Finite Group Databasebeta

← #34056176

Subgroups — #34056176

Order 19072.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011939C211yesmaximal, characteristic, complemented
2C22×D1192C211yesmaximal, characteristic, complemented
3#23750271C211yesmaximal, characteristic, complemented
4D4×D596C211yesmaximal, characteristic, complemented
5#23750014C211yesmaximal, characteristic, complemented
6#23749878C211yesmaximal, characteristic, complemented
7#23749854C211yesmaximal, characteristic, complemented
8#23749841C211yesmaximal, characteristic, complemented
9#23749821C211yesmaximal, characteristic, complemented
10#23749778C211yesmaximal, characteristic, complemented
11#23749772C211yesmaximal, characteristic, complemented
12#23749761C211yesmaximal, characteristic, complemented
13#23749761C211yesmaximal, characteristic, complemented
14#23749738C211yesmaximal, characteristic, complemented
15#435×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic, complemented
17C22×D596C2211yescharacteristic
18C22×D596C2211yescharacteristic, complemented
19C22×D596C2211yescharacteristic, complemented
20C2×D4×D149—21no—
21#18011939—24no—
22C2×#14558725C2211yescharacteristic, complemented
23C2×#14558725C2211yescharacteristic, complemented
24C2×#14558725C2211yescharacteristic, complemented
25C2×D1192—24no—
26C2×D1192C2211yescharacteristic
27C2×D1192C2211yescharacteristic
28C2×D1192C2211yescharacteristic, complemented
29C2×D1192C2211yescharacteristic, complemented
30C2×D1192C2211yescharacteristic, complemented
31C2×D1192C2211yescharacteristic, complemented
32#18011908C2211yescharacteristic, complemented
33#18011899C2211yescharacteristic, complemented
34#18011896—21no—
35#18011890C2211yescharacteristic, complemented
36#18011886—21no—
37#18011885C2211yescharacteristic
38#18011885C2211yescharacteristic, complemented
39#18011885C2211yescharacteristic, complemented
40#18011884—21no—
41#18011881—21no—
42#18011881—21no—
43#18011879—21no—
44C4×D596C2211yescharacteristic, complemented
45C4×D596C2211yescharacteristic, complemented
46C22⋊C4×D149—21no—
47#18011843C2211yescharacteristic, complemented
48#18011836C2211yescharacteristic, complemented
49#18011833C2211yescharacteristic, complemented
50#18011833C2211yescharacteristic, complemented
51#18011833C2211yescharacteristic, complemented
52#18011833C2211yescharacteristic, complemented
53#18011833C2211yescharacteristic, complemented
54C2×M16×C149C2211yescharacteristic, complemented
55C22×C8×C149C2211yescharacteristic, complemented
56C4×D4×C149C2211yescharacteristic
57C4⋊C8×C149C2211yescharacteristic, complemented
58C22⋊C8×C149C2211yescharacteristic, complemented
59C22⋊C8×C149C2211yescharacteristic, complemented
60#97×C149C2211yescharacteristic, complemented
61C23×D149—21no—
62C23×D149—21no—
63C23×D149—21no—
64#14558736—22no—
65#14558736—41no—
66C2×Dic298C2311yescharacteristic
67C2×D596—22no—
68C2×D596—22no—
69C2×D596—22no—
70C2×D596—21no—
71C2×D596—21no—
72C2×D596—21no—
73C2×D596—21no—
74C2×D596—21no—
75C2×D596—41no—
76C2×D596—41no—
77C2×D596—41no—
78C2×D596C2311yescharacteristic
79C2×D596C2311yescharacteristic
80C2×D596C2311yescharacteristic
81C2×D596C2311yescharacteristic
82C2×D596C2311yescharacteristic
83C2×C22⋊D149—21no—
84C2×C22⋊D149—21no—
85C2×C22⋊D149—21no—
86C2×C22⋊D149—21no—
87D4×D149—44no—
88C2×C4×D149—21no—
89C2×C4×D149—21no—
90C2×C4×D149—21no—
91#14558725—22no—
92#14558725—22no—
93#14558725—41no—
94D1192—22no—
95D1192—22no—
96D1192—22no—
97D1192—22no—
98D1192—41no—
99D1192D414yescomplemented
100C4⋊Dic149C2311yescharacteristic
101C4⋊Dic149C2311yescharacteristic
102#14558715—21no—
103C22⋊Dic149—21no—
104#14558713—21no—
105#14558713—21no—
106#14558713—21no—
107#14558713—21no—
108#14558713—21no—
109#14558713—21no—
110#14558713—21no—
111C2×D4×C149D411yescharacteristic
112C22×C4×C149C2311yescharacteristic
113C22×C4×C149C2311yescharacteristic
114M16×C149—22no—
115C2×C8×C149—22no—
116C2×C8×C149C2311yescharacteristic
117C2×C8×C149C2311yescharacteristic
118C2×C8×C149C2311yescharacteristic
119C2×C8×C149C2311yescharacteristic
120C4⋊C4×C149D411yescharacteristic
121C22⋊C4×C149D411yescharacteristic
122C22⋊C4×C149D411yescharacteristic
123C42×C149C2311yescharacteristic
124C22×D149—21no—
125C22×D149—21no—
126C22×D149—21no—
127C22×D149—21no—
128C22×D149—21no—
129C22×D149—42no—
130C22×D149—42no—
131C22×D149—42no—
132C22×D149—42no—
133C22×D149—42no—
134C22×D149—42no—
135C22×D149—81no—
136C22×D149—81no—
137C22×D149—81no—
138Dic298—21no—
139Dic298—21no—
140D596—21no—
141D596—21no—
142D596—21no—
143D596—21no—
144D596—21no—
145D596—21no—
146D596—21no—
147D596—21no—
148D596—42no—
149D596—42no—
150D596—42no—
151D596—42no—
152D596—81no—
153D596C2×D412yes—
154D596C2×D412yescomplemented
155C22⋊D149—42no—
156C22⋊D149—42no—
157C22⋊D149—42no—
158C22⋊D149—81no—
159C2×Dic149—21no—
160C2×Dic149—21no—
161C2×Dic149—21no—
162C4×D149—42no—
163C4×D149—42no—
164C4×D149—81no—
165C23×C149C2×D411yescharacteristic
166C23×C149C2×D411yescharacteristic
167D4×C149—22no—
168C2×C4×C149—21no—
169C2×C4×C149—21no—
170C2×C4×C149—21no—
171C2×C4×C149—21no—
172C2×C4×C149C2×D411yescharacteristic
173C2×C4×C149C2×D411yescharacteristic
174C2×C4×C149C2×D411yescharacteristic
175C2×C4×C149C2×D411yescharacteristic
176C2×C4×C149C2411yescharacteristic
177C8×C149—21no—
178C8×C149—21no—
179C8×C149—21no—
180C8×C149C2×D412yescomplemented
181C22×C149—21no—
182C22×C149—21no—
183C22×C149—21no—
184C22×C149—21no—
185C22×C149—21no—
186C22×C149AGL(1,ℤ/8)12yescomplemented
187C22×C149C22×D411yescharacteristic
188C2×D149—22no—
189C2×D149—22no—
190C2×D149—41no—
191C2×D149—41no—
192C2×D149—41no—
193C2×D149—41no—
194C2×D149—41no—
195C2×D149—41no—
196C2×D149—41no—
197C2×D149—41no—
198C2×D149—41no—
199C2×D149—41no—
200C2×D149—41no—
201C2×D149—41no—
202C2×D149—41no—
203C2×D149—84no—
204C2×D149—84no—
205C2×D149—84no—
206C4×C149—21no—
207C4×C149—21no—
208C4×C149—21no—
209C4×C149—21no—
210C4×C149C22×D411yescharacteristic
211C4×C149H(5,𝔽2)11yescharacteristic
212Dic149—41no—
213Dic149—41no—
214Dic149—41no—
215C2×C149—22no—
216C2×C149—41no—
217C2×C149D4211yescharacteristic
218C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
219C2×C149#57611yescharacteristic
220D149—42no—
221D149—42no—
222D149—81no—
223D149—81no—
224D149—81no—
225C149#326411yescharacteristic, complemented, Sylow
226#3264—1491nomaximal, Sylow
227C2×AGL(1,ℤ/8)—1491no—
228C22×D8—1491no—
229#546—1491no—
230D42—1491no—
231#496—1491no—
232#469—1491no—
233#465—1491no—
234#463—1491no—
235#459—1491no—
236#450—1491no—
237#449—1491no—
238#447—1491no—
239#447—1491no—
240#442—1491no—
241#435D14911yescharacteristic, complemented
242C2×#41—1491no—
243C22×D4—2981no—
244C22×D4—1491no—
245C22×D4—1491no—
246C22×D4—1491no—
247AGL(1,ℤ/8)—2984no—
248C2×SD16—1491no—
249C2×SD16—1491no—
250C2×SD16—1491no—
251C2×D8—2984no—
252C2×D8—1491no—
253C2×D8—1491no—
254C2×D8—1491no—
255C2×D8—1491no—
256C2×D8—1491no—
257C2×D8—1491no—
258C2×M16C2×D14911yescharacteristic, complemented
259C22×C8C2×D14911yescharacteristic, complemented
260#127—1491no—
261#124—1491no—
262#123—2981no—
263C22⋊Q8—1491no—
264#121—2981no—
265#121—2981no—
266#121—1491no—
267#121—1491no—
268#121—1491no—
269#120—2981no—
270#120—2981no—
271#120—2981no—
272C4×D4—1491no—
273C4×D4—1491no—
274C4×D4C2×D14911yescharacteristic
275C2×C22⋊C4—2981no—
276#106—1491no—
277C4⋊C8C2×D14911yescharacteristic, complemented
278#103—1491no—
279#102—1491no—
280#102—1491no—
281#102—1491no—
282#102—1491no—
283#102—1491no—
284C22⋊C8C2×D14911yescharacteristic, complemented
285C22⋊C8C2×D14911yescharacteristic, complemented
286#97C2×D14911yescharacteristic, complemented
287C24—2981no—
288C24—2981no—
289C24—2981no—
290#41—2982no—
291#41—5961no—
292C2×Q8—1491no—
293C2×D4—2982no—
294C2×D4—2982no—
295C2×D4—2982no—
296C2×D4—2981no—
297C2×D4—2981no—
298C2×D4—2981no—
299C2×D4—2981no—
300C2×D4—2981no—
301C2×D4—2981no—
302C2×D4—2981no—
303C2×D4—2981no—
304C2×D4—2981no—
305C2×D4—5961no—
306C2×D4—5961no—
307C2×D4—5961no—
308C2×D4—5964no—
309C2×D4—1491no—
310C2×D4—1491no—
311C2×D4—1491no—
312C2×D4—1491no—
313C2×D4—1491no—
314C2×D4D59611yescharacteristic
315C22×C4—2981no—
316C22×C4—2981no—
317C22×C4—2981no—
318C22×C4C22×D14911yescharacteristic
319C22×C4C22×D14911yescharacteristic
320SD16—2982no—
321SD16—2982no—
322SD16—5961no—
323D8—2982no—
324D8—2982no—
325D8—2982no—
326D8—2982no—
327D8—5961no—
328D8—1494no—
329M16—22no—
330C2×C8—22no—
331C2×C8C22×D14911yescharacteristic
332C2×C8C22×D14911yescharacteristic
333C2×C8C22×D14911yescharacteristic
334C2×C8C22×D14911yescharacteristic
335C4⋊C4—2981no—
336C4⋊C4—1491no—
337C4⋊C4—1491no—
338C4⋊C4D59611yescharacteristic
339C22⋊C4—2981no—
340C22⋊C4—2981no—
341C22⋊C4—2981no—
342C22⋊C4—2981no—
343C22⋊C4—2981no—
344C22⋊C4—2981no—
345C22⋊C4—2981no—
346C22⋊C4—2981no—
347C22⋊C4D59611yescharacteristic
348C22⋊C4D59611yescharacteristic
349C42C22×D14911yescharacteristic
350C23—2981no—
351C23—2981no—
352C23—2981no—
353C23—2981no—
354C23—2981no—
355C23—5962no—
356C23—5962no—
357C23—5962no—
358C23—5962no—
359C23—5962no—
360C23—5962no—
361C23—11921no—
362C23—11921no—
363C23—11921no—
364C23C2×D59611yescharacteristic
365C23C2×D59611yescharacteristic
366Q8—2981no—
367Q8—2981no—
368D4—22no—
369D4—2981no—
370D4—2981no—
371D4—2981no—
372D4—2981no—
373D4—2981no—
374D4—2981no—
375D4—2981no—
376D4—2981no—
377D4—5962no—
378D4—5962no—
379D4—5962no—
380D4—5962no—
381D4—5962no—
382D4—5962no—
383D4—5962no—
384D4—1492no—
385D4—1492no—
386D4—11921no—
387D4—11921no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—2981no—
393C2×C4—2981no—
394C2×C4—2981no—
395C2×C4—5962no—
396C2×C4—5962no—
397C2×C4—11921no—
398C2×C4C2×D59611yescharacteristic
399C2×C4C2×D59611yescharacteristic
400C2×C4C2×D59611yescharacteristic
401C2×C4C2×D59611yescharacteristic
402C2×C4C23×D14911yescharacteristic
403C8—21no—
404C8—21no—
405C8—21no—
406C8D4×D14912yescomplemented
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—2982no—
413C22—2982no—
414C22—5961no—
415C22—5961no—
416C22—5961no—
417C22—5961no—
418C22—5961no—
419C22—5961no—
420C22—5961no—
421C22—5961no—
422C22—5961no—
423C22—5961no—
424C22—5961no—
425C22—5961no—
426C22—5961no—
427C22—11924no—
428C22—11924no—
429C22—11924no—
430C22#1801193912yescomplemented
431C22C22×D59611yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—5961no—
437C4—5961no—
438C4—5961no—
439C4C2×D4×D14911yescharacteristic
440C4#1801195711yescharacteristic
441C2—22no—
442C2—41no—
443C2—5962no—
444C2—5962no—
445C2—11921no—
446C2—11921no—
447C2—11921no—
448C2D4×D59611yescharacteristic
449C2C2×#1801193911yescharacteristic
450C2#2375043011yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#435×C149C2
socleC22×C149C22×D4
hypercenter#435D149
hypocenterC149#3264
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#18011939C2semidirect
2. C22×D1192C2semidirect
3. #23750271C2semidirect
4. D4×D596C2semidirect
5. #23750014C2semidirect
6. #23749878C2semidirect
7. #23749854C2semidirect
8. #23749841C2semidirect
9. #23749821C2semidirect
10. #23749778C2semidirect
11. #23749772C2semidirect
12. #23749761C2semidirect
13. #23749761C2semidirect
14. #23749738C2semidirect
15. #435×C149C2semidirect
16. C2×#14558736C22semidirect
18. C22×D596C22semidirect
19. C22×D596C22semidirect
22. C2×#14558725C22semidirect
23. C2×#14558725C22semidirect
24. C2×#14558725C22semidirect
28. C2×D1192C22semidirect
29. C2×D1192C22semidirect
30. C2×D1192C22semidirect
31. C2×D1192C22semidirect
32. #18011908C22semidirect
33. #18011899C22semidirect
35. #18011890C22semidirect
38. #18011885C22semidirect
39. #18011885C22semidirect
44. C4×D596C22semidirect
45. C4×D596C22semidirect
47. #18011843C22semidirect
48. #18011836C22semidirect
49. #18011833C22semidirect
50. #18011833C22semidirect
51. #18011833C22semidirect
52. #18011833C22semidirect
53. #18011833C22semidirect
54. C2×M16×C149C22semidirect
55. C22×C8×C149C22semidirect
57. C4⋊C8×C149C22semidirect
58. C22⋊C8×C149C22semidirect
59. C22⋊C8×C149C22semidirect
60. #97×C149C22semidirect
99. D1192D4semidirect
154. D596C2×D4semidirect
180. C8×C149C2×D4semidirect
186. C22×C149AGL(1,ℤ/8)semidirect
225. C149#3264semidirect
241. #435D149semidirect
258. C2×M16C2×D149semidirect
259. C22×C8C2×D149semidirect
277. C4⋊C8C2×D149semidirect
284. C22⋊C8C2×D149semidirect
285. C22⋊C8C2×D149semidirect
286. #97C2×D149semidirect
406. C8D4×D149semidirect
430. C22#18011939semidirect

Maximal subgroups

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

subgroupindex
C2×#180119392
C22×D11922
#237502712
D4×D5962
#237500142
#237498782
#237498542
#237498412
#237498212
#237497782
#237497722
#237497612
#237497382
#435×C1492
#3264149