Finite Group Databasebeta

← #37544770

Subgroups — #37544770

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#26041880C211yesmaximal, characteristic, complemented
2#26041842C211yesmaximal, characteristic, complemented
3#26041667C211yesmaximal, characteristic, complemented
4#26041654C211yesmaximal, characteristic, complemented
5#26041642C211yesmaximal, characteristic, complemented
6#26041632C211yesmaximal, characteristic, complemented
7#26041495C211yesmaximal, characteristic, complemented
8#26041494C211yesmaximal, characteristic, complemented
9#26041471C211yesmaximal, characteristic, complemented
10#26041425C211yesmaximal, characteristic, complemented
11#26041421C211yesmaximal, characteristic, complemented
12#26041414C211yesmaximal, characteristic, complemented
13#26041411C211yesmaximal, characteristic, complemented
14#26041339C211yesmaximal, characteristic, complemented
15#459×C181C211yesmaximal, characteristic, complemented
16C2×#15668448C2211yescharacteristic
17C2×D4×D181C2211yescharacteristic
18C2×#15668438C2211yescharacteristic, complemented
19C2×#15668437C2211yescharacteristic, complemented
20C2×D1448C2211yescharacteristic
21C2×#15668434C2211yescharacteristic
22C2×#15668434C2211yescharacteristic
23C2×#15668434C2211yescharacteristic, complemented
24#19153812C2211yescharacteristic
25#19153812C2211yescharacteristic, complemented
26#19153807C2211yescharacteristic, complemented
27#19153804C2211yescharacteristic
28#19153803C2211yescharacteristic
29#19153799—21no—
30#19153798—21no—
31#19153791C2211yescharacteristic
32#19153790—21no—
33#19153789—21no—
34#19153788—21no—
35#19153788—21no—
36#19153787C2211yescharacteristic
37#19153784—21no—
38#19153784—21no—
39C4×D724C2211yescharacteristic, 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×D8×C181C2211yescharacteristic
53C2×D8×C181C2211yescharacteristic, complemented
54#127×C181C2211yescharacteristic
55C4×D4×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×D724—21no—
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—
73D4×D181—41no—
74D4×D181—41no—
75C22×Dic181—21no—
76C2×C4×D181—21no—
77C2×C4×D181C2311yescharacteristic
78#15668438—41no—
79#15668437—41no—
80D1448—41no—
81#15668434—41no—
82#15668434—41no—
83#15668434—41no—
84C2×#13089678C2311yescharacteristic
85C2×#13089678C2311yescharacteristic
86C4⋊Dic181—21no—
87C4⋊Dic181C2311yescharacteristic
88#15668428—21no—
89#15668428D411yescharacteristic
90#15668428D411yescharacteristic
91C22⋊Dic181—21no—
92C22⋊Dic181—21no—
93C22⋊Dic181—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97#15668426—21no—
98#15668426D411yescharacteristic
99#15668426D411yescharacteristic
100C4×Dic181C2311yescharacteristic
101C2×D4×C181—21no—
102C2×D4×C181—21no—
103C2×D4×C181C2311yescharacteristic
104C2×D4×C181C2311yescharacteristic
105C2×D4×C181C2311yescharacteristic
106C22×C4×C181—21no—
107D8×C181—41no—
108D8×C181—41no—
109C2×C8×C181C2311yescharacteristic
110C2×C8×C181C2311yescharacteristic
111C4⋊C4×C181C2311yescharacteristic
112C22⋊C4×C181—21no—
113C42×C181C2311yescharacteristic
114C22×D181—21no—
115C22×D181—21no—
116C22×D181—42no—
117C22×D181—81no—
118C22×D181—81no—
119C22×D181C2×D411yescharacteristic
120Dic362—21no—
121Dic362—21no—
122D724—21no—
123D724—21no—
124D724—21no—
125D724—21no—
126D724—81no—
127C22⋊D181—42no—
128C22⋊D181—42no—
129C22⋊D181—81no—
130C22⋊D181—81no—
131C22⋊D181—81no—
132C22⋊D181—81no—
133C22⋊D181—81no—
134C2×Dic181—21no—
135C2×Dic181—21no—
136C2×Dic181—42no—
137C2×Dic181C2×D411yescharacteristic
138C2×Dic181C2×D411yescharacteristic
139C2×Dic181C2×D411yescharacteristic
140C4×D181—21no—
141C4×D181—21no—
142C4×D181—81no—
143#13089678—21no—
144#13089678—21no—
145C23×C181—21no—
146C23×C181—21no—
147C23×C181—21no—
148D4×C181—21no—
149D4×C181—21no—
150D4×C181—21no—
151D4×C181—21no—
152D4×C181—21no—
153D4×C181—21no—
154D4×C181—81no—
155D4×C181—81no—
156C2×C4×C181—21no—
157C2×C4×C181—81no—
158C2×C4×C181C2×D411yescharacteristic
159C2×C4×C181C2×D411yescharacteristic
160C2×C4×C181C2411yescharacteristic
161C8×C181—21no—
162C8×C181—21no—
163C22×C181—41no—
164C22×C181—41no—
165C22×C181—41no—
166C22×C181—41no—
167C22×C181—41no—
168C22×C181—41no—
169C22×C181—41no—
170C22×C181—41no—
171C22×C181—41no—
172C22×C181C22×D411yescharacteristic
173C2×D181—21no—
174C2×D181—21no—
175C2×D181—21no—
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—21no—
185C4×C181—41no—
186C4×C181H(5,𝔽2)11yescharacteristic
187C4×C181H(5,𝔽2)11yescharacteristic
188Dic181—21no—
189Dic181—21no—
190Dic181—21no—
191Dic181—41no—
192Dic181—41no—
193C2×C181—81no—
194C2×C181—81no—
195C2×C181—81no—
196C2×C181#53511yescharacteristic
197C2×C181#57611yescharacteristic
198C2×C181#57611yescharacteristic
199D181—41no—
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#459D18111yescharacteristic, complemented
214#449—1811no—
215#449—1811no—
216#447—1811no—
217#447—1811no—
218#433—1811no—
219C2×#41—1811no—
220C22×D4—1811no—
221C2×SD16—1811no—
222C2×SD16—1811no—
223C2×D8—1811no—
224C2×D8—1811no—
225C2×D8—1811no—
226C2×D8—1811no—
227C2×D8C2×D18111yescharacteristic
228C2×D8C2×D18111yescharacteristic, complemented
229#127—1811no—
230#127—1811no—
231#127C2×D18111yescharacteristic
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#121—1811no—
243#120—3621no—
244#120—3621no—
245C4×D4—1811no—
246C4×D4C2×D18111yescharacteristic, complemented
247#117—1811no—
248C4⋊C8—1811no—
249C4⋊C8C2×D18111yescharacteristic, complemented
250#103—1811no—
251#103—1811no—
252#102—1811no—
253#102—1811no—
254#102—1811no—
255#102—1811no—
256#102C2×D18111yescharacteristic
257#102C2×D18111yescharacteristic, complemented
258C22⋊C8—1811no—
259C22⋊C8—1811no—
260#97—1811no—
261C4×C8—1811no—
262C24—3621no—
263#41—7241no—
264#41—7241no—
265C2×Q8—1811no—
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—7241no—
279C2×D4—7241no—
280C2×D4C22×D18111yescharacteristic
281C2×D4C22×D18111yescharacteristic
282C2×D4C22×D18111yescharacteristic
283C22×C4—21no—
284C22×C4—3621no—
285C22×C4—3621no—
286C22×C4—1811no—
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—
316C42C22×D18111yescharacteristic
317C23—21no—
318C23—21no—
319C23—21no—
320C23—3621no—
321C23—3621no—
322C23—14481no—
323C23—14481no—
324C23—1811no—
325C23—7242no—
326Q8—3621no—
327Q8—3621no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—81no—
335D4—81no—
336D4—3621no—
337D4—3621no—
338D4—3621no—
339D4—3621no—
340D4—14481no—
341D4—14481no—
342D4—14481no—
343D4—14481no—
344D4—14481no—
345D4—14481no—
346D4—7242no—
347D4—7242no—
348C2×C4—21no—
349C2×C4—81no—
350C2×C4—3621no—
351C2×C4—3621no—
352C2×C4—3621no—
353C2×C4—3621no—
354C2×C4—14481no—
355C2×C4—1811no—
356C2×C4—1811no—
357C2×C4—1811no—
358C2×C4—7242no—
359C2×C4D4×D18111yescharacteristic
360C2×C4D4×D18111yescharacteristic
361C2×C4C23×D18111yescharacteristic
362C8—21no—
363C8—21no—
364C8—3621no—
365C8—3621no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—3621no—
376C22—3621no—
377C22—3621no—
378C22—14484no—
379C22—7241no—
380C22—7241no—
381C22—7241no—
382C22—7241no—
383C22—7241no—
384C22—7241no—
385C22C2×D4×D18111yescharacteristic
386C4—21no—
387C4—21no—
388C4—41no—
389C4—3621no—
390C4—3621no—
391C4—3621no—
392C4—7241no—
393C4—7241no—
394C4#1915386111yescharacteristic
395C4#1915386211yescharacteristic
396C2—81no—
397C2—81no—
398C2—81no—
399C2—14481no—
400C2—14481no—
401C2—7241no—
402C2#2604184511yescharacteristic
403C2#2604208011yescharacteristic
404C2#2604208311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#459×C181C2
socleC22×C181C22×D4
hypercenter#459D181
hypocenterC181#3220
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #26041880C2semidirect
2. #26041842C2semidirect
3. #26041667C2semidirect
4. #26041654C2semidirect
5. #26041642C2semidirect
6. #26041632C2semidirect
7. #26041495C2semidirect
8. #26041494C2semidirect
9. #26041471C2semidirect
10. #26041425C2semidirect
11. #26041421C2semidirect
12. #26041414C2semidirect
13. #26041411C2semidirect
14. #26041339C2semidirect
15. #459×C181C2semidirect
18. C2×#15668438C22semidirect
19. C2×#15668437C22semidirect
23. C2×#15668434C22semidirect
25. #19153812C22semidirect
26. #19153807C22semidirect
39. C4×D724C22semidirect
41. C4⋊#13089678C22semidirect
42. #19153741C22semidirect
43. #19153739C22semidirect
46. #19153737C22semidirect
50. #19153726C22semidirect
51. C8×Dic181C22semidirect
53. C2×D8×C181C22semidirect
55. C4×D4×C181C22semidirect
56. C4⋊C8×C181C22semidirect
58. #102×C181C22semidirect
202. C181#3220semidirect
213. #459D181semidirect
228. C2×D8C2×D181semidirect
246. C4×D4C2×D181semidirect
249. C4⋊C8C2×D181semidirect
257. #102C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260418802
#260418422
#260416672
#260416542
#260416422
#260416322
#260414952
#260414942
#260414712
#260414252
#260414212
#260414142
#260414112
#260413392
#459×C1812
#3220181