Finite Group Databasebeta

← #37544769

Subgroups — #37544769

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#26041843C211yesmaximal, characteristic, complemented
3#26041665C211yesmaximal, characteristic, complemented
4#26041654C211yesmaximal, characteristic, complemented
5#26041642C211yesmaximal, characteristic, complemented
6#26041635C211yesmaximal, characteristic, complemented
7#26041497C211yesmaximal, characteristic, complemented
8#26041496C211yesmaximal, characteristic, complemented
9#26041473C211yesmaximal, characteristic, complemented
10#26041472C211yesmaximal, characteristic, complemented
11#26041424C211yesmaximal, characteristic, complemented
12#26041415C211yesmaximal, characteristic, complemented
13#26041412C211yesmaximal, characteristic, complemented
14#26041337C211yesmaximal, characteristic, complemented
15#449×C181C211yesmaximal, characteristic, complemented
16C22×D724C2211yescharacteristic
17C2×#15668436C2211yescharacteristic, complemented
18C2×D1448C2211yescharacteristic
19C2×D1448C2211yescharacteristic
20C2×#15668434C2211yescharacteristic
21C2×#15668434C2211yescharacteristic
22C2×#15668434C2211yescharacteristic, complemented
23#19153812C2211yescharacteristic
24#19153812C2211yescharacteristic
25#19153812C2211yescharacteristic, complemented
26#19153807C2211yescharacteristic, complemented
27#19153805C2211yescharacteristic
28#19153805C2211yescharacteristic
29#19153800—21no—
30#19153798—21no—
31#19153790—21no—
32#19153790—21no—
33#19153790C2211yescharacteristic
34#19153788—21no—
35#19153787—21no—
36#19153784—21no—
37#19153784—21no—
38D4×Dic181C2211yescharacteristic, complemented
39#19153778C2211yescharacteristic, complemented
40#19153775C2211yescharacteristic
41#19153745C2211yescharacteristic, complemented
42#19153745C2211yescharacteristic, complemented
43#19153740C2211yescharacteristic, complemented
44#19153738C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153737C2211yescharacteristic, complemented
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153726C2211yescharacteristic, complemented
51C8×Dic181C2211yescharacteristic, complemented
52C2×#41×C181C2211yescharacteristic
53C2×SD16×C181C2211yescharacteristic, complemented
54C2×D8×C181C2211yescharacteristic, complemented
55#121×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic, complemented
57#102×C181C2211yescharacteristic, complemented
58C22⋊C8×C181C2211yescharacteristic
59C23×D181—21no—
60C2×D724—21no—
61C2×D724—41no—
62C2×D724—41no—
63C2×D724C2311yescharacteristic
64C2×D724C2311yescharacteristic
65C2×D724C2311yescharacteristic
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C22⋊D181—21no—
71C2×C22⋊D181—21no—
72C2×C22⋊D181—21no—
73C22×Dic181—21no—
74C2×C4×D181—21no—
75#15668436—41no—
76D1448—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⋊Dic181D411yescharacteristic
90C22⋊Dic181D411yescharacteristic
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97C4×Dic181C2311yescharacteristic
98C4×Dic181C2311yescharacteristic
99#41×C181—41no—
100#41×C181—41no—
101C2×Q8×C181C2311yescharacteristic
102C2×D4×C181—21no—
103C2×D4×C181—21no—
104C2×D4×C181C2311yescharacteristic
105C2×D4×C181C2311yescharacteristic
106C22×C4×C181—21no—
107C22×C4×C181C2311yescharacteristic
108SD16×C181—41no—
109D8×C181—41no—
110C2×C8×C181C2311yescharacteristic
111C2×C8×C181C2311yescharacteristic
112C4⋊C4×C181C2311yescharacteristic
113C22⋊C4×C181—21no—
114C22×D181—21no—
115C22×D181—21no—
116C22×D181—21no—
117C22×D181—42no—
118C22×D181—81no—
119C22×D181—81no—
120D724—21no—
121D724—21no—
122D724—21no—
123D724—21no—
124D724—21no—
125D724—21no—
126D724—42no—
127C22⋊D181—81no—
128C22⋊D181—81no—
129C22⋊D181—81no—
130C22⋊D181—81no—
131C22⋊D181—81no—
132C22⋊D181—81no—
133C22⋊D181—81no—
134C2×Dic181—21no—
135C2×Dic181—81no—
136C2×Dic181C2×D411yescharacteristic
137C2×Dic181C2×D411yescharacteristic
138C2×Dic181C2×D411yescharacteristic
139C2×Dic181C2×D411yescharacteristic
140C4×D181—81no—
141#13089678—21no—
142#13089678—21no—
143C23×C181—21no—
144C23×C181—21no—
145C23×C181C2×D411yescharacteristic
146Q8×C181—21no—
147Q8×C181—21no—
148D4×C181—21no—
149D4×C181—21no—
150D4×C181—21no—
151D4×C181—21no—
152D4×C181—42no—
153D4×C181—81no—
154C2×C4×C181—21no—
155C2×C4×C181—21no—
156C2×C4×C181—21no—
157C2×C4×C181—21no—
158C2×C4×C181—42no—
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×C181C22×D411yescharacteristic
173C2×D181—41no—
174C2×D181—41no—
175C2×D181—41no—
176C2×D181—41no—
177C2×D181—41no—
178C2×D181—41no—
179C2×D181—41no—
180C2×D181—41no—
181C2×D181—41no—
182C2×D181—84no—
183C4×C181—21no—
184C4×C181—41no—
185C4×C181—41no—
186C4×C181H(5,𝔽2)11yescharacteristic
187C4×C181H(5,𝔽2)11yescharacteristic
188Dic181—21no—
189Dic181—21no—
190Dic181—21no—
191Dic181—21no—
192Dic181—41no—
193C2×C181—41no—
194C2×C181—81no—
195C2×C181—81no—
196C2×C181#53511yescharacteristic
197C2×C181#57611yescharacteristic
198C2×C181#57611yescharacteristic
199D181—81no—
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#449D18111yescharacteristic, complemented
216#447—1811no—
217#447—1811no—
218#433—1811no—
219C2×#41C2×D18111yescharacteristic
220C22×D4—1811no—
221C2×SD16—1811no—
222C2×SD16C2×D18111yescharacteristic, complemented
223C2×D8—1811no—
224C2×D8—1811no—
225C2×D8—1811no—
226C2×D8—1811no—
227C2×D8—1811no—
228C2×D8C2×D18111yescharacteristic, complemented
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#103C2×D18111yescharacteristic, complemented
252#102—1811no—
253#102—1811no—
254#102—1811no—
255#102—1811no—
256#102—1811no—
257#102C2×D18111yescharacteristic, complemented
258C22⋊C8—1811no—
259C22⋊C8C2×D18111yescharacteristic
260#97—1811no—
261C4×C8—1811no—
262C24—3621no—
263#41—41no—
264#41—41no—
265C2×Q8C22×D18111yescharacteristic
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—3621no—
269C2×D4—3621no—
270C2×D4—3621no—
271C2×D4—3621no—
272C2×D4—3621no—
273C2×D4—3621no—
274C2×D4—3621no—
275C2×D4—3621no—
276C2×D4—1811no—
277C2×D4—1811no—
278C2×D4—1811no—
279C2×D4—7241no—
280C2×D4—7241no—
281C2×D4C22×D18111yescharacteristic
282C2×D4C22×D18111yescharacteristic
283C22×C4—21no—
284C22×C4—3621no—
285C22×C4—3621no—
286C22×C4C22×D18111yescharacteristic
287SD16—41no—
288SD16—7241no—
289D8—41no—
290D8—7241no—
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—3621no—
320C23—3621no—
321C23—3621no—
322C23—14481no—
323C23—14481no—
324C23—7242no—
325C23D4×D18111yescharacteristic
326Q8—21no—
327Q8—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—81no—
334D4—3621no—
335D4—3621no—
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—21no—
352C2×C4—42no—
353C2×C4—3621no—
354C2×C4—14481no—
355C2×C4—14481no—
356C2×C4—1811no—
357C2×C4—1811no—
358C2×C4—1811no—
359C2×C4—1811no—
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—14484no—
376C22—7241no—
377C22—7241no—
378C22—7241no—
379C22—7241no—
380C22—7241no—
381C22—7241no—
382C22—7241no—
383C22—7241no—
384C22—7241no—
385C22C2×D4×D18111yescharacteristic
386C4—21no—
387C4—41no—
388C4—41no—
389C4—3621no—
390C4—3621no—
391C4—3621no—
392C4—3621no—
393C4—7241no—
394C4#1915386111yescharacteristic
395C4#1915386111yescharacteristic
396C2—41no—
397C2—81no—
398C2—81no—
399C2—14481no—
400C2—14481no—
401C2—14481no—
402C2#2604184411yescharacteristic
403C2#2604208111yescharacteristic
404C2#2604208311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#449×C181C2
socleC22×C181C22×D4
hypercenter#449D181
hypocenterC181#3220
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #26041882C2semidirect
2. #26041843C2semidirect
3. #26041665C2semidirect
4. #26041654C2semidirect
5. #26041642C2semidirect
6. #26041635C2semidirect
7. #26041497C2semidirect
8. #26041496C2semidirect
9. #26041473C2semidirect
10. #26041472C2semidirect
11. #26041424C2semidirect
12. #26041415C2semidirect
13. #26041412C2semidirect
14. #26041337C2semidirect
15. #449×C181C2semidirect
17. C2×#15668436C22semidirect
22. C2×#15668434C22semidirect
25. #19153812C22semidirect
26. #19153807C22semidirect
38. D4×Dic181C22semidirect
39. #19153778C22semidirect
41. #19153745C22semidirect
42. #19153745C22semidirect
43. #19153740C22semidirect
46. #19153737C22semidirect
50. #19153726C22semidirect
51. C8×Dic181C22semidirect
53. C2×SD16×C181C22semidirect
54. C2×D8×C181C22semidirect
56. #103×C181C22semidirect
57. #102×C181C22semidirect
202. C181#3220semidirect
215. #449D181semidirect
222. C2×SD16C2×D181semidirect
228. C2×D8C2×D181semidirect
251. #103C2×D181semidirect
257. #102C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260418822
#260418432
#260416652
#260416542
#260416422
#260416352
#260414972
#260414962
#260414732
#260414722
#260414242
#260414152
#260414122
#260413372
#449×C1812
#3220181