Finite Group Databasebeta

← #37544792

Subgroups — #37544792

Order 23168.

396 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041887C211yesmaximal, characteristic, complemented
2#26041842C211yesmaximal, characteristic
3#26041670C211yesmaximal, characteristic, complemented
4#26041650C211yesmaximal, characteristic, complemented
5#26041642C211yesmaximal, characteristic, complemented
6#26041632C211yesmaximal, characteristic, complemented
7#26041502C211yesmaximal, characteristic, complemented
8#26041501C211yesmaximal, characteristic, complemented
9#26041476C211yesmaximal, characteristic, complemented
10#26041442C211yesmaximal, characteristic, complemented
11#26041438C211yesmaximal, characteristic, complemented
12#26041431C211yesmaximal, characteristic, complemented
13#26041428C211yesmaximal, characteristic, complemented
14#26041339C211yesmaximal, characteristic, complemented
15#460×C181C211yesmaximal, characteristic, complemented
16C2×#15668448C2211yescharacteristic
17C2×D4×D181C2211yescharacteristic
18C2×Dic724C2211yescharacteristic, complemented
19C2×#15668439C2211yescharacteristic, complemented
20C2×#15668438C2211yescharacteristic
21C2×#15668437C2211yescharacteristic
22C2×#15668437C2211yescharacteristic, complemented
23C2×#15668436C2211yescharacteristic
24#19153814C2211yescharacteristic, complemented
25#19153812C2211yescharacteristic
26#19153811—21no—
27#19153810—21no—
28#19153808—21no—
29#19153807C2211yescharacteristic, complemented
30#19153806—21no—
31#19153804C2211yescharacteristic
32#19153803C2211yescharacteristic
33#19153796C2211yescharacteristic
34#19153792C2211yescharacteristic
35#19153788—21no—
36#19153788—21no—
37#19153784—21no—
38#19153784—21no—
39C4×Dic362C2211yescharacteristic, complemented
40#19153773C2211yescharacteristic
41C4⋊#13089678C2211yescharacteristic, complemented
42#19153741C2211yescharacteristic, complemented
43#19153739C2211yescharacteristic, complemented
44#19153738C2211yescharacteristic
45#19153737C2211yescharacteristic
46#19153737C2211yescharacteristic, complemented
47#19153736C2211yescharacteristic
48#19153728C2211yescharacteristic
49#19153728C2211yescharacteristic
50#19153726C2211yescharacteristic, complemented
51C8×Dic181C2211yescharacteristic, complemented
52C2×SD16×C181C2211yescharacteristic
53C2×SD16×C181C2211yescharacteristic, complemented
54#127×C181C2211yescharacteristic
55C4×Q8×C181C2211yescharacteristic, complemented
56C4⋊C8×C181C2211yescharacteristic, complemented
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60#15668448—41no—
61#15668448—41no—
62C2×Dic362C2311yescharacteristic
63C2×Dic362C2311yescharacteristic
64C2×D724C2311yescharacteristic
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69D4×D181—41no—
70D4×D181—41no—
71C22×Dic181—21no—
72C2×C4×D181C2311yescharacteristic
73Dic724—41no—
74#15668439—41no—
75#15668438—41no—
76#15668437—41no—
77#15668437—41no—
78#15668436—41no—
79C2×#13089678C2311yescharacteristic
80C2×#13089678C2311yescharacteristic
81C4⋊Dic181—21no—
82C4⋊Dic181—21no—
83C4⋊Dic181C2311yescharacteristic
84#15668428—21no—
85#15668428—21no—
86#15668428—21no—
87#15668428—21no—
88#15668428—21no—
89#15668428D411yescharacteristic
90#15668428D411yescharacteristic
91C22⋊Dic181—21no—
92C22⋊Dic181—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97#15668426D411yescharacteristic
98#15668426D411yescharacteristic
99C4×Dic181—21no—
100C4×Dic181C2311yescharacteristic
101C2×Q8×C181C2311yescharacteristic
102C2×D4×C181—21no—
103C2×D4×C181—21no—
104C2×D4×C181C2311yescharacteristic
105C2×D4×C181C2311yescharacteristic
106SD16×C181—41no—
107SD16×C181—41no—
108C2×C8×C181C2311yescharacteristic
109C2×C8×C181C2311yescharacteristic
110C4⋊C4×C181—21no—
111C4⋊C4×C181C2311yescharacteristic
112C42×C181—21no—
113C42×C181C2311yescharacteristic
114C22×D181—21no—
115C22×D181—42no—
116C22×D181—81no—
117C22×D181—81no—
118C22×D181C2×D411yescharacteristic
119Dic362—21no—
120Dic362—21no—
121Dic362—21no—
122Dic362—21no—
123D724—21no—
124D724—21no—
125C22⋊D181—42no—
126C22⋊D181—42no—
127C22⋊D181—81no—
128C22⋊D181—81no—
129C2×Dic181—21no—
130C2×Dic181—21no—
131C2×Dic181—21no—
132C2×Dic181—42no—
133C2×Dic181C2×D411yescharacteristic
134C2×Dic181C2×D411yescharacteristic
135C2×Dic181C2×D411yescharacteristic
136C4×D181—21no—
137C4×D181—21no—
138#13089678—21no—
139#13089678—21no—
140C23×C181—21no—
141C23×C181—21no—
142Q8×C181—21no—
143Q8×C181—21no—
144D4×C181—21no—
145D4×C181—21no—
146D4×C181—21no—
147D4×C181—21no—
148D4×C181—81no—
149D4×C181—81no—
150C2×C4×C181—21no—
151C2×C4×C181—21no—
152C2×C4×C181C2×D411yescharacteristic
153C2×C4×C181C2×D411yescharacteristic
154C2×C4×C181C2411yescharacteristic
155C8×C181—21no—
156C8×C181—21no—
157C22×C181—41no—
158C22×C181—41no—
159C22×C181—41no—
160C22×C181—41no—
161C22×C181—41no—
162C22×C181—41no—
163C22×C181C22×D411yescharacteristic
164C2×D181—21no—
165C2×D181—21no—
166C2×D181—21no—
167C2×D181—41no—
168C2×D181—41no—
169C2×D181—41no—
170C2×D181—84no—
171C4×C181—21no—
172C4×C181—21no—
173C4×C181—41no—
174C4×C181—41no—
175C4×C181H(5,𝔽2)11yescharacteristic
176C4×C181H(5,𝔽2)11yescharacteristic
177Dic181—21no—
178Dic181—21no—
179Dic181—21no—
180Dic181—41no—
181Dic181—41no—
182Dic181—41no—
183C2×C181—81no—
184C2×C181—81no—
185C2×C181#53511yescharacteristic
186C2×C181#57711yescharacteristic
187C2×C181#57711yescharacteristic
188D181—41no—
189D181—81no—
190C181#322211yescharacteristic, complemented, Sylow
191#3222—1811nomaximal, Sylow
192#541—1811no—
193#535—1811no—
194#497—1811no—
195#492—1811no—
196#490—1811no—
197#488—1811no—
198#464—1811no—
199#464—1811no—
200#460—1811no—
201#460D18111yescharacteristic, complemented
202#452—1811no—
203#452—1811no—
204#450—1811no—
205#450—1811no—
206#433—1811no—
207C2×#41—1811no—
208C22×D4—1811no—
209C2×Q16—1811no—
210C2×Q16—1811no—
211C2×SD16—1811no—
212C2×SD16—1811no—
213C2×SD16—1811no—
214C2×SD16—1811no—
215C2×SD16C2×D18111yescharacteristic
216C2×SD16C2×D18111yescharacteristic, complemented
217C4⋊Q8—1811no—
218#127—1811no—
219#127C2×D18111yescharacteristic
220#126—3621no—
221#126—3621no—
222#125—3621no—
223#125—3621no—
224#125—1811no—
225#124—1811no—
226#124—1811no—
227C22⋊Q8—1811no—
228C22⋊Q8—1811no—
229#121—3621no—
230#121—3621no—
231#120—3621no—
232#120—3621no—
233C4×Q8—1811no—
234C4×Q8C2×D18111yescharacteristic, complemented
235#117—1811no—
236C4⋊C8—1811no—
237C4⋊C8C2×D18111yescharacteristic, complemented
238#103—1811no—
239#103—1811no—
240#102—1811no—
241#102—1811no—
242#102—1811no—
243#102—1811no—
244#102C2×D18111yescharacteristic
245#102C2×D18111yescharacteristic, complemented
246C22⋊C8—1811no—
247C22⋊C8—1811no—
248#97—1811no—
249C4×C8—1811no—
250C24—3621no—
251#41—7241no—
252#41—7241no—
253C2×Q8—1811no—
254C2×Q8—1811no—
255C2×Q8C22×D18111yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—3621no—
259C2×D4—3621no—
260C2×D4—3621no—
261C2×D4—3621no—
262C2×D4—1811no—
263C2×D4—7241no—
264C2×D4—7241no—
265C2×D4C22×D18111yescharacteristic
266C2×D4C22×D18111yescharacteristic
267C22×C4—3621no—
268C22×C4—1811no—
269Q16—7241no—
270Q16—7241no—
271SD16—41no—
272SD16—41no—
273SD16—7241no—
274SD16—7241no—
275SD16—7241no—
276SD16—7241no—
277C2×C8—1811no—
278C2×C8—1811no—
279C2×C8C22×D18111yescharacteristic
280C2×C8C22×D18111yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—3621no—
283C4⋊C4—3621no—
284C4⋊C4—3621no—
285C4⋊C4—3621no—
286C4⋊C4—3621no—
287C4⋊C4—3621no—
288C4⋊C4—3621no—
289C4⋊C4—1811no—
290C4⋊C4—1811no—
291C4⋊C4—1811no—
292C4⋊C4C22×D18111yescharacteristic
293C22⋊C4—3621no—
294C22⋊C4—3621no—
295C22⋊C4—3621no—
296C22⋊C4—3621no—
297C22⋊C4—3621no—
298C22⋊C4—3621no—
299C22⋊C4—1811no—
300C22⋊C4—1811no—
301C42—21no—
302C42—3621no—
303C42—1811no—
304C42C22×D18111yescharacteristic
305C23—21no—
306C23—21no—
307C23—3621no—
308C23—14481no—
309C23—14481no—
310C23—1811no—
311C23—7242no—
312Q8—21no—
313Q8—21no—
314Q8—3621no—
315Q8—3621no—
316Q8—3621no—
317Q8—3621no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—81no—
323D4—81no—
324D4—3621no—
325D4—3621no—
326D4—14481no—
327D4—14481no—
328D4—7242no—
329D4—7242no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—3621no—
333C2×C4—3621no—
334C2×C4—3621no—
335C2×C4—3621no—
336C2×C4—3621no—
337C2×C4—1811no—
338C2×C4—1811no—
339C2×C4—1811no—
340C2×C4—7242no—
341C2×C4D4×D18111yescharacteristic
342C2×C4D4×D18111yescharacteristic
343C2×C4C23×D18111yescharacteristic
344C8—21no—
345C8—21no—
346C8—3621no—
347C8—3621no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—3621no—
355C22—3621no—
356C22—3621no—
357C22—14484no—
358C22—7241no—
359C22—7241no—
360C22—7241no—
361C22C2×D4×D18111yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—3621no—
367C4—3621no—
368C4—3621no—
369C4—7241no—
370C4—7241no—
371C4—7241no—
372C4#1915386111yescharacteristic
373C4#1915386211yescharacteristic
374C2—81no—
375C2—81no—
376C2—14481no—
377C2—7241no—
378C2#2604184511yescharacteristic
379C2#2604208511yescharacteristic
380C2#2604208911yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#460×C181C2
socleC22×C181C22×D4
prime radical#26041842C2
hypercenter#460D181
hypocenterC181#3222
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #26041887C2semidirect
3. #26041670C2semidirect
4. #26041650C2semidirect
5. #26041642C2semidirect
6. #26041632C2semidirect
7. #26041502C2semidirect
8. #26041501C2semidirect
9. #26041476C2semidirect
10. #26041442C2semidirect
11. #26041438C2semidirect
12. #26041431C2semidirect
13. #26041428C2semidirect
14. #26041339C2semidirect
15. #460×C181C2semidirect
18. C2×Dic724C22semidirect
19. C2×#15668439C22semidirect
22. C2×#15668437C22semidirect
24. #19153814C22semidirect
29. #19153807C22semidirect
39. C4×Dic362C22semidirect
41. C4⋊#13089678C22semidirect
42. #19153741C22semidirect
43. #19153739C22semidirect
46. #19153737C22semidirect
50. #19153726C22semidirect
51. C8×Dic181C22semidirect
53. C2×SD16×C181C22semidirect
55. C4×Q8×C181C22semidirect
56. C4⋊C8×C181C22semidirect
58. #102×C181C22semidirect
190. C181#3222semidirect
201. #460D181semidirect
216. C2×SD16C2×D181semidirect
234. C4×Q8C2×D181semidirect
237. C4⋊C8C2×D181semidirect
245. #102C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260418872
#260418422
#260416702
#260416502
#260416422
#260416322
#260415022
#260415012
#260414762
#260414422
#260414382
#260414312
#260414282
#260413392
#460×C1812
#3222181