Finite Group Databasebeta

← #541×D149 #34058053

Subgroups — #541×D149 #34058053

Order 19072.

1004 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#23750238C211yesmaximal, characteristic, complemented
2#23750237C211yesmaximal, characteristic, complemented
3#23750236C211yesmaximal, characteristic, complemented
4#23750235C212yesmaximal, complemented
5#23750234C214yesmaximal, complemented
6#23750233C212yesmaximal, complemented
7#23750232C214yesmaximal, complemented
8C4⋊Q8×D149C211yesmaximal, characteristic, complemented
9#126×D149C214yesmaximal
10#125×D149C214yesmaximal, complemented
11#125×D149C211yesmaximal, characteristic, complemented
12C22⋊Q8×D149C212yesmaximal
13C4×Q8×D149C212yesmaximal, complemented
14#117×D149C211yesmaximal, characteristic
15#541×C149C211yesmaximal, characteristic, complemented
16C2×Q8×D149C2212yes—
17C22×C4×D149C2211yescharacteristic
18#18011911C2211yescharacteristic, complemented
19#18011910C2214yescomplemented
20#18011909C2212yescomplemented
21#18011906C2214yes—
22#18011906C2214yes—
23#18011906C2214yes—
24#18011905C2214yes—
25#18011904C2214yes—
26#18011904C2214yes—
27#18011904C2214yes—
28#18011903C2214yescomplemented
29#18011903C2211yescharacteristic, complemented
30#18011902C2214yescomplemented
31#18011902C2212yescomplemented
32#18011902C2214yescomplemented
33#18011901C2214yescomplemented
34#18011901C2214yescomplemented
35#18011901C2214yescomplemented
36#18011901C2214yescomplemented
37#18011901C2214yescomplemented
38#18011891C2212yes—
39#18011890C2212yes—
40#18011889C2214yes—
41#18011888C2214yes—
42#18011887C2212yes—
43Q8×Dic149C2212yescomplemented
44C4×Dic298C2214yescomplemented
45C4×Dic298C2212yescomplemented
46#18011876C2214yescomplemented
47#18011876C2212yescomplemented
48#18011870C2211yescharacteristic
49#18011869C2212yes—
50#18011868C2211yescharacteristic
51#18011868C2211yescharacteristic
52#18011867C2212yes—
53C4⋊C4×D149C2214yes—
54C4⋊C4×D149C2212yes—
55C4⋊C4×D149C2214yes—
56C4⋊C4×D149C2214yes—
57C4⋊C4×D149C2214yes—
58C4⋊C4×D149C2212yes—
59C22⋊C4×D149C2212yes—
60C22⋊C4×D149C2214yes—
61C42×D149C2214yes—
62C42×D149C2211yescharacteristic
63C42×D149C2211yescharacteristic
64C4⋊Q8×C149C2211yescharacteristic, complemented
65#126×C149C2214yes—
66#125×C149C2214yescomplemented
67#125×C149C2211yescharacteristic, complemented
68C22⋊Q8×C149C2212yes—
69C4×Q8×C149C2212yescomplemented
70#117×C149C2211yescharacteristic
71C23×D149C2311yescharacteristic
72C2×Dic298C2312yes—
73C2×Dic298C2314yes—
74Q8×D149—28no—
75C22×Dic149C2311yescharacteristic
76C2×C4×D149—24no—
77C2×C4×D149C2311yescharacteristic
78C2×C4×D149C2311yescharacteristic
79C2×C4×D149C2311yescharacteristic
80C2×C4×D149C2314yes—
81C2×C4×D149C2312yes—
82C2×C4×D149C2314yes—
83C2×C4×D149C2312yes—
84C2×C4×D149C2311yescharacteristic
85C4⋊Dic149C2314yes—
86C4⋊Dic149C2314yes—
87C4⋊Dic149C2314yes—
88C4⋊Dic149C2312yes—
89C4⋊Dic149C2312yes—
90C4⋊Dic149C2314yes—
91#14558715C2314yes—
92#14558715C2314yes—
93#14558715C2314yes—
94#14558715C2314yes—
95#14558715C2314yes—
96#14558715C2314yes—
97#14558715C2312yes—
98#14558715C2312yes—
99#14558715C2314yes—
100#14558715C2314yes—
101#14558715C2314yes—
102C22⋊Dic149C2312yes—
103C22⋊Dic149C2314yes—
104#14558713C2312yes—
105#14558713C2314yes—
106#14558713C2314yes—
107#14558713C2312yes—
108C4×Dic149C2314yes—
109C4×Dic149C2314yes—
110C4×Dic149C2314yes—
111C4×Dic149C2311yescharacteristic
112C4×Dic149C2312yes—
113C4×Dic149C2312yes—
114C4×Dic149C2311yescharacteristic
115C2×Q8×C149C2312yes—
116C22×C4×C149C2311yescharacteristic
117C4⋊C4×C149C2314yes—
118C4⋊C4×C149C2314yes—
119C4⋊C4×C149C2314yes—
120C4⋊C4×C149C2312yes—
121C4⋊C4×C149C2312yes—
122C4⋊C4×C149C2314yes—
123C22⋊C4×C149C2312yes—
124C22⋊C4×C149C2314yes—
125C42×C149C2314yes—
126C42×C149C2311yescharacteristic
127C42×C149C2311yescharacteristic
128C22×D149—22no—
129C22×D149—24no—
130C22×D149C2411yescharacteristic
131C22×D149C2411yescharacteristic
132Dic298—24no—
133Dic298—28no—
134C2×Dic149—22no—
135C2×Dic149C2411yescharacteristic
136C2×Dic149C2414yes—
137C2×Dic149C2412yes—
138C2×Dic149C2414yes—
139C2×Dic149C2412yes—
140C2×Dic149C2411yescharacteristic
141C4×D149—22no—
142C4×D149—28no—
143C4×D149—24no—
144C4×D149—28no—
145C4×D149—24no—
146C4×D149—22no—
147C4×D149—22no—
148C4×D149#4114yes—
149C23×C149C2411yescharacteristic
150Q8×C149—24no—
151C2×C4×C149—22no—
152C2×C4×C149C2411yescharacteristic
153C2×C4×C149C2414yes—
154C2×C4×C149C2412yes—
155C2×C4×C149C2414yes—
156C2×C4×C149C2412yes—
157C2×C4×C149C2411yescharacteristic
158C22×C149—21no—
159C22×C149—22no—
160C22×C149C2511yescharacteristic
161C2×D149—21no—
162C2×D149—22no—
163C2×D149—44no—
164C2×D149C2×#4112yes—
165C2×D1492−1+414yes—
166C4×C149—21no—
167C4×C149—24no—
168C4×C149—22no—
169C4×C149—24no—
170C4×C149—22no—
171C4×C149C2×#4112yes—
172Dic149—21no—
173Dic149—24no—
174Dic149—22no—
175Dic149—24no—
176Dic149—22no—
177Dic149C2×#4112yes—
178C2×C149—41no—
179C2×C149C22×#4111yescharacteristic
180C2×C149C2×2−1+412yes—
181D149—41no—
182D149#54114yesdirect product factor
183C149C2×#54111yescharacteristic, complemented, Sylow
184C2×#541—1491nomaximal, Sylow
185#541—1491no—
186#541—1494no—
187#541—1494no—
188#541—1491no—
189#541—1492no—
190#541—1492no—
191#541—1491no—
192#541D14911yescharacteristic, direct product factor
193C2×C4⋊Q8—1491no—
194C2×#126—1494no—
195C2×#125—1491no—
196C2×#125—1494no—
197C2×C22⋊Q8—1492no—
198C2×C4×Q8—1492no—
199C2×#117—1491no—
200C22×Q8—1492no—
201C23×C4—1491no—
202C4⋊Q8—1492no—
203C4⋊Q8—1494no—
204C4⋊Q8—1491no—
205C4⋊Q8C2×D14911yescharacteristic, complemented
206#126—1494no—
207#126—1494no—
208#126—1494no—
209#126—1494no—
210#126—1494no—
211#126—1494no—
212#126—1494no—
213#126C2×D14914yes—
214#125—1494no—
215#125—1494no—
216#125—1494no—
217#125—1494no—
218#125—1494no—
219#125—1492no—
220#125—1494no—
221#125—1494no—
222#125—1491no—
223#125—1494no—
224#125C2×D14911yescharacteristic, complemented
225#125C2×D14914yescomplemented
226C22⋊Q8—1492no—
227C22⋊Q8—1492no—
228C22⋊Q8—1494no—
229C22⋊Q8—1492no—
230C22⋊Q8—1494no—
231C22⋊Q8C2×D14912yes—
232C4×Q8—1492no—
233C4×Q8—1494no—
234C4×Q8—1492no—
235C4×Q8—1494no—
236C4×Q8—1492no—
237C4×Q8C2×D14912yescomplemented
238#117—1491no—
239#117—1492no—
240#117—1492no—
241#117—1491no—
242#117—1491no—
243#117C2×D14911yescharacteristic
244C2×C4⋊C4—1492no—
245C2×C4⋊C4—1492no—
246C2×C4⋊C4—1494no—
247C2×C4⋊C4—1494no—
248C2×C4⋊C4—1494no—
249C2×C4⋊C4—1494no—
250C2×C22⋊C4—1492no—
251C2×C22⋊C4—1494no—
252C2×C42—1491no—
253C2×C42—1491no—
254C2×C42—1494no—
255C24—1491no—
256C2×Q8—2988no—
257C2×Q8—1492no—
258C2×Q8—1494no—
259C2×Q8C22×D14912yes—
260C22×C4—2984no—
261C22×C4—1491no—
262C22×C4—1492no—
263C22×C4—1492no—
264C22×C4—1494no—
265C22×C4—1494no—
266C22×C4—1491no—
267C22×C4—1491no—
268C22×C4—1491no—
269C22×C4—1491no—
270C22×C4C22×D14911yescharacteristic
271C4⋊C4—1492no—
272C4⋊C4—1492no—
273C4⋊C4—1492no—
274C4⋊C4—1494no—
275C4⋊C4—1492no—
276C4⋊C4—1494no—
277C4⋊C4—1494no—
278C4⋊C4—1494no—
279C4⋊C4—1494no—
280C4⋊C4—1494no—
281C4⋊C4—1494no—
282C4⋊C4—1494no—
283C4⋊C4—1494no—
284C4⋊C4—1494no—
285C4⋊C4—1494no—
286C4⋊C4—1494no—
287C4⋊C4—1494no—
288C4⋊C4C22×D14912yes—
289C4⋊C4C22×D14912yes—
290C4⋊C4C22×D14914yes—
291C4⋊C4C22×D14914yes—
292C4⋊C4C22×D14914yes—
293C4⋊C4C22×D14914yes—
294C22⋊C4—1492no—
295C22⋊C4—1494no—
296C22⋊C4—1492no—
297C22⋊C4—1492no—
298C22⋊C4—1494no—
299C22⋊C4—1494no—
300C22⋊C4C22×D14912yes—
301C22⋊C4C22×D14914yes—
302C42—1491no—
303C42—1492no—
304C42—1491no—
305C42—1492no—
306C42—1494no—
307C42—1494no—
308C42—1494no—
309C42C22×D14911yescharacteristic
310C42C22×D14911yescharacteristic
311C42C22×D14914yes—
312C23—2982no—
313C23—2984no—
314C23—1491no—
315C23—1491no—
316C23C23×D14911yescharacteristic
317Q8—24no—
318Q8—2988no—
319Q8—2984no—
320C2×C4—22no—
321C2×C4—2982no—
322C2×C4—2984no—
323C2×C4—2984no—
324C2×C4—2988no—
325C2×C4—2988no—
326C2×C4—2982no—
327C2×C4—2982no—
328C2×C4—2982no—
329C2×C4—1492no—
330C2×C4—1492no—
331C2×C4—1494no—
332C2×C4—1494no—
333C2×C4—1491no—
334C2×C4—1491no—
335C2×C4—1494no—
336C2×C4C23×D14912yes—
337C2×C4C23×D14912yes—
338C2×C4C23×D14914yes—
339C2×C4C23×D14914yes—
340C2×C4C23×D14911yescharacteristic
341C2×C4C23×D14911yescharacteristic
342C22—21no—
343C22—22no—
344C22—2981no—
345C22—2982no—
346C22—5964no—
347C22—1492no—
348C22—1494no—
349C22C24×D14911yescharacteristic
350C4—21no—
351C4—24no—
352C4—22no—
353C4—22no—
354C4—24no—
355C4—2981no—
356C4—2984no—
357C4—2982no—
358C4—2982no—
359C4—2984no—
360C4—1492no—
361C4#41×D14912yes—
362C2—41no—
363C2—5961no—
364C2—1494no—
365C2C2×#41×D14911yescharacteristic
366C22−1+4×D14912yes—
subgroupG/H
center, FrattiniC22C24×D149
commutator, socle, cosocleC22×C149C25
Fitting#541×C149C2
prime radicalC23×D149C23
hypercenter#541D149
hypocenterC149C2×#541
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ #541

Complements

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

NH ≅ G/Ntype
1. #23750238C2semidirect
2. #23750237C2semidirect
3. #23750236C2semidirect
4. #23750235C2semidirect
5. #23750234C2semidirect
6. #23750233C2semidirect
7. #23750232C2semidirect
8. C4⋊Q8×D149C2semidirect
10. #125×D149C2semidirect
11. #125×D149C2semidirect
13. C4×Q8×D149C2semidirect
15. #541×C149C2semidirect
18. #18011911C22semidirect
19. #18011910C22semidirect
20. #18011909C22semidirect
28. #18011903C22semidirect
29. #18011903C22semidirect
30. #18011902C22semidirect
31. #18011902C22semidirect
32. #18011902C22semidirect
33. #18011901C22semidirect
34. #18011901C22semidirect
35. #18011901C22semidirect
36. #18011901C22semidirect
37. #18011901C22semidirect
43. Q8×Dic149C22semidirect
44. C4×Dic298C22semidirect
45. C4×Dic298C22semidirect
46. #18011876C22semidirect
47. #18011876C22semidirect
64. C4⋊Q8×C149C22semidirect
66. #125×C149C22semidirect
67. #125×C149C22semidirect
69. C4×Q8×C149C22semidirect
182. D149#541direct (N × H)
183. C149C2×#541semidirect
192. #541D149direct (N × H)
205. C4⋊Q8C2×D149semidirect
224. #125C2×D149semidirect
225. #125C2×D149semidirect
237. C4×Q8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502382
#237502372
#237502362
#237502352
#237502342
#237502332
#237502322
C4⋊Q8×D1492
#126×D1492
#125×D1492
C22⋊Q8×D1492
C4×Q8×D1492
#117×D1492
#541×C1492
C2×#541149