Finite Group Databasebeta

← #26027950

Subgroups — #26027950

Order 11392.

472 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19151540C211yesmaximal, characteristic, complemented
2#19151521C211yesmaximal, characteristic, complemented
3#19151521C211yesmaximal, characteristic, complemented
4#19151519C211yesmaximal, characteristic, complemented
5#19151510C211yesmaximal, characteristic, complemented
6#19151510C211yesmaximal, characteristic, complemented
7#19151501C211yesmaximal, characteristic
8#19151485C211yesmaximal, characteristic, complemented
9#19151481C211yesmaximal, characteristic, complemented
10#19151478C211yesmaximal, characteristic
11#19151473C211yesmaximal, characteristic, complemented
12#19151471C211yesmaximal, characteristic, complemented
13#19151458C211yesmaximal, characteristic, complemented
14#19151456C211yesmaximal, characteristic, complemented
15#386×C89C211yesmaximal, characteristic
16C22×Dic178C2211yescharacteristic
17C23×Dic89C2211yescharacteristic
18C2×C4⋊Dic89C2211yescharacteristic
19C2×C4⋊Dic89C2211yescharacteristic
20C2×C4⋊Dic89C2211yescharacteristic
21C2×C4⋊Dic89C2211yescharacteristic
22C2×#13083553C2211yescharacteristic
23C2×#13083553C2211yescharacteristic
24C2×#13083553C2211yescharacteristic
25C2×#13083553C2211yescharacteristic
26C2×C22⋊Dic89C2211yescharacteristic
27C2×C22⋊Dic89C2211yescharacteristic
28C2×C22⋊Dic89C2211yescharacteristic
29C2×C22⋊Dic89C2211yescharacteristic
30C2×C22⋊Dic89C2211yescharacteristic
31C2×C22⋊Dic89C2211yescharacteristic
32C2×C22⋊Dic89C2211yescharacteristic
33C2×C4×Dic89C2211yescharacteristic
34#15667919C2211yescharacteristic
35#15667919C2211yescharacteristic
36#15667919C2211yescharacteristic
37#15667919C2211yescharacteristic
38#15667919C2211yescharacteristic
39#15667919C2211yescharacteristic
40#15667919C2211yescharacteristic
41#15667919C2211yescharacteristic
42#15667919C2211yescharacteristic
43#15667919C2211yescharacteristic
44C22×D4×C89C2211yescharacteristic
45C23×C4×C89C2211yescharacteristic
46C2×C22⋊C4×C89C2211yescharacteristic
47C2×C22⋊C4×C89C2211yescharacteristic
48C2×C22⋊C4×C89C2211yescharacteristic
49#95×C89C2211yescharacteristic
50#95×C89C2211yescharacteristic
51C2×Dic178—41no—
52C2×Dic178—41no—
53C2×Dic178—41no—
54C22×Dic89—22no—
55C22×Dic89—41no—
56C22×Dic89—41no—
57C22×Dic89C2311yescharacteristic
58C22×Dic89C2311yescharacteristic
59C22×Dic89C2311yescharacteristic
60C22×Dic89C2311yescharacteristic
61C22×Dic89C2311yescharacteristic
62C22×Dic89C2311yescharacteristic
63C22×Dic89C2311yescharacteristic
64C22×Dic89C2311yescharacteristic
65C4⋊Dic89—22no—
66C4⋊Dic89—41no—
67C4⋊Dic89—41no—
68C4⋊Dic89—41no—
69#13083553—22no—
70#13083553—41no—
71#13083553—41no—
72#13083553—41no—
73C22⋊Dic89—22no—
74C22⋊Dic89—41no—
75C22⋊Dic89—41no—
76C22⋊Dic89—41no—
77C22⋊Dic89—41no—
78C22⋊Dic89—41no—
79C22⋊Dic89—41no—
80C4×Dic89—41no—
81C24×C89C2311yescharacteristic
82C24×C89C2311yescharacteristic
83C2×D4×C89—41no—
84C2×D4×C89—41no—
85C2×D4×C89Q814yescomplemented
86C22×C4×C89—22no—
87C22×C4×C89—41no—
88C22×C4×C89—41no—
89C22×C4×C89C2311yescharacteristic
90C22×C4×C89C2311yescharacteristic
91C22×C4×C89C2311yescharacteristic
92C22×C4×C89C2311yescharacteristic
93C22×C4×C89C2311yescharacteristic
94C22⋊C4×C89—22no—
95C22⋊C4×C89—41no—
96C22⋊C4×C89—41no—
97C23×C89—21no—
98C23×C89—21no—
99C23×C89—21no—
100C23×C89—21no—
101C23×C89—21no—
102C23×C89—21no—
103C23×C89—21no—
104C23×C89—21no—
105C23×C89—21no—
106C23×C89—21no—
107C23×C89—21no—
108C23×C89—21no—
109C23×C89C2×Q812yes—
110C23×C89C2×Q812yes—
111C23×C89C2411yescharacteristic
112D4×C89—44no—
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×C89—21no—
126C2×C4×C89—44no—
127C2×C4×C89C2×Q812yes—
128C2×C4×C89#4112yes—
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—21no—
150C2×Dic89—21no—
151C2×Dic89—21no—
152C2×Dic89—44no—
153C2×Dic89#4112yes—
154Dic178—44no—
155C22×C89—22no—
156C22×C89—22no—
157C22×C89—22no—
158C22×C89—22no—
159C22×C89—22no—
160C22×C89—22no—
161C22×C89—41no—
162C22×C89—41no—
163C22×C89—41no—
164C22×C89—41no—
165C22×C89—41no—
166C22×C89—41no—
167C22×C89—41no—
168C22×C89—41no—
169C22×C89C22×Q811yescharacteristic
170C22×C89C2×#4111yescharacteristic
171C22×C89C2×#4111yescharacteristic
172C22×C89H(5,𝔽2)11yescharacteristic
173C22×C89H(5,𝔽2)11yescharacteristic
174C22×C89H(5,𝔽2)11yescharacteristic
175C22×C89H(5,𝔽2)11yescharacteristic
176C4×C89—22no—
177C4×C89—22no—
178C4×C89—41no—
179C4×C89—41no—
180C4×C89—41no—
181Dic89—22no—
182Dic89—41no—
183Dic89—41no—
184Dic89—41no—
185Dic89—41no—
186Dic89—41no—
187Dic89—41no—
188Dic89—41no—
189C2×C89—42no—
190C2×C89—42no—
191C2×C89#53811yescharacteristic
192C2×C89#53811yescharacteristic
193C2×C89#54311yescharacteristic
194C2×C89#55411yescharacteristic
195C2×C89#55411yescharacteristic
196C2×C89#55511yescharacteristic
197C2×C89#56011yescharacteristic
198#2784—891nomaximal, Sylow
199C89#278411yescharacteristic, complemented, Sylow
200#400—891no—
201#396—891no—
202#396—891no—
203#395—891no—
204#393—891no—
205#393—891no—
206#390—891no—
207#387—891no—
208#387—891no—
209#386—891no—
210#386D8911yescharacteristic
211#385—891no—
212#385—891no—
213#380—891no—
214#380—891no—
215C22×Q8—891no—
216C22×D4C2×D8911yescharacteristic
217C23×C4—891no—
218C23×C4C2×D8911yescharacteristic
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×C22⋊C4—891no—
228C2×C22⋊C4—891no—
229C2×C22⋊C4—891no—
230C2×C22⋊C4—891no—
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—
238#95—891no—
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#95—891no—
248#95C2×D8911yescharacteristic
249#95C2×D8911yescharacteristic
250C24C22×D8911yescharacteristic
251C24C22×D8911yescharacteristic
252C2×Q8—3561no—
253C2×Q8—3561no—
254C2×Q8—3561no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4Dic17814yescomplemented
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—891no—
262C22×C4—891no—
263C22×C4—891no—
264C22×C4—891no—
265C22×C4—891no—
266C22×C4—891no—
267C22×C4—891no—
268C22×C4—891no—
269C22×C4—3561no—
270C22×C4—3561no—
271C22×C4—1782no—
272C22×C4C22×D8911yescharacteristic
273C22×C4C22×D8911yescharacteristic
274C22×C4C22×D8911yescharacteristic
275C22×C4C22×D8911yescharacteristic
276C22×C4C22×D8911yescharacteristic
277C4⋊C4—3561no—
278C4⋊C4—3561no—
279C4⋊C4—3561no—
280C4⋊C4—3561no—
281C4⋊C4—3561no—
282C4⋊C4—3561no—
283C4⋊C4—1782no—
284C4⋊C4—1782no—
285C22⋊C4—22no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—3561no—
289C22⋊C4—3561no—
290C22⋊C4—3561no—
291C22⋊C4—3561no—
292C22⋊C4—3561no—
293C22⋊C4—3561no—
294C22⋊C4—1782no—
295C42—3561no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23C2×Dic17812yes—
309C23C2×Dic17812yes—
310C23C23×D8911yescharacteristic
311Q8—3564no—
312D4—44no—
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—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—44no—
327C2×C4—892no—
328C2×C4—3564no—
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×C4—1781no—
348C2×C4—1781no—
349C2×C4—1781no—
350C2×C4—1781no—
351C2×C4—1781no—
352C2×C4C2×Dic17812yes—
353C2×C4#1308357312yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22C22×Dic17811yescharacteristic
369C22#41×D8911yescharacteristic
370C22C2×#1308357311yescharacteristic
371C22#1566805711yescharacteristic
372C22#1566805711yescharacteristic
373C22#1566805711yescharacteristic
374C22#1566805811yescharacteristic
375C4—22no—
376C4—22no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—3561no—
381C4—3561no—
382C4—3561no—
383C4—3561no—
384C4—3561no—
385C4—3561no—
386C4—3561no—
387C4—1782no—
388C2—42no—
389C2—42no—
390C2#1915218311yescharacteristic
391C2#1915218411yescharacteristic
392C2#1915222411yescharacteristic
393C2#1915230511yescharacteristic
394C2#1915230711yescharacteristic
395C2#1915231211yescharacteristic
396C2#1915233611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#386×C89C2
prime radicalC22×D4×C89C22
hypercenter#386D89
hypocenterC89#2784
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. #19151540C2semidirect
2. #19151521C2semidirect
3. #19151521C2semidirect
4. #19151519C2semidirect
5. #19151510C2semidirect
6. #19151510C2semidirect
8. #19151485C2semidirect
9. #19151481C2semidirect
11. #19151473C2semidirect
12. #19151471C2semidirect
13. #19151458C2semidirect
14. #19151456C2semidirect
85. C2×D4×C89Q8semidirect
199. C89#2784semidirect
257. C2×D4Dic178semidirect

Maximal subgroups

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

subgroupindex
#191515402
#191515212
#191515192
#191515102
#191515012
#191514852
#191514812
#191514782
#191514732
#191514712
#191514582
#191514562
#386×C892
#278489