Finite Group Databasebeta

← #37545754

Subgroups — #37545754

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#26042003C211yesmaximal, characteristic, complemented
2#26041924C211yesmaximal, characteristic
3#26041641C211yesmaximal, characteristic, complemented
4#26041623C211yesmaximal, characteristic, complemented
5#26041605C211yesmaximal, characteristic, complemented
6#26041538C211yesmaximal, characteristic, complemented
7#26041509C211yesmaximal, characteristic, complemented
8#26041502C211yesmaximal, characteristic, complemented
9#26041442C211yesmaximal, characteristic, complemented
10#26041431C211yesmaximal, characteristic, complemented
11#26041379C211yesmaximal, characteristic, complemented
12#26041349C211yesmaximal, characteristic, complemented
13#26041282C211yesmaximal, characteristic, complemented
14#26041272C211yesmaximal, characteristic, complemented
15#476×C181C211yesmaximal, characteristic, complemented
16C2×#15668448C2211yescharacteristic
17C2×D4×D181C2211yescharacteristic
18C2×Dic724C2211yescharacteristic, complemented
19C2×#15668438C2211yescharacteristic
20C2×#15668437C2211yescharacteristic
21C2×#15668432C2211yescharacteristic
22C2×C8×D181C2211yescharacteristic, complemented
23#19153811—21no—
24#19153811—21no—
25#19153805—21no—
26#19153804C2211yescharacteristic
27#19153800—21no—
28#19153796C2211yescharacteristic
29#19153796C2211yescharacteristic
30#19153796C2211yescharacteristic, complemented
31#19153791C2211yescharacteristic
32#19153790—21no—
33#19153786—21no—
34Q8×Dic181—21no—
35C4×Dic362C2211yescharacteristic, complemented
36C4×D724C2211yescharacteristic
37#19153774C2211yescharacteristic
38#19153774C2211yescharacteristic, complemented
39C2×#15668426—21no—
40#19153749C2211yescharacteristic, complemented
41#19153741C2211yescharacteristic, complemented
42#19153739C2211yescharacteristic, complemented
43#19153739C2211yescharacteristic, complemented
44#19153739C2211yescharacteristic, complemented
45#19153738C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49#19153728C2211yescharacteristic
50#19153728C2211yescharacteristic, complemented
51#19153727C2211yescharacteristic, complemented
52C4⋊Q8×C181C2211yescharacteristic, complemented
53C4×D4×C181C2211yescharacteristic
54#106×C181C2211yescharacteristic, complemented
55#106×C181C2211yescharacteristic, complemented
56C4⋊C8×C181C2211yescharacteristic, complemented
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59C23×D181—21no—
60#15668448—22no—
61#15668448—41no—
62C2×Dic362C2311yescharacteristic
63C2×Dic362C2311yescharacteristic
64C2×D724—21no—
65C2×D724D411yescharacteristic
66C2×D724C2311yescharacteristic
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69D4×D181—22no—
70D4×D181—41no—
71C22×Dic181—21no—
72C2×C4×D181C2311yescharacteristic
73C2×C4×D181C2311yescharacteristic
74Dic724—41no—
75#15668438—41no—
76#15668437—22no—
77#15668432—41no—
78C2×#13089678C2311yescharacteristic
79C2×#13089678C2311yescharacteristic
80C8×D181—41no—
81C4⋊Dic181—21no—
82C4⋊Dic181—21no—
83C4⋊Dic181—21no—
84C4⋊Dic181D411yescharacteristic
85C4⋊Dic181C2311yescharacteristic
86#15668428—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426D411yescharacteristic
96#15668426D411yescharacteristic
97C4×Dic181—21no—
98C4×Dic181—21no—
99C4×Dic181—21no—
100C2×Q8×C181—21no—
101C2×D4×C181C2311yescharacteristic
102C22×C4×C181—21no—
103C2×C8×C181C2311yescharacteristic
104C2×C8×C181C2311yescharacteristic
105C4⋊C4×C181—21no—
106C4⋊C4×C181C2311yescharacteristic
107C4⋊C4×C181C2311yescharacteristic
108C4⋊C4×C181C2311yescharacteristic
109C22⋊C4×C181—21no—
110C42×C181C2311yescharacteristic
111C22×D181—21no—
112C22×D181—42no—
113C22×D181—42no—
114C22×D181—81no—
115C22×D181C2×D411yescharacteristic
116C22×D181C2×D411yescharacteristic
117Dic362—21no—
118Dic362—21no—
119Dic362—21no—
120Dic362—21no—
121D724—21no—
122D724—21no—
123D724—41no—
124D724—81no—
125C22⋊D181—42no—
126C22⋊D181—42no—
127C2×Dic181—21no—
128C2×Dic181—21no—
129C2×Dic181—21no—
130C2×Dic181—42no—
131C2×Dic181C2×D411yescharacteristic
132C2×Dic181C2×D411yescharacteristic
133C4×D181—21no—
134C4×D181—21no—
135C4×D181—21no—
136C4×D181—21no—
137#13089678—21no—
138#13089678—21no—
139C23×C181—21no—
140Q8×C181—42no—
141D4×C181—21no—
142D4×C181#4112yes—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—81no—
147C2×C4×C181C2×D411yescharacteristic
148C2×C4×C181C2×D411yescharacteristic
149C2×C4×C181C2411yescharacteristic
150C8×C181—21no—
151C8×C181—21no—
152C22×C181—22no—
153C22×C181—41no—
154C22×C181—41no—
155C22×C181C22×D411yescharacteristic
156C2×D181—21no—
157C2×D181—21no—
158C2×D181—21no—
159C2×D181—21no—
160C2×D181—21no—
161C2×D181—21no—
162C2×D181—41no—
163C2×D181—41no—
164C2×D181—41no—
165C2×D181—84no—
166C4×C181—21no—
167C4×C181—21no—
168C4×C181—41no—
169C4×C181—41no—
170C4×C181—41no—
171C4×C181C2×#4111yescharacteristic
172C4×C181H(5,𝔽2)11yescharacteristic
173Dic181—21no—
174Dic181—21no—
175Dic181—41no—
176Dic181—41no—
177Dic181—41no—
178C2×C181—42no—
179C2×C181#54611yescharacteristic
180C2×C181#57511yescharacteristic
181C2×C181#57711yescharacteristic
182D181—41no—
183D181—41no—
184D181—81no—
185C181#331111yescharacteristic, complemented, Sylow
186#3311—1811nomaximal, Sylow
187#556—1811no—
188#546—1811no—
189#489—1811no—
190#485—1811no—
191#482—1811no—
192#476D18111yescharacteristic, complemented
193#470—1811no—
194#465—1811no—
195#464—1811no—
196#452—1811no—
197#450—1811no—
198#440—1811no—
199#435—1811no—
200#418—1811no—
201#416—1811no—
202C2×#41—1811no—
203C22×D4—1811no—
204C2×Q16—1811no—
205C2×SD16—1811no—
206C2×SD16—1811no—
207C2×M16—1811no—
208C22×C8—1811no—
209C4⋊Q8C2×D18111yescharacteristic, complemented
210#126—3621no—
211#126—3621no—
212#124—3621no—
213#124—1811no—
214#123—3621no—
215C22⋊Q8—1811no—
216C22⋊Q8—1811no—
217C22⋊Q8—1811no—
218#121—3621no—
219#121—1811no—
220#120—3621no—
221C4×Q8—3621no—
222C4×Q8—1811no—
223C4×D4—1811no—
224C4×D4C2×D18111yescharacteristic
225#117—1811no—
226#117—1811no—
227C2×C22⋊C4—3621no—
228#107—1811no—
229#106C2×D18111yescharacteristic, complemented
230#106C2×D18111yescharacteristic, complemented
231C4⋊C8C2×D18111yescharacteristic, complemented
232#103—1811no—
233#103—1811no—
234#103—1811no—
235#103—1811no—
236#102—1811no—
237#102—1811no—
238#102—1811no—
239#102—1811no—
240#102C2×D18111yescharacteristic
241#102C2×D18111yescharacteristic
242C22⋊C8—1811no—
243C22⋊C8—1811no—
244#97—1811no—
245C24—3621no—
246#41—3622no—
247#41—7241no—
248C2×Q8—21no—
249C2×Q8—1811no—
250C2×Q8—1811no—
251C2×D4—3621no—
252C2×D4—3622no—
253C2×D4—3621no—
254C2×D4—3621no—
255C2×D4—1811no—
256C2×D4—1811no—
257C2×D4—7241no—
258C2×D4C22×D18111yescharacteristic
259C22×C4—21no—
260C22×C4—3621no—
261C22×C4—1811no—
262C22×C4—1811no—
263Q16—7241no—
264SD16—3622no—
265SD16—7241no—
266M16—7241no—
267C2×C8—1811no—
268C2×C8—1811no—
269C2×C8—7241no—
270C2×C8C22×D18111yescharacteristic
271C2×C8C22×D18111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—3621no—
274C4⋊C4—3621no—
275C4⋊C4—3621no—
276C4⋊C4—3621no—
277C4⋊C4—1811no—
278C4⋊C4—1811no—
279C4⋊C4C22×D18111yescharacteristic
280C4⋊C4C22×D18111yescharacteristic
281C4⋊C4C22×D18111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—3621no—
284C22⋊C4—3621no—
285C22⋊C4—3621no—
286C22⋊C4—3621no—
287C22⋊C4—3621no—
288C22⋊C4—3621no—
289C22⋊C4—3621no—
290C22⋊C4—3621no—
291C22⋊C4—1811no—
292C22⋊C4—1811no—
293C42—3621no—
294C42—3621no—
295C42—3621no—
296C42C22×D18111yescharacteristic
297C23—21no—
298C23—3621no—
299C23—14481no—
300C23—1811no—
301C23—1811no—
302C23—7242no—
303C23—7242no—
304Q8—42no—
305Q8—3621no—
306Q8—3621no—
307Q8—3621no—
308Q8—3621no—
309D4—21no—
310D4—3621no—
311D4—3621no—
312D4—14481no—
313D4—7241no—
314D4—7242no—
315D4—7242no—
316D4#1566845012yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—3621no—
322C2×C4—3621no—
323C2×C4—3621no—
324C2×C4—3621no—
325C2×C4—3621no—
326C2×C4—3621no—
327C2×C4—3621no—
328C2×C4—1811no—
329C2×C4—1811no—
330C2×C4—7242no—
331C2×C4D4×D18111yescharacteristic
332C2×C4D4×D18111yescharacteristic
333C2×C4C23×D18111yescharacteristic
334C8—21no—
335C8—21no—
336C8—3621no—
337C8—3621no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—3621no—
342C22—3621no—
343C22—3621no—
344C22—3621no—
345C22—3621no—
346C22—3621no—
347C22—14484no—
348C22—7241no—
349C22—7241no—
350C22—7241no—
351C22C2×D4×D18111yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—3621no—
358C4—3621no—
359C4—7241no—
360C4—7241no—
361C4—7241no—
362C4C2×#1566845011yescharacteristic
363C4#1915386211yescharacteristic
364C2—42no—
365C2—14481no—
366C2—7241no—
367C2—7241no—
368C2#2604192011yescharacteristic
369C2#2604207511yescharacteristic
370C2#2604208511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#476×C181C2
socleC22×C181C22×D4
prime radical#26041924C2
hypercenter#476D181
hypocenterC181#3311
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #26042003C2semidirect
3. #26041641C2semidirect
4. #26041623C2semidirect
5. #26041605C2semidirect
6. #26041538C2semidirect
7. #26041509C2semidirect
8. #26041502C2semidirect
9. #26041442C2semidirect
10. #26041431C2semidirect
11. #26041379C2semidirect
12. #26041349C2semidirect
13. #26041282C2semidirect
14. #26041272C2semidirect
15. #476×C181C2semidirect
18. C2×Dic724C22semidirect
22. C2×C8×D181C22semidirect
30. #19153796C22semidirect
35. C4×Dic362C22semidirect
38. #19153774C22semidirect
40. #19153749C22semidirect
41. #19153741C22semidirect
42. #19153739C22semidirect
43. #19153739C22semidirect
44. #19153739C22semidirect
50. #19153728C22semidirect
51. #19153727C22semidirect
52. C4⋊Q8×C181C22semidirect
54. #106×C181C22semidirect
55. #106×C181C22semidirect
56. C4⋊C8×C181C22semidirect
185. C181#3311semidirect
192. #476D181semidirect
209. C4⋊Q8C2×D181semidirect
229. #106C2×D181semidirect
230. #106C2×D181semidirect
231. C4⋊C8C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260420032
#260419242
#260416412
#260416232
#260416052
#260415382
#260415092
#260415022
#260414422
#260414312
#260413792
#260413492
#260412822
#260412722
#476×C1812
#3311181