
242C23—1788no—
243C23—1781no—
244C23—1781no—
245C23—1782no—
246C23—1782no—
247C23—1782no—
248C23—1782no—
249C23Q8×D8912yes—
250C23C23×D8911yescharacteristic
251Q8—44no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—892no—
262C2×C4—3564no—
263C2×C4—3564no—
264C2×C4—1781no—
265C2×C4—1782no—
266C2×C4—1782no—
267C2×C4—1782no—
268C2×C4—1782no—
269C2×C4—1782no—
270C2×C4—1782no—
271C2×C4—1782no—
272C2×C4—1782no—
273C2×C4D4×D8912yes—
274C22—24no—
275C22—22no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—894no—
280C22—35616no—
281C22—3561no—
282C22—3561no—
283C22—3562no—
284C22—1784no—
285C22—1782no—
286C22—1782no—
287C22—1782no—
288C22—1784no—
289C22—1784no—
290C22C2×D4×D8911yescharacteristic
291C22C2×Q8×D8911yescharacteristic
292C22#41×D8911yescharacteristic
293C22#1566805712yes—
294C22#1566805812yes—
295C4—22no—
296C4—42no—
297C4—41no—
298C4—42no—
299C4—3561no—
300C4—3562no—
301C4—3562no—
302C4—1782no—
303C2—42no—
304C2—3562no—
305C2—1784no—
306C2C22⋊Q8×D8911yescharacteristic
307C2#1915215811yescharacteristic
308C2#1915216611yescharacteristic
309C2#1915218212yes—
310C2#1915222312yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#393×C89C2
prime radicalC24×D89C22
hypercenter#393D89
hypocenterC89#2626
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#15667988C2semidirect
3. #19151535C2semidirect
4. #19151534C2semidirect
5. #19151522C2semidirect
6. #19151521C2semidirect
7. #19151509C2semidirect
8. #19151472C2semidirect
9. #19151457C2semidirect
11. #393×C89C2semidirect
16. C2×C4⋊Dic89C22semidirect
17. C2×C4⋊Dic89C22semidirect
18. C2×#13083553C22semidirect
19. C2×#13083553C22semidirect
20. C2×#13083553C22semidirect
30. #15667919C22semidirect
31. #15667919C22semidirect
32. C22×Q8×C89C22semidirect
35. #95×C89C22semidirect
36. #95×C89C22semidirect
41. C23×D89Q8semidirect
156. C89#2626semidirect
164. #393D89semidirect
169. C22×Q8C2×D89semidirect
191. #95C2×D89semidirect
192. #95C2×D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679882
C2×C22⋊C4×D892
#191515352
#191515342
#191515222
#191515212
#191515092
#191514722
#191514572
#191514532
#393×C892
#262689