Finite Group Databasebeta

← #26032408

Subgroups — #26032408

Order 11392.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152313C211yesmaximal, characteristic, complemented
2#19151957C211yesmaximal, characteristic, complemented
3#19151936C211yesmaximal, characteristic, complemented
4#19151919C211yesmaximal, characteristic, complemented
5#19151878C211yesmaximal, characteristic, complemented
6#19151846C211yesmaximal, characteristic, complemented
7#19151832C211yesmaximal, characteristic, complemented
8#19151810C211yesmaximal, characteristic, complemented
9#19151743C211yesmaximal, characteristic, complemented
10#19151732C211yesmaximal, characteristic, complemented
11#19151708C211yesmaximal, characteristic, complemented
12#19151670C211yesmaximal, characteristic, complemented
13#19151603C211yesmaximal, characteristic, complemented
14#19151594C211yesmaximal, characteristic, complemented
15#546×C89C211yesmaximal, characteristic, complemented
16C2×#13083561C2211yescharacteristic, complemented
17C2×#13083559C2211yescharacteristic
18C2×#13083559C2211yescharacteristic
19C2×#13083558C2211yescharacteristic
20C22×#10623494C2211yescharacteristic, complemented
21#15668012C2211yescharacteristic, complemented
22#15667998—21no—
23#15667998—21no—
24#15667986C2211yescharacteristic
25#15667986C2211yescharacteristic, complemented
26#15667983—21no—
27C4×D356C2211yescharacteristic, complemented
28#15667971C2211yescharacteristic
29#15667971C2211yescharacteristic, complemented
30#15667970—21no—
31#15667945C2211yescharacteristic, complemented
32#15667945C2211yescharacteristic, complemented
33#15667943C2211yescharacteristic, complemented
34C4⋊#10623494C2211yescharacteristic, complemented
35#15667936C2211yescharacteristic, complemented
36#15667936C2211yescharacteristic, complemented
37#15667936C2211yescharacteristic, complemented
38#15667933C2211yescharacteristic
39#15667933C2211yescharacteristic
40#15667933C2211yescharacteristic
41#15667933C2211yescharacteristic
42#15667933C2211yescharacteristic
43#15667933C2211yescharacteristic
44#15667932C2211yescharacteristic, complemented
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×D356C2311yescharacteristic
61C2×C22⋊D89—21no—
62C2×C22⋊D89—21no—
63C2×C4×D89—21no—
64#13083561—41no—
65#13083559—22no—
66#13083559—41no—
67#13083558—41no—
68C2×#10623494—41no—
69C2×#10623494C2311yescharacteristic
70C2×#10623494C2311yescharacteristic
71C2×#10623494C2311yescharacteristic
72C2×#10623494C2311yescharacteristic
73C4⋊Dic89—21no—
74C4⋊Dic89C2311yescharacteristic
75C4⋊Dic89C2311yescharacteristic
76C4⋊Dic89C2311yescharacteristic
77C22⋊Dic89—21no—
78C22⋊Dic89—21no—
79#13083551—21no—
80#13083551—21no—
81#13083551—21no—
82C4×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
118C22×D89—21no—
119Q8×C89—21no—
120Q8×C89—21no—
121D4×C89—21no—
122D4×C89—21no—
123D4×C89—21no—
124D4×C89—41no—
125D4×C89—42no—
126D4×C89—42no—
127D4×C89—81no—
128D4×C89#4112yes—
129C2×C4×C89—21no—
130C2×C4×C89—21no—
131C2×C4×C89—21no—
132C2×C4×C89—21no—
133C2×C4×C89—21no—
134C2×C4×C89—21no—
135C2×C4×C89—42no—
136C2×C4×C89—81no—
137C2×C4×C89C2×D411yescharacteristic
138C2×C4×C89C2×D411yescharacteristic
139C2×C4×C89C2×D411yescharacteristic
140C2×C4×C89C2×D411yescharacteristic
141C2×C4×C89C2411yescharacteristic
142C22⋊D89—81no—
143C22⋊D89—81no—
144C2×Dic89—21no—
145C2×Dic89—21no—
146C2×Dic89—21no—
147D356—21no—
148D356—21no—
149C4×D89—42no—
150Dic178—81no—
151#10623494—21no—
152#10623494—21no—
153#10623494—21no—
154#10623494—21no—
155C22×C89—21no—
156C22×C89—21no—
157C22×C89—22no—
158C22×C89—21no—
159C22×C89—21no—
160C22×C89—21no—
161C22×C89—21no—
162C22×C89—41no—
163C22×C89—41no—
164C22×C89—41no—
165C22×C89—41no—
166C22×C89—41no—
167C22×C89—84no—
168C22×C89C22×D411yescharacteristic
169C2×D89—41no—
170C2×D89—41no—
171C2×D89—41no—
172C4×C89—21no—
173C4×C89—21no—
174C4×C89—21no—
175C4×C89—21no—
176C4×C89—41no—
177C4×C89—41no—
178C4×C89C2×#4111yescharacteristic
179C4×C89H(5,𝔽2)11yescharacteristic
180Dic89—41no—
181Dic89—41no—
182Dic89—41no—
183C2×C89—41no—
184C2×C89—41no—
185C2×C89—42no—
186C2×C89—81no—
187C2×C89#54611yescharacteristic
188C2×C89#57511yescharacteristic
189C2×C89#57611yescharacteristic
190D89—81no—
191#3319—891nomaximal, Sylow
192C89#331911yescharacteristic, complemented, Sylow
193#555—891no—
194#546D8911yescharacteristic, complemented
195#489—891no—
196#485—891no—
197#482—891no—
198#474—891no—
199#468—891no—
200#466—891no—
201#463—891no—
202#449—891no—
203#447—891no—
204#442—891no—
205#435—891no—
206#418—891no—
207#416—891no—
208C2×#41C2×D8911yescharacteristic
209C22×D4C2×D8911yescharacteristic
210C2×SD16—891no—
211C2×D8—891no—
212C2×D8—891no—
213C2×M16—891no—
214C22×C8—891no—
215C4⋊Q8—891no—
216#124—1781no—
217#124—1781no—
218#124C2×D8911yescharacteristic
219#123—21no—
220C22⋊Q8C2×D8911yescharacteristic
221#121—21no—
222#121—891no—
223#121—891no—
224#121—1781no—
225#121C2×D8911yescharacteristic
226#120—21no—
227C4×D4—891no—
228C4×D4C2×D8911yescharacteristic
229C4×D4C2×D8911yescharacteristic
230#117—891no—
231#117—891no—
232#117—1781no—
233C2×C22⋊C4—21no—
234#107—891no—
235#107—891no—
236#106—891no—
237C4⋊C8—891no—
238#103—891no—
239#103—891no—
240#103—891no—
241#102—891no—
242#102—891no—
243#102—891no—
244#102—891no—
245#102—891no—
246#102—891no—
247#102—891no—
248C22⋊C8—891no—
249C22⋊C8—891no—
250#97—891no—
251C24—21no—
252#41—22no—
253#41—41no—
254C2×Q8—1781no—
255C2×Q8C22×D8911yescharacteristic
256C2×D4—22no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—41no—
261C2×D4—891no—
262C2×D4—1781no—
263C2×D4—1781no—
264C2×D4C22⋊D8911yescharacteristic
265C2×D4C22×D8911yescharacteristic
266C2×D4C22×D8911yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—1781no—
270C22×C4C22×D8911yescharacteristic
271C22×C4C22×D8911yescharacteristic
272SD16—3561no—
273D8—3561no—
274D8—1782no—
275M16—3561no—
276C2×C8—891no—
277C2×C8—891no—
278C2×C8—891no—
279C2×C8—891no—
280C2×C8—3561no—
281C4⋊C4—21no—
282C4⋊C4—891no—
283C4⋊C4—891no—
284C4⋊C4—891no—
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⋊C4—1781no—
296C22⋊C4—1781no—
297C22⋊C4—1781no—
298C22⋊C4C22⋊D8911yescharacteristic
299C22⋊C4C22⋊D8911yescharacteristic
300C42—1781no—
301C42—1781no—
302C42C22×D8911yescharacteristic
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—1781no—
309C23C2×C22⋊D8911yescharacteristic
310C23C2×C22⋊D8911yescharacteristic
311Q8—21no—
312Q8—21no—
313Q8—7121no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—41no—
318D4—42no—
319D4—42no—
320D4—81no—
321D4—1781no—
322D4—1781no—
323D4—7121no—
324D4—7121no—
325D4#1308357312yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—81no—
334C2×C4—3562no—
335C2×C4—1781no—
336C2×C4—1781no—
337C2×C4—1781no—
338C2×C4C2×C22⋊D8911yescharacteristic
339C2×C4C2×C22⋊D8911yescharacteristic
340C2×C4C2×C22⋊D8911yescharacteristic
341C2×C4C2×C22⋊D8911yescharacteristic
342C2×C4C23×D8911yescharacteristic
343C8—1781no—
344C8—1781no—
345C8—1781no—
346C8—1781no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—22no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—84no—
360C22—3561no—
361C22—3561no—
362C22—3561no—
363C22C22×C22⋊D8911yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—3561no—
371C4—3561no—
372C4—3561no—
373C4C2×#1308357311yescharacteristic
374C4#1566805711yescharacteristic
375C2—41no—
376C2—41no—
377C2—42no—
378C2—81no—
379C2—7121no—
380C2#1915224211yescharacteristic
381C2#1915239611yescharacteristic
382C2#1915240111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#546×C89C2
socleC22×C89C22×D4
hypercenter#546D89
hypocenterC89#3319
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. #19152313C2semidirect
2. #19151957C2semidirect
3. #19151936C2semidirect
4. #19151919C2semidirect
5. #19151878C2semidirect
6. #19151846C2semidirect
7. #19151832C2semidirect
8. #19151810C2semidirect
9. #19151743C2semidirect
10. #19151732C2semidirect
11. #19151708C2semidirect
12. #19151670C2semidirect
13. #19151603C2semidirect
14. #19151594C2semidirect
15. #546×C89C2semidirect
16. C2×#13083561C22semidirect
20. C22×#10623494C22semidirect
21. #15668012C22semidirect
25. #15667986C22semidirect
27. C4×D356C22semidirect
29. #15667971C22semidirect
31. #15667945C22semidirect
32. #15667945C22semidirect
33. #15667943C22semidirect
34. C4⋊#10623494C22semidirect
35. #15667936C22semidirect
36. #15667936C22semidirect
37. #15667936C22semidirect
44. #15667932C22semidirect
46. C22⋊#10623494C22semidirect
47. #15667923C22semidirect
192. C89#3319semidirect
194. #546D89semidirect

Maximal subgroups

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

subgroupindex
#191523132
#191519572
#191519362
#191519192
#191518782
#191518462
#191518322
#191518102
#191517432
#191517322
#191517082
#191516702
#191516032
#191515942
#546×C892
#331989