Finite Group Databasebeta

← #26026564

Subgroups — #26026564

Order 11392.

544 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15668012C211yesmaximal, characteristic, complemented
2C2×#15668011C211yesmaximal, characteristic, complemented
3C2×#15667989C211yesmaximal, characteristic
4C2×#15667989C211yesmaximal, characteristic
5#19151534C211yesmaximal, characteristic
6#19151532C211yesmaximal, characteristic, complemented
7#19151530C211yesmaximal, characteristic, complemented
8#19151519C211yesmaximal, characteristic, complemented
9#19151518C211yesmaximal, characteristic, complemented
10#19151510C211yesmaximal, characteristic
11#19151491C211yesmaximal, characteristic
12#19151482C211yesmaximal, characteristic, complemented
13#19151481C211yesmaximal, characteristic, complemented
14#19151473C211yesmaximal, characteristic
15#388×C89C211yesmaximal, characteristic
16C22×Dic178C2211yescharacteristic
17C22×Dic178C2211yescharacteristic
18C22×Dic178C2211yescharacteristic
19C23×Dic89C2211yescharacteristic
20#15668012—24no—
21#15668011—24no—
22#15667989—24no—
23#15667989—24no—
24C2×C4⋊Dic89C2211yescharacteristic
25C2×C4⋊Dic89C2211yescharacteristic
26C2×C4⋊Dic89C2211yescharacteristic
27C2×C4⋊Dic89C2211yescharacteristic
28C2×C4⋊Dic89C2211yescharacteristic
29C2×C4⋊Dic89C2211yescharacteristic
30C2×#13083553C2211yescharacteristic
31C2×#13083553C2211yescharacteristic
32C2×#13083553C2211yescharacteristic
33C2×#13083553C2211yescharacteristic
34C2×#13083553C2211yescharacteristic
35C2×#13083553C2211yescharacteristic
36C2×C22⋊Dic89C2211yescharacteristic
37C2×C22⋊Dic89C2211yescharacteristic
38C2×C22⋊Dic89C2211yescharacteristic
39C2×C4×Dic89C2211yescharacteristic
40#15667919C2211yescharacteristic
41#15667919C2211yescharacteristic
42#15667919C2211yescharacteristic
43#15667919C2211yescharacteristic
44#15667919C2211yescharacteristic
45#15667919C2211yescharacteristic
46#15667919C2211yescharacteristic
47#15667919C2211yescharacteristic
48C2×C4⋊C4×C89C2211yescharacteristic
49C2×C22⋊C4×C89C2211yescharacteristic
50C2×C22⋊C4×C89C2211yescharacteristic
51C2×C22⋊C4×C89C2211yescharacteristic
52C2×C42×C89C2211yescharacteristic
53#95×C89C2211yescharacteristic
54#95×C89C2211yescharacteristic
55C2×Dic178—22no—
56C2×Dic178—22no—
57C2×Dic178—22no—
58C2×Dic178—22no—
59C2×Dic178—22no—
60C2×Dic178—22no—
61C2×Dic178—41no—
62C2×Dic178—41no—
63C2×Dic178—41no—
64C22×Dic89—22no—
65C22×Dic89—22no—
66C22×Dic89—41no—
67C22×Dic89C2311yescharacteristic
68C22×Dic89C2311yescharacteristic
69C22×Dic89C2311yescharacteristic
70C22×Dic89C2311yescharacteristic
71C22×Dic89C2311yescharacteristic
72C22×Dic89C2311yescharacteristic
73C22×Dic89C2311yescharacteristic
74C22×Dic89C2311yescharacteristic
75C4⋊Dic89—22no—
76C4⋊Dic89—22no—
77C4⋊Dic89—22no—
78C4⋊Dic89—22no—
79C4⋊Dic89—22no—
80C4⋊Dic89D414yes—
81#13083553—22no—
82#13083553—22no—
83#13083553—22no—
84#13083553—22no—
85#13083553—41no—
86#13083553D414yes—
87C22⋊Dic89—22no—
88C22⋊Dic89—22no—
89C22⋊Dic89—41no—
90C4×Dic89—22no—
91C24×C89C2311yescharacteristic
92C22×C4×C89C2311yescharacteristic
93C22×C4×C89C2311yescharacteristic
94C22×C4×C89C2311yescharacteristic
95C22×C4×C89C2311yescharacteristic
96C22×C4×C89C2311yescharacteristic
97C22×C4×C89C2311yescharacteristic
98C4⋊C4×C89—22no—
99C22⋊C4×C89—22no—
100C22⋊C4×C89—22no—
101C22⋊C4×C89Q814yescomplemented
102C42×C89—22no—
103C23×C89—21no—
104C23×C89—21no—
105C23×C89—21no—
106C23×C89—21no—
107C23×C89—21no—
108C23×C89—21no—
109C23×C89C2×Q812yes—
110C23×C89C2411yescharacteristic
111C2×C4×C89—21no—
112C2×C4×C89—21no—
113C2×C4×C89—21no—
114C2×C4×C89—21no—
115C2×C4×C89—21no—
116C2×C4×C89—21no—
117C2×C4×C89—21no—
118C2×C4×C89—21no—
119C2×C4×C89—21no—
120C2×C4×C89—21no—
121C2×C4×C89—21no—
122C2×C4×C89—21no—
123C2×C4×C89—21no—
124C2×C4×C89—21no—
125C2×C4×C89C2×D412yes—
126C2×C4×C89C2×D412yes—
127C2×C4×C89C2×Q812yes—
128C2×C4×C89C2×Q812yes—
129C2×Dic89—21no—
130C2×Dic89—21no—
131C2×Dic89—21no—
132C2×Dic89—21no—
133C2×Dic89—21no—
134C2×Dic89—21no—
135C2×Dic89—21no—
136C2×Dic89—21no—
137C2×Dic89—21no—
138C2×Dic89—21no—
139C2×Dic89—21no—
140C2×Dic89—21no—
141C2×Dic89—21no—
142C2×Dic89—21no—
143C2×Dic89—21no—
144C2×Dic89—21no—
145C2×Dic89—21no—
146C2×Dic89—21no—
147C2×Dic89—21no—
148C2×Dic89—21no—
149C2×Dic89—44no—
150C2×Dic89C2×D412yes—
151C2×Dic89C2×D412yes—
152C2×Dic89C2×D412yes—
153C2×Dic89C2×D412yes—
154Dic178—44no—
155Dic178—44no—
156Dic178—44no—
157C22×C89—22no—
158C22×C89—22no—
159C22×C89—22no—
160C22×C89—41no—
161C22×C89—41no—
162C22×C89—41no—
163C22×C89—41no—
164C22×C89C22×D411yescharacteristic
165C22×C89C22×D411yescharacteristic
166C22×C89C22×Q811yescharacteristic
167C22×C89H(5,𝔽2)11yescharacteristic
168C22×C892−1+411yescharacteristic
169C22×C892−1+411yescharacteristic
170C22×C892−1+411yescharacteristic
171C4×C89—22no—
172C4×C89—22no—
173C4×C89—22no—
174C4×C89—22no—
175C4×C89—41no—
176C4×C89—41no—
177Dic89—22no—
178Dic89—22no—
179Dic89—22no—
180Dic89—22no—
181Dic89—41no—
182Dic89—41no—
183Dic89—41no—
184Dic89—41no—
185C2×C89—42no—
186C2×C89#53611yescharacteristic
187C2×C89#53611yescharacteristic
188C2×C89#54411yescharacteristic
189C2×C89D4211yescharacteristic
190C2×C89D4×Q811yescharacteristic
191C2×C89D4×Q811yescharacteristic
192C2×C89#56311yescharacteristic
193#2677—891nomaximal, Sylow
194C89#267711yescharacteristic, complemented, Sylow
195C2×C4⋊Q8—891no—
196C2×C4⋊Q8—891no—
197C2×C22⋊Q8—891no—
198C2×C22⋊Q8—891no—
199#399—891no—
200#398—891no—
201#398—891no—
202#395—891no—
203#395—891no—
204#393—891no—
205#388—891no—
206#388D8911yescharacteristic
207#387—891no—
208#387—891no—
209#385—891no—
210C22×Q8—891no—
211C22×Q8—891no—
212C22×Q8—891no—
213C23×C4—891no—
214C4⋊Q8—1784no—
215C4⋊Q8—1784no—
216C22⋊Q8—1784no—
217C22⋊Q8—1784no—
218C2×C4⋊C4—891no—
219C2×C4⋊C4—891no—
220C2×C4⋊C4—891no—
221C2×C4⋊C4—891no—
222C2×C4⋊C4—891no—
223C2×C4⋊C4—891no—
224C2×C4⋊C4—891no—
225C2×C4⋊C4—891no—
226C2×C4⋊C4—891no—
227C2×C4⋊C4—891no—
228C2×C4⋊C4—891no—
229C2×C4⋊C4—891no—
230C2×C4⋊C4C2×D8911yescharacteristic
231C2×C22⋊C4—891no—
232C2×C22⋊C4—891no—
233C2×C22⋊C4—891no—
234C2×C22⋊C4C2×D8911yescharacteristic
235C2×C22⋊C4C2×D8911yescharacteristic
236C2×C22⋊C4C2×D8911yescharacteristic
237C2×C42—891no—
238C2×C42C2×D8911yescharacteristic
239#95—891no—
240#95—891no—
241#95—891no—
242#95—891no—
243#95—891no—
244#95—891no—
245#95—891no—
246#95—891no—
247#95C2×D8911yescharacteristic
248#95C2×D8911yescharacteristic
249C24C22×D8911yescharacteristic
250C2×Q8—3561no—
251C2×Q8—3561no—
252C2×Q8—3561no—
253C2×Q8—1782no—
254C2×Q8—1782no—
255C2×Q8—1782no—
256C2×Q8—1782no—
257C2×Q8—1782no—
258C2×Q8—1782no—
259C22×C4—891no—
260C22×C4—891no—
261C22×C4—891no—
262C22×C4—891no—
263C22×C4—891no—
264C22×C4—891no—
265C22×C4—891no—
266C22×C4—891no—
267C22×C4—3561no—
268C22×C4—1782no—
269C22×C4—1782no—
270C22×C4C22×D8911yescharacteristic
271C22×C4C22×D8911yescharacteristic
272C22×C4C22×D8911yescharacteristic
273C22×C4C22×D8911yescharacteristic
274C22×C4C22×D8911yescharacteristic
275C22×C4C22×D8911yescharacteristic
276C4⋊C4—22no—
277C4⋊C4—894no—
278C4⋊C4—894no—
279C4⋊C4—3561no—
280C4⋊C4—1782no—
281C4⋊C4—1782no—
282C4⋊C4—1782no—
283C4⋊C4—1782no—
284C4⋊C4—1782no—
285C4⋊C4—1782no—
286C4⋊C4—1782no—
287C4⋊C4—1782no—
288C4⋊C4—1782no—
289C22⋊C4—22no—
290C22⋊C4—22no—
291C22⋊C4—3561no—
292C22⋊C4—1782no—
293C22⋊C4—1782no—
294C22⋊C4Dic17814yescomplemented
295C42—22no—
296C42—1782no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23C2×Dic17812yes—
304C23C23×D8911yescharacteristic
305Q8—3564no—
306Q8—3564no—
307Q8—3564no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—892no—
323C2×C4—892no—
324C2×C4—892no—
325C2×C4—892no—
326C2×C4—3564no—
327C2×C4—1781no—
328C2×C4—1781no—
329C2×C4—1781no—
330C2×C4—1781no—
331C2×C4—1781no—
332C2×C4—1781no—
333C2×C4—1781no—
334C2×C4—1781no—
335C2×C4—1781no—
336C2×C4—1781no—
337C2×C4—1781no—
338C2×C4—1781no—
339C2×C4—1781no—
340C2×C4—1781no—
341C2×C4—1781no—
342C2×C4—1781no—
343C2×C4—1781no—
344C2×C4—1781no—
345C2×C4—1781no—
346C2×C4—1781no—
347C2×C4D4×D8912yes—
348C2×C4D4×D8912yes—
349C2×C4C2×Dic17812yes—
350C2×C4C2×Dic17812yes—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22C2×D4×D8911yescharacteristic
359C22C2×D4×D8911yescharacteristic
360C22C22×Dic17811yescharacteristic
361C22#1566805811yescharacteristic
362C22#1566805911yescharacteristic
363C22#1566805911yescharacteristic
364C22#1566805911yescharacteristic
365C4—22no—
366C4—22no—
367C4—22no—
368C4—22no—
369C4—41no—
370C4—41no—
371C4—3561no—
372C4—3561no—
373C4—3561no—
374C4—3561no—
375C4—1782no—
376C4—1782no—
377C4—1782no—
378C4—1782no—
379C2—42no—
380C2#1915216811yescharacteristic
381C2#1915217011yescharacteristic
382C2#1915222611yescharacteristic
383C2#1915223211yescharacteristic
384C2D4×Dic17811yescharacteristic
385C2D4×Dic17811yescharacteristic
386C2#1915235011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#388×C89C2
prime radicalC24×C89C23
hypercenter#388D89
hypocenterC89#2677
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#15668012C2semidirect
2. C2×#15668011C2semidirect
6. #19151532C2semidirect
7. #19151530C2semidirect
8. #19151519C2semidirect
9. #19151518C2semidirect
12. #19151482C2semidirect
13. #19151481C2semidirect
101. C22⋊C4×C89Q8semidirect
194. C89#2677semidirect
294. C22⋊C4Dic178semidirect

Maximal subgroups

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

subgroupindex
C2×#156680122
C2×#156680112
C2×#156679892
#191515342
#191515322
#191515302
#191515192
#191515182
#191515102
#191514912
#191514822
#191514812
#191514732
#388×C892
#267789