Finite Group Databasebeta

← #26030436

Subgroups — #26030436

Order 11392.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152219C211yesmaximal, characteristic, complemented
2#19151939C211yesmaximal, characteristic, complemented
3#19151922C211yesmaximal, characteristic, complemented
4#19151888C211yesmaximal, characteristic, complemented
5#19151878C211yesmaximal, characteristic, complemented
6#19151813C211yesmaximal, characteristic, complemented
7#19151813C211yesmaximal, characteristic, complemented
8#19151749C211yesmaximal, characteristic, complemented
9#19151732C211yesmaximal, characteristic
10#19151708C211yesmaximal, characteristic, complemented
11#19151698C211yesmaximal, characteristic, complemented
12C4×#13083562C211yesmaximal, characteristic, complemented
13C4×#13083559C211yesmaximal, characteristic, complemented
14#19151659C211yesmaximal, characteristic, complemented
15#518×C89C211yesmaximal, characteristic, complemented
16C2×#13083562C2211yescharacteristic
17C2×#13083562C2211yescharacteristic
18C2×#13083559C2211yescharacteristic
19C2×#13083559C2211yescharacteristic
20#15668012C2211yescharacteristic, complemented
21#15668007—21no—
22#15668000C2211yescharacteristic, complemented
23#15667998—21no—
24#15667994—21no—
25#15667991C2211yescharacteristic
26#15667990—21no—
27#15667986C2211yescharacteristic
28C4×Dic178C2211yescharacteristic, complemented
29C4×D356C2211yescharacteristic, complemented
30#15667945C2211yescharacteristic, complemented
31#15667945C2211yescharacteristic, complemented
32#15667943C2211yescharacteristic, complemented
33#15667943C2211yescharacteristic, complemented
34C4⋊#10623494C2211yescharacteristic, complemented
35C4⋊#10623494C2211yescharacteristic, complemented
36#15667935C2211yescharacteristic, complemented
37#15667935C2211yescharacteristic, complemented
38#15667933C2211yescharacteristic
39#15667933C2211yescharacteristic
40#15667933C2211yescharacteristic
41#15667933C2211yescharacteristic
42#15667932C2211yescharacteristic, complemented
43#15667932C2211yescharacteristic, complemented
44C22⋊#10623494C2211yescharacteristic
45C22⋊#10623494C2211yescharacteristic
46#15667923C2211yescharacteristic, complemented
47C4×#10623494C2211yescharacteristic, complemented
48C22×D4×C89C2211yescharacteristic
49C4×D4×C89—21no—
50C4×D4×C89—21no—
51C4×D4×C89C2211yescharacteristic
52C4×D4×C89C2211yescharacteristic
53C4×D4×C89C2211yescharacteristic
54C4×D4×C89C2211yescharacteristic
55#117×C89C2211yescharacteristic
56#117×C89C2211yescharacteristic
57C2×C22⋊C4×C89—21no—
58C2×C22⋊C4×C89—21no—
59C2×Dic178—21no—
60C2×Dic178C2311yescharacteristic
61C2×D356C2311yescharacteristic
62C2×C22⋊D89—21no—
63C2×C4×D89—21no—
64#13083562—22no—
65#13083562—22no—
66#13083559—22no—
67#13083559—22no—
68C2×#10623494C2311yescharacteristic
69C2×#10623494C2311yescharacteristic
70C2×#10623494C2311yescharacteristic
71C2×#10623494C2311yescharacteristic
72C4⋊Dic89—21no—
73C4⋊Dic89C2311yescharacteristic
74C4⋊Dic89C2311yescharacteristic
75#13083553—21no—
76#13083553—21no—
77C22⋊Dic89—21no—
78#13083551—21no—
79#13083551—21no—
80#13083551—21no—
81#13083551—21no—
82C4×Dic89—21no—
83C24×C89—21no—
84C2×D4×C89—22no—
85C2×D4×C89—22no—
86C2×D4×C89—21no—
87C2×D4×C89C2311yescharacteristic
88C2×D4×C89C2311yescharacteristic
89C22×C4×C89—21no—
90C22×C4×C89—21no—
91C22×C4×C89—21no—
92C22×C4×C89—21no—
93C22×C4×C89C2311yescharacteristic
94C4⋊C4×C89D411yescharacteristic
95C4⋊C4×C89D411yescharacteristic
96C4⋊C4×C89C2311yescharacteristic
97C4⋊C4×C89C2311yescharacteristic
98C22⋊C4×C89—21no—
99C22⋊C4×C89—21no—
100C22⋊C4×C89—21no—
101C22⋊C4×C89—21no—
102C22⋊C4×C89—21no—
103C22⋊C4×C89D411yescharacteristic
104C22⋊C4×C89D411yescharacteristic
105C42×C89—21no—
106C42×C89C2311yescharacteristic
107C42×C89C2311yescharacteristic
108C23×C89—24no—
109C23×C89—21no—
110C23×C89—21no—
111C23×C89—81no—
112C23×C89—81no—
113C23×C89C2×D411yescharacteristic
114C22×D89—21no—
115D4×C89—24no—
116D4×C89—21no—
117D4×C89—21no—
118D4×C89#4112yes—
119D4×C89#4112yes—
120C2×C4×C89—21no—
121C2×C4×C89—21no—
122C2×C4×C89—21no—
123C2×C4×C89—21no—
124C2×C4×C89—81no—
125C2×C4×C89—81no—
126C2×C4×C89—81no—
127C2×C4×C89—81no—
128C2×C4×C89C2×D411yescharacteristic
129C2×C4×C89C2×D411yescharacteristic
130C2×C4×C89C2×D411yescharacteristic
131C2×C4×C89C2×D411yescharacteristic
132C2×C4×C89C2×D411yescharacteristic
133C2×C4×C89C2411yescharacteristic
134C22⋊D89—81no—
135C2×Dic89—21no—
136C2×Dic89—21no—
137C2×Dic89—21no—
138D356—21no—
139D356—21no—
140C4×D89—81no—
141Dic178—21no—
142Dic178—21no—
143Dic178—81no—
144#10623494—21no—
145#10623494—21no—
146#10623494—21no—
147#10623494—21no—
148C22×C89—21no—
149C22×C89—22no—
150C22×C89—22no—
151C22×C89—21no—
152C22×C89—21no—
153C22×C89—41no—
154C22×C89—41no—
155C22×C89—41no—
156C22×C89—41no—
157C22×C89—84no—
158C22×C89C22×D411yescharacteristic
159C2×D89—41no—
160C2×D89—41no—
161C2×D89—41no—
162C4×C89—21no—
163C4×C89—21no—
164C4×C89—21no—
165C4×C89—21no—
166C4×C89—21no—
167C4×C89—41no—
168C4×C89—41no—
169C4×C89C2×#4111yescharacteristic
170C4×C89C2×#4111yescharacteristic
171Dic89—41no—
172Dic89—41no—
173Dic89—41no—
174C2×C89—41no—
175C2×C89—42no—
176C2×C89—42no—
177C2×C89#52511yescharacteristic
178C2×C89#57611yescharacteristic
179C2×C89#57711yescharacteristic
180D89—81no—
181#3118—891nomaximal, Sylow
182C89#311811yescharacteristic, complemented, Sylow
183#542—891no—
184#518D8911yescharacteristic, complemented
185#485—891no—
186#482—891no—
187#476—891no—
188#474—891no—
189#463—891no—
190#463—891no—
191#450—891no—
192#447—891no—
193#442—891no—
194#440—891no—
195C4×SD16—891no—
196C4×D8—891no—
197#433—891no—
198C22×D4C2×D8911yescharacteristic
199C2×SD16—891no—
200C2×SD16—891no—
201C2×D8—891no—
202C2×D8—891no—
203C4⋊Q8—891no—
204#126—1781no—
205#124—891no—
206#124—1781no—
207#123—1781no—
208C22⋊Q8—891no—
209C22⋊Q8—1781no—
210#121—891no—
211C4×Q8—891no—
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—891no—
215C4×D4C2×D8911yescharacteristic
216C4×D4C2×D8911yescharacteristic
217C4×D4C2×D8911yescharacteristic
218C4×D4C2×D8911yescharacteristic
219#117C2×D8911yescharacteristic
220#117C2×D8911yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223#107—891no—
224#107—891no—
225#106—891no—
226#106—891no—
227C4⋊C8—891no—
228C4⋊C8—891no—
229#103—891no—
230#103—891no—
231#102—891no—
232#102—891no—
233#102—891no—
234#102—891no—
235#102—891no—
236#102—891no—
237C22⋊C8—891no—
238C22⋊C8—891no—
239#97—891no—
240C4×C8—891no—
241C24—21no—
242C2×Q8—891no—
243C2×Q8—1781no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—891no—
248C2×D4—1781no—
249C2×D4C22×D8911yescharacteristic
250C2×D4C22×D8911yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—1781no—
256C22×C4C22×D8911yescharacteristic
257SD16—1782no—
258SD16—1782no—
259D8—1782no—
260D8—1782no—
261C2×C8—891no—
262C2×C8—891no—
263C2×C8—891no—
264C2×C8—891no—
265C4⋊C4—891no—
266C4⋊C4—891no—
267C4⋊C4—1781no—
268C4⋊C4—1781no—
269C4⋊C4—1781no—
270C4⋊C4C22⋊D8911yescharacteristic
271C4⋊C4C22⋊D8911yescharacteristic
272C4⋊C4C22×D8911yescharacteristic
273C4⋊C4C22×D8911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—1781no—
280C22⋊C4—1781no—
281C22⋊C4—1781no—
282C22⋊C4—1781no—
283C22⋊C4—1781no—
284C22⋊C4C22⋊D8911yescharacteristic
285C22⋊C4C22⋊D8911yescharacteristic
286C42—21no—
287C42—1781no—
288C42C22×D8911yescharacteristic
289C42C22×D8911yescharacteristic
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—1781no—
296C23C2×C22⋊D8911yescharacteristic
297Q8—1781no—
298Q8—1781no—
299Q8—7121no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—1781no—
304D4—1781no—
305D4—7121no—
306D4#1308357412yes—
307D4#1308357412yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—1781no—
317C2×C4—1781no—
318C2×C4—1781no—
319C2×C4—7121no—
320C2×C4C2×C22⋊D8911yescharacteristic
321C2×C4C2×C22⋊D8911yescharacteristic
322C2×C4C2×C22⋊D8911yescharacteristic
323C2×C4C2×C22⋊D8911yescharacteristic
324C2×C4C2×C22⋊D8911yescharacteristic
325C2×C4C23×D8911yescharacteristic
326C8—1781no—
327C8—1781no—
328C8—1781no—
329C8—1781no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—3561no—
341C22—3561no—
342C22—3561no—
343C22C22×C22⋊D8911yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—3561no—
352C4—3561no—
353C4—3561no—
354C4C2×#1308357411yescharacteristic
355C4C2×#1308357411yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—7121no—
360C2#1915210911yescharacteristic
361C2#1915240111yescharacteristic
362C2#1915240911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#518×C89C2
socleC22×C89C22×D4
prime radical#19151732C2
hypercenter#518D89
hypocenterC89#3118
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #19152219C2semidirect
2. #19151939C2semidirect
3. #19151922C2semidirect
4. #19151888C2semidirect
5. #19151878C2semidirect
6. #19151813C2semidirect
7. #19151813C2semidirect
8. #19151749C2semidirect
10. #19151708C2semidirect
11. #19151698C2semidirect
12. C4×#13083562C2semidirect
13. C4×#13083559C2semidirect
14. #19151659C2semidirect
15. #518×C89C2semidirect
20. #15668012C22semidirect
22. #15668000C22semidirect
28. C4×Dic178C22semidirect
29. C4×D356C22semidirect
30. #15667945C22semidirect
31. #15667945C22semidirect
32. #15667943C22semidirect
33. #15667943C22semidirect
34. C4⋊#10623494C22semidirect
35. C4⋊#10623494C22semidirect
36. #15667935C22semidirect
37. #15667935C22semidirect
42. #15667932C22semidirect
43. #15667932C22semidirect
46. #15667923C22semidirect
47. C4×#10623494C22semidirect
182. C89#3118semidirect
184. #518D89semidirect

Maximal subgroups

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

subgroupindex
#191522192
#191519392
#191519222
#191518882
#191518782
#191518132
#191517492
#191517322
#191517082
#191516982
C4×#130835622
C4×#130835592
#191516592
#518×C892
#311889