Finite Group Databasebeta

← #37545559

Subgroups — #37545559

Order 23168.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041968C211yesmaximal, characteristic, complemented
2#26041926C211yesmaximal, characteristic
3#26041632C211yesmaximal, characteristic, complemented
4#26041611C211yesmaximal, characteristic, complemented
5#26041582C211yesmaximal, characteristic, complemented
6#26041521C211yesmaximal, characteristic, complemented
7#26041506C211yesmaximal, characteristic, complemented
8#26041500C211yesmaximal, characteristic, complemented
9#26041443C211yesmaximal, characteristic, complemented
10#26041431C211yesmaximal, characteristic, complemented
11#26041366C211yesmaximal, characteristic, complemented
12#26041342C211yesmaximal, characteristic, complemented
13#26041273C211yesmaximal, characteristic, complemented
14#102×D181C211yesmaximal, characteristic, complemented
15#482×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C2×D4×D181C2211yescharacteristic
18C2×Dic724C2211yescharacteristic, complemented
19C2×#15668438C2211yescharacteristic
20C2×#15668437C2211yescharacteristic
21C22×#13089678C2211yescharacteristic, complemented
22C2×C8×D181C2211yescharacteristic
23#19153809—21no—
24#19153808—21no—
25#19153807C2211yescharacteristic, complemented
26#19153803C2211yescharacteristic
27#19153798—21no—
28#19153798—21no—
29#19153796C2211yescharacteristic
30#19153796C2211yescharacteristic
31#19153795C2211yescharacteristic, complemented
32#19153787—21no—
33#19153784—21no—
34#19153781C2211yescharacteristic, complemented
35#19153778C2211yescharacteristic
36C4×C22⋊D181C2211yescharacteristic
37#19153773—21no—
38C4⋊C4×D181C2211yescharacteristic
39C22⋊C4×D181—21no—
40#19153747C2211yescharacteristic, complemented
41#19153745C2211yescharacteristic, complemented
42#19153741C2211yescharacteristic, complemented
43#19153739C2211yescharacteristic, complemented
44#19153739C2211yescharacteristic, complemented
45#19153739C2211yescharacteristic, complemented
46#19153738C2211yescharacteristic
47#19153737C2211yescharacteristic
48#19153736C2211yescharacteristic
49#19153736C2211yescharacteristic
50#19153728C2211yescharacteristic
51C8×Dic181C2211yescharacteristic, complemented
52#121×C181C2211yescharacteristic
53#117×C181C2211yescharacteristic, complemented
54#107×C181C2211yescharacteristic, complemented
55#106×C181C2211yescharacteristic, complemented
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60#15668449—22no—
61#15668449—41no—
62C2×Dic362C2311yescharacteristic
63C2×Dic362C2311yescharacteristic
64C2×D724C2311yescharacteristic
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C2×C22⋊D181D411yescharacteristic
68D4×D181—22no—
69D4×D181—41no—
70C2×C4×D181—21no—
71C2×C4×D181—21no—
72C2×C4×D181—21no—
73C2×C4×D181C2311yescharacteristic
74Dic724—41no—
75#15668438—22no—
76#15668437—41no—
77C2×#13089678—41no—
78C2×#13089678C2311yescharacteristic
79C2×#13089678C2311yescharacteristic
80C8×D181—41no—
81C4⋊Dic181—21no—
82C4⋊Dic181—21no—
83C4⋊Dic181—21no—
84C4⋊Dic181C2311yescharacteristic
85#15668428—21no—
86#15668428—21no—
87#15668428—21no—
88#15668428—21no—
89#15668428D411yescharacteristic
90C22⋊Dic181—21no—
91C22⋊Dic181—21no—
92C22⋊Dic181—21no—
93C22⋊Dic181D411yescharacteristic
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97#15668426D411yescharacteristic
98C4×Dic181—21no—
99C4×Dic181C2311yescharacteristic
100C2×D4×C181—21no—
101C2×D4×C181C2311yescharacteristic
102C22×C4×C181C2311yescharacteristic
103C2×C8×C181C2311yescharacteristic
104C2×C8×C181C2311yescharacteristic
105C4⋊C4×C181C2311yescharacteristic
106C4⋊C4×C181C2311yescharacteristic
107C4⋊C4×C181C2311yescharacteristic
108C22⋊C4×C181—21no—
109C22⋊C4×C181—21no—
110C42×C181—21no—
111C22×D181—21no—
112C22×D181—42no—
113C22×D181—42no—
114C22×D181—81no—
115C22×D181C2×D411yescharacteristic
116Dic362—21no—
117Dic362—21no—
118Dic362—21no—
119Dic362—21no—
120D724—21no—
121D724#4112yes—
122C22⋊D181—22no—
123C22⋊D181—42no—
124C22⋊D181—42no—
125C2×Dic181—21no—
126C2×Dic181—21no—
127C2×Dic181—21no—
128C2×Dic181C2×D411yescharacteristic
129C2×Dic181C2×D411yescharacteristic
130C2×Dic181C2×D411yescharacteristic
131C4×D181—21no—
132C4×D181—21no—
133C4×D181—42no—
134C4×D181—42no—
135C4×D181—81no—
136#13089678—21no—
137#13089678—21no—
138C23×C181—21no—
139C23×C181C2×D411yescharacteristic
140D4×C181—21no—
141D4×C181—21no—
142D4×C181—81no—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—21no—
147C2×C4×C181—21no—
148C2×C4×C181C2×D411yescharacteristic
149C2×C4×C181C2411yescharacteristic
150C8×C181—21no—
151C8×C181—21no—
152C22×C181—21no—
153C22×C181—21no—
154C22×C181—21no—
155C22×C181—41no—
156C22×C181—41no—
157C22×C181—41no—
158C22×C181C22×D411yescharacteristic
159C2×D181—21no—
160C2×D181—21no—
161C2×D181—22no—
162C2×D181—41no—
163C2×D181—41no—
164C2×D181—84no—
165C2×D181#13512yes—
166C4×C181—21no—
167C4×C181—41no—
168C4×C181—41no—
169C4×C181—41no—
170C4×C181C2×#4111yescharacteristic
171C4×C181H(5,𝔽2)11yescharacteristic
172Dic181—21no—
173Dic181—21no—
174Dic181—21no—
175Dic181—41no—
176Dic181—41no—
177Dic181—41no—
178C2×C181—41no—
179C2×C181—81no—
180C2×C181#54611yescharacteristic
181C2×C181C2×#13511yescharacteristic
182C2×C181#57711yescharacteristic
183D181—22no—
184D181—42no—
185C181#329611yescharacteristic, complemented, Sylow
186#3296—1811nomaximal, Sylow
187#552—1811no—
188#546—1811no—
189#488—1811no—
190#483—1811no—
191#482D18111yescharacteristic, complemented
192#478—1811no—
193#467—1811no—
194#465—1811no—
195#464—1811no—
196#452—1811no—
197#450—1811no—
198C4×SD16—1811no—
199C8×D4—1811no—
200#416—1811no—
201C2×#102—1811no—
202C2×#41—1811no—
203C22×D4—1811no—
204C2×Q16—1811no—
205C2×SD16—1811no—
206C2×SD16—1811no—
207C22×C8—1811no—
208C22×C8—1811no—
209#126—3621no—
210#125—3621no—
211#125—1811no—
212#124—1811no—
213#123—3621no—
214#123—3621no—
215C22⋊Q8—1811no—
216C22⋊Q8—1811no—
217C22⋊Q8—1811no—
218#121—3621no—
219#121C2×D18111yescharacteristic
220#120—3621no—
221C4×Q8—1811no—
222C4×D4—1811no—
223C4×D4—1811no—
224#117—3621no—
225#117C2×D18111yescharacteristic, complemented
226C2×C4⋊C4—1811no—
227C2×C22⋊C4—3621no—
228#107C2×D18111yescharacteristic, complemented
229#106—1811no—
230#106C2×D18111yescharacteristic, complemented
231C4⋊C8—1811no—
232#103—1811no—
233#103—1811no—
234#103—1811no—
235#103—1811no—
236#102—1811no—
237#102—1811no—
238#102—1811no—
239#102—1811no—
240#102C2×D18111yescharacteristic
241#102C2×D18111yescharacteristic
242C22⋊C8—1811no—
243C22⋊C8C2×D18111yescharacteristic, complemented
244C4×C8—1811no—
245C24—3621no—
246#41—3622no—
247#41—7241no—
248C2×Q8—1811no—
249C2×Q8—1811no—
250C2×D4—21no—
251C2×D4—3622no—
252C2×D4—3621no—
253C2×D4—3621no—
254C2×D4—1811no—
255C2×D4—1811no—
256C2×D4—7241no—
257C2×D4C22×D18111yescharacteristic
258C22×C4—3621no—
259C22×C4—3621no—
260C22×C4—3621no—
261C22×C4—1811no—
262C22×C4C22×D18111yescharacteristic
263Q16—7241no—
264SD16—3622no—
265SD16—7241no—
266C2×C8—1811no—
267C2×C8—1811no—
268C2×C8—7241no—
269C2×C8—7241no—
270C2×C8C22×D18111yescharacteristic
271C2×C8C22×D18111yescharacteristic
272C4⋊C4—3621no—
273C4⋊C4—3621no—
274C4⋊C4—3621no—
275C4⋊C4—3621no—
276C4⋊C4—3621no—
277C4⋊C4—3621no—
278C4⋊C4—3621no—
279C4⋊C4—1811no—
280C4⋊C4—1811no—
281C4⋊C4C22×D18111yescharacteristic
282C4⋊C4C22×D18111yescharacteristic
283C4⋊C4C22×D18111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—3621no—
287C22⋊C4—3621no—
288C22⋊C4—3621no—
289C22⋊C4—3621no—
290C22⋊C4—3621no—
291C22⋊C4—3621no—
292C22⋊C4—1811no—
293C22⋊C4—1811no—
294C42—21no—
295C42—3621no—
296C42—1811no—
297C23—21no—
298C23—3621no—
299C23—14481no—
300C23—1811no—
301C23—7242no—
302C23—7242no—
303C23D4×D18111yescharacteristic
304Q8—3621no—
305Q8—3621no—
306Q8—3621no—
307Q8—3621no—
308D4—21no—
309D4—21no—
310D4—81no—
311D4—3622no—
312D4—3621no—
313D4—1812no—
314D4—7242no—
315D4—7242no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—3621no—
322C2×C4—3621no—
323C2×C4—3621no—
324C2×C4—3621no—
325C2×C4—3621no—
326C2×C4—14481no—
327C2×C4—1811no—
328C2×C4—1811no—
329C2×C4—1811no—
330C2×C4—7242no—
331C2×C4—7242no—
332C2×C4D4×D18111yescharacteristic
333C2×C4C23×D18111yescharacteristic
334C8—21no—
335C8—21no—
336C8—3621no—
337C8—3621no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—3621no—
345C22—3621no—
346C22—3622no—
347C22—14484no—
348C22—1812no—
349C22—7241no—
350C22—7241no—
351C22C2×D4×D18111yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—3621no—
357C4—3621no—
358C4—3621no—
359C4—7241no—
360C4—7241no—
361C4—7241no—
362C4#41×D18111yescharacteristic
363C4#1915386211yescharacteristic
364C2—41no—
365C2—81no—
366C2—3622no—
367C2—7242no—
368C2#2604192111yescharacteristic
369C2#135×D18111yescharacteristic
370C2#2604208911yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#482×C181C2
socleC22×C181C22×D4
prime radical#26041926C2
hypercenter#482D181
hypocenterC181#3296
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #26041968C2semidirect
3. #26041632C2semidirect
4. #26041611C2semidirect
5. #26041582C2semidirect
6. #26041521C2semidirect
7. #26041506C2semidirect
8. #26041500C2semidirect
9. #26041443C2semidirect
10. #26041431C2semidirect
11. #26041366C2semidirect
12. #26041342C2semidirect
13. #26041273C2semidirect
14. #102×D181C2semidirect
15. #482×C181C2semidirect
18. C2×Dic724C22semidirect
21. C22×#13089678C22semidirect
25. #19153807C22semidirect
31. #19153795C22semidirect
34. #19153781C22semidirect
40. #19153747C22semidirect
41. #19153745C22semidirect
42. #19153741C22semidirect
43. #19153739C22semidirect
44. #19153739C22semidirect
45. #19153739C22semidirect
51. C8×Dic181C22semidirect
53. #117×C181C22semidirect
54. #107×C181C22semidirect
55. #106×C181C22semidirect
58. C22⋊C8×C181C22semidirect
185. C181#3296semidirect
191. #482D181semidirect
225. #117C2×D181semidirect
228. #107C2×D181semidirect
230. #106C2×D181semidirect
243. C22⋊C8C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419682
#260419262
#260416322
#260416112
#260415822
#260415212
#260415062
#260415002
#260414432
#260414312
#260413662
#260413422
#260412732
#102×D1812
#482×C1812
#3296181