Finite Group Databasebeta

← #37544653

Subgroups — #37544653

Order 23168.

438 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041828C211yesmaximal, characteristic, complemented
2#26041826C211yesmaximal, characteristic, complemented
3#26041654C211yesmaximal, characteristic, complemented
4#26041650C211yesmaximal, characteristic, complemented
5#26041628C211yesmaximal, characteristic, complemented
6#26041624C211yesmaximal, characteristic, complemented
7#26041495C211yesmaximal, characteristic, complemented
8#26041494C211yesmaximal, characteristic, complemented
9#26041491C211yesmaximal, characteristic, complemented
10#26041427C211yesmaximal, characteristic, complemented
11#26041425C211yesmaximal, characteristic, complemented
12#26041423C211yesmaximal, characteristic, complemented
13#26041421C211yesmaximal, characteristic, complemented
14#26041331C211yesmaximal, characteristic, complemented
15#463×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668449—21no—
18C2×#15668448C2211yescharacteristic
19C2×#15668438C2211yescharacteristic
20C2×#15668437C2211yescharacteristic
21C2×#15668436C2211yescharacteristic
22C2×D1448C2211yescharacteristic
23C2×#15668434C2211yescharacteristic
24C2×#15668434C2211yescharacteristic
25#19153815C2211yescharacteristic
26#19153814C2211yescharacteristic
27#19153812C2211yescharacteristic
28#19153812C2211yescharacteristic
29#19153804C2211yescharacteristic
30#19153802—21no—
31#19153791C2211yescharacteristic
32#19153789—21no—
33#19153789—21no—
34#19153789—21no—
35#19153787C2211yescharacteristic
36C4×D724C2211yescharacteristic
37C4×C22⋊D181—21no—
38#19153776—21no—
39#19153776—21no—
40C42×D181C2211yescharacteristic
41C4⋊#13089678C2211yescharacteristic
42#19153741C2211yescharacteristic
43#19153740C2211yescharacteristic
44#19153739C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153728C2211yescharacteristic
49#19153728C2211yescharacteristic
50C8×Dic181C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C2×SD16×C181C2211yescharacteristic
53C2×D8×C181C2211yescharacteristic
54#124×C181C2211yescharacteristic
55C4×D4×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59#15668450—41no—
60#15668450—41no—
61#15668449—44no—
62#15668448—41no—
63#15668448—41no—
64C2×Dic362—21no—
65C2×Dic362C2311yescharacteristic
66C2×D724—21no—
67C2×D724—21no—
68C2×D724C2311yescharacteristic
69C2×D724C2311yescharacteristic
70C2×C22⋊D181—21no—
71C2×C22⋊D181—21no—
72C2×C22⋊D181—21no—
73C2×C22⋊D181—21no—
74C2×C22⋊D181—21no—
75C2×C22⋊D181—21no—
76C22×Dic181—21no—
77C2×C4×D181—21no—
78C2×C4×D181—21no—
79C2×C4×D181D411yescharacteristic
80C2×C4×D181D411yescharacteristic
81C2×C4×D181C2311yescharacteristic
82#15668438—41no—
83#15668437—41no—
84#15668436—41no—
85D1448—41no—
86#15668434—41no—
87#15668434—41no—
88C2×#13089678C2311yescharacteristic
89C2×#13089678C2311yescharacteristic
90C4⋊Dic181C2311yescharacteristic
91#15668428—21no—
92#15668428—21no—
93#15668428—21no—
94C22⋊Dic181—21no—
95#15668426—21no—
96#15668426—21no—
97#15668426—21no—
98#15668426—21no—
99C4×Dic181D411yescharacteristic
100C4×Dic181D411yescharacteristic
101C4×Dic181C2311yescharacteristic
102C2×Q8×C181C2311yescharacteristic
103C2×D4×C181C2311yescharacteristic
104C2×D4×C181C2311yescharacteristic
105C22×C4×C181—21no—
106SD16×C181—41no—
107D8×C181—41no—
108C2×C8×C181C2311yescharacteristic
109C2×C8×C181C2311yescharacteristic
110C4⋊C4×C181C2311yescharacteristic
111C22⋊C4×C181—21no—
112C22⋊C4×C181—21no—
113C22⋊C4×C181—21no—
114C42×C181C2311yescharacteristic
115C22×D181—21no—
116C22×D181—21no—
117C22×D181C2×D411yescharacteristic
118Dic362—21no—
119Dic362—21no—
120Dic362—42no—
121D724—21no—
122D724—21no—
123D724—21no—
124D724—21no—
125D724—42no—
126D724—42no—
127C22⋊D181—42no—
128C22⋊D181—42no—
129C22⋊D181—42no—
130C22⋊D181—42no—
131C22⋊D181—42no—
132C22⋊D181—42no—
133C2×Dic181—21no—
134C2×Dic181—21no—
135C2×Dic181—42no—
136C2×Dic181C2×D411yescharacteristic
137C2×Dic181C2×D411yescharacteristic
138C2×Dic181C2×D411yescharacteristic
139C4×D181—21no—
140C4×D181—21no—
141C4×D181—22no—
142C4×D181—22no—
143C4×D181—42no—
144C4×D181—42no—
145#13089678—21no—
146#13089678—21no—
147C23×C181—21no—
148C23×C181—21no—
149Q8×C181—21no—
150Q8×C181—21no—
151D4×C181—21no—
152D4×C181—21no—
153D4×C181—21no—
154D4×C181—21no—
155C2×C4×C181—21no—
156C2×C4×C181—21no—
157C2×C4×C181—42no—
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×C181C22×D411yescharacteristic
170C2×D181—21no—
171C2×D181—21no—
172C2×D181—21no—
173C2×D181—41no—
174C2×D181—41no—
175C2×D181—41no—
176C2×D181—41no—
177C2×D181—41no—
178C2×D181—41no—
179C4×C181—21no—
180C4×C181—21no—
181C4×C181—41no—
182C4×C181—41no—
183C4×C181H(5,𝔽2)11yescharacteristic
184C4×C181H(5,𝔽2)11yescharacteristic
185Dic181—21no—
186Dic181—41no—
187Dic181—41no—
188Dic181#13512yes—
189Dic181AGL(1,ℤ/8)12yes—
190C2×C181—81no—
191C2×C181—81no—
192C2×C181#53511yescharacteristic
193C2×C181C2×#13511yescharacteristic
194C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
195D181—41no—
196D181—81no—
197D181—81no—
198C181#320711yescharacteristic, complemented, Sylow
199#3207—1811nomaximal, Sylow
200#532—1811no—
201#532—1811no—
202#493—1811no—
203#492—1811no—
204#487—1811no—
205#486—1811no—
206#463—1811no—
207#463—1811no—
208#463—1811no—
209#463D18111yescharacteristic, complemented
210#449—1811no—
211#449—1811no—
212#449—1811no—
213#449—1811no—
214#431—1811no—
215C2×#41—3621no—
216C2×#41—1811no—
217C2×#41—1811no—
218C2×SD16—1811no—
219C2×SD16—1811no—
220C2×SD16—1811no—
221C2×SD16C2×D18111yescharacteristic
222C2×D8—1811no—
223C2×D8—1811no—
224C2×D8—1811no—
225C2×D8C2×D18111yescharacteristic
226C4⋊Q8—1811no—
227C4⋊Q8—1811no—
228#127—1811no—
229#127—1811no—
230#124—3621no—
231#124—1811no—
232#124C2×D18111yescharacteristic
233#121—3621no—
234#121—3621no—
235#121—3621no—
236#121—1811no—
237#121—1811no—
238C4×D4—3621no—
239C4×D4—3621no—
240C4×D4—3621no—
241C4×D4—1811no—
242C4×D4C2×D18111yescharacteristic
243C2×C42—1811no—
244C4⋊C8—1811no—
245C4⋊C8C2×D18111yescharacteristic
246#103—1811no—
247#103—1811no—
248#103—1811no—
249#103C2×D18111yescharacteristic
250#102—1811no—
251#102—1811no—
252#102—1811no—
253#102C2×D18111yescharacteristic
254C22⋊C8—1811no—
255C22⋊C8—1811no—
256C4×C8—1811no—
257C4×C8—1811no—
258#41—7244no—
259#41—7241no—
260#41—7241no—
261#41—7241no—
262#41—7241no—
263C2×Q8—3621no—
264C2×Q8—1811no—
265C2×Q8C22×D18111yescharacteristic
266C2×D4—3621no—
267C2×D4—3621no—
268C2×D4—3621no—
269C2×D4—3621no—
270C2×D4—3621no—
271C2×D4—3621no—
272C2×D4—3621no—
273C2×D4—3621no—
274C2×D4—1811no—
275C2×D4—1811no—
276C2×D4C22×D18111yescharacteristic
277C2×D4C22×D18111yescharacteristic
278C22×C4—21no—
279C22×C4—3621no—
280C22×C4—3621no—
281C22×C4—3621no—
282C22×C4—1811no—
283C22×C4—1811no—
284C22×C4—1811no—
285SD16—41no—
286SD16—7241no—
287SD16—7241no—
288SD16—7241no—
289D8—41no—
290D8—7241no—
291D8—7241no—
292D8—7241no—
293C2×C8—1811no—
294C2×C8—1811no—
295C2×C8C22×D18111yescharacteristic
296C2×C8C22×D18111yescharacteristic
297C4⋊C4—3621no—
298C4⋊C4—3621no—
299C4⋊C4—3621no—
300C4⋊C4—1811no—
301C4⋊C4C22×D18111yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—3621no—
306C22⋊C4—3621no—
307C22⋊C4—3621no—
308C22⋊C4—3621no—
309C22⋊C4—3621no—
310C42—1811no—
311C42—1811no—
312C42—1811no—
313C42C22×D18111yescharacteristic
314C23—21no—
315C23—21no—
316C23—3621no—
317C23—3621no—
318C23—1811no—
319Q8—21no—
320Q8—21no—
321Q8—3621no—
322Q8—3621no—
323Q8—7242no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—3621no—
329D4—3621no—
330D4—3621no—
331D4—3621no—
332D4—7242no—
333D4—7242no—
334D4—7242no—
335D4—7242no—
336D4—7242no—
337D4—7242no—
338D4—7242no—
339D4—7242no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—3622no—
344C2×C4—3622no—
345C2×C4—3621no—
346C2×C4—3621no—
347C2×C4—3621no—
348C2×C4—3621no—
349C2×C4—1811no—
350C2×C4—1811no—
351C2×C4—1811no—
352C2×C4—7242no—
353C2×C4—7242no—
354C2×C4—7242no—
355C2×C4D4×D18111yescharacteristic
356C2×C4D4×D18111yescharacteristic
357C2×C4C23×D18111yescharacteristic
358C8—21no—
359C8—21no—
360C8—3621no—
361C8—3621no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—3621no—
369C22—3621no—
370C22—3621no—
371C22—7241no—
372C22—7241no—
373C22—7241no—
374C22—7241no—
375C22—7241no—
376C22—7241no—
377C22C2×D4×D18111yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—3621no—
383C4—1812no—
384C4—1812no—
385C4—7241no—
386C4—7241no—
387C4#1915386111yescharacteristic
388C4#1915386211yescharacteristic
389C2—81no—
390C2—81no—
391C2—14481no—
392C2—14481no—
393C2—7241no—
394C2#2604184511yescharacteristic
395C2#135×D18111yescharacteristic
396C2AGL(1,ℤ/8)×D18111yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#463×C181C2
socleC22×C181C22×D4
hypercenter#463D181
hypocenterC181#3207
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #26041828C2semidirect
2. #26041826C2semidirect
3. #26041654C2semidirect
4. #26041650C2semidirect
5. #26041628C2semidirect
6. #26041624C2semidirect
7. #26041495C2semidirect
8. #26041494C2semidirect
9. #26041491C2semidirect
10. #26041427C2semidirect
11. #26041425C2semidirect
12. #26041423C2semidirect
13. #26041421C2semidirect
14. #26041331C2semidirect
15. #463×C181C2semidirect
198. C181#3207semidirect
209. #463D181semidirect

Maximal subgroups

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

subgroupindex
#260418282
#260418262
#260416542
#260416502
#260416282
#260416242
#260414952
#260414942
#260414912
#260414272
#260414252
#260414232
#260414212
#260413312
#463×C1812
#3207181