Finite Group Databasebeta

← #26032476

Subgroups — #26032476

Order 11392.

448 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152319C211yesmaximal, characteristic, complemented
2D4×C22⋊D89C211yesmaximal, characteristic
3#19151943C211yesmaximal, characteristic, complemented
4#19151923C211yesmaximal, characteristic, complemented
5#19151921C211yesmaximal, characteristic, complemented
6#19151876C211yesmaximal, characteristic, complemented
7#19151846C211yesmaximal, characteristic, complemented
8#19151841C211yesmaximal, characteristic, complemented
9#19151796C211yesmaximal, characteristic, complemented
10#19151747C211yesmaximal, characteristic, complemented
11SD16×Dic89C211yesmaximal, characteristic, complemented
12#19151673C211yesmaximal, characteristic, complemented
13#19151603C211yesmaximal, characteristic, complemented
14#19151601C211yesmaximal, characteristic, complemented
15#450×C89C211yesmaximal, characteristic, complemented
16C22×C22⋊D89—21no—
17C2×D4×D89C2211yescharacteristic
18C2×#13083561C2211yescharacteristic, complemented
19C2×#13083558C2211yescharacteristic, complemented
20C2×#13083557C2211yescharacteristic, complemented
21#15668011C2211yescharacteristic, complemented
22#15668008C2211yescharacteristic
23#15668007—21no—
24#15668005—21no—
25#15667998—21no—
26#15667988C2211yescharacteristic, complemented
27#15667986C2211yescharacteristic
28#15667984—21no—
29#15667983C2211yescharacteristic
30#15667981—21no—
31#15667980—21no—
32Q8×Dic89C2211yescharacteristic, complemented
33#15667977—21no—
34D4×Dic89C2211yescharacteristic
35C4×C22⋊D89C2211yescharacteristic
36#15667971C2211yescharacteristic, complemented
37#15667970C2211yescharacteristic, complemented
38#15667946C2211yescharacteristic, complemented
39#15667945C2211yescharacteristic, complemented
40#15667944C2211yescharacteristic, complemented
41#15667941C2211yescharacteristic, complemented
42#15667936C2211yescharacteristic, complemented
43#15667934C2211yescharacteristic, complemented
44#15667934C2211yescharacteristic, complemented
45#15667933C2211yescharacteristic
46#15667933C2211yescharacteristic
47#15667933C2211yescharacteristic, complemented
48#15667933C2211yescharacteristic, complemented
49#15667932C2211yescharacteristic, complemented
50#15667924C2211yescharacteristic, complemented
51C8×Dic89C2211yescharacteristic, complemented
52C22×D4×C89C2211yescharacteristic
53C2×SD16×C89C2211yescharacteristic
54C2×SD16×C89C2211yescharacteristic, complemented
55C22⋊Q8×C89C2211yescharacteristic, complemented
56#102×C89C2211yescharacteristic
57#102×C89C2211yescharacteristic, complemented
58C22⋊C8×C89C2211yescharacteristic, complemented
59C23×D89—21no—
60C2×Dic178—21no—
61C2×D356C2311yescharacteristic
62C2×C22⋊D89—21no—
63C2×C22⋊D89—21no—
64C2×C22⋊D89—21no—
65C2×C22⋊D89—21no—
66C2×C22⋊D89—21no—
67C2×C22⋊D89—44no—
68C2×C22⋊D89D411yescharacteristic
69D4×D89—22no—
70D4×D89—41no—
71C22×Dic89—21no—
72C2×C4×D89C2311yescharacteristic
73#13083561—41no—
74#13083558—41no—
75#13083557—41no—
76C2×#10623494C2311yescharacteristic
77C2×#10623494C2311yescharacteristic
78C4⋊Dic89—21no—
79C4⋊Dic89C2311yescharacteristic
80C4⋊Dic89C2311yescharacteristic
81C4⋊Dic89C2311yescharacteristic
82#13083553—21no—
83#13083553—21no—
84#13083553D411yescharacteristic
85C22⋊Dic89—21no—
86C22⋊Dic89—21no—
87C22⋊Dic89—21no—
88C22⋊Dic89D411yescharacteristic
89#13083551—21no—
90#13083551—21no—
91#13083551—21no—
92#13083551D411yescharacteristic
93C4×Dic89—21no—
94C4×Dic89—21no—
95C4×Dic89—21no—
96C4×Dic89C2311yescharacteristic
97C24×C89—21no—
98C2×Q8×C89C2311yescharacteristic
99C2×D4×C89—22no—
100C2×D4×C89—21no—
101C2×D4×C89—41no—
102C2×D4×C89C2311yescharacteristic
103C2×D4×C89C2311yescharacteristic
104C22×C4×C89C2311yescharacteristic
105SD16×C89—22no—
106SD16×C89—41no—
107C2×C8×C89C2311yescharacteristic
108C2×C8×C89C2311yescharacteristic
109C4⋊C4×C89—21no—
110C4⋊C4×C89C2311yescharacteristic
111C22⋊C4×C89—21no—
112C23×C89—21no—
113C23×C89—21no—
114C23×C89—42no—
115C23×C89—42no—
116C23×C89—81no—
117C23×C89C2×D411yescharacteristic
118C22×D89—21no—
119C22×D89—42no—
120C22×D89—42no—
121C22×D89—81no—
122C22×D89C2×D411yescharacteristic
123Q8×C89—21no—
124Q8×C89—21no—
125D4×C89—21no—
126D4×C89—21no—
127D4×C89—21no—
128D4×C89—42no—
129D4×C89#4112yes—
130C2×C4×C89—21no—
131C2×C4×C89—21no—
132C2×C4×C89—21no—
133C2×C4×C89—21no—
134C2×C4×C89C2×D411yescharacteristic
135C2×C4×C89C2411yescharacteristic
136C22⋊D89—22no—
137C22⋊D89—42no—
138C22⋊D89—42no—
139C22⋊D89—42no—
140C22⋊D89—42no—
141C22⋊D89—81no—
142C2×Dic89—21no—
143C2×Dic89—21no—
144C2×Dic89—21no—
145C2×Dic89—42no—
146C2×Dic89C2×D411yescharacteristic
147C2×Dic89C2×D411yescharacteristic
148C2×Dic89C2×D411yescharacteristic
149D356—21no—
150D356—21no—
151C4×D89—21no—
152C4×D89—21no—
153Dic178—42no—
154C8×C89—21no—
155C8×C89—21no—
156#10623494—21no—
157#10623494—21no—
158C22×C89—22no—
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—21no—
170C2×D89—21no—
171C2×D89—21no—
172C2×D89—41no—
173C2×D89—41no—
174C2×D89—41no—
175C2×D89—84no—
176C4×C89—21no—
177C4×C89—41no—
178C4×C89—41no—
179C4×C89C2×#4111yescharacteristic
180C4×C89H(5,𝔽2)11yescharacteristic
181Dic89—21no—
182Dic89—21no—
183Dic89—41no—
184Dic89—41no—
185Dic89—41no—
186Dic89AGL(1,ℤ/8)12yes—
187C2×C89—42no—
188C2×C89—41no—
189C2×C89—81no—
190C2×C89#54611yescharacteristic
191C2×C89C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C89#57711yescharacteristic
193D89—41no—
194D89—81no—
195#3324—891nomaximal, Sylow
196C89#332411yescharacteristic, complemented, Sylow
197#556—891no—
198D42—891no—
199#486—891no—
200#482—891no—
201#482—891no—
202#474—891no—
203#468—891no—
204#468—891no—
205#460—891no—
206#450—891no—
207#450D8911yescharacteristic, complemented
208C4×SD16—891no—
209#436—891no—
210#418—891no—
211#418—891no—
212C22×D4—891no—
213C22×D4—1781no—
214C22×D4C2×D8911yescharacteristic
215C2×SD16—891no—
216C2×SD16C2×D8911yescharacteristic
217C2×SD16C2×D8911yescharacteristic, complemented
218C2×M16—891no—
219C2×M16—891no—
220C4⋊Q8—891no—
221#127—891no—
222#126—1781no—
223#126—1781no—
224#124—1781no—
225C22⋊Q8—891no—
226C22⋊Q8C2×D8911yescharacteristic, complemented
227#121—891no—
228#121—891no—
229#121—1781no—
230#120—1781no—
231#120—1781no—
232C4×Q8—891no—
233C4×Q8—1781no—
234C4×D4—891no—
235C4×D4—891no—
236#117—891no—
237#117—891no—
238#107—891no—
239#107—891no—
240#106—891no—
241C4⋊C8—891no—
242#103—891no—
243#102—891no—
244#102—891no—
245#102—891no—
246#102—891no—
247#102—891no—
248#102—891no—
249#102—891no—
250#102C2×D8911yescharacteristic
251#102C2×D8911yescharacteristic, complemented
252C22⋊C8—891no—
253C22⋊C8C2×D8911yescharacteristic, complemented
254C4×C8—891no—
255C24—21no—
256C24—1781no—
257C2×Q8—1781no—
258C2×Q8C22×D8911yescharacteristic
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—891no—
263C2×D4—891no—
264C2×D4—3564no—
265C2×D4—3561no—
266C2×D4—1781no—
267C2×D4—1781no—
268C2×D4—1781no—
269C2×D4—1781no—
270C2×D4—1781no—
271C2×D4—1782no—
272C2×D4C22×D8911yescharacteristic
273C2×D4C22×D8911yescharacteristic
274C22×C4—891no—
275C22×C4—1781no—
276C22×C4C22×D8911yescharacteristic
277SD16—22no—
278SD16—41no—
279SD16—3561no—
280M16—3561no—
281M16—3561no—
282C2×C8—891no—
283C2×C8—891no—
284C2×C8C22×D8911yescharacteristic
285C2×C8C22×D8911yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—891no—
288C4⋊C4—891no—
289C4⋊C4—891no—
290C4⋊C4—891no—
291C4⋊C4—1781no—
292C4⋊C4—1781no—
293C4⋊C4—1781no—
294C4⋊C4C22×D8911yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—891no—
297C22⋊C4—891no—
298C22⋊C4—1781no—
299C22⋊C4—1781no—
300C22⋊C4—1781no—
301C22⋊C4—1781no—
302C22⋊C4—1781no—
303C22⋊C4—1781no—
304C42—891no—
305C42—1781no—
306C42—1781no—
307C42—1781no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—891no—
314C23—3562no—
315C23—3562no—
316C23—1781no—
317C23—7121no—
318C23D4×D8911yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—3562no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—42no—
326D4—3562no—
327D4—3562no—
328D4—3562no—
329D4—3562no—
330D4—1782no—
331D4—1781no—
332D4—1781no—
333D4—7121no—
334D4#1308357312yes—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—891no—
340C2×C4—891no—
341C2×C4—891no—
342C2×C4—3562no—
343C2×C4—1781no—
344C2×C4—1781no—
345C2×C4—1781no—
346C2×C4—1781no—
347C2×C4—1781no—
348C2×C4D4×D8911yescharacteristic
349C2×C4C23×D8911yescharacteristic
350C8—21no—
351C8—21no—
352C8—1781no—
353C8—1781no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—84no—
364C22—3561no—
365C22—3561no—
366C22—3561no—
367C22—1781no—
368C22—1781no—
369C22—1781no—
370C22—7124no—
371C22C2×D4×D8911yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—892no—
376C4—3561no—
377C4—3561no—
378C4—3561no—
379C4—1781no—
380C4—1781no—
381C4C2×#1308357311yescharacteristic
382C4#1566805711yescharacteristic
383C2—41no—
384C2—42no—
385C2—81no—
386C2—3561no—
387C2—7121no—
388C2#1915223511yescharacteristic
389C2AGL(1,ℤ/8)×D8911yescharacteristic
390C2#1915240411yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#450×C89C2
socleC22×C89C22×D4
prime radicalD4×C22⋊D89C2
hypercenter#450D89
hypocenterC89#3324
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #19152319C2semidirect
3. #19151943C2semidirect
4. #19151923C2semidirect
5. #19151921C2semidirect
6. #19151876C2semidirect
7. #19151846C2semidirect
8. #19151841C2semidirect
9. #19151796C2semidirect
10. #19151747C2semidirect
11. SD16×Dic89C2semidirect
12. #19151673C2semidirect
13. #19151603C2semidirect
14. #19151601C2semidirect
15. #450×C89C2semidirect
18. C2×#13083561C22semidirect
19. C2×#13083558C22semidirect
20. C2×#13083557C22semidirect
21. #15668011C22semidirect
26. #15667988C22semidirect
32. Q8×Dic89C22semidirect
36. #15667971C22semidirect
37. #15667970C22semidirect
38. #15667946C22semidirect
39. #15667945C22semidirect
40. #15667944C22semidirect
41. #15667941C22semidirect
42. #15667936C22semidirect
43. #15667934C22semidirect
44. #15667934C22semidirect
47. #15667933C22semidirect
48. #15667933C22semidirect
49. #15667932C22semidirect
50. #15667924C22semidirect
51. C8×Dic89C22semidirect
54. C2×SD16×C89C22semidirect
55. C22⋊Q8×C89C22semidirect
57. #102×C89C22semidirect
58. C22⋊C8×C89C22semidirect
196. C89#3324semidirect
207. #450D89semidirect
217. C2×SD16C2×D89semidirect
226. C22⋊Q8C2×D89semidirect
251. #102C2×D89semidirect
253. C22⋊C8C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191523192
D4×C22⋊D892
#191519432
#191519232
#191519212
#191518762
#191518462
#191518412
#191517962
#191517472
SD16×Dic892
#191516732
#191516032
#191516012
#450×C892
#332489