Finite Group Databasebeta

← #26029324

Subgroups — #26029324

Order 11392.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152145C211yesmaximal, characteristic
2#19151674C211yesmaximal, characteristic, complemented
3#19151673C211yesmaximal, characteristic, complemented
4#19151671C211yesmaximal, characteristic, complemented
5#19151670C211yesmaximal, characteristic, complemented
6#19151668C211yesmaximal, characteristic, complemented
7C8×C22⋊D89C211yesmaximal, characteristic, complemented
8#19151661C211yesmaximal, characteristic, complemented
9#19151653C211yesmaximal, characteristic, complemented
10#19151650C211yesmaximal, characteristic, complemented
11#19151566C211yesmaximal, characteristic, complemented
12#19151564C211yesmaximal, characteristic, complemented
13#19151563C211yesmaximal, characteristic, complemented
14#19151563C211yesmaximal, characteristic, complemented
15#435×C89C211yesmaximal, characteristic, complemented
16C2×#13083574C2211yescharacteristic
17C2×#13083574C2211yescharacteristic
18C2×#13083558C2211yescharacteristic
19C2×#13083557C2211yescharacteristic
20C2×#13083557C2211yescharacteristic
21C22×#10623494C2211yescharacteristic
22C2×C8×D89C2211yescharacteristic
23C2×C8×D89C2211yescharacteristic
24#15668011C411yescharacteristic
25#15668008C411yescharacteristic
26#15667998C411yescharacteristic
27#15667998C411yescharacteristic
28#15667987C411yescharacteristic
29#15667985C411yescharacteristic
30#15667985C411yescharacteristic
31#15667983C411yescharacteristic
32C4×D356C2211yescharacteristic
33C4×C22⋊D89C2211yescharacteristic
34C4×C22⋊D89C2211yescharacteristic
35C42×D89C2211yescharacteristic
36C4⋊#10623494C2211yescharacteristic
37#15667941C2211yescharacteristic
38#15667941C2211yescharacteristic
39C22⋊#10623494C2211yescharacteristic
40C22⋊#10623494C2211yescharacteristic
41#15667924C2211yescharacteristic
42#15667924C2211yescharacteristic
43#15667924C2211yescharacteristic
44#15667924C2211yescharacteristic
45#15667924C2211yescharacteristic
46#15667924C2211yescharacteristic
47#15667924C2211yescharacteristic
48#15667924C2211yescharacteristic
49#15667923C2211yescharacteristic
50C8×Dic89C2211yescharacteristic
51C8×Dic89C2211yescharacteristic
52C2×M16×C89C2211yescharacteristic
53C22×C8×C89C2211yescharacteristic
54C4×D4×C89C2211yescharacteristic
55C4⋊C8×C89C2211yescharacteristic
56C22⋊C8×C89C2211yescharacteristic
57C22⋊C8×C89C2211yescharacteristic
58#97×C89C2211yescharacteristic
59#13083574—41no—
60#13083574—41no—
61#13083574—41no—
62#13083574—41no—
63C2×Dic178C2×C411yescharacteristic
64C2×Dic178C2×C411yescharacteristic
65C2×D356C2×C411yescharacteristic
66C2×D356C2×C411yescharacteristic
67C2×D356C2×C411yescharacteristic
68C2×C22⋊D89C2×C411yescharacteristic
69C2×C22⋊D89C2×C411yescharacteristic
70C2×C22⋊D89C2×C411yescharacteristic
71C2×C22⋊D89C2×C411yescharacteristic
72C2×C22⋊D89C2×C411yescharacteristic
73C2×C22⋊D89C2×C411yescharacteristic
74C2×C4×D89C2×C411yescharacteristic
75C2×C4×D89C2×C411yescharacteristic
76C2×C4×D89C2311yescharacteristic
77C2×C4×D89C2311yescharacteristic
78C2×C4×D89C2311yescharacteristic
79#13083558—41no—
80#13083557—41no—
81#13083557—41no—
82C2×#10623494—41no—
83C2×#10623494C2311yescharacteristic
84C2×#10623494C2311yescharacteristic
85C2×#10623494C2311yescharacteristic
86C2×#10623494C2311yescharacteristic
87C8×D89—41no—
88C8×D89—41no—
89C4⋊Dic89C2×C411yescharacteristic
90#13083553C2×C411yescharacteristic
91#13083553C2×C411yescharacteristic
92C22⋊Dic89C2×C411yescharacteristic
93C22⋊Dic89C2×C411yescharacteristic
94#13083551C2×C411yescharacteristic
95#13083551C2×C411yescharacteristic
96#13083551C2×C411yescharacteristic
97#13083551C2×C411yescharacteristic
98C4×Dic89C2×C411yescharacteristic
99C4×Dic89C2×C411yescharacteristic
100C4×Dic89C2311yescharacteristic
101C2×D4×C89C2×C411yescharacteristic
102C22×C4×C89C2311yescharacteristic
103C22×C4×C89C2311yescharacteristic
104M16×C89—41no—
105C2×C8×C89—41no—
106C2×C8×C89C2311yescharacteristic
107C2×C8×C89C2311yescharacteristic
108C2×C8×C89C2311yescharacteristic
109C2×C8×C89C2311yescharacteristic
110C4⋊C4×C89C2×C411yescharacteristic
111C22⋊C4×C89C2×C411yescharacteristic
112C22⋊C4×C89C2×C411yescharacteristic
113C42×C89C2311yescharacteristic
114C23×C89C22×C411yescharacteristic
115C23×C89C22×C411yescharacteristic
116C22×D89C22×C411yescharacteristic
117C22×D89C22×C411yescharacteristic
118C22×D89C22×C411yescharacteristic
119D4×C89—41no—
120C2×C4×C89—21no—
121C2×C4×C89—21no—
122C2×C4×C89—21no—
123C2×C4×C89—21no—
124C2×C4×C89C22×C411yescharacteristic
125C2×C4×C89C22×C411yescharacteristic
126C2×C4×C89C22×C411yescharacteristic
127C2×C4×C89C22×C411yescharacteristic
128C2×C4×C89C2411yescharacteristic
129C22⋊D89—22no—
130C22⋊D89—22no—
131C22⋊D89—41no—
132C22⋊D89—41no—
133C22⋊D89—41no—
134C22⋊D89—41no—
135C2×Dic89C22×C411yescharacteristic
136C2×Dic89C22×C411yescharacteristic
137C2×Dic89C22×C411yescharacteristic
138C2×Dic89C22×C411yescharacteristic
139C2×Dic89C22×C411yescharacteristic
140D356—41no—
141D356—41no—
142D356—41no—
143C4×D89—21no—
144C4×D89—21no—
145C4×D89—21no—
146C4×D89—21no—
147C4×D89—21no—
148C4×D89—21no—
149C4×D89—22no—
150C4×D89—41no—
151Dic178—41no—
152Dic178—41no—
153C8×C89—21no—
154C8×C89—21no—
155C8×C89—21no—
156C8×C89—21no—
157#10623494—21no—
158#10623494—21no—
159#10623494—21no—
160#10623494—21no—
161C22×C89—21no—
162C22×C89—21no—
163C22×C89—21no—
164C22×C89—21no—
165C22×C89—21no—
166C22×C89—21no—
167C22×C89C23×C411yescharacteristic
168C2×D89—21no—
169C2×D89—21no—
170C2×D89—21no—
171C2×D89—21no—
172C2×D89—21no—
173C2×D89—21no—
174C2×D89—21no—
175C2×D89—21no—
176C2×D89—21no—
177C4×C89—21no—
178C4×C89—21no—
179C4×C89—21no—
180C4×C89—21no—
181C4×C89H(5,𝔽2)11yescharacteristic
182C4×C89H(5,𝔽2)11yescharacteristic
183Dic89—21no—
184Dic89—21no—
185Dic89—21no—
186Dic89—21no—
187Dic89#13112yes—
188C2×C89—41no—
189C2×C89—41no—
190C2×C89#51811yescharacteristic
191C2×C89C2×#13111yescharacteristic
192C2×C89#56811yescharacteristic
193D89—41no—
194D89—41no—
195D89—41no—
196#2981—891nomaximal, Sylow
197C89#298111yescharacteristic, complemented, Sylow
198#532—891no—
199#436—891no—
200#436—891no—
201#435—891no—
202#435—891no—
203#435—891no—
204#435D8911yescharacteristic, complemented
205C8×D4—891no—
206C8×D4—891no—
207#432—891no—
208#431—891no—
209#408—891no—
210#408—891no—
211#408—891no—
212#408—891no—
213C2×#41—891no—
214C2×#41—891no—
215C2×M16—891no—
216C2×M16—891no—
217C2×M16—891no—
218C2×M16C2×D8911yescharacteristic
219C22×C8—891no—
220C22×C8—891no—
221C22×C8—891no—
222C22×C8C2×D8911yescharacteristic
223C4⋊Q8—891no—
224#127—891no—
225#124—891no—
226#124—891no—
227#121—891no—
228#121—891no—
229#121—891no—
230#121—891no—
231C4×D4—891no—
232C4×D4—891no—
233C4×D4—891no—
234C4×D4C2×D8911yescharacteristic
235C2×C42—891no—
236C4⋊C8—891no—
237C4⋊C8—891no—
238C4⋊C8—891no—
239C4⋊C8C2×D8911yescharacteristic
240C22⋊C8—891no—
241C22⋊C8—891no—
242C22⋊C8—891no—
243C22⋊C8—891no—
244C22⋊C8—891no—
245C22⋊C8—891no—
246C22⋊C8—891no—
247C22⋊C8—891no—
248C22⋊C8—891no—
249C22⋊C8—891no—
250C22⋊C8C2×D8911yescharacteristic
251C22⋊C8C2×D8911yescharacteristic
252#97—891no—
253#97C2×D8911yescharacteristic
254C4×C8—891no—
255C4×C8—891no—
256#41—3561no—
257#41—3561no—
258#41—3561no—
259#41—3561no—
260C2×Q8—891no—
261C2×Q8—891no—
262C2×D4—891no—
263C2×D4—891no—
264C2×D4—891no—
265C2×D4—891no—
266C2×D4—891no—
267C2×D4—891no—
268C2×D4—891no—
269C2×D4—891no—
270C2×D4—891no—
271C2×D4C4×D8911yescharacteristic
272C22×C4—891no—
273C22×C4—891no—
274C22×C4—891no—
275C22×C4—891no—
276C22×C4—891no—
277C22×C4C22×D8911yescharacteristic
278C22×C4C22×D8911yescharacteristic
279M16—41no—
280M16—3561no—
281M16—3561no—
282M16—3561no—
283C2×C8—41no—
284C2×C8—891no—
285C2×C8—891no—
286C2×C8—891no—
287C2×C8—891no—
288C2×C8—3561no—
289C2×C8—3561no—
290C2×C8—3561no—
291C2×C8C22×D8911yescharacteristic
292C2×C8C22×D8911yescharacteristic
293C2×C8C22×D8911yescharacteristic
294C2×C8C22×D8911yescharacteristic
295C4⋊C4—891no—
296C4⋊C4—891no—
297C4⋊C4—891no—
298C4⋊C4C4×D8911yescharacteristic
299C22⋊C4—891no—
300C22⋊C4—891no—
301C22⋊C4—891no—
302C22⋊C4—891no—
303C22⋊C4—891no—
304C22⋊C4—891no—
305C22⋊C4C4×D8911yescharacteristic
306C22⋊C4C4×D8911yescharacteristic
307C42—891no—
308C42—891no—
309C42—891no—
310C42C22×D8911yescharacteristic
311C23—891no—
312C23—891no—
313C23—891no—
314C23C2×C4×D8911yescharacteristic
315C23C2×C4×D8911yescharacteristic
316Q8—3561no—
317Q8—3561no—
318D4—41no—
319D4—3561no—
320D4—3561no—
321D4—3561no—
322D4—3561no—
323D4—3561no—
324D4—3561no—
325D4—3561no—
326D4—1782no—
327D4—1782no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—891no—
333C2×C4—891no—
334C2×C4—891no—
335C2×C4—891no—
336C2×C4—891no—
337C2×C4—3561no—
338C2×C4—1782no—
339C2×C4—1781no—
340C2×C4—1781no—
341C2×C4—1781no—
342C2×C4—1781no—
343C2×C4—1781no—
344C2×C4—1781no—
345C2×C4C2×C4×D8911yescharacteristic
346C2×C4C2×C4×D8911yescharacteristic
347C2×C4C2×C4×D8911yescharacteristic
348C2×C4C2×C4×D8911yescharacteristic
349C2×C4C23×D8911yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C8—1781no—
355C8—1781no—
356C8—1781no—
357C8—1781no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—1781no—
365C22—1781no—
366C22—1781no—
367C22—1781no—
368C22—1781no—
369C22—1781no—
370C22—1781no—
371C22—1781no—
372C22—1781no—
373C22C22×C4×D8911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—892no—
379C4—1781no—
380C4—1781no—
381C4—1781no—
382C4—1781no—
383C4#1566805711yescharacteristic
384C4#1566805811yescharacteristic
385C2—41no—
386C2—41no—
387C2—3561no—
388C2—3561no—
389C2—3561no—
390C2#1915207011yescharacteristic
391C2#131×D8911yescharacteristic
392C2#1915236411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D89
commutator, socleC22×C89C23×C4
Fitting#435×C89C2
prime radical#19152145C2
cosocleC2×C4×C89C24
hypercenter#435D89
hypocenterC89#2981
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #19151674C2semidirect
3. #19151673C2semidirect
4. #19151671C2semidirect
5. #19151670C2semidirect
6. #19151668C2semidirect
7. C8×C22⋊D89C2semidirect
8. #19151661C2semidirect
9. #19151653C2semidirect
10. #19151650C2semidirect
11. #19151566C2semidirect
12. #19151564C2semidirect
13. #19151563C2semidirect
14. #19151563C2semidirect
15. #435×C89C2semidirect
197. C89#2981semidirect
204. #435D89semidirect

Maximal subgroups

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

subgroupindex
#191521452
#191516742
#191516732
#191516712
#191516702
#191516682
C8×C22⋊D892
#191516612
#191516532
#191516502
#191515662
#191515642
#191515632
#435×C892
#298189