Finite Group Databasebeta

← #540×D149 #34058045

Subgroups — #540×D149 #34058045

Order 19072.

1260 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750231C211yesmaximal, characteristic, complemented
2#23750230C211yesmaximal, characteristic, complemented
3#23750229C211yesmaximal, characteristic, complemented
4#23750228C212yesmaximal, complemented
5#23750227C214yesmaximal, complemented
6#23750226C212yesmaximal, complemented
7#23750225C214yesmaximal, complemented
8#127×D149C211yesmaximal, characteristic, complemented
9#125×D149C211yesmaximal, characteristic, complemented
10#123×D149C214yesmaximal, complemented
11#121×D149C212yesmaximal, complemented
12#121×D149C214yesmaximal, complemented
13C4×D4×D149C212yesmaximal, complemented
14#117×D149C211yesmaximal, characteristic, complemented
15#540×C149C211yesmaximal, characteristic, complemented
16C2×D4×D149C2212yes—
17C2×D4×D149C2214yes—
18C2×D4×D149C2214yes—
19C22×C4×D149C2211yescharacteristic
20C22×C4×D149C2214yes—
21#18011908C2211yescharacteristic, complemented
22#18011907C2214yescomplemented
23#18011907C2212yescomplemented
24#18011903C2211yescharacteristic, complemented
25#18011902C2212yescomplemented
26#18011901C2214yescomplemented
27#18011896C2214yescomplemented
28#18011896C2214yescomplemented
29#18011895C2214yescomplemented
30#18011894C2214yescomplemented
31#18011893C2214yescomplemented
32#18011893C2214yescomplemented
33#18011892C2214yescomplemented
34#18011886C2212yescomplemented
35#18011886C2214yescomplemented
36#18011885C2214yescomplemented
37#18011885C2212yescomplemented
38#18011884C2214yescomplemented
39#18011884C2214yescomplemented
40#18011884C2214yescomplemented
41#18011883C2214yescomplemented
42#18011883C2214yescomplemented
43#18011883C2214yescomplemented
44#18011882C2214yescomplemented
45#18011882C2212yescomplemented
46C4×D596C2212yescomplemented
47D4×Dic149C2212yescomplemented
48#18011873C2212yescomplemented
49C4×C22⋊D149C2214yescomplemented
50#18011871C2214yescomplemented
51#18011870C2211yescharacteristic, complemented
52#18011869C2212yescomplemented
53#18011868C2211yescharacteristic, complemented
54#18011868C2211yescharacteristic, complemented
55#18011867C2212yescomplemented
56C4⋊C4×D149C2212yes—
57C4⋊C4×D149C2214yes—
58C4⋊C4×D149C2212yes—
59C22⋊C4×D149C2212yes—
60C22⋊C4×D149C2214yes—
61C22⋊C4×D149C2214yes—
62C42×D149C2211yescharacteristic
63C42×D149C2211yescharacteristic
64#127×C149C2211yescharacteristic, complemented
65#125×C149C2211yescharacteristic, complemented
66#123×C149C2214yescomplemented
67#121×C149C2214yescomplemented
68#121×C149C2212yescomplemented
69C4×D4×C149C2212yescomplemented
70#117×C149C2211yescharacteristic, complemented
71C23×D149C2311yescharacteristic
72C23×D149C2314yes—
73C2×D596C2312yes—
74C2×D596C2314yes—
75C2×D596C2314yes—
76C2×C22⋊D149C2314yes—
77C2×C22⋊D149C2314yes—
78C2×C22⋊D149C2314yes—
79C2×C22⋊D149C2314yes—
80C2×C22⋊D149C2314yes—
81D4×D149—28no—
82D4×D149—48no—
83D4×D149—48no—
84C22×Dic149C2311yescharacteristic
85C22×Dic149C2314yes—
86C2×C4×D149—24no—
87C2×C4×D149—48no—
88C2×C4×D149C2312yes—
89C2×C4×D149C2314yes—
90C2×C4×D149C2311yescharacteristic
91C2×C4×D149C2311yescharacteristic
92C2×C4×D149C2311yescharacteristic
93C2×C4×D149C2312yes—
94C2×C4×D149C2314yes—
95C2×C4×D149C2314yes—
96C2×C4×D149C2311yescharacteristic
97C4⋊Dic149C2312yes—
98C4⋊Dic149C2312yes—
99C4⋊Dic149C2314yes—
100#14558715C2312yes—
101#14558715C2312yes—
102#14558715C2314yes—
103#14558715C2314yes—
104#14558715C2314yes—
105C22⋊Dic149C2312yes—
106C22⋊Dic149C2314yes—
107C22⋊Dic149C2314yes—
108#14558713C2312yes—
109#14558713C2312yes—
110#14558713C2314yes—
111#14558713C2314yes—
112#14558713C2314yes—
113#14558713C2314yes—
114C4×Dic149C2312yes—
115C4×Dic149C2311yescharacteristic
116C4×Dic149C2312yes—
117C4×Dic149C2311yescharacteristic
118C2×D4×C149C2312yes—
119C2×D4×C149C2314yes—
120C2×D4×C149C2314yes—
121C22×C4×C149C2311yescharacteristic
122C22×C4×C149C2314yes—
123C4⋊C4×C149C2312yes—
124C4⋊C4×C149C2312yes—
125C4⋊C4×C149C2314yes—
126C22⋊C4×C149C2312yes—
127C22⋊C4×C149C2314yes—
128C22⋊C4×C149C2314yes—
129C42×C149C2311yescharacteristic
130C42×C149C2311yescharacteristic
131C22×D149—22no—
132C22×D149—28no—
133C22×D149—28no—
134C22×D149—24no—
135C22×D149—28no—
136C22×D149C2411yescharacteristic
137C22×D149C2414yes—
138C22×D149C2411yescharacteristic
139D596—24no—
140D596—44no—
141D596—44no—
142C22⋊D149—28no—
143C22⋊D149—44no—
144C22⋊D149—44no—
145C22⋊D149—44no—
146C22⋊D149—44no—
147C2×Dic149—22no—
148C2×Dic149—44no—
149C2×Dic149C2412yes—
150C2×Dic149C2414yes—
151C2×Dic149C2411yescharacteristic
152C2×Dic149C2412yes—
153C2×Dic149C2411yescharacteristic
154C4×D149—22no—
155C4×D149—24no—
156C4×D149—28no—
157C4×D149—24no—
158C4×D149—22no—
159C4×D149—22no—
160C4×D149—44no—
161C4×D149—44no—
162C4×D149#4114yes—
163C23×C149C2411yescharacteristic
164C23×C149C2414yes—
165D4×C149—24no—
166D4×C149—44no—
167D4×C149—44no—
168C2×C4×C149—22no—
169C2×C4×C149—44no—
170C2×C4×C149C2412yes—
171C2×C4×C149C2414yes—
172C2×C4×C149C2411yescharacteristic
173C2×C4×C149C2412yes—
174C2×C4×C149C2411yescharacteristic
175C22×C149—21no—
176C22×C149—24no—
177C22×C149—24no—
178C22×C149—22no—
179C22×C149—24no—
180C22×C149C2511yescharacteristic
181C2×D149—21no—
182C2×D149—24no—
183C2×D149—24no—
184C2×D149—22no—
185C2×D149—24no—
186C2×D149—44no—
187C2×D149—416no—
188C2×D149C2×#4112yes—
189C2×D149H(5,𝔽2)14yes—
190C4×C149—21no—
191C4×C149—22no—
192C4×C149—24no—
193C4×C149—22no—
194C4×C149C2×#4112yes—
195Dic149—21no—
196Dic149—22no—
197Dic149—24no—
198Dic149—22no—
199Dic149C2×#4112yes—
200C2×C149—41no—
201C2×C149—44no—
202C2×C149C22×#4111yescharacteristic
203C2×C149C2×H(5,𝔽2)12yes—
204D149—41no—
205D149—44no—
206D149#54014yesdirect product factor
207C149C2×#54011yescharacteristic, complemented, Sylow
208C2×#540—1491nomaximal, Sylow
209#540—1491no—
210#540—1491no—
211#540—1494no—
212#540—1494no—
213#540—1492no—
214#540—1492no—
215#540—1491no—
216#540D14911yescharacteristic, direct product factor
217C2×#127—1491no—
218C2×#125—1491no—
219C2×#123—1494no—
220C2×#121—1494no—
221C2×#121—1492no—
222C2×C4×D4—1492no—
223C2×#117—1491no—
224C22×D4—1492no—
225C22×D4—1494no—
226C22×D4—1494no—
227C23×C4—1491no—
228C23×C4—1494no—
229#127—1494no—
230#127—1492no—
231#127—1491no—
232#127C2×D14911yescharacteristic, complemented
233#125—1494no—
234#125—1492no—
235#125—1491no—
236#125C2×D14911yescharacteristic, complemented
237#123—1494no—
238#123—1494no—
239#123—1494no—
240#123—1494no—
241#123—1494no—
242#123—1494no—
243#123—1494no—
244#123C2×D14914yescomplemented
245#121—1494no—
246#121—1492no—
247#121—1494no—
248#121—1494no—
249#121—1494no—
250#121—1494no—
251#121—1492no—
252#121—1494no—
253#121—1492no—
254#121—1494no—
255#121—1494no—
256#121—1494no—
257#121C2×D14914yescomplemented
258#121C2×D14912yescomplemented
259C4×D4—1492no—
260C4×D4—1494no—
261C4×D4—1492no—
262C4×D4—1494no—
263C4×D4—1492no—
264C4×D4C2×D14912yescomplemented
265#117—1491no—
266#117—1492no—
267#117—1492no—
268#117—1491no—
269#117—1491no—
270#117C2×D14911yescharacteristic, complemented
271C2×C4⋊C4—1492no—
272C2×C4⋊C4—1492no—
273C2×C4⋊C4—1494no—
274C2×C22⋊C4—1492no—
275C2×C22⋊C4—1494no—
276C2×C22⋊C4—1494no—
277C2×C42—1491no—
278C2×C42—1491no—
279C24—1491no—
280C24—1494no—
281C2×D4—2988no—
282C2×D4—5968no—
283C2×D4—5968no—
284C2×D4—1494no—
285C2×D4—1494no—
286C2×D4—1494no—
287C2×D4—1494no—
288C2×D4—1494no—
289C2×D4—1492no—
290C2×D4—1494no—
291C2×D4—1494no—
292C2×D4C22×D14912yes—
293C2×D4C22×D14914yes—
294C2×D4C22×D14914yes—
295C22×C4—2984no—
296C22×C4—5968no—
297C22×C4—1491no—
298C22×C4—1492no—
299C22×C4—1492no—
300C22×C4—1491no—
301C22×C4—1494no—
302C22×C4—1491no—
303C22×C4—1491no—
304C22×C4—1494no—
305C22×C4—1494no—
306C22×C4—1494no—
307C22×C4—1491no—
308C22×C4C22×D14911yescharacteristic
309C22×C4C22×D14914yes—
310C4⋊C4—1492no—
311C4⋊C4—1492no—
312C4⋊C4—1492no—
313C4⋊C4—1494no—
314C4⋊C4—1492no—
315C4⋊C4—1494no—
316C4⋊C4—1494no—
317C4⋊C4—1494no—
318C4⋊C4C22×D14912yes—
319C4⋊C4C22×D14912yes—
320C4⋊C4C22×D14914yes—
321C22⋊C4—1492no—
322C22⋊C4—1494no—
323C22⋊C4—1494no—
324C22⋊C4—1492no—
325C22⋊C4—1492no—
326C22⋊C4—1494no—
327C22⋊C4—1494no—
328C22⋊C4—1494no—
329C22⋊C4—1494no—
330C22⋊C4C22×D14912yes—
331C22⋊C4C22×D14914yes—
332C22⋊C4C22×D14914yes—
333C42—1491no—
334C42—1492no—
335C42—1491no—
336C42—1492no—
337C42C22×D14911yescharacteristic
338C42C22×D14911yescharacteristic
339C23—2982no—
340C23—2988no—
341C23—2988no—
342C23—2984no—
343C23—2988no—
344C23—1491no—
345C23—1494no—
346C23—1491no—
347C23C23×D14911yescharacteristic
348C23C23×D14914yes—
349D4—24no—
350D4—44no—
351D4—44no—
352D4—2988no—
353D4—2984no—
354D4—5964no—
355D4—5964no—
356D4—5964no—
357D4—5964no—
358D4—5964no—
359D4—5964no—
360C2×C4—22no—
361C2×C4—44no—
362C2×C4—2982no—
363C2×C4—2984no—
364C2×C4—2988no—
365C2×C4—2984no—
366C2×C4—2982no—
367C2×C4—2982no—
368C2×C4—2982no—
369C2×C4—5964no—
370C2×C4—5964no—
371C2×C4—5964no—
372C2×C4—1492no—
373C2×C4—1492no—
374C2×C4—1491no—
375C2×C4—1494no—
376C2×C4—1491no—
377C2×C4—1494no—
378C2×C4C23×D14912yes—
379C2×C4C23×D14912yes—
380C2×C4C23×D14911yescharacteristic
381C2×C4C23×D14914yes—
382C2×C4C23×D14911yescharacteristic
383C22—21no—
384C22—24no—
385C22—24no—
386C22—22no—
387C22—24no—
388C22—2981no—
389C22—2984no—
390C22—2984no—
391C22—2982no—
392C22—2984no—
393C22—5964no—
394C22—59616no—
395C22—1492no—
396C22—1494no—
397C22C24×D14911yescharacteristic
398C4—21no—
399C4—22no—
400C4—24no—
401C4—22no—
402C4—2981no—
403C4—2982no—
404C4—2984no—
405C4—2982no—
406C4—1492no—
407C4#41×D14912yes—
408C2—41no—
409C2—44no—
410C2—5961no—
411C2—5964no—
412C2—1494no—
413C2C2×#41×D14911yescharacteristic
414C2H(5,𝔽2)×D14912yes—
subgroupG/H
center, FrattiniC22C24×D149
commutator, socle, cosocleC22×C149C25
Fitting#540×C149C2
hypercenter#540D149
hypocenterC149C2×#540
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #23750231C2semidirect
2. #23750230C2semidirect
3. #23750229C2semidirect
4. #23750228C2semidirect
5. #23750227C2semidirect
6. #23750226C2semidirect
7. #23750225C2semidirect
8. #127×D149C2semidirect
9. #125×D149C2semidirect
10. #123×D149C2semidirect
11. #121×D149C2semidirect
12. #121×D149C2semidirect
13. C4×D4×D149C2semidirect
14. #117×D149C2semidirect
15. #540×C149C2semidirect
21. #18011908C22semidirect
22. #18011907C22semidirect
23. #18011907C22semidirect
24. #18011903C22semidirect
25. #18011902C22semidirect
26. #18011901C22semidirect
27. #18011896C22semidirect
28. #18011896C22semidirect
29. #18011895C22semidirect
30. #18011894C22semidirect
31. #18011893C22semidirect
32. #18011893C22semidirect
33. #18011892C22semidirect
34. #18011886C22semidirect
35. #18011886C22semidirect
36. #18011885C22semidirect
37. #18011885C22semidirect
38. #18011884C22semidirect
39. #18011884C22semidirect
40. #18011884C22semidirect
41. #18011883C22semidirect
42. #18011883C22semidirect
43. #18011883C22semidirect
44. #18011882C22semidirect
45. #18011882C22semidirect
46. C4×D596C22semidirect
47. D4×Dic149C22semidirect
48. #18011873C22semidirect
49. C4×C22⋊D149C22semidirect
50. #18011871C22semidirect
51. #18011870C22semidirect
52. #18011869C22semidirect
53. #18011868C22semidirect
54. #18011868C22semidirect
55. #18011867C22semidirect
64. #127×C149C22semidirect
65. #125×C149C22semidirect
66. #123×C149C22semidirect
67. #121×C149C22semidirect
68. #121×C149C22semidirect
69. C4×D4×C149C22semidirect
70. #117×C149C22semidirect
206. D149#540direct (N × H)
207. C149C2×#540semidirect
216. #540D149direct (N × H)
232. #127C2×D149semidirect
236. #125C2×D149semidirect
244. #123C2×D149semidirect
257. #121C2×D149semidirect
258. #121C2×D149semidirect
264. C4×D4C2×D149semidirect
270. #117C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502312
#237502302
#237502292
#237502282
#237502272
#237502262
#237502252
#127×D1492
#125×D1492
#123×D1492
#121×D1492
C4×D4×D1492
#117×D1492
#540×C1492
C2×#540149