Finite Group Databasebeta

← #37544074

Subgroups — #37544074

Order 23168.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041909C211yesmaximal, characteristic, complemented
2#26041847C211yesmaximal, characteristic
3#26041645C211yesmaximal, characteristic, complemented
4#26041642C211yesmaximal, characteristic, complemented
5#26041640C211yesmaximal, characteristic, complemented
6#26041638C211yesmaximal, characteristic, complemented
7#26041635C211yesmaximal, characteristic, complemented
8#26041626C211yesmaximal, characteristic, complemented
9#26041624C211yesmaximal, characteristic, complemented
10#26041282C211yesmaximal, characteristic, complemented
11#26041279C211yesmaximal, characteristic, complemented
12#26041274C211yesmaximal, characteristic, complemented
13#102×D181C211yesmaximal, characteristic, complemented
14#26041233C211yesmaximal, characteristic, complemented
15#488×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×D4×D181C2211yescharacteristic
18C2×#15668432C2211yescharacteristic
19C2×C8×D181C2211yescharacteristic
20#19153816C2211yescharacteristic, complemented
21#19153815—21no—
22#19153815C2211yescharacteristic, complemented
23#19153813C2211yescharacteristic
24#19153812C2211yescharacteristic
25#19153807C2211yescharacteristic, complemented
26#19153806—21no—
27#19153805C2211yescharacteristic
28#19153796—21no—
29#19153794—21no—
30#19153789—21no—
31#19153789—21no—
32#19153786—21no—
33#19153786—21no—
34#19153774C2211yescharacteristic
35#19153773C2211yescharacteristic
36C4⋊C4×D181C2211yescharacteristic
37#19153740C2211yescharacteristic, complemented
38#19153740C2211yescharacteristic, complemented
39#19153738C2211yescharacteristic
40#19153738C2211yescharacteristic
41#19153738C2211yescharacteristic, complemented
42#19153738C2211yescharacteristic, complemented
43#19153737C2211yescharacteristic
44#19153737C2211yescharacteristic
45#19153736C2211yescharacteristic
46#19153736C2211yescharacteristic
47#19153736C2211yescharacteristic, complemented
48#19153736C2211yescharacteristic, complemented
49#19153727C2211yescharacteristic, complemented
50#19153726C2211yescharacteristic, complemented
51C8×Dic181C2211yescharacteristic, complemented
52#125×C181C2211yescharacteristic, complemented
53#124×C181C2211yescharacteristic
54#103×C181C2211yescharacteristic, complemented
55#103×C181C2211yescharacteristic, complemented
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C4×C8×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60#15668450—22no—
61#15668450—22no—
62C2×Dic362—21no—
63C2×Dic362—21no—
64C2×D724—21no—
65C2×D724—21no—
66C2×D724—21no—
67C2×D724C2311yescharacteristic
68C2×D724C2311yescharacteristic
69C2×C22⋊D181—21no—
70C2×C22⋊D181—21no—
71C2×C22⋊D181—21no—
72D4×D181—22no—
73D4×D181—22no—
74C2×C4×D181—21no—
75C2×C4×D181—21no—
76C2×C4×D181C2311yescharacteristic
77#15668432—22no—
78C2×#13089678C2311yescharacteristic
79C2×#13089678C2311yescharacteristic
80C8×D181—22no—
81C4⋊Dic181—21no—
82C4⋊Dic181—21no—
83C4⋊Dic181C2311yescharacteristic
84C4⋊Dic181C2311yescharacteristic
85#15668428—21no—
86#15668428—21no—
87#15668428—21no—
88#15668428D411yescharacteristic
89#15668428D411yescharacteristic
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426D411yescharacteristic
94#15668426D411yescharacteristic
95C4×Dic181—21no—
96C4×Dic181C2311yescharacteristic
97C2×Q8×C181C2311yescharacteristic
98C2×D4×C181C2311yescharacteristic
99C2×C8×C181C2311yescharacteristic
100C2×C8×C181C2311yescharacteristic
101C4⋊C4×C181—21no—
102C4⋊C4×C181—21no—
103C4⋊C4×C181C2311yescharacteristic
104C4⋊C4×C181C2311yescharacteristic
105C22⋊C4×C181—21no—
106C22⋊C4×C181—21no—
107C42×C181C2311yescharacteristic
108C22×D181—21no—
109C22×D181—21no—
110C22×D181—42no—
111C22×D181—81no—
112C22×D181—81no—
113C22×D181C2×D411yescharacteristic
114Dic362—81no—
115Dic362—81no—
116D724—21no—
117D724—21no—
118D724—21no—
119D724—21no—
120D724—42no—
121D724—81no—
122D724—81no—
123C22⋊D181—42no—
124C22⋊D181—81no—
125C22⋊D181—81no—
126C2×Dic181—21no—
127C2×Dic181—21no—
128C2×Dic181C2×D411yescharacteristic
129C2×Dic181C2×D411yescharacteristic
130C2×Dic181C2×D411yescharacteristic
131C4×D181—42no—
132C4×D181—81no—
133C4×D181#4112yes—
134C4×D181#4112yes—
135#13089678—21no—
136#13089678—21no—
137C23×C181—21no—
138Q8×C181—21no—
139Q8×C181—21no—
140D4×C181—21no—
141D4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181C2×D411yescharacteristic
146C2×C4×C181C2×D411yescharacteristic
147C2×C4×C181C2411yescharacteristic
148C8×C181—21no—
149C8×C181—21no—
150C22×C181—41no—
151C22×C181—41no—
152C22×C181—41no—
153C22×C181C22×D411yescharacteristic
154C2×D181—21no—
155C2×D181—21no—
156C2×D181—41no—
157C2×D181—41no—
158C2×D181—41no—
159C2×D181—41no—
160C2×D181—41no—
161C2×D181—41no—
162C2×D181—84no—
163C2×D181#12412yes—
164C4×C181—21no—
165C4×C181—21no—
166C4×C181—41no—
167C4×C181—41no—
168C4×C181—41no—
169C4×C181C2×#4111yescharacteristic
170C4×C181C2×#4111yescharacteristic
171Dic181—21no—
172Dic181—21no—
173Dic181—41no—
174Dic181—41no—
175Dic181#12412yes—
176C2×C181—81no—
177C2×C181C2×#12411yescharacteristic
178C2×C181#57611yescharacteristic
179C2×C181#57711yescharacteristic
180D181—22no—
181D181—81no—
182D181—81no—
183C181#313611yescharacteristic, complemented, Sylow
184#3136—1811nomaximal, Sylow
185#544—1811no—
186#535—1811no—
187#490—1811no—
188#490—1811no—
189#489—1811no—
190#489—1811no—
191#488—1811no—
192#488D18111yescharacteristic, complemented
193#486—1811no—
194#486—1811no—
195#418—1811no—
196#417—1811no—
197#416—1811no—
198C2×#102—1811no—
199#405—1811no—
200C2×#41—1811no—
201C22×D4—1811no—
202C2×M16—1811no—
203C22×C8—1811no—
204C4⋊Q8—3621no—
205C4⋊Q8—1811no—
206C4⋊Q8—1811no—
207#127—1811no—
208#127—1811no—
209#125—3621no—
210#125—1811no—
211#125C2×D18111yescharacteristic, complemented
212#124—1811no—
213#124C2×D18111yescharacteristic
214C22⋊Q8—3621no—
215C22⋊Q8—3621no—
216#121—3621no—
217#121—3621no—
218#120—3621no—
219#120—3621no—
220#117—1811no—
221#117—1811no—
222C2×C4⋊C4—1811no—
223#103—1811no—
224#103—1811no—
225#103C2×D18111yescharacteristic, complemented
226#103C2×D18111yescharacteristic, complemented
227#102—1811no—
228#102—1811no—
229#102—1811no—
230#102—1811no—
231#102—1811no—
232#102—1811no—
233#102—1811no—
234#102—1811no—
235#102—1811no—
236#102—1811no—
237#102C2×D18111yescharacteristic
238#102C2×D18111yescharacteristic
239#97—1811no—
240#97—1811no—
241C4×C8—1811no—
242C4×C8C2×D18111yescharacteristic, complemented
243C24—3621no—
244#41—3622no—
245#41—3622no—
246C2×Q8—3621no—
247C2×Q8—3621no—
248C2×Q8C22×D18111yescharacteristic
249C2×D4—3621no—
250C2×D4—3622no—
251C2×D4—3622no—
252C2×D4—3621no—
253C2×D4—3621no—
254C2×D4—3621no—
255C2×D4—3621no—
256C2×D4—3621no—
257C2×D4—1811no—
258C2×D4—1811no—
259C2×D4C22×D18111yescharacteristic
260C22×C4—3621no—
261C22×C4—3621no—
262C22×C4—1811no—
263M16—3622no—
264C2×C8—3622no—
265C2×C8—1811no—
266C2×C8—1811no—
267C2×C8C22×D18111yescharacteristic
268C2×C8C22×D18111yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—3621no—
272C4⋊C4—3621no—
273C4⋊C4—3621no—
274C4⋊C4—3621no—
275C4⋊C4—3621no—
276C4⋊C4—1811no—
277C4⋊C4—1811no—
278C4⋊C4—1811no—
279C4⋊C4—1811no—
280C4⋊C4C22×D18111yescharacteristic
281C4⋊C4C22×D18111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—3621no—
285C22⋊C4—3621no—
286C22⋊C4—3621no—
287C22⋊C4—1811no—
288C22⋊C4—1811no—
289C42—3621no—
290C42—1811no—
291C42C22×D18111yescharacteristic
292C23—21no—
293C23—3621no—
294C23—3621no—
295C23—14481no—
296C23—14481no—
297C23—1811no—
298C23—7242no—
299Q8—21no—
300Q8—21no—
301Q8—14481no—
302Q8—14481no—
303D4—21no—
304D4—21no—
305D4—3621no—
306D4—3621no—
307D4—3621no—
308D4—3621no—
309D4—14481no—
310D4—14481no—
311D4—14481no—
312D4—14481no—
313D4—7242no—
314D4—7242no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—3621no—
319C2×C4—3621no—
320C2×C4—14481no—
321C2×C4—1811no—
322C2×C4—1811no—
323C2×C4—1811no—
324C2×C4—1812no—
325C2×C4—1812no—
326C2×C4—7242no—
327C2×C4D4×D18111yescharacteristic
328C2×C4D4×D18111yescharacteristic
329C2×C4C23×D18111yescharacteristic
330C8—21no—
331C8—21no—
332C8—3621no—
333C8—3621no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—3621no—
338C22—3621no—
339C22—14484no—
340C22—1812no—
341C22—7241no—
342C22—7241no—
343C22—7241no—
344C22—7241no—
345C22—7241no—
346C22—7241no—
347C22C2×D4×D18111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—3621no—
354C4—3621no—
355C4—1812no—
356C4—7241no—
357C4—7241no—
358C4#41×D18111yescharacteristic
359C4#41×D18111yescharacteristic
360C2—81no—
361C2—3622no—
362C2—14481no—
363C2—14481no—
364C2#124×D18111yescharacteristic
365C2#2604208111yescharacteristic
366C2#2604208611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#488×C181C2
socleC22×C181C22×D4
prime radical#26041847C2
hypercenter#488D181
hypocenterC181#3136
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #26041909C2semidirect
3. #26041645C2semidirect
4. #26041642C2semidirect
5. #26041640C2semidirect
6. #26041638C2semidirect
7. #26041635C2semidirect
8. #26041626C2semidirect
9. #26041624C2semidirect
10. #26041282C2semidirect
11. #26041279C2semidirect
12. #26041274C2semidirect
13. #102×D181C2semidirect
14. #26041233C2semidirect
15. #488×C181C2semidirect
20. #19153816C22semidirect
22. #19153815C22semidirect
25. #19153807C22semidirect
37. #19153740C22semidirect
38. #19153740C22semidirect
41. #19153738C22semidirect
42. #19153738C22semidirect
47. #19153736C22semidirect
48. #19153736C22semidirect
49. #19153727C22semidirect
50. #19153726C22semidirect
51. C8×Dic181C22semidirect
52. #125×C181C22semidirect
54. #103×C181C22semidirect
55. #103×C181C22semidirect
58. C4×C8×C181C22semidirect
183. C181#3136semidirect
192. #488D181semidirect
211. #125C2×D181semidirect
225. #103C2×D181semidirect
226. #103C2×D181semidirect
242. C4×C8C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419092
#260418472
#260416452
#260416422
#260416402
#260416382
#260416352
#260416262
#260416242
#260412822
#260412792
#260412742
#102×D1812
#260412332
#488×C1812
#3136181