Finite Group Databasebeta

← #37544767

Subgroups — #37544767

Order 23168.

420 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041882C211yesmaximal, characteristic, complemented
2#26041846C211yesmaximal, characteristic, complemented
3#26041667C211yesmaximal, characteristic, complemented
4#26041654C211yesmaximal, characteristic, complemented
5#26041642C211yesmaximal, characteristic, complemented
6#26041632C211yesmaximal, characteristic, complemented
7#26041493C211yesmaximal, characteristic, complemented
8#26041492C211yesmaximal, characteristic, complemented
9#26041473C211yesmaximal, characteristic, complemented
10#26041472C211yesmaximal, characteristic, complemented
11#26041426C211yesmaximal, characteristic, complemented
12#26041422C211yesmaximal, characteristic, complemented
13#26041413C211yesmaximal, characteristic, complemented
14#26041337C211yesmaximal, characteristic, complemented
15#447×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C2×#15668438C2211yescharacteristic, complemented
18C2×#15668437C2211yescharacteristic, complemented
19C2×D1448C2211yescharacteristic, complemented
20C2×#15668434C2211yescharacteristic
21C2×#15668434C2211yescharacteristic
22C2×#15668434C2211yescharacteristic, complemented
23#19153812C2211yescharacteristic
24#19153812C2211yescharacteristic
25#19153812C2211yescharacteristic, complemented
26#19153807C2211yescharacteristic, complemented
27#19153803C2211yescharacteristic
28#19153803C2211yescharacteristic
29#19153800—21no—
30#19153798—21no—
31#19153790C2211yescharacteristic
32#19153788—21no—
33#19153787—21no—
34#19153787—21no—
35#19153787—21no—
36#19153785—21no—
37#19153785—21no—
38D4×Dic181C2211yescharacteristic, complemented
39#19153778C2211yescharacteristic, complemented
40#19153775C2211yescharacteristic
41#19153745C2211yescharacteristic, complemented
42#19153745C2211yescharacteristic, complemented
43#19153741C2211yescharacteristic, complemented
44#19153739C2211yescharacteristic, complemented
45#19153738C2211yescharacteristic, complemented
46#19153737C2211yescharacteristic
47#19153737C2211yescharacteristic
48#19153736C2211yescharacteristic, complemented
49C22⋊#13089678C2211yescharacteristic
50#19153726C2211yescharacteristic, complemented
51C8×Dic181C2211yescharacteristic, complemented
52C22×D4×C181C2211yescharacteristic
53C2×D8×C181C2211yescharacteristic
54C2×D8×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59#15668449—41no—
60#15668449—41no—
61C2×Dic362C2311yescharacteristic
62C2×D724C2311yescharacteristic
63C2×D724C2311yescharacteristic
64C2×C22⋊D181—21no—
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C22⋊D181—21no—
71C2×C22⋊D181—21no—
72C22×Dic181—21no—
73C2×C4×D181—21no—
74C2×C4×D181—21no—
75#15668438—41no—
76#15668437—41no—
77D1448—41no—
78#15668434—41no—
79#15668434—41no—
80#15668434—41no—
81C2×#13089678C2311yescharacteristic
82C2×#13089678C2311yescharacteristic
83C4⋊Dic181—21no—
84C4⋊Dic181D411yescharacteristic
85C4⋊Dic181D411yescharacteristic
86C4⋊Dic181C2311yescharacteristic
87#15668428—21no—
88C22⋊Dic181—21no—
89C22⋊Dic181—21no—
90C22⋊Dic181—21no—
91C22⋊Dic181—21no—
92C22⋊Dic181—21no—
93C22⋊Dic181D411yescharacteristic
94C22⋊Dic181D411yescharacteristic
95#15668426—21no—
96#15668426—21no—
97C4×Dic181C2311yescharacteristic
98C4×Dic181C2311yescharacteristic
99C24×C181—21no—
100C2×D4×C181—21no—
101C2×D4×C181—21no—
102C2×D4×C181—41no—
103C2×D4×C181—41no—
104C2×D4×C181C2311yescharacteristic
105C2×D4×C181C2311yescharacteristic
106C2×D4×C181C2311yescharacteristic
107C22×C4×C181C2311yescharacteristic
108D8×C181—41no—
109D8×C181—41no—
110C2×C8×C181C2311yescharacteristic
111C2×C8×C181C2311yescharacteristic
112C4⋊C4×C181C2311yescharacteristic
113C22⋊C4×C181—21no—
114C22×D181—21no—
115C22×D181—21no—
116Dic362—21no—
117Dic362—21no—
118D724—21no—
119D724—21no—
120D724—21no—
121D724—21no—
122C22⋊D181—42no—
123C22⋊D181—81no—
124C22⋊D181—81no—
125C22⋊D181—81no—
126C22⋊D181—81no—
127C22⋊D181—81no—
128C22⋊D181—81no—
129C22⋊D181—81no—
130C2×Dic181—21no—
131C2×Dic181—21no—
132C2×Dic181—81no—
133C2×Dic181C2×D411yescharacteristic
134C2×Dic181C2×D411yescharacteristic
135C2×Dic181C2×D411yescharacteristic
136C2×Dic181C2×D411yescharacteristic
137C4×D181—42no—
138C4×D181—81no—
139#13089678—21no—
140#13089678—21no—
141C23×C181—21no—
142C23×C181—21no—
143C23×C181—21no—
144C23×C181—42no—
145C23×C181—81no—
146C23×C181—81no—
147C23×C181C2×D411yescharacteristic
148D4×C181—21no—
149D4×C181—21no—
150D4×C181—21no—
151D4×C181—21no—
152D4×C181—21no—
153D4×C181—21no—
154D4×C181—42no—
155D4×C181—81no—
156C2×C4×C181—21no—
157C2×C4×C181—21no—
158C2×C4×C181—21no—
159C2×C4×C181C2×D411yescharacteristic
160C2×C4×C181C2411yescharacteristic
161C8×C181—21no—
162C8×C181—21no—
163C22×C181—21no—
164C22×C181—21no—
165C22×C181—21no—
166C22×C181—41no—
167C22×C181—41no—
168C22×C181—41no—
169C22×C181—41no—
170C22×C181—41no—
171C22×C181—41no—
172C22×C181—41no—
173C22×C181—41no—
174C22×C181—41no—
175C22×C181—84no—
176C22×C181C22×D411yescharacteristic
177C2×D181—41no—
178C2×D181—41no—
179C2×D181—41no—
180C2×D181—41no—
181C2×D181—41no—
182C2×D181—41no—
183C4×C181—21no—
184C4×C181—41no—
185C4×C181H(5,𝔽2)11yescharacteristic
186C4×C181H(5,𝔽2)11yescharacteristic
187Dic181—21no—
188Dic181—21no—
189Dic181—21no—
190Dic181—21no—
191Dic181—41no—
192Dic181—41no—
193C2×C181—41no—
194C2×C181—81no—
195C2×C181—81no—
196C2×C181—81no—
197C2×C181#53511yescharacteristic
198C2×C181#57611yescharacteristic
199C2×C181#57611yescharacteristic
200D181—81no—
201D181—81no—
202C181#322011yescharacteristic, complemented, Sylow
203#3220—1811nomaximal, Sylow
204#540—1811no—
205#535—1811no—
206#496—1811no—
207#493—1811no—
208#490—1811no—
209#488—1811no—
210#463—1811no—
211#463—1811no—
212#459—1811no—
213#459—1811no—
214#449—1811no—
215#449—1811no—
216#447—1811no—
217#447D18111yescharacteristic, complemented
218#433—1811no—
219C2×#41—1811no—
220C22×D4C2×D18111yescharacteristic
221C2×SD16—1811no—
222C2×SD16—1811no—
223C2×D8—1811no—
224C2×D8—1811no—
225C2×D8—1811no—
226C2×D8—1811no—
227C2×D8C2×D18111yescharacteristic
228C2×D8C2×D18111yescharacteristic
229#127—1811no—
230#127—1811no—
231#127—1811no—
232#125—1811no—
233#124—1811no—
234#124—1811no—
235#123—3621no—
236#123—3621no—
237#121—3621no—
238#121—3621no—
239#121—3621no—
240#121—3621no—
241#121—1811no—
242#121C2×D18111yescharacteristic
243#120—3621no—
244#120—3621no—
245C4×D4—1811no—
246C4×D4—1811no—
247#117—1811no—
248C4⋊C8—1811no—
249C4⋊C8—1811no—
250#103—1811no—
251#103—1811no—
252#102—1811no—
253#102—1811no—
254#102—1811no—
255#102—1811no—
256#102C2×D18111yescharacteristic
257#102C2×D18111yescharacteristic
258C22⋊C8—1811no—
259C22⋊C8C2×D18111yescharacteristic
260#97—1811no—
261C4×C8—1811no—
262C24—21no—
263#41—7241no—
264#41—7241no—
265C2×Q8—1811no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—3621no—
271C2×D4—3621no—
272C2×D4—3621no—
273C2×D4—3621no—
274C2×D4—3621no—
275C2×D4—3621no—
276C2×D4—3621no—
277C2×D4—3621no—
278C2×D4—1811no—
279C2×D4—1811no—
280C2×D4C22×D18111yescharacteristic
281C2×D4C22×D18111yescharacteristic
282C2×D4C22×D18111yescharacteristic
283C22×C4—3621no—
284C22×C4—3621no—
285C22×C4—3621no—
286C22×C4C22×D18111yescharacteristic
287SD16—7241no—
288SD16—7241no—
289D8—41no—
290D8—41no—
291D8—7241no—
292D8—7241no—
293D8—7241no—
294D8—7241no—
295C2×C8—1811no—
296C2×C8—1811no—
297C2×C8C22×D18111yescharacteristic
298C2×C8C22×D18111yescharacteristic
299C4⋊C4—3621no—
300C4⋊C4—3621no—
301C4⋊C4—1811no—
302C4⋊C4—1811no—
303C4⋊C4—1811no—
304C4⋊C4C22×D18111yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—3621no—
307C22⋊C4—3621no—
308C22⋊C4—3621no—
309C22⋊C4—3621no—
310C22⋊C4—3621no—
311C22⋊C4—3621no—
312C22⋊C4—3621no—
313C22⋊C4—1811no—
314C22⋊C4—1811no—
315C42—1811no—
316C42—1811no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—3621no—
324C23—3621no—
325C23D4×D18111yescharacteristic
326Q8—3621no—
327Q8—3621no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—81no—
336D4—3621no—
337D4—3621no—
338D4—3621no—
339D4—3621no—
340D4—14481no—
341D4—14481no—
342D4—14481no—
343D4—14481no—
344D4—14481no—
345D4—14481no—
346D4—14481no—
347D4—7242no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—3621no—
352C2×C4—3621no—
353C2×C4—14481no—
354C2×C4—14481no—
355C2×C4—1811no—
356C2×C4—1811no—
357C2×C4—1811no—
358C2×C4—1811no—
359C2×C4—7242no—
360C2×C4D4×D18111yescharacteristic
361C2×C4C23×D18111yescharacteristic
362C8—21no—
363C8—21no—
364C8—3621no—
365C8—3621no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—84no—
379C22—7241no—
380C22—7241no—
381C22—7241no—
382C22—7241no—
383C22—7241no—
384C22—7241no—
385C22C2×D4×D18111yescharacteristic
386C4—21no—
387C4—41no—
388C4—3621no—
389C4—3621no—
390C4—3621no—
391C4—3621no—
392C4—7241no—
393C4—7241no—
394C4#1915386111yescharacteristic
395C4#1915386111yescharacteristic
396C2—41no—
397C2—81no—
398C2—81no—
399C2—81no—
400C2—14481no—
401C2—14481no—
402C2#2604184411yescharacteristic
403C2#2604208011yescharacteristic
404C2#2604208311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#447×C181C2
socleC22×C181C22×D4
hypercenter#447D181
hypocenterC181#3220
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #26041882C2semidirect
2. #26041846C2semidirect
3. #26041667C2semidirect
4. #26041654C2semidirect
5. #26041642C2semidirect
6. #26041632C2semidirect
7. #26041493C2semidirect
8. #26041492C2semidirect
9. #26041473C2semidirect
10. #26041472C2semidirect
11. #26041426C2semidirect
12. #26041422C2semidirect
13. #26041413C2semidirect
14. #26041337C2semidirect
15. #447×C181C2semidirect
17. C2×#15668438C22semidirect
18. C2×#15668437C22semidirect
19. C2×D1448C22semidirect
22. C2×#15668434C22semidirect
25. #19153812C22semidirect
26. #19153807C22semidirect
38. D4×Dic181C22semidirect
39. #19153778C22semidirect
41. #19153745C22semidirect
42. #19153745C22semidirect
43. #19153741C22semidirect
44. #19153739C22semidirect
45. #19153738C22semidirect
48. #19153736C22semidirect
50. #19153726C22semidirect
51. C8×Dic181C22semidirect
202. C181#3220semidirect
217. #447D181semidirect

Maximal subgroups

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

subgroupindex
#260418822
#260418462
#260416672
#260416542
#260416422
#260416322
#260414932
#260414922
#260414732
#260414722
#260414262
#260414222
#260414132
#260413372
#447×C1812
#3220181