Finite Group Databasebeta

← #548×D149 #34058153

Subgroups — #548×D149 #34058153

Order 19072.

1620 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D149C211yesmaximal, characteristic, complemented
2C22×Q8×D149C211yesmaximal, characteristic, complemented
3#23750287C211yesmaximal, characteristic, complemented
4#23750286C211yesmaximal, characteristic, complemented
5#23750285C213yesmaximal, complemented
6#23750284C213yesmaximal, complemented
7#23750283C213yesmaximal, complemented
8#23750282C211yesmaximal, characteristic, complemented
9#23750281C213yesmaximal, complemented
10#124×D149C213yesmaximal, complemented
11C22⋊Q8×D149C213yesmaximal, complemented
12#121×D149C213yesmaximal, complemented
13C4×Q8×D149C211yesmaximal, characteristic, complemented
14C4×D4×D149C213yesmaximal, complemented
15#548×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic, complemented
17C2×#14558736C2213yescomplemented
18C2×#14558735C2213yescomplemented
19#41×D149—28no—
20C22×Dic298C2213yescomplemented
21C2×Q8×D149—28no—
22C2×Q8×D149C2213yes—
23C2×Q8×D149C2211yescharacteristic
24C2×Q8×D149C2211yescharacteristic, complemented
25C2×Q8×D149C2213yescomplemented
26C2×D4×D149C2213yes—
27C2×D4×D149C2213yes—
28C22×C4×D149C2213yes—
29C22×C4×D149C2213yes—
30#18011900C2213yescomplemented
31#18011899C2213yescomplemented
32#18011898C2213yescomplemented
33#18011897C2216yescomplemented
34#18011897C2216yescomplemented
35#18011891C2213yescomplemented
36#18011890C2213yescomplemented
37#18011889C2216yescomplemented
38#18011888C2216yescomplemented
39#18011887C2213yescomplemented
40#18011886C2213yescomplemented
41#18011885C2213yescomplemented
42#18011884C2216yescomplemented
43#18011883C2216yescomplemented
44#18011882C2213yescomplemented
45Q8×Dic149C2211yescharacteristic, complemented
46C4×Dic298C2213yescomplemented
47#18011876C2213yescomplemented
48C4×D596C2213yescomplemented
49D4×Dic149C2213yescomplemented
50#18011873C2213yescomplemented
51C4×C22⋊D149C2213yescomplemented
52C4×C22⋊D149C2213yescomplemented
53#18011871C2213yescomplemented
54#18011871C2213yescomplemented
55C4⋊C4×D149C2213yes—
56C4⋊C4×D149C2213yes—
57C22⋊C4×D149C2211yescharacteristic
58C22⋊C4×D149C2213yes—
59C22⋊C4×D149C2216yes—
60C42×D149C2213yes—
61C2×#41×C149C2211yescharacteristic, complemented
62C22×Q8×C149C2211yescharacteristic, complemented
63#124×C149C2213yescomplemented
64C22⋊Q8×C149C2213yescomplemented
65#121×C149C2213yescomplemented
66C4×Q8×C149C2211yescharacteristic, complemented
67C4×D4×C149C2213yescomplemented
68C23×D149C2313yes—
69C23×D149C2311yescharacteristic
70#14558737—24no—
71#14558736—212no—
72#14558735—212no—
73C2×Dic298—212no—
74C2×Dic298C2316yes—
75C2×Dic298C2313yes—
76C2×Dic298C2313yes—
77Q8×D149—212no—
78Q8×D149—212no—
79Q8×D149—24no—
80Q8×D149D418yescomplemented
81C2×D596C2313yes—
82C2×D596C2313yes—
83C2×C22⋊D149C2316yes—
84C2×C22⋊D149C2313yes—
85C2×C22⋊D149C2313yes—
86D4×D149—212no—
87D4×D149—212no—
88C22×Dic149C2313yes—
89C22×Dic149C2313yes—
90C2×C4×D149—212no—
91C2×C4×D149—212no—
92C2×C4×D149C2311yescharacteristic
93C2×C4×D149C2313yes—
94C2×C4×D149C2313yes—
95C2×C4×D149C2313yes—
96C2×C4×D149C2313yes—
97C2×C4×D149C2313yes—
98C2×C4×D149C2313yes—
99C2×C4×D149C2311yescharacteristic
100C2×C4×D149C2313yes—
101C4⋊Dic149C2313yes—
102C4⋊Dic149C2313yes—
103#14558715C2313yes—
104#14558715C2313yes—
105#14558715C2316yes—
106C22⋊Dic149C2311yescharacteristic
107C22⋊Dic149C2313yes—
108C22⋊Dic149C2316yes—
109#14558713C2311yescharacteristic
110#14558713C2313yes—
111#14558713C2311yescharacteristic
112#14558713C2313yes—
113#14558713C2316yes—
114#14558713C2316yes—
115C4×Dic149C2313yes—
116C4×Dic149C2313yes—
117C4×Dic149C2313yes—
118#41×C149—24no—
119C2×Q8×C149—24no—
120C2×Q8×C149C2313yes—
121C2×Q8×C149C2311yescharacteristic
122C2×D4×C149C2313yes—
123C2×D4×C149C2313yes—
124C22×C4×C149C2313yes—
125C22×C4×C149C2313yes—
126C4⋊C4×C149C2313yes—
127C4⋊C4×C149C2313yes—
128C22⋊C4×C149C2311yescharacteristic
129C22⋊C4×C149C2313yes—
130C22⋊C4×C149C2316yes—
131C42×C149C2313yes—
132C22×D149—22no—
133C22×D149—22no—
134C22×D149—26no—
135C22×D149—26no—
136C22×D149—26no—
137C22×D149#4114yescomplemented
138C22×D149C2413yes—
139C22×D149C2411yescharacteristic
140C22×D149C2411yescharacteristic
141Dic298—26no—
142Dic298—212no—
143Dic298C2×D4112yescomplemented
144D596—26no—
145D596—26no—
146C22⋊D149—26no—
147C22⋊D149—26no—
148C22⋊D149—212no—
149C2×Dic149—26no—
150C2×Dic149—26no—
151C2×Dic149C2411yescharacteristic
152C2×Dic149C2413yes—
153C2×Dic149C2413yes—
154C2×Dic149C2411yescharacteristic
155C2×Dic149C2413yes—
156C4×D149—22no—
157C4×D149—26no—
158C4×D149—26no—
159C4×D149—22no—
160C4×D149—26no—
161C4×D149—26no—
162C4×D149—26no—
163C4×D149—26no—
164C4×D149C2×D4112yes—
165C23×C149C2413yes—
166C23×C149C2411yescharacteristic
167Q8×C149—26no—
168Q8×C149C2×D414yescomplemented
169D4×C149—26no—
170D4×C149—26no—
171C2×C4×C149—26no—
172C2×C4×C149—26no—
173C2×C4×C149C2411yescharacteristic
174C2×C4×C149C2413yes—
175C2×C4×C149C2413yes—
176C2×C4×C149C2411yescharacteristic
177C2×C4×C149C2413yes—
178C22×C149—21no—
179C22×C149—21no—
180C22×C149—23no—
181C22×C149—23no—
182C22×C149—23no—
183C22×C149C2×#4112yescomplemented
184C22×C149C2511yescharacteristic
185C2×D149—21no—
186C2×D149—21no—
187C2×D149—28no—
188C2×D149—23no—
189C2×D149—23no—
190C2×D149—23no—
191C2×D149—412no—
192C2×D149C22×D412yes—
193C2×D149C2×#4112yes—
194C2×D149C2×#4112yescomplemented
195C2×D1492−1+412yes—
196C4×C149—21no—
197C4×C149—23no—
198C4×C149—23no—
199C4×C149—21no—
200C4×C149C22×D416yes—
201Dic149—21no—
202Dic149—23no—
203Dic149—23no—
204Dic149—21no—
205Dic149C22×D416yes—
206C2×C149—22no—
207C2×C149—43no—
208C2×C149C23×D411yescharacteristic
209C2×C149C22×#4111yescharacteristic
210C2×C149C2×2−1+411yescharacteristic
211D149—22no—
212D149—43no—
213D149#54814yesdirect product factor
214C149C2×#54811yescharacteristic, complemented, Sylow
215C2×#548—1491nomaximal, Sylow
216C22×#41—1491no—
217C23×Q8—1491no—
218#548—1491no—
219#548—1491no—
220#548—1493no—
221#548—1493no—
222#548—1493no—
223#548—1491no—
224#548—1493no—
225#548D14911yescharacteristic, direct product factor
226C2×#124—1493no—
227C2×C22⋊Q8—1493no—
228C2×#121—1493no—
229C2×C4×Q8—1491no—
230C2×C4×D4—1493no—
231C2×#41—2988no—
232C2×#41—1491no—
233C2×#41—1493no—
234C2×#41—1493no—
235C2×#41C2×D14911yescharacteristic, complemented
236C22×Q8—2988no—
237C22×Q8—1493no—
238C22×Q8—1493no—
239C22×Q8—1491no—
240C22×Q8—1491no—
241C22×Q8—1493no—
242C22×Q8C2×D14911yescharacteristic, complemented
243C22×D4—1493no—
244C22×D4—1493no—
245C23×C4—1493no—
246C23×C4—1493no—
247#124—1493no—
248#124—1493no—
249#124—1496no—
250#124—1496no—
251#124—1493no—
252#124C2×D14913yescomplemented
253C22⋊Q8—1493no—
254C22⋊Q8—1493no—
255C22⋊Q8—1496no—
256C22⋊Q8—1493no—
257C22⋊Q8—1496no—
258C22⋊Q8C2×D14913yescomplemented
259#121—1493no—
260#121—1496no—
261#121—1493no—
262#121—1493no—
263#121—1496no—
264#121C2×D14913yescomplemented
265C4×Q8—1491no—
266C4×Q8—1493no—
267C4×Q8—1493no—
268C4×Q8C2×D14911yescharacteristic, complemented
269C4×D4—1493no—
270C4×D4—1493no—
271C4×D4—1493no—
272C4×D4—1493no—
273C4×D4—1493no—
274C4×D4—1493no—
275C4×D4—1493no—
276C4×D4C2×D14913yescomplemented
277C2×C4⋊C4—1493no—
278C2×C4⋊C4—1493no—
279C2×C22⋊C4—1491no—
280C2×C22⋊C4—1493no—
281C2×C22⋊C4—1496no—
282C2×C42—1493no—
283C24—1493no—
284C24—1491no—
285#41—24no—
286#41—29812no—
287#41—29812no—
288#41—2984no—
289C2×Q8—24no—
290C2×Q8—29812no—
291C2×Q8—29812no—
292C2×Q8—2984no—
293C2×Q8—29812no—
294C2×Q8—1498no—
295C2×Q8—1493no—
296C2×Q8—1496no—
297C2×Q8—1493no—
298C2×Q8C22×D14913yes—
299C2×Q8C22×D14911yescharacteristic
300C2×D4—29812no—
301C2×D4—29812no—
302C2×D4—1493no—
303C2×D4—1493no—
304C2×D4—1496no—
305C2×D4—1493no—
306C2×D4—1493no—
307C2×D4C22×D14913yes—
308C2×D4C22×D14913yes—
309C22×C4—29812no—
310C22×C4—29812no—
311C22×C4—1493no—
312C22×C4—1493no—
313C22×C4—1491no—
314C22×C4—1493no—
315C22×C4—1493no—
316C22×C4—1491no—
317C22×C4—1493no—
318C22×C4—1493no—
319C22×C4—1493no—
320C22×C4—1493no—
321C22×C4—1493no—
322C22×C4C22×D14913yes—
323C22×C4C22×D14913yes—
324C4⋊C4—1493no—
325C4⋊C4—1493no—
326C4⋊C4—1493no—
327C4⋊C4—1496no—
328C4⋊C4—1493no—
329C4⋊C4C22×D14913yes—
330C4⋊C4C22×D14913yes—
331C22⋊C4—1491no—
332C22⋊C4—1493no—
333C22⋊C4—1496no—
334C22⋊C4—1491no—
335C22⋊C4—1491no—
336C22⋊C4—1493no—
337C22⋊C4—1493no—
338C22⋊C4—1496no—
339C22⋊C4—1496no—
340C22⋊C4C22×D14911yescharacteristic
341C22⋊C4C22×D14913yes—
342C22⋊C4C22×D14916yes—
343C42—1493no—
344C42—1493no—
345C42—1493no—
346C42C22×D14913yes—
347C23—2982no—
348C23—2982no—
349C23—2986no—
350C23—2986no—
351C23—2986no—
352C23—1493no—
353C23—1494no—
354C23—1491no—
355C23—1491no—
356C23C23×D14913yes—
357C23C23×D14911yescharacteristic
358Q8—26no—
359Q8—29812no—
360Q8—2986no—
361Q8—14912no—
362Q8D4×D14914yescomplemented
363D4—26no—
364D4—26no—
365D4—2986no—
366D4—2986no—
367D4—2986no—
368D4—29812no—
369D4—2986no—
370C2×C4—26no—
371C2×C4—26no—
372C2×C4—2982no—
373C2×C4—2986no—
374C2×C4—2982no—
375C2×C4—2986no—
376C2×C4—2986no—
377C2×C4—2986no—
378C2×C4—2986no—
379C2×C4—2986no—
380C2×C4—2986no—
381C2×C4—2986no—
382C2×C4—1491no—
383C2×C4—1493no—
384C2×C4—1493no—
385C2×C4—1491no—
386C2×C4—1493no—
387C2×C4—14912no—
388C2×C4C23×D14911yescharacteristic
389C2×C4C23×D14913yes—
390C2×C4C23×D14913yes—
391C2×C4C23×D14911yescharacteristic
392C2×C4C23×D14913yes—
393C22—21no—
394C22—21no—
395C22—23no—
396C22—23no—
397C22—23no—
398C22—2988no—
399C22—2981no—
400C22—2981no—
401C22—2983no—
402C22—2983no—
403C22—2983no—
404C22—59612no—
405C22—1492no—
406C22—1492no—
407C22—1492no—
408C22—1492no—
409C22#41×D14912yescomplemented
410C22C24×D14911yescharacteristic
411C4—21no—
412C4—23no—
413C4—23no—
414C4—21no—
415C4—2981no—
416C4—2983no—
417C4—2983no—
418C4—2981no—
419C4—1496no—
420C4C2×D4×D14916yes—
421C2—22no—
422C2—43no—
423C2—2982no—
424C2—5963no—
425C2—1494no—
426C2C22×D4×D14911yescharacteristic
427C2C2×#41×D14911yescharacteristic
428C22−1+4×D14911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D149
commutator, socle, cosocleC22×C149C25
Fitting#548×C149C2
hypercenter#548D149
hypocenterC149C2×#548
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#41×D149C2semidirect
2. C22×Q8×D149C2semidirect
3. #23750287C2semidirect
4. #23750286C2semidirect
5. #23750285C2semidirect
6. #23750284C2semidirect
7. #23750283C2semidirect
8. #23750282C2semidirect
9. #23750281C2semidirect
10. #124×D149C2semidirect
11. C22⋊Q8×D149C2semidirect
12. #121×D149C2semidirect
13. C4×Q8×D149C2semidirect
14. C4×D4×D149C2semidirect
15. #548×C149C2semidirect
16. C2×#14558737C22semidirect
17. C2×#14558736C22semidirect
18. C2×#14558735C22semidirect
20. C22×Dic298C22semidirect
24. C2×Q8×D149C22semidirect
25. C2×Q8×D149C22semidirect
30. #18011900C22semidirect
31. #18011899C22semidirect
32. #18011898C22semidirect
33. #18011897C22semidirect
34. #18011897C22semidirect
35. #18011891C22semidirect
36. #18011890C22semidirect
37. #18011889C22semidirect
38. #18011888C22semidirect
39. #18011887C22semidirect
40. #18011886C22semidirect
41. #18011885C22semidirect
42. #18011884C22semidirect
43. #18011883C22semidirect
44. #18011882C22semidirect
45. Q8×Dic149C22semidirect
46. C4×Dic298C22semidirect
47. #18011876C22semidirect
48. C4×D596C22semidirect
49. D4×Dic149C22semidirect
50. #18011873C22semidirect
51. C4×C22⋊D149C22semidirect
52. C4×C22⋊D149C22semidirect
53. #18011871C22semidirect
54. #18011871C22semidirect
61. C2×#41×C149C22semidirect
62. C22×Q8×C149C22semidirect
63. #124×C149C22semidirect
64. C22⋊Q8×C149C22semidirect
65. #121×C149C22semidirect
66. C4×Q8×C149C22semidirect
67. C4×D4×C149C22semidirect
80. Q8×D149D4semidirect
137. C22×D149#41semidirect
143. Dic298C2×D4semidirect
168. Q8×C149C2×D4semidirect
183. C22×C149C2×#41semidirect
194. C2×D149C2×#41semidirect
213. D149#548direct (N × H)
214. C149C2×#548semidirect
225. #548D149direct (N × H)
235. C2×#41C2×D149semidirect
242. C22×Q8C2×D149semidirect
252. #124C2×D149semidirect
258. C22⋊Q8C2×D149semidirect
264. #121C2×D149semidirect
268. C4×Q8C2×D149semidirect
276. C4×D4C2×D149semidirect
362. Q8D4×D149semidirect
409. C22#41×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D1492
C22×Q8×D1492
#237502872
#237502862
#237502852
#237502842
#237502832
#237502822
#237502812
#124×D1492
C22⋊Q8×D1492
#121×D1492
C4×Q8×D1492
C4×D4×D1492
#548×C1492
C2×#548149