Finite Group Databasebeta

← #26032333

Subgroups — #26032333

Order 11392.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152305C211yesmaximal, characteristic, complemented
2#19151957C211yesmaximal, characteristic, complemented
3#19151931C211yesmaximal, characteristic, complemented
4#19151909C211yesmaximal, characteristic, complemented
5#19151878C211yesmaximal, characteristic, complemented
6#19151842C211yesmaximal, characteristic, complemented
7#19151837C211yesmaximal, characteristic, complemented
8#19151817C211yesmaximal, characteristic, complemented
9#19151760C211yesmaximal, characteristic, complemented
10#19151749C211yesmaximal, characteristic, complemented
11#19151698C211yesmaximal, characteristic, complemented
12#19151670C211yesmaximal, characteristic, complemented
13#19151599C211yesmaximal, characteristic, complemented
14C2×#15667933C211yesmaximal, characteristic, complemented
15#546×C89C211yesmaximal, characteristic
16C2×#13083564C2211yescharacteristic, complemented
17C2×#13083562C2211yescharacteristic
18C2×#13083562C2211yescharacteristic
19C2×#13083558C2211yescharacteristic, complemented
20C22×#10623494C2211yescharacteristic
21#15668012C2211yescharacteristic, complemented
22#15668003—21no—
23#15667991C2211yescharacteristic
24#15667991C2211yescharacteristic, complemented
25#15667989—21no—
26#15667989—21no—
27C4×Dic178C2211yescharacteristic, complemented
28D4×Dic89—21no—
29C2×C4⋊Dic89C2211yescharacteristic
30C2×C4⋊Dic89C2211yescharacteristic, complemented
31#15667945C2211yescharacteristic, complemented
32#15667945C2211yescharacteristic, complemented
33#15667945C2211yescharacteristic, complemented
34C4⋊#10623494C2211yescharacteristic, complemented
35#15667936C2211yescharacteristic, complemented
36#15667936C2211yescharacteristic, complemented
37#15667936C2211yescharacteristic, complemented
38#15667935C2211yescharacteristic, complemented
39#15667933C2211yescharacteristic
40#15667933C2211yescharacteristic
41#15667933C2211yescharacteristic
42#15667933C2211yescharacteristic
43#15667933C2211yescharacteristic
44#15667933C2211yescharacteristic
45C22⋊#10623494C2211yescharacteristic
46C22⋊#10623494C2211yescharacteristic, complemented
47#15667923C2211yescharacteristic, complemented
48C2×#41×C89C2211yescharacteristic
49C22×D4×C89C2211yescharacteristic
50#124×C89C2211yescharacteristic
51#123×C89—21no—
52C22⋊Q8×C89C2211yescharacteristic
53#121×C89—21no—
54#121×C89C2211yescharacteristic
55#120×C89—21no—
56C4×D4×C89C2211yescharacteristic
57C4×D4×C89C2211yescharacteristic
58C2×C22⋊C4×C89—21no—
59C2×Dic178—21no—
60C2×Dic178C2311yescharacteristic
61C22×Dic89—21no—
62C22×Dic89—21no—
63#13083564—41no—
64#13083562—22no—
65#13083562—41no—
66#13083558—41no—
67C2×#10623494—41no—
68C2×#10623494C2311yescharacteristic
69C2×#10623494C2311yescharacteristic
70C2×#10623494C2311yescharacteristic
71C2×#10623494C2311yescharacteristic
72C4⋊Dic89—21no—
73C4⋊Dic89—21no—
74C4⋊Dic89—21no—
75C4⋊Dic89C2311yescharacteristic
76C4⋊Dic89C2311yescharacteristic
77C4⋊Dic89C2311yescharacteristic
78#13083553—21no—
79#13083553—21no—
80#13083553—21no—
81C22⋊Dic89—21no—
82C22⋊Dic89—21no—
83C4×Dic89—21no—
84C24×C89—21no—
85#41×C89—22no—
86#41×C89—41no—
87C2×Q8×C89C2311yescharacteristic
88C2×D4×C89—22no—
89C2×D4×C89—21no—
90C2×D4×C89—21no—
91C2×D4×C89—21no—
92C2×D4×C89—41no—
93C2×D4×C89D411yescharacteristic
94C2×D4×C89C2311yescharacteristic
95C2×D4×C89C2311yescharacteristic
96C22×C4×C89—21no—
97C22×C4×C89—21no—
98C22×C4×C89C2311yescharacteristic
99C22×C4×C89C2311yescharacteristic
100C4⋊C4×C89—21no—
101C4⋊C4×C89D411yescharacteristic
102C4⋊C4×C89C2311yescharacteristic
103C22⋊C4×C89—21no—
104C22⋊C4×C89—21no—
105C22⋊C4×C89—21no—
106C22⋊C4×C89—21no—
107C22⋊C4×C89—21no—
108C22⋊C4×C89D411yescharacteristic
109C22⋊C4×C89D411yescharacteristic
110C42×C89C2311yescharacteristic
111C23×C89—21no—
112C23×C89—21no—
113C23×C89—42no—
114C23×C89—42no—
115C23×C89—81no—
116C23×C89C2×D411yescharacteristic
117C23×C89C2×D411yescharacteristic
118Q8×C89—21no—
119Q8×C89—21no—
120D4×C89—22no—
121D4×C89—21no—
122D4×C89—21no—
123D4×C89—21no—
124D4×C89—42no—
125D4×C89—42no—
126D4×C89—81no—
127D4×C89#4112yes—
128C2×C4×C89—21no—
129C2×C4×C89—21no—
130C2×C4×C89—21no—
131C2×C4×C89—21no—
132C2×C4×C89—21no—
133C2×C4×C89—21no—
134C2×C4×C89—42no—
135C2×C4×C89—81no—
136C2×C4×C89C2×D411yescharacteristic
137C2×C4×C89C2×D411yescharacteristic
138C2×C4×C89C2×D411yescharacteristic
139C2×C4×C89C2×D411yescharacteristic
140C2×C4×C89C2411yescharacteristic
141C2×Dic89—21no—
142C2×Dic89—21no—
143C2×Dic89—21no—
144C2×Dic89—21no—
145C2×Dic89—81no—
146C2×Dic89—81no—
147Dic178—21no—
148Dic178—21no—
149Dic178—81no—
150#10623494—21no—
151#10623494—21no—
152#10623494—21no—
153#10623494—21no—
154C22×C89—21no—
155C22×C89—21no—
156C22×C89—21no—
157C22×C89—22no—
158C22×C89—21no—
159C22×C89—21no—
160C22×C89—41no—
161C22×C89—41no—
162C22×C89—41no—
163C22×C89—41no—
164C22×C89—41no—
165C22×C89—84no—
166C22×C89#13712yes—
167C22×C89C22×D411yescharacteristic
168C4×C89—21no—
169C4×C89—21no—
170C4×C89—21no—
171C4×C89—21no—
172C4×C89—41no—
173C4×C89—41no—
174C4×C89C2×#4111yescharacteristic
175C4×C89H(5,𝔽2)11yescharacteristic
176Dic89—41no—
177Dic89—41no—
178Dic89—41no—
179Dic89—41no—
180C2×C89—22no—
181C2×C89—41no—
182C2×C89—42no—
183C2×C89—81no—
184C2×C89#54611yescharacteristic
185C2×C89C2×#13711yescharacteristic
186C2×C89#57611yescharacteristic
187#3314—891nomaximal, Sylow
188C89#331411yescharacteristic, complemented, Sylow
189#554—891no—
190#546D8911yescharacteristic
191#489—891no—
192#484—891no—
193#480—891no—
194#474—891no—
195#468—891no—
196#467—891no—
197#464—891no—
198#452—891no—
199#450—891no—
200#440—891no—
201#435—891no—
202#417—891no—
203C2×#102—891no—
204C2×#41C2×D8911yescharacteristic
205C22×D4C2×D8911yescharacteristic
206C2×Q16—891no—
207C2×SD16—891no—
208C2×SD16—891no—
209C2×M16—891no—
210C22×C8—891no—
211C4⋊Q8—891no—
212#125—1781no—
213#124C2×D8911yescharacteristic
214#123—21no—
215C22⋊Q8—891no—
216C22⋊Q8—891no—
217C22⋊Q8—1781no—
218C22⋊Q8—1781no—
219C22⋊Q8C2×D8911yescharacteristic
220#121—21no—
221#121C2×D8911yescharacteristic
222#120—21no—
223C4×Q8—891no—
224C4×D4—1781no—
225C4×D4C2×D8911yescharacteristic
226C4×D4C2×D8911yescharacteristic
227C2×C4⋊C4—891no—
228C2×C4⋊C4—891no—
229C2×C22⋊C4—21no—
230#107—891no—
231#107—891no—
232#107—891no—
233C4⋊C8—891no—
234#103—891no—
235#103—891no—
236#103—891no—
237#103—891no—
238#102—891no—
239#102—891no—
240#102—891no—
241#102—891no—
242#102—891no—
243#102—891no—
244C22⋊C8—891no—
245C22⋊C8—891no—
246#97—891no—
247C24—21no—
248#41—22no—
249#41—41no—
250C2×Q8—891no—
251C2×Q8—1781no—
252C2×Q8C22×D8911yescharacteristic
253C2×D4—22no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4C22⋊D8911yescharacteristic
259C2×D4C22×D8911yescharacteristic
260C2×D4C22×D8911yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—1781no—
264C22×C4—1781no—
265C22×C4C22×D8911yescharacteristic
266C22×C4C22×D8911yescharacteristic
267Q16—3561no—
268SD16—3561no—
269SD16—1782no—
270M16—3561no—
271C2×C8—891no—
272C2×C8—891no—
273C2×C8—891no—
274C2×C8—891no—
275C2×C8—3561no—
276C4⋊C4—21no—
277C4⋊C4—891no—
278C4⋊C4—891no—
279C4⋊C4—891no—
280C4⋊C4—1781no—
281C4⋊C4—1781no—
282C4⋊C4—1781no—
283C4⋊C4—1781no—
284C4⋊C4—1781no—
285C4⋊C4—1781no—
286C4⋊C4C22⋊D8911yescharacteristic
287C4⋊C4C22×D8911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—1781no—
294C22⋊C4—1781no—
295C22⋊C4C22⋊D8911yescharacteristic
296C22⋊C4C22⋊D8911yescharacteristic
297C42—1781no—
298C42C22×D8911yescharacteristic
299C23—21no—
300C23—21no—
301C23—42no—
302C23—42no—
303C23—81no—
304C23C2×C22⋊D8911yescharacteristic
305C23C2×C22⋊D8911yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—1781no—
309Q8—1781no—
310Q8—7121no—
311D4—22no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4#1308357312yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—81no—
327C2×C4—1781no—
328C2×C4—1781no—
329C2×C4—1781no—
330C2×C4—1781no—
331C2×C4—7121no—
332C2×C4—7121no—
333C2×C4C2×C22⋊D8911yescharacteristic
334C2×C4C2×C22⋊D8911yescharacteristic
335C2×C4C2×C22⋊D8911yescharacteristic
336C2×C4C2×C22⋊D8911yescharacteristic
337C2×C4C23×D8911yescharacteristic
338C8—1781no—
339C8—1781no—
340C8—1781no—
341C8—1781no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—84no—
354C22#1566804212yes—
355C22C22×C22⋊D8911yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—3561no—
363C4—3561no—
364C4—3561no—
365C4—3561no—
366C4C2×#1308357311yescharacteristic
367C4#1566805711yescharacteristic
368C2—22no—
369C2—41no—
370C2—42no—
371C2—81no—
372C2#1915224211yescharacteristic
373C2C2×#1566804211yescharacteristic
374C2#1915240111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting, prime radical#546×C89C2
socleC22×C89C22×D4
hypercenter#546D89
hypocenterC89#3314
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #19152305C2semidirect
2. #19151957C2semidirect
3. #19151931C2semidirect
4. #19151909C2semidirect
5. #19151878C2semidirect
6. #19151842C2semidirect
7. #19151837C2semidirect
8. #19151817C2semidirect
9. #19151760C2semidirect
10. #19151749C2semidirect
11. #19151698C2semidirect
12. #19151670C2semidirect
13. #19151599C2semidirect
14. C2×#15667933C2semidirect
16. C2×#13083564C22semidirect
19. C2×#13083558C22semidirect
21. #15668012C22semidirect
24. #15667991C22semidirect
27. C4×Dic178C22semidirect
30. C2×C4⋊Dic89C22semidirect
31. #15667945C22semidirect
32. #15667945C22semidirect
33. #15667945C22semidirect
34. C4⋊#10623494C22semidirect
35. #15667936C22semidirect
36. #15667936C22semidirect
37. #15667936C22semidirect
38. #15667935C22semidirect
46. C22⋊#10623494C22semidirect
47. #15667923C22semidirect
188. C89#3314semidirect

Maximal subgroups

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

subgroupindex
#191523052
#191519572
#191519312
#191519092
#191518782
#191518422
#191518372
#191518172
#191517602
#191517492
#191516982
#191516702
#191515992
C2×#156679332
#546×C892
#331489