Finite Group Databasebeta

← #37545934

Subgroups — #37545934

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#26041967C211yesmaximal, characteristic, complemented
2#26041924C211yesmaximal, characteristic
3#26041636C211yesmaximal, characteristic, complemented
4#26041622C211yesmaximal, characteristic, complemented
5#26041599C211yesmaximal, characteristic, complemented
6#26041538C211yesmaximal, characteristic, complemented
7#26041526C211yesmaximal, characteristic, complemented
8#26041502C211yesmaximal, characteristic, complemented
9#26041442C211yesmaximal, characteristic, complemented
10#26041431C211yesmaximal, characteristic, complemented
11C4×#15668437C211yesmaximal, characteristic, complemented
12#26041356C211yesmaximal, characteristic, complemented
13#26041282C211yesmaximal, characteristic, complemented
14#26041277C211yesmaximal, characteristic, complemented
15#478×C181C211yesmaximal, characteristic, complemented
16C2×#15668448C2211yescharacteristic
17C2×D4×D181C2211yescharacteristic
18C2×Dic724C2211yescharacteristic, complemented
19C2×#15668438C2211yescharacteristic
20C2×#15668437C2211yescharacteristic
21C2×#15668432C2211yescharacteristic
22C2×#15668432C2211yescharacteristic, complemented
23#19153811—21no—
24#19153807—21no—
25#19153804C2211yescharacteristic
26#19153801—21no—
27#19153800—21no—
28#19153796C2211yescharacteristic
29#19153796C2211yescharacteristic
30#19153796C2211yescharacteristic, complemented
31#19153791C2211yescharacteristic
32#19153790—21no—
33#19153786—21no—
34C4×Dic362C2211yescharacteristic, complemented
35C4×D724C2211yescharacteristic
36#19153774—21no—
37#19153774C2211yescharacteristic
38C4⋊C4×D181C2211yescharacteristic, complemented
39C2×#15668426—21no—
40#19153747C2211yescharacteristic, 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
51C4×#13089678C2211yescharacteristic, complemented
52#125×C181C2211yescharacteristic, complemented
53C4×D4×C181C2211yescharacteristic
54#107×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×D181—21no—
73C2×C4×D181C2311yescharacteristic
74C2×C4×D181C2311yescharacteristic
75Dic724—41no—
76#15668438—41no—
77#15668437—22no—
78#15668432—41no—
79#15668432—41no—
80C2×#13089678C2311yescharacteristic
81C2×#13089678C2311yescharacteristic
82C4⋊Dic181—21no—
83C4⋊Dic181—21no—
84C4⋊Dic181—21no—
85C4⋊Dic181D411yescharacteristic
86C4⋊Dic181C2311yescharacteristic
87#15668428—21no—
88#15668428—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426D411yescharacteristic
97#15668426D411yescharacteristic
98C4×Dic181—21no—
99C4×Dic181—21no—
100C2×D4×C181C2311yescharacteristic
101C22×C4×C181—21no—
102C2×C8×C181C2311yescharacteristic
103C2×C8×C181C2311yescharacteristic
104C4⋊C4×C181—21no—
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—
137C4×D181—42no—
138#13089678—21no—
139#13089678—21no—
140C23×C181—21no—
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#332311yescharacteristic, complemented, Sylow
186#3323—1811nomaximal, Sylow
187#552—1811no—
188#546—1811no—
189#488—1811no—
190#485—1811no—
191#481—1811no—
192#478D18111yescharacteristic, complemented
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#125C2×D18111yescharacteristic, complemented
212#124—1811no—
213#123—3621no—
214#123—3621no—
215C22⋊Q8—1811no—
216C22⋊Q8—1811no—
217C22⋊Q8—1811no—
218#121—3621no—
219#121—1811no—
220#120—3621no—
221C4×Q8—1811no—
222C4×D4—1811no—
223C4×D4C2×D18111yescharacteristic
224#117—3621no—
225#117—1811no—
226C2×C4⋊C4—1811no—
227C2×C22⋊C4—3621no—
228#107C2×D18111yescharacteristic, complemented
229#106—1811no—
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—
244C4×C8—1811no—
245C24—3621no—
246#41—3622no—
247#41—7241no—
248C2×Q8—1811no—
249C2×Q8—1811no—
250C2×D4—3621no—
251C2×D4—3622no—
252C2×D4—3621no—
253C2×D4—3621no—
254C2×D4—1811no—
255C2×D4—1811no—
256C2×D4—7241no—
257C2×D4C22×D18111yescharacteristic
258C22×C4—21no—
259C22×C4—3621no—
260C22×C4—3621no—
261C22×C4—1811no—
262C22×C4—1811no—
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—21no—
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—3621no—
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—3621no—
295C42—3621no—
296C42C22×D18111yescharacteristic
297C23—21no—
298C23—3621no—
299C23—14481no—
300C23—1811no—
301C23—1811no—
302C23—7242no—
303C23—7242no—
304Q8—3621no—
305Q8—3621no—
306Q8—3621no—
307Q8—3621no—
308D4—21no—
309D4—3621no—
310D4—3621no—
311D4—14481no—
312D4—7241no—
313D4—7242no—
314D4—7242no—
315D4#1566845012yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—3621no—
321C2×C4—3621no—
322C2×C4—3621no—
323C2×C4—3621no—
324C2×C4—3621no—
325C2×C4—3621no—
326C2×C4—3621no—
327C2×C4—1811no—
328C2×C4—1811no—
329C2×C4—7242no—
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#2604207611yescharacteristic
370C2#2604208911yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#478×C181C2
socleC22×C181C22×D4
prime radical#26041924C2
hypercenter#478D181
hypocenterC181#3323
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #26041967C2semidirect
3. #26041636C2semidirect
4. #26041622C2semidirect
5. #26041599C2semidirect
6. #26041538C2semidirect
7. #26041526C2semidirect
8. #26041502C2semidirect
9. #26041442C2semidirect
10. #26041431C2semidirect
11. C4×#15668437C2semidirect
12. #26041356C2semidirect
13. #26041282C2semidirect
14. #26041277C2semidirect
15. #478×C181C2semidirect
18. C2×Dic724C22semidirect
22. C2×#15668432C22semidirect
30. #19153796C22semidirect
34. C4×Dic362C22semidirect
38. C4⋊C4×D181C22semidirect
40. #19153747C22semidirect
41. #19153741C22semidirect
42. #19153739C22semidirect
43. #19153739C22semidirect
44. #19153739C22semidirect
50. #19153728C22semidirect
51. C4×#13089678C22semidirect
52. #125×C181C22semidirect
54. #107×C181C22semidirect
55. #106×C181C22semidirect
56. C4⋊C8×C181C22semidirect
185. C181#3323semidirect
192. #478D181semidirect
211. #125C2×D181semidirect
228. #107C2×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
#260419672
#260419242
#260416362
#260416222
#260415992
#260415382
#260415262
#260415022
#260414422
#260414312
C4×#156684372
#260413562
#260412822
#260412772
#478×C1812
#3323181