Finite Group Databasebeta

← #34058082

Subgroups — #34058082

Order 19072.

1040 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750248C212yesmaximal, complemented
2#23750247C212yesmaximal, complemented
3#23750236C211yesmaximal, characteristic, complemented
4#23750231C211yesmaximal, characteristic, complemented
5#23750230C211yesmaximal, characteristic, complemented
6#23750223C214yesmaximal, complemented
7#23750214C214yesmaximal, complemented
8#23750181C211yesmaximal, characteristic, complemented
9#23750176C211yesmaximal, characteristic, complemented
10#23750160C214yesmaximal, complemented
11#23750158C214yesmaximal, complemented
12#23750138C212yesmaximal, complemented
13C4×#14558737C212yesmaximal, complemented
14#117×D149C211yesmaximal, characteristic, complemented
15#541×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2212yes—
17C22×C4×D149C2211yescharacteristic
18#18011910C2212yescomplemented
19#18011908C2211yescharacteristic, complemented
20#18011906C2214yes—
21#18011906C2214yescomplemented
22#18011905C2214yescomplemented
23#18011903C2211yescharacteristic, complemented
24#18011901C2214yescomplemented
25#18011900C2212yescomplemented
26#18011899C2214yes—
27#18011897C2214yes—
28#18011896C2214yes—
29#18011896C2214yes—
30#18011896C2214yescomplemented
31#18011896C2214yescomplemented
32#18011893C2214yes—
33#18011891C2214yescomplemented
34#18011889C2214yes—
35#18011889C2214yescomplemented
36#18011887C2212yes—
37#18011886C2214yes—
38#18011886C2214yes—
39#18011886C2212yes—
40#18011885C2212yes—
41#18011884C2214yes—
42#18011881C2214yes—
43Q8×Dic149C2212yescomplemented
44#18011876C2214yescomplemented
45C4×D596C2214yes—
46C4×D596C2212yescomplemented
47#18011873C2214yes—
48#18011873C2214yes—
49#18011873C2214yescomplemented
50#18011873C2212yescomplemented
51#18011871C2214yes—
52#18011870C2211yescharacteristic
53#18011869C2212yes—
54#18011869C2212yes—
55#18011869C2214yescomplemented
56#18011868C2211yescharacteristic
57#18011868C2211yescharacteristic
58#18011867C2212yes—
59C4⋊C4×D149C2212yes—
60C22⋊C4×D149C2212yes—
61C42×D149C2211yescharacteristic
62C42×D149C2211yescharacteristic
63C42×D149C2214yescomplemented
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
72#14558737—28no—
73C2×Dic298C2314yes—
74C2×D596C2312yes—
75C2×D596C2314yes—
76C2×D596C2314yes—
77C2×D596C2314yes—
78C2×C22⋊D149C2314yes—
79C22×Dic149C2311yescharacteristic
80C2×C4×D149—24no—
81C2×C4×D149C2311yescharacteristic
82C2×C4×D149C2311yescharacteristic
83C2×C4×D149C2311yescharacteristic
84C2×C4×D149C2314yes—
85C2×C4×D149C2312yes—
86C2×C4×D149C2312yes—
87C2×C4×D149C2314yes—
88C2×C4×D149C2314yes—
89C2×C4×D149C2311yescharacteristic
90C4⋊Dic149C2314yes—
91C4⋊Dic149C2312yes—
92C4⋊Dic149C2312yes—
93#14558715C2312yes—
94#14558715C2314yes—
95#14558715C2314yes—
96#14558715C2314yes—
97#14558715C2312yes—
98C22⋊Dic149C2312yes—
99#14558713C2314yes—
100#14558713C2314yes—
101#14558713C2314yes—
102#14558713C2312yes—
103#14558713C2314yes—
104#14558713C2314yes—
105#14558713C2314yes—
106#14558713C2314yes—
107#14558713C2312yes—
108#14558713C2314yes—
109C4×Dic149C2314yes—
110C4×Dic149C2311yescharacteristic
111C4×Dic149C2312yes—
112C4×Dic149C2312yes—
113C4×Dic149C2311yescharacteristic
114C4×Dic149C2314yes—
115C2×Q8×C149C2312yes—
116C22×C4×C149C2311yescharacteristic
117C4⋊C4×C149C2314yes—
118C4⋊C4×C149C2314yes—
119C4⋊C4×C149C2312yes—
120C4⋊C4×C149C2312yes—
121C4⋊C4×C149C2314yes—
122C4⋊C4×C149C2314yes—
123C22⋊C4×C149C2312yes—
124C22⋊C4×C149C2314yes—
125C42×C149C2314yes—
126C42×C149C2311yescharacteristic
127C42×C149C2311yescharacteristic
128C22×D149—22no—
129C22×D149—42no—
130C22×D149C2414yes—
131C22×D149C2411yescharacteristic
132C22×D149C2411yescharacteristic
133Dic298—44no—
134D596—28no—
135D596—24no—
136D596—44no—
137D596—44no—
138C22⋊D149—44no—
139C2×Dic149—22no—
140C2×Dic149C2412yes—
141C2×Dic149C2411yescharacteristic
142C2×Dic149C2414yes—
143C2×Dic149C2412yes—
144C2×Dic149C2411yescharacteristic
145C4×D149—22no—
146C4×D149—22no—
147C4×D149—22no—
148C4×D149—28no—
149C4×D149—42no—
150C4×D149—44no—
151C4×D149—44no—
152C4×D149—42no—
153C4×D149#4114yes—
154C23×C149C2411yescharacteristic
155Q8×C149—24no—
156C2×C4×C149—22no—
157C2×C4×C149C2412yes—
158C2×C4×C149C2411yescharacteristic
159C2×C4×C149C2412yes—
160C2×C4×C149C2414yes—
161C2×C4×C149C2414yes—
162C2×C4×C149C2411yescharacteristic
163C22×C149—21no—
164C22×C149—22no—
165C22×C149C2511yescharacteristic
166C2×D149—22no—
167C2×D149—21no—
168C2×D149—24no—
169C2×D149—24no—
170C2×D149—24no—
171C2×D149—22no—
172C2×D149—44no—
173C2×D149C2×#4112yes—
174C4×C149—21no—
175C4×C149—24no—
176C4×C149—22no—
177C4×C149—22no—
178C4×C149—24no—
179C4×C149C2×#4112yes—
180Dic149—21no—
181Dic149—22no—
182Dic149—24no—
183Dic149—22no—
184Dic149C2×#4112yes—
185C2×C149—41no—
186C2×C149C22×#4111yescharacteristic
187C2×C149#58512yes—
188D149—22no—
189D149—44no—
190D149—41no—
191C149#345511yescharacteristic, complemented, Sylow
192#3455—1491nomaximal, Sylow
193#542—1492no—
194#542—1492no—
195#541—1491no—
196#541D14911yescharacteristic, complemented
197#540—1491no—
198#540—1491no—
199#539—1494no—
200#538—1494no—
201#533—1491no—
202#532—1491no—
203#529—1494no—
204#529—1494no—
205#525—1492no—
206C4×#41—1492no—
207C2×#117—1491no—
208C2×#41—1492no—
209C23×C4—1491no—
210C4⋊Q8—1492no—
211C4⋊Q8C2×D14911yescharacteristic, complemented
212#127—1491no—
213#126—1494no—
214#126—1494no—
215#126—1494no—
216#126C2×D14914yes—
217#125—1494no—
218#125—1491no—
219#125C2×D14914yescomplemented
220#125C2×D14911yescharacteristic, complemented
221#124—1492no—
222#124—1494no—
223#124—1494no—
224#123—1494no—
225#123—1494no—
226#123—1494no—
227#123—1494no—
228#123—1494no—
229C22⋊Q8—1492no—
230C22⋊Q8—1494no—
231C22⋊Q8—1494no—
232C22⋊Q8—1494no—
233C22⋊Q8C2×D14912yes—
234#121—1492no—
235#121—1492no—
236#121—1494no—
237#121—1494no—
238#121—1494no—
239#120—1494no—
240C4×Q8—1492no—
241C4×Q8—1494no—
242C4×Q8C2×D14912yescomplemented
243C4×D4—1494no—
244C4×D4—1492no—
245C4×D4—1494no—
246C4×D4—1494no—
247C4×D4—1494no—
248C4×D4—1494no—
249C4×D4—1492no—
250#117—1491no—
251#117—1492no—
252#117—1492no—
253#117—1494no—
254#117—1492no—
255#117—1491no—
256#117—1491no—
257#117C2×D14911yescharacteristic
258C2×C4⋊C4—1492no—
259C2×C22⋊C4—1492no—
260C2×C42—1491no—
261C2×C42—1491no—
262C2×C42—1494no—
263C24—1491no—
264#41—2988no—
265C2×Q8—1494no—
266C2×Q8C22×D14912yes—
267C2×D4—1494no—
268C2×D4—1494no—
269C2×D4—1492no—
270C2×D4—1494no—
271C2×D4—1494no—
272C22×C4—2984no—
273C22×C4—1491no—
274C22×C4—1494no—
275C22×C4—1491no—
276C22×C4—1491no—
277C22×C4—1491no—
278C22×C4—1492no—
279C22×C4—1492no—
280C22×C4—1494no—
281C22×C4—1494no—
282C22×C4—1491no—
283C22×C4C22×D14911yescharacteristic
284C4⋊C4—1492no—
285C4⋊C4—1492no—
286C4⋊C4—1492no—
287C4⋊C4—1492no—
288C4⋊C4—1494no—
289C4⋊C4—1494no—
290C4⋊C4—1494no—
291C4⋊C4—1494no—
292C4⋊C4C22×D14912yes—
293C4⋊C4C22×D14912yes—
294C4⋊C4C22×D14914yes—
295C4⋊C4C22×D14914yes—
296C4⋊C4C22×D14914yes—
297C4⋊C4C22×D14914yes—
298C22⋊C4—1492no—
299C22⋊C4—1492no—
300C22⋊C4—1492no—
301C22⋊C4—1494no—
302C22⋊C4—1494no—
303C22⋊C4—1494no—
304C22⋊C4—1494no—
305C22⋊C4—1494no—
306C22⋊C4—1494no—
307C22⋊C4—1494no—
308C22⋊C4—1494no—
309C22⋊C4C22×D14912yes—
310C22⋊C4C22×D14914yes—
311C42—1492no—
312C42—1491no—
313C42—1492no—
314C42—1494no—
315C42—1491no—
316C42—1494no—
317C42C22×D14911yescharacteristic
318C42C22×D14911yescharacteristic
319C42C22×D14914yes—
320C23—2982no—
321C23—5962no—
322C23—1491no—
323C23—1494no—
324C23—1491no—
325C23C23×D14911yescharacteristic
326Q8—24no—
327Q8—5964no—
328D4—2988no—
329D4—2984no—
330D4—5964no—
331D4—5964no—
332D4—5964no—
333C2×C4—22no—
334C2×C4—2982no—
335C2×C4—2982no—
336C2×C4—2988no—
337C2×C4—2982no—
338C2×C4—2982no—
339C2×C4—5962no—
340C2×C4—5964no—
341C2×C4—5962no—
342C2×C4—5964no—
343C2×C4—1492no—
344C2×C4—1492no—
345C2×C4—1494no—
346C2×C4—1491no—
347C2×C4—1491no—
348C2×C4—1494no—
349C2×C4C23×D14912yes—
350C2×C4C23×D14914yes—
351C2×C4C23×D14914yes—
352C2×C4C23×D14912yes—
353C2×C4C23×D14911yescharacteristic
354C2×C4C23×D14911yescharacteristic
355C22—21no—
356C22—22no—
357C22—2982no—
358C22—2981no—
359C22—2984no—
360C22—2984no—
361C22—2984no—
362C22—2982no—
363C22—5964no—
364C22—1492no—
365C22C24×D14911yescharacteristic
366C4—21no—
367C4—24no—
368C4—22no—
369C4—22no—
370C4—24no—
371C4—2981no—
372C4—2982no—
373C4—2984no—
374C4—2982no—
375C4—1492no—
376C4#41×D14912yes—
377C2—41no—
378C2—2982no—
379C2—5961no—
380C2—5964no—
381C2C2×#41×D14911yescharacteristic
382C2#2375046212yes—
subgroupG/H
center, FrattiniC22C24×D149
commutator, socle, cosocleC22×C149C25
Fitting#541×C149C2
hypercenter#541D149
hypocenterC149#3455
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ #541

Complements

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

NH ≅ G/Ntype
1. #23750248C2semidirect
2. #23750247C2semidirect
3. #23750236C2semidirect
4. #23750231C2semidirect
5. #23750230C2semidirect
6. #23750223C2semidirect
7. #23750214C2semidirect
8. #23750181C2semidirect
9. #23750176C2semidirect
10. #23750160C2semidirect
11. #23750158C2semidirect
12. #23750138C2semidirect
13. C4×#14558737C2semidirect
14. #117×D149C2semidirect
15. #541×C149C2semidirect
18. #18011910C22semidirect
19. #18011908C22semidirect
21. #18011906C22semidirect
22. #18011905C22semidirect
23. #18011903C22semidirect
24. #18011901C22semidirect
25. #18011900C22semidirect
30. #18011896C22semidirect
31. #18011896C22semidirect
33. #18011891C22semidirect
35. #18011889C22semidirect
43. Q8×Dic149C22semidirect
44. #18011876C22semidirect
46. C4×D596C22semidirect
49. #18011873C22semidirect
50. #18011873C22semidirect
55. #18011869C22semidirect
63. C42×D149C22semidirect
64. C4⋊Q8×C149C22semidirect
66. #125×C149C22semidirect
67. #125×C149C22semidirect
69. C4×Q8×C149C22semidirect
191. C149#3455semidirect
196. #541D149semidirect
211. C4⋊Q8C2×D149semidirect
219. #125C2×D149semidirect
220. #125C2×D149semidirect
242. C4×Q8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502482
#237502472
#237502362
#237502312
#237502302
#237502232
#237502142
#237501812
#237501762
#237501602
#237501582
#237501382
C4×#145587372
#117×D1492
#541×C1492
#3455149