Finite Group Databasebeta

← #26031077

Subgroups — #26031077

Order 11392.

414 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
1#19152108C211yesmaximal, characteristic
2C22⋊Q8×D89C211yesmaximal, characteristic, complemented
3#19151941C211yesmaximal, characteristic, complemented
4#19151937C211yesmaximal, characteristic, complemented
5#19151935C211yesmaximal, characteristic, complemented
6#19151915C211yesmaximal, characteristic, complemented
7#19151856C211yesmaximal, characteristic, complemented
8#19151854C211yesmaximal, characteristic, complemented
9#19151842C211yesmaximal, characteristic, complemented
10#19151761C211yesmaximal, characteristic, complemented
11#19151757C211yesmaximal, characteristic, complemented
12#19151755C211yesmaximal, characteristic, complemented
13#19151735C211yesmaximal, characteristic, complemented
14#19151561C211yesmaximal, characteristic, complemented
15#468×C89C211yesmaximal, characteristic, complemented
16C2×#13083573C2211yescharacteristic
17C2×Q8×D89C2211yescharacteristic
18C22×C4×D89C2211yescharacteristic
19C2×Dic356C2211yescharacteristic, complemented
20C2×#13083564C2211yescharacteristic, complemented
21C2×#13083562C2211yescharacteristic, complemented
22C2×#13083558C2211yescharacteristic
23#15667994—21no—
24#15667992C2211yescharacteristic
25#15667992C2211yescharacteristic
26#15667991C2211yescharacteristic
27#15667991C2211yescharacteristic
28#15667990—21no—
29#15667989—21no—
30#15667988C2211yescharacteristic
31#15667983C2211yescharacteristic
32#15667980—21no—
33D4×Dic89—21no—
34#15667972—21no—
35#15667970C2211yescharacteristic
36C4⋊C4×D89—21no—
37C4⋊C4×D89C2211yescharacteristic
38C22⋊C4×D89—21no—
39#15667945C2211yescharacteristic, complemented
40#15667944C2211yescharacteristic, complemented
41#15667943C2211yescharacteristic, complemented
42#15667937C2211yescharacteristic, complemented
43#15667937C2211yescharacteristic, complemented
44#15667936C2211yescharacteristic, complemented
45#15667935C2211yescharacteristic, complemented
46#15667935C2211yescharacteristic, complemented
47#15667933C2211yescharacteristic, complemented
48#15667924C2211yescharacteristic
49#15667924C2211yescharacteristic
50#15667924C2211yescharacteristic
51#15667924C2211yescharacteristic
52C2×SD16×C89C2211yescharacteristic, complemented
53C2×M16×C89C2211yescharacteristic
54C22⋊Q8×C89C2211yescharacteristic
55#121×C89C2211yescharacteristic
56#107×C89C2211yescharacteristic, complemented
57#103×C89C2211yescharacteristic, complemented
58#102×C89C2211yescharacteristic, complemented
59C23×D89D411yescharacteristic
60#13083573—41no—
61#13083573—41no—
62C2×Dic178—21no—
63C2×Dic178C2311yescharacteristic
64C2×Dic178C2311yescharacteristic
65Q8×D89—41no—
66Q8×D89—41no—
67C2×C22⋊D89—21no—
68C2×C22⋊D89—21no—
69C22×Dic89—21no—
70C22×Dic89D411yescharacteristic
71C2×C4×D89—21no—
72C2×C4×D89—21no—
73C2×C4×D89—41no—
74C2×C4×D89—41no—
75C2×C4×D89D411yescharacteristic
76C2×C4×D89D411yescharacteristic
77C2×C4×D89C2311yescharacteristic
78C2×C4×D89C2311yescharacteristic
79Dic356—41no—
80#13083564—41no—
81#13083562—41no—
82#13083558—41no—
83C2×#10623494C2311yescharacteristic
84C2×#10623494C2311yescharacteristic
85C4⋊Dic89—21no—
86C4⋊Dic89—21no—
87C4⋊Dic89C2311yescharacteristic
88C4⋊Dic89C2311yescharacteristic
89#13083553—21no—
90#13083553—21no—
91#13083553—21no—
92#13083553—21no—
93C22⋊Dic89—21no—
94C22⋊Dic89—21no—
95C22⋊Dic89—21no—
96#13083551—21no—
97#13083551—21no—
98#13083551—21no—
99#13083551—21no—
100C4×Dic89—21no—
101C2×Q8×C89C2311yescharacteristic
102C2×D4×C89—21no—
103C2×D4×C89C2311yescharacteristic
104C22×C4×C89C2311yescharacteristic
105SD16×C89—41no—
106M16×C89—41no—
107C2×C8×C89C2311yescharacteristic
108C2×C8×C89C2311yescharacteristic
109C4⋊C4×C89—21no—
110C4⋊C4×C89C2311yescharacteristic
111C4⋊C4×C89C2311yescharacteristic
112C22⋊C4×C89—21no—
113C22⋊C4×C89—21no—
114C23×C89—21no—
115C23×C89C2×D411yescharacteristic
116C22×D89—22no—
117C22×D89—41no—
118C22×D89—41no—
119C22×D89C2×D411yescharacteristic
120C22×D89C2×D411yescharacteristic
121Q8×C89—21no—
122Q8×C89—21no—
123D4×C89—21no—
124D4×C89—21no—
125D4×C89—42no—
126C2×C4×C89—21no—
127C2×C4×C89—21no—
128C2×C4×C89—21no—
129C2×C4×C89—21no—
130C2×C4×C89—21no—
131C2×C4×C89C2×D411yescharacteristic
132C2×C4×C89C2411yescharacteristic
133C22⋊D89—42no—
134C22⋊D89—42no—
135C2×Dic89—21no—
136C2×Dic89—21no—
137C2×Dic89—21no—
138C2×Dic89—21no—
139C2×Dic89—41no—
140C2×Dic89—42no—
141C2×Dic89C2×D411yescharacteristic
142C2×Dic89C2×D411yescharacteristic
143C4×D89—21no—
144C4×D89—21no—
145C4×D89—21no—
146C4×D89—21no—
147C4×D89—41no—
148C4×D89—41no—
149C4×D89—42no—
150C4×D89—42no—
151Dic178—21no—
152Dic178—21no—
153Dic178—21no—
154Dic178—21no—
155Dic178—42no—
156C8×C89—21no—
157C8×C89—21no—
158#10623494—21no—
159#10623494—21no—
160C22×C89—21no—
161C22×C89—21no—
162C22×C89—21no—
163C22×C89—41no—
164C22×C89—41no—
165C22×C89—41no—
166C22×C89C22×D411yescharacteristic
167C2×D89—21no—
168C2×D89—21no—
169C2×D89—21no—
170C2×D89—21no—
171C2×D89—21no—
172C2×D89—44no—
173C2×D89#13712yes—
174C4×C89—21no—
175C4×C89—41no—
176C4×C89—41no—
177C4×C89—41no—
178C4×C89H(5,𝔽2)11yescharacteristic
179C4×C89H(5,𝔽2)11yescharacteristic
180Dic89—21no—
181Dic89—21no—
182Dic89—41no—
183Dic89—41no—
184Dic89—41no—
185Dic89—41no—
186C2×C89—41no—
187C2×C89—81no—
188C2×C89#53411yescharacteristic
189C2×C89C2×#13711yescharacteristic
190C2×C89#57511yescharacteristic
191D89—22no—
192D89—41no—
193#3196—891nomaximal, Sylow
194C89#319611yescharacteristic, complemented, Sylow
195#525—891no—
196C2×C22⋊Q8—891no—
197#485—891no—
198#485—891no—
199#484—891no—
200#481—891no—
201#470—891no—
202#470—891no—
203#468—891no—
204#468D8911yescharacteristic, complemented
205#452—891no—
206#452—891no—
207#451—891no—
208#448—891no—
209#407—891no—
210C2×#41—891no—
211C22×Q8—891no—
212C23×C4—891no—
213C2×Q16—891no—
214C2×Q16—891no—
215C2×SD16—891no—
216C2×SD16C2×D8911yescharacteristic, complemented
217C2×M16—891no—
218C2×M16C2×D8911yescharacteristic
219#123—1781no—
220C22⋊Q8—891no—
221C22⋊Q8—891no—
222C22⋊Q8—891no—
223C22⋊Q8—891no—
224C22⋊Q8—891no—
225C22⋊Q8—1781no—
226C22⋊Q8—1781no—
227C22⋊Q8C2×D8911yescharacteristic
228#121—891no—
229#121C2×D8911yescharacteristic
230#120—1781no—
231C4×D4—1781no—
232C4×D4—1781no—
233#117—891no—
234C2×C4⋊C4—891no—
235C2×C4⋊C4—1781no—
236C2×C22⋊C4—1781no—
237#107—891no—
238#107C2×D8911yescharacteristic, complemented
239#106—891no—
240#106—891no—
241#103—891no—
242#103—891no—
243#103—891no—
244#103—891no—
245#103—891no—
246#103C2×D8911yescharacteristic, complemented
247#102—891no—
248#102C2×D8911yescharacteristic, complemented
249C22⋊C8—891no—
250C22⋊C8—891no—
251C22⋊C8—891no—
252C22⋊C8—891no—
253C24—891no—
254#41—3561no—
255#41—3561no—
256C2×Q8—891no—
257C2×Q8—891no—
258C2×Q8—3561no—
259C2×Q8—3561no—
260C2×Q8—1781no—
261C2×Q8C22×D8911yescharacteristic
262C2×D4—21no—
263C2×D4—1781no—
264C2×D4—1781no—
265C2×D4C22×D8911yescharacteristic
266C22×C4—891no—
267C22×C4—891no—
268C22×C4—891no—
269C22×C4—891no—
270C22×C4—891no—
271C22×C4—3561no—
272C22×C4—3561no—
273C22×C4—1781no—
274C22×C4—1781no—
275C22×C4—1781no—
276C22×C4C22×D8911yescharacteristic
277Q16—3561no—
278Q16—3561no—
279SD16—41no—
280SD16—3561no—
281M16—41no—
282M16—3561no—
283C2×C8—891no—
284C2×C8—891no—
285C2×C8C22×D8911yescharacteristic
286C2×C8C22×D8911yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—891no—
289C4⋊C4—891no—
290C4⋊C4—1781no—
291C4⋊C4—1781no—
292C4⋊C4—1781no—
293C4⋊C4—1781no—
294C4⋊C4—1781no—
295C4⋊C4—1781no—
296C4⋊C4C22×D8911yescharacteristic
297C4⋊C4C22×D8911yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—1781no—
301C22⋊C4—1781no—
302C22⋊C4—1781no—
303C22⋊C4—1781no—
304C22⋊C4—1781no—
305C22⋊C4—1781no—
306C22⋊C4—1781no—
307C42—1781no—
308C23—21no—
309C23—891no—
310C23—891no—
311C23—3561no—
312C23—3561no—
313C23—1782no—
314C23D4×D8911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—3562no—
318Q8—1781no—
319Q8—1781no—
320Q8—1781no—
321Q8—1781no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—3562no—
326D4—3562no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—891no—
333C2×C4—891no—
334C2×C4—3561no—
335C2×C4—3561no—
336C2×C4—3562no—
337C2×C4—3562no—
338C2×C4—3562no—
339C2×C4—3561no—
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×C4D4×D8911yescharacteristic
349C2×C4C23×D8911yescharacteristic
350C8—21no—
351C8—21no—
352C8—1781no—
353C8—1781no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—892no—
361C22—3564no—
362C22—1781no—
363C22—1781no—
364C22—1781no—
365C22—1781no—
366C22—1781no—
367C22C2×D4×D8911yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—3561no—
373C4—3561no—
374C4—3561no—
375C4—3561no—
376C4—1781no—
377C4—1781no—
378C4#1566805711yescharacteristic
379C4#1566805811yescharacteristic
380C2—41no—
381C2—81no—
382C2—3561no—
383C2—1782no—
384C2#1915215611yescharacteristic
385C2#137×D8911yescharacteristic
386C2#1915239411yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#468×C89C2
socleC22×C89C22×D4
prime radical#19152108C2
hypercenter#468D89
hypocenterC89#3196
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
2. C22⋊Q8×D89C2semidirect
3. #19151941C2semidirect
4. #19151937C2semidirect
5. #19151935C2semidirect
6. #19151915C2semidirect
7. #19151856C2semidirect
8. #19151854C2semidirect
9. #19151842C2semidirect
10. #19151761C2semidirect
11. #19151757C2semidirect
12. #19151755C2semidirect
13. #19151735C2semidirect
14. #19151561C2semidirect
15. #468×C89C2semidirect
19. C2×Dic356C22semidirect
20. C2×#13083564C22semidirect
21. C2×#13083562C22semidirect
39. #15667945C22semidirect
40. #15667944C22semidirect
41. #15667943C22semidirect
42. #15667937C22semidirect
43. #15667937C22semidirect
44. #15667936C22semidirect
45. #15667935C22semidirect
46. #15667935C22semidirect
47. #15667933C22semidirect
52. C2×SD16×C89C22semidirect
56. #107×C89C22semidirect
57. #103×C89C22semidirect
58. #102×C89C22semidirect
194. C89#3196semidirect
204. #468D89semidirect
216. C2×SD16C2×D89semidirect
238. #107C2×D89semidirect
246. #103C2×D89semidirect
248. #102C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191521082
C22⋊Q8×D892
#191519412
#191519372
#191519352
#191519152
#191518562
#191518542
#191518422
#191517612
#191517572
#191517552
#191517352
#191515612
#468×C892
#319689