Finite Group Databasebeta

← #37545935

Subgroups — #37545935

Order 23168.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041968C211yesmaximal, characteristic, complemented
2#26041920C211yesmaximal, characteristic
3#26041635C211yesmaximal, characteristic, complemented
4#26041599C211yesmaximal, characteristic, complemented
5#26041582C211yesmaximal, characteristic, complemented
6#26041535C211yesmaximal, characteristic, complemented
7#26041526C211yesmaximal, characteristic, complemented
8#26041504C211yesmaximal, characteristic, complemented
9#26041444C211yesmaximal, characteristic, complemented
10#26041432C211yesmaximal, characteristic, complemented
11#26041366C211yesmaximal, characteristic, complemented
12#26041354C211yesmaximal, characteristic, complemented
13#26041283C211yesmaximal, characteristic, complemented
14#26041279C211yesmaximal, characteristic, complemented
15#485×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C22×D724C2211yescharacteristic
18C2×#15668439C2211yescharacteristic, complemented
19C2×#15668438C2211yescharacteristic
20C2×#15668438C2211yescharacteristic
21C2×#15668433C2211yescharacteristic
22C2×#15668432C2211yescharacteristic, complemented
23#19153809—21no—
24#19153808—21no—
25#19153807C2211yescharacteristic, complemented
26#19153805C2211yescharacteristic
27#19153801—21no—
28#19153798—21no—
29#19153796C2211yescharacteristic, complemented
30#19153795C2211yescharacteristic
31#19153791—21no—
32#19153791C2211yescharacteristic
33#19153786—21no—
34#19153781C2211yescharacteristic, complemented
35#19153778C2211yescharacteristic
36C4×C22⋊D181C2211yescharacteristic
37#19153773—21no—
38C4⋊C4×D181C2211yescharacteristic, complemented
39C22⋊C4×D181—21no—
40#19153747C2211yescharacteristic, complemented
41#19153745C2211yescharacteristic, complemented
42#19153740C2211yescharacteristic, complemented
43#19153739C2211yescharacteristic, complemented
44#19153738C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153736C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49#19153736C2211yescharacteristic
50#19153728C2211yescharacteristic, complemented
51C8×Dic181C2211yescharacteristic, complemented
52C22⋊Q8×C181C2211yescharacteristic
53#117×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic, complemented
55#106×C181C2211yescharacteristic, complemented
56#103×C181C2211yescharacteristic, complemented
57#103×C181C2211yescharacteristic, complemented
58C22⋊C8×C181C2211yescharacteristic
59C23×D181—21no—
60#15668450—22no—
61#15668450—41no—
62C2×Dic362C2311yescharacteristic
63C2×D724—22no—
64C2×D724—21no—
65C2×D724—21no—
66C2×D724—21no—
67C2×D724—41no—
68C2×D724C2311yescharacteristic
69C2×D724C2311yescharacteristic
70C2×C22⋊D181D411yescharacteristic
71C2×C4×D181—21no—
72C2×C4×D181—21no—
73C2×C4×D181—21no—
74C2×C4×D181C2311yescharacteristic
75#15668439—41no—
76#15668438—22no—
77#15668438—41no—
78#15668433—41no—
79#15668432—41no—
80C2×#13089678C2311yescharacteristic
81C2×#13089678C2311yescharacteristic
82C4⋊Dic181—21no—
83C4⋊Dic181—21no—
84C4⋊Dic181C2311yescharacteristic
85#15668428—21no—
86#15668428—21no—
87#15668428—21no—
88#15668428—21no—
89#15668428D411yescharacteristic
90C22⋊Dic181—21no—
91C22⋊Dic181D411yescharacteristic
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97#15668426D411yescharacteristic
98C4×Dic181—21no—
99C4×Dic181C2311yescharacteristic
100C2×Q8×C181C2311yescharacteristic
101C22×C4×C181C2311yescharacteristic
102C2×C8×C181C2311yescharacteristic
103C2×C8×C181C2311yescharacteristic
104C4⋊C4×C181—21no—
105C4⋊C4×C181C2311yescharacteristic
106C4⋊C4×C181C2311yescharacteristic
107C4⋊C4×C181C2311yescharacteristic
108C22⋊C4×C181—21no—
109C22⋊C4×C181—21no—
110C42×C181—21no—
111C22×D181—21no—
112C22×D181—21no—
113C22×D181—42no—
114C22×D181—42no—
115C22×D181—81no—
116C22×D181C2×D411yescharacteristic
117Dic362—21no—
118Dic362—21no—
119D724—21no—
120D724—21no—
121D724—21no—
122D724—42no—
123D724—42no—
124D724—81no—
125D724#4112yes—
126C22⋊D181—41no—
127C2×Dic181—21no—
128C2×Dic181—21no—
129C2×Dic181C2×D411yescharacteristic
130C2×Dic181C2×D411yescharacteristic
131C2×Dic181C2×D411yescharacteristic
132C4×D181—21no—
133C4×D181—21no—
134C4×D181—42no—
135C4×D181—42no—
136C4×D181—81no—
137#13089678—21no—
138#13089678—21no—
139C23×C181C2×D411yescharacteristic
140Q8×C181—21no—
141Q8×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—21no—
147C2×C4×C181—21no—
148C2×C4×C181C2×D411yescharacteristic
149C2×C4×C181C2411yescharacteristic
150C8×C181—21no—
151C8×C181—21no—
152C22×C181—21no—
153C22×C181—21no—
154C22×C181—21no—
155C22×C181C22×D411yescharacteristic
156C2×D181—21no—
157C2×D181—22no—
158C2×D181—21no—
159C2×D181—21no—
160C2×D181—41no—
161C2×D181—41no—
162C2×D181—41no—
163C2×D181—41no—
164C2×D181—41no—
165C2×D181—84no—
166C4×C181—21no—
167C4×C181—41no—
168C4×C181—41no—
169C4×C181—41no—
170C4×C181—41no—
171C4×C181C2×#4111yescharacteristic
172C4×C181H(5,𝔽2)11yescharacteristic
173Dic181—21no—
174Dic181—21no—
175Dic181—21no—
176Dic181—41no—
177Dic181—41no—
178C2×C181—41no—
179C2×C181#54611yescharacteristic
180C2×C181#57511yescharacteristic
181C2×C181#57711yescharacteristic
182D181—41no—
183D181—42no—
184D181—81no—
185C181#332311yescharacteristic, complemented, Sylow
186#3323—1811nomaximal, Sylow
187#552—1811no—
188#546—1811no—
189#488—1811no—
190#485D18111yescharacteristic, complemented
191#481—1811no—
192#478—1811no—
193#470—1811no—
194#468—1811no—
195#464—1811no—
196#452—1811no—
197#450—1811no—
198C4×SD16—1811no—
199#436—1811no—
200#418—1811no—
201#417—1811no—
202C2×#41—1811no—
203C22×D4—1811no—
204C2×Q16—1811no—
205C2×SD16—1811no—
206C2×SD16—1811no—
207C2×M16—1811no—
208C2×M16—1811no—
209#126—3621no—
210#125—3621no—
211#125—1811no—
212#124—1811no—
213#123—3621no—
214#123—3621no—
215C22⋊Q8—1811no—
216C22⋊Q8—1811no—
217C22⋊Q8C2×D18111yescharacteristic
218#121—3621no—
219#121—1811no—
220#120—3621no—
221C4×Q8—1811no—
222C4×D4—1811no—
223C4×D4—1811no—
224#117—3621no—
225#117C2×D18111yescharacteristic
226C2×C4⋊C4—1811no—
227C2×C22⋊C4—3621no—
228#107C2×D18111yescharacteristic, complemented
229#106—1811no—
230#106C2×D18111yescharacteristic, complemented
231C4⋊C8—1811no—
232#103—1811no—
233#103—1811no—
234#103C2×D18111yescharacteristic, complemented
235#103C2×D18111yescharacteristic, complemented
236#102—1811no—
237#102—1811no—
238#102—1811no—
239#102—1811no—
240#102—1811no—
241#102—1811no—
242C22⋊C8—1811no—
243C22⋊C8C2×D18111yescharacteristic
244C4×C8—1811no—
245C24—3621no—
246#41—3622no—
247#41—7241no—
248C2×Q8—1811no—
249C2×Q8C22×D18111yescharacteristic
250C2×D4—3622no—
251C2×D4—3621no—
252C2×D4—3621no—
253C2×D4—3621no—
254C2×D4—1811no—
255C2×D4—1811no—
256C2×D4—1811no—
257C2×D4—7241no—
258C22×C4—3621no—
259C22×C4—3621no—
260C22×C4—3621no—
261C22×C4—1811no—
262C22×C4C22×D18111yescharacteristic
263Q16—7241no—
264SD16—3622no—
265SD16—7241no—
266M16—7241no—
267M16—7241no—
268C2×C8—1811no—
269C2×C8—1811no—
270C2×C8C22×D18111yescharacteristic
271C2×C8C22×D18111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—3621no—
274C4⋊C4—3621no—
275C4⋊C4—3621no—
276C4⋊C4—3621no—
277C4⋊C4—3621no—
278C4⋊C4—3621no—
279C4⋊C4—1811no—
280C4⋊C4—1811no—
281C4⋊C4C22×D18111yescharacteristic
282C4⋊C4C22×D18111yescharacteristic
283C4⋊C4C22×D18111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—3621no—
287C22⋊C4—3621no—
288C22⋊C4—3621no—
289C22⋊C4—3621no—
290C22⋊C4—3621no—
291C22⋊C4—3621no—
292C22⋊C4—1811no—
293C22⋊C4—1811no—
294C42—21no—
295C42—3621no—
296C42—1811no—
297C23—3621no—
298C23—3621no—
299C23—14481no—
300C23—1811no—
301C23—7242no—
302C23—7242no—
303C23D4×D18111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—3621no—
307Q8—3621no—
308D4—3621no—
309D4—3621no—
310D4—3621no—
311D4—14481no—
312D4—1812no—
313D4—7242no—
314D4—7242no—
315D4—7241no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—3621no—
323C2×C4—3621no—
324C2×C4—3621no—
325C2×C4—3621no—
326C2×C4—14481no—
327C2×C4—1811no—
328C2×C4—1811no—
329C2×C4—1811no—
330C2×C4—7242no—
331C2×C4—7242no—
332C2×C4D4×D18111yescharacteristic
333C2×C4C23×D18111yescharacteristic
334C8—21no—
335C8—21no—
336C8—3621no—
337C8—3621no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—3621no—
342C22—3622no—
343C22—3621no—
344C22—3621no—
345C22—14484no—
346C22—7241no—
347C22—7241no—
348C22—7241no—
349C22—7241no—
350C22—7241no—
351C22C2×D4×D18111yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—3621no—
358C4—3621no—
359C4—3621no—
360C4—7241no—
361C4—7241no—
362C4#41×D18111yescharacteristic
363C4#1915386211yescharacteristic
364C2—41no—
365C2—14481no—
366C2—7241no—
367C2—7242no—
368C2#2604192111yescharacteristic
369C2#2604207811yescharacteristic
370C2#2604208611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#485×C181C2
socleC22×C181C22×D4
prime radical#26041920C2
hypercenter#485D181
hypocenterC181#3323
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #26041968C2semidirect
3. #26041635C2semidirect
4. #26041599C2semidirect
5. #26041582C2semidirect
6. #26041535C2semidirect
7. #26041526C2semidirect
8. #26041504C2semidirect
9. #26041444C2semidirect
10. #26041432C2semidirect
11. #26041366C2semidirect
12. #26041354C2semidirect
13. #26041283C2semidirect
14. #26041279C2semidirect
15. #485×C181C2semidirect
18. C2×#15668439C22semidirect
22. C2×#15668432C22semidirect
25. #19153807C22semidirect
29. #19153796C22semidirect
34. #19153781C22semidirect
38. C4⋊C4×D181C22semidirect
40. #19153747C22semidirect
41. #19153745C22semidirect
42. #19153740C22semidirect
43. #19153739C22semidirect
50. #19153728C22semidirect
51. C8×Dic181C22semidirect
54. #107×C181C22semidirect
55. #106×C181C22semidirect
56. #103×C181C22semidirect
57. #103×C181C22semidirect
185. C181#3323semidirect
190. #485D181semidirect
228. #107C2×D181semidirect
230. #106C2×D181semidirect
234. #103C2×D181semidirect
235. #103C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419682
#260419202
#260416352
#260415992
#260415822
#260415352
#260415262
#260415042
#260414442
#260414322
#260413662
#260413542
#260412832
#260412792
#485×C1812
#3323181