Finite Group Databasebeta

← #26032338

Subgroups — #26032338

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#19152308C211yesmaximal, characteristic, complemented
2#19152243C211yesmaximal, characteristic
3#19151958C211yesmaximal, characteristic, complemented
4#19151935C211yesmaximal, characteristic, complemented
5#19151913C211yesmaximal, characteristic, complemented
6#19151878C211yesmaximal, characteristic, complemented
7#19151847C211yesmaximal, characteristic, complemented
8#19151838C211yesmaximal, characteristic, complemented
9#19151820C211yesmaximal, characteristic, complemented
10#19151757C211yesmaximal, characteristic, complemented
11#19151747C211yesmaximal, characteristic, complemented
12#19151671C211yesmaximal, characteristic, complemented
13#19151596C211yesmaximal, characteristic, complemented
14#102×D89C211yesmaximal, characteristic, complemented
15#440×C89C211yesmaximal, characteristic, complemented
16C2×#13083573C2211yescharacteristic
17C2×D4×D89C2211yescharacteristic
18C2×#13083564C2211yescharacteristic, complemented
19C2×#13083561C2211yescharacteristic
20C2×#13083557C2211yescharacteristic, complemented
21C2×C8×D89C2211yescharacteristic
22#15668012C2211yescharacteristic, complemented
23#15668004—21no—
24#15668000C2211yescharacteristic
25#15667996—21no—
26#15667992C2211yescharacteristic
27#15667990—21no—
28#15667990—21no—
29#15667988C2211yescharacteristic
30#15667988C2211yescharacteristic, complemented
31#15667987C2211yescharacteristic
32#15667986—21no—
33#15667982—21no—
34C4×D356—21no—
35C4×D356C2211yescharacteristic
36C4⋊C4×D89C2211yescharacteristic
37C4⋊C4×D89C2211yescharacteristic, complemented
38C2×#13083551—21no—
39#15667945C2211yescharacteristic, complemented
40#15667945C2211yescharacteristic, complemented
41C4⋊#10623494C2211yescharacteristic, complemented
42#15667937C2211yescharacteristic, complemented
43#15667937C2211yescharacteristic, complemented
44#15667935C2211yescharacteristic, complemented
45#15667934C2211yescharacteristic
46#15667934C2211yescharacteristic
47#15667933C2211yescharacteristic
48#15667933C2211yescharacteristic
49#15667932C2211yescharacteristic
50#15667924C2211yescharacteristic
51#15667924C2211yescharacteristic, complemented
52C2×SD16×C89C2211yescharacteristic
53C4×Q8×C89C2211yescharacteristic, complemented
54C4×D4×C89C2211yescharacteristic
55#107×C89C2211yescharacteristic, complemented
56#103×C89C2211yescharacteristic, complemented
57#102×C89C2211yescharacteristic
58#97×C89C2211yescharacteristic, complemented
59C23×D89—21no—
60#13083573—22no—
61#13083573—41no—
62C2×Dic178—21no—
63C2×Dic178C2311yescharacteristic
64C2×D356—21no—
65C2×D356D411yescharacteristic
66C2×D356C2311yescharacteristic
67C2×C22⋊D89—21no—
68C2×C22⋊D89—21no—
69D4×D89—22no—
70D4×D89—41no—
71C22×Dic89—21no—
72C2×C4×D89—21no—
73C2×C4×D89—21no—
74C2×C4×D89C2311yescharacteristic
75C2×C4×D89C2311yescharacteristic
76#13083564—41no—
77#13083561—41no—
78#13083557—41no—
79C2×#10623494C2311yescharacteristic
80C2×#10623494C2311yescharacteristic
81C8×D89—41no—
82C4⋊Dic89—21no—
83C4⋊Dic89—21no—
84C4⋊Dic89D411yescharacteristic
85C4⋊Dic89C2311yescharacteristic
86C4⋊Dic89C2311yescharacteristic
87#13083553—21no—
88#13083553—21no—
89#13083553—21no—
90#13083553—21no—
91#13083551—21no—
92#13083551—21no—
93#13083551—21no—
94#13083551—21no—
95#13083551—21no—
96#13083551—21no—
97#13083551D411yescharacteristic
98#13083551D411yescharacteristic
99C2×Q8×C89C2311yescharacteristic
100C2×D4×C89C2311yescharacteristic
101C22×C4×C89—21no—
102SD16×C89—22no—
103C2×C8×C89C2311yescharacteristic
104C2×C8×C89C2311yescharacteristic
105C4⋊C4×C89—21no—
106C4⋊C4×C89C2311yescharacteristic
107C4⋊C4×C89C2311yescharacteristic
108C22⋊C4×C89—21no—
109C42×C89—21no—
110C42×C89C2311yescharacteristic
111C23×C89—21no—
112C22×D89—21no—
113C22×D89—42no—
114C22×D89—42no—
115C22×D89—81no—
116C22×D89C2×D411yescharacteristic
117C22×D89C2×D411yescharacteristic
118Q8×C89—21no—
119Q8×C89—21no—
120D4×C89—21no—
121D4×C89#4112yes—
122C2×C4×C89—21no—
123C2×C4×C89—21no—
124C2×C4×C89—21no—
125C2×C4×C89—81no—
126C2×C4×C89C2×D411yescharacteristic
127C2×C4×C89C2×D411yescharacteristic
128C2×C4×C89C2411yescharacteristic
129C22⋊D89—42no—
130C22⋊D89—42no—
131C2×Dic89—21no—
132C2×Dic89—21no—
133C2×Dic89—21no—
134C2×Dic89—42no—
135C2×Dic89C2×D411yescharacteristic
136C2×Dic89C2×D411yescharacteristic
137D356—22no—
138D356—21no—
139D356—21no—
140D356—81no—
141C4×D89—21no—
142C4×D89—21no—
143C4×D89—21no—
144C4×D89—21no—
145C4×D89—81no—
146C4×D89—81no—
147Dic178—21no—
148Dic178—21no—
149Dic178—81no—
150C8×C89—21no—
151C8×C89—21no—
152#10623494—21no—
153#10623494—21no—
154C22×C89—22no—
155C22×C89—41no—
156C22×C89—41no—
157C22×C89C22×D411yescharacteristic
158C2×D89—21no—
159C2×D89—21no—
160C2×D89—21no—
161C2×D89—21no—
162C2×D89—21no—
163C2×D89—41no—
164C2×D89—41no—
165C2×D89—41no—
166C2×D89—84no—
167C2×D89#13712yes—
168C4×C89—21no—
169C4×C89—21no—
170C4×C89—41no—
171C4×C89—41no—
172C4×C89—41no—
173C4×C89C2×#4111yescharacteristic
174C4×C89H(5,𝔽2)11yescharacteristic
175Dic89—21no—
176Dic89—21no—
177Dic89—41no—
178Dic89—41no—
179Dic89—41no—
180C2×C89—42no—
181C2×C89#54611yescharacteristic
182C2×C89C2×#13711yescharacteristic
183C2×C89#57611yescharacteristic
184D89—22no—
185D89—41no—
186D89—81no—
187#3314—891nomaximal, Sylow
188C89#331411yescharacteristic, complemented, Sylow
189#554—891no—
190#546—891no—
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#440D8911yescharacteristic, complemented
201#435—891no—
202#417—891no—
203C2×#102—891no—
204C2×#41—891no—
205C22×D4—891no—
206C2×Q16—891no—
207C2×SD16—891no—
208C2×SD16C2×D8911yescharacteristic
209C2×M16—891no—
210C22×C8—891no—
211C4⋊Q8—891no—
212#125—1781no—
213#124—891no—
214#123—1781no—
215C22⋊Q8—891no—
216C22⋊Q8—891no—
217C22⋊Q8—891no—
218C22⋊Q8—1781no—
219C22⋊Q8—1781no—
220#121—891no—
221#121—1781no—
222#120—1781no—
223C4×Q8C2×D8911yescharacteristic, complemented
224C4×D4—891no—
225C4×D4—1781no—
226C4×D4C2×D8911yescharacteristic
227C2×C4⋊C4—891no—
228C2×C4⋊C4—891no—
229C2×C22⋊C4—1781no—
230#107—891no—
231#107—891no—
232#107C2×D8911yescharacteristic, complemented
233C4⋊C8—891no—
234#103—891no—
235#103—891no—
236#103—891no—
237#103C2×D8911yescharacteristic, complemented
238#102—891no—
239#102—891no—
240#102—891no—
241#102—891no—
242#102—891no—
243#102C2×D8911yescharacteristic
244C22⋊C8—891no—
245C22⋊C8—891no—
246#97C2×D8911yescharacteristic, complemented
247C24—1781no—
248#41—3561no—
249#41—1782no—
250C2×Q8—891no—
251C2×Q8—1781no—
252C2×Q8C22×D8911yescharacteristic
253C2×D4—891no—
254C2×D4—891no—
255C2×D4—3561no—
256C2×D4—1781no—
257C2×D4—1781no—
258C2×D4—1781no—
259C2×D4—1782no—
260C2×D4C22×D8911yescharacteristic
261C22×C4—21no—
262C22×C4—891no—
263C22×C4—891no—
264C22×C4—1781no—
265C22×C4—1781no—
266C22×C4—1781no—
267Q16—3561no—
268SD16—22no—
269SD16—3561no—
270M16—3561no—
271C2×C8—891no—
272C2×C8—891no—
273C2×C8—3561no—
274C2×C8C22×D8911yescharacteristic
275C2×C8C22×D8911yescharacteristic
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—891no—
290C22⋊C4—891no—
291C22⋊C4—1781no—
292C22⋊C4—1781no—
293C22⋊C4—1781no—
294C22⋊C4—1781no—
295C22⋊C4—1781no—
296C22⋊C4—1781no—
297C42—21no—
298C42C22×D8911yescharacteristic
299C23—21no—
300C23—891no—
301C23—891no—
302C23—3562no—
303C23—3562no—
304C23—1781no—
305C23—7121no—
306Q8—21no—
307Q8—21no—
308Q8—1781no—
309Q8—1781no—
310Q8—7121no—
311D4—21no—
312D4—3562no—
313D4—3562no—
314D4—1782no—
315D4—1781no—
316D4—1781no—
317D4—7121no—
318D4#1308357412yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—891no—
324C2×C4—891no—
325C2×C4—3562no—
326C2×C4—1781no—
327C2×C4—1781no—
328C2×C4—1781no—
329C2×C4—1781no—
330C2×C4—1781no—
331C2×C4—1781no—
332C2×C4—1781no—
333C2×C4—7121no—
334C2×C4—7121no—
335C2×C4D4×D8911yescharacteristic
336C2×C4D4×D8911yescharacteristic
337C2×C4C23×D8911yescharacteristic
338C8—21no—
339C8—21no—
340C8—1781no—
341C8—1781no—
342C22—22no—
343C22—41no—
344C22—41no—
345C22—892no—
346C22—3561no—
347C22—3561no—
348C22—3561no—
349C22—1781no—
350C22—1781no—
351C22—1781no—
352C22—1781no—
353C22—1781no—
354C22—7124no—
355C22C2×D4×D8911yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—3561no—
362C4—3561no—
363C4—3561no—
364C4—1781no—
365C4—1781no—
366C4C2×#1308357411yescharacteristic
367C4#1566805811yescharacteristic
368C2—42no—
369C2—3561no—
370C2—1782no—
371C2—7121no—
372C2#1915224411yescharacteristic
373C2#137×D8911yescharacteristic
374C2#1915240211yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#440×C89C2
socleC22×C89C22×D4
prime radical#19152243C2
hypercenter#440D89
hypocenterC89#3314
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #19152308C2semidirect
3. #19151958C2semidirect
4. #19151935C2semidirect
5. #19151913C2semidirect
6. #19151878C2semidirect
7. #19151847C2semidirect
8. #19151838C2semidirect
9. #19151820C2semidirect
10. #19151757C2semidirect
11. #19151747C2semidirect
12. #19151671C2semidirect
13. #19151596C2semidirect
14. #102×D89C2semidirect
15. #440×C89C2semidirect
18. C2×#13083564C22semidirect
20. C2×#13083557C22semidirect
22. #15668012C22semidirect
30. #15667988C22semidirect
37. C4⋊C4×D89C22semidirect
39. #15667945C22semidirect
40. #15667945C22semidirect
41. C4⋊#10623494C22semidirect
42. #15667937C22semidirect
43. #15667937C22semidirect
44. #15667935C22semidirect
51. #15667924C22semidirect
53. C4×Q8×C89C22semidirect
55. #107×C89C22semidirect
56. #103×C89C22semidirect
58. #97×C89C22semidirect
188. C89#3314semidirect
200. #440D89semidirect
223. C4×Q8C2×D89semidirect
232. #107C2×D89semidirect
237. #103C2×D89semidirect
246. #97C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191523082
#191522432
#191519582
#191519352
#191519132
#191518782
#191518472
#191518382
#191518202
#191517572
#191517472
#191516712
#191515962
#102×D892
#440×C892
#331489