Finite Group Databasebeta

← #562×D149 #34058813

Subgroups — #562×D149 #34058813

Order 19072.

1152 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750373C211yesmaximal, characteristic, complemented
2#23750372C214yesmaximal, complemented
3#23750371C214yesmaximal, complemented
4#23750370C214yesmaximal, complemented
5#23750369C212yesmaximal, complemented
6#125×D149C211yesmaximal, characteristic, complemented
7#124×D149C212yesmaximal, complemented
8#123×D149C214yesmaximal, complemented
9C22⋊Q8×D149C214yesmaximal, complemented
10#121×D149C214yesmaximal, complemented
11#562×C149C211yesmaximal, characteristic, complemented
12C2×Q8×D149C2212yes—
13C2×D4×D149C2214yes—
14C2×D4×D149C2212yes—
15C22×C4×D149C2214yes—
16#18011903C2211yescharacteristic, complemented
17#18011902C2212yescomplemented
18#18011901C2214yescomplemented
19#18011900C2212yescomplemented
20#18011899C2212yescomplemented
21#18011898C2212yescomplemented
22#18011897C2214yescomplemented
23#18011897C2214yescomplemented
24#18011896C2214yescomplemented
25#18011896C2214yescomplemented
26#18011895C2214yescomplemented
27#18011894C2214yescomplemented
28#18011893C2214yescomplemented
29#18011893C2214yescomplemented
30#18011892C2214yescomplemented
31#18011891C2214yescomplemented
32#18011890C2214yescomplemented
33#18011889C2214yescomplemented
34#18011889C2214yescomplemented
35#18011888C2214yescomplemented
36#18011888C2214yescomplemented
37#18011887C2214yescomplemented
38#18011886C2214yescomplemented
39#18011885C2214yescomplemented
40#18011884C2214yescomplemented
41#18011884C2214yescomplemented
42#18011883C2214yescomplemented
43#18011883C2214yescomplemented
44#18011882C2214yescomplemented
45C4⋊C4×D149C2214yes—
46C4⋊C4×D149C2212yes—
47C4⋊C4×D149C2214yes—
48C22⋊C4×D149C2214yes—
49C22⋊C4×D149C2214yes—
50C22⋊C4×D149C2214yes—
51C42×D149C2211yescharacteristic
52#125×C149C2211yescharacteristic, complemented
53#124×C149C2212yescomplemented
54#123×C149C2214yescomplemented
55C22⋊Q8×C149C2214yescomplemented
56#121×C149C2214yescomplemented
57C23×D149C2314yes—
58C2×Dic298C2312yes—
59C2×Dic298C2314yes—
60Q8×D149—44no—
61C2×D596C2312yes—
62C2×D596C2314yes—
63C2×C22⋊D149C2314yes—
64C2×C22⋊D149C2314yes—
65C2×C22⋊D149C2314yes—
66D4×D149—48no—
67D4×D149—44no—
68C22×Dic149C2314yes—
69C2×C4×D149—48no—
70C2×C4×D149C2314yes—
71C2×C4×D149C2314yes—
72C2×C4×D149C2312yes—
73C2×C4×D149C2311yescharacteristic
74C2×C4×D149C2314yes—
75C2×C4×D149C2314yes—
76C4⋊Dic149C2314yes—
77C4⋊Dic149C2314yes—
78C4⋊Dic149C2312yes—
79#14558715C2314yes—
80#14558715C2314yes—
81#14558715C2314yes—
82#14558715C2314yes—
83#14558715C2314yes—
84C22⋊Dic149C2314yes—
85C22⋊Dic149C2314yes—
86C22⋊Dic149C2314yes—
87#14558713C2314yes—
88#14558713C2314yes—
89#14558713C2314yes—
90#14558713C2314yes—
91#14558713C2314yes—
92#14558713C2314yes—
93C4×Dic149C2311yescharacteristic
94C4×Dic149C2312yes—
95C2×Q8×C149C2312yes—
96C2×D4×C149C2314yes—
97C2×D4×C149C2312yes—
98C22×C4×C149C2314yes—
99C4⋊C4×C149C2314yes—
100C4⋊C4×C149C2314yes—
101C4⋊C4×C149C2312yes—
102C22⋊C4×C149C2314yes—
103C22⋊C4×C149C2314yes—
104C22⋊C4×C149C2314yes—
105C42×C149C2311yescharacteristic
106C22×D149—28no—
107C22×D149—28no—
108C22×D149—28no—
109C22×D149C2414yes—
110C22×D149C2411yescharacteristic
111Dic298—42no—
112Dic298—44no—
113D596—44no—
114D596—42no—
115C22⋊D149—44no—
116C22⋊D149—44no—
117C22⋊D149—44no—
118C2×Dic149—44no—
119C2×Dic149C2414yes—
120C2×Dic149C2414yes—
121C2×Dic149C2412yes—
122C2×Dic149C2411yescharacteristic
123C4×D149—28no—
124C4×D149—28no—
125C4×D149—24no—
126C4×D149—22no—
127C4×D149—44no—
128C4×D149—44no—
129C23×C149C2414yes—
130Q8×C149—42no—
131D4×C149—44no—
132D4×C149—42no—
133C2×C4×C149—44no—
134C2×C4×C149C2414yes—
135C2×C4×C149C2414yes—
136C2×C4×C149C2412yes—
137C2×C4×C149C2411yescharacteristic
138C22×C149—24no—
139C22×C149—24no—
140C22×C149—24no—
141C22×C149C2511yescharacteristic
142C2×D149—24no—
143C2×D149—24no—
144C2×D149—24no—
145C2×D149—416no—
146C2×D149H(5,𝔽2)14yes—
147C2×D1492−1+412yes—
148C4×C149—24no—
149C4×C149—24no—
150C4×C149—22no—
151C4×C149—21no—
152Dic149—24no—
153Dic149—24no—
154Dic149—22no—
155Dic149—21no—
156C2×C149—44no—
157C2×C149C2×H(5,𝔽2)12yes—
158C2×C149C2×2−1+411yescharacteristic
159D149—44no—
160D149#56214yesdirect product factor
161C149C2×#56211yescharacteristic, complemented, Sylow
162C2×#562—1491nomaximal, Sylow
163#562—1491no—
164#562—1492no—
165#562—1494no—
166#562—1494no—
167#562—1494no—
168#562D14911yescharacteristic, direct product factor
169C2×#125—1491no—
170C2×#124—1492no—
171C2×#123—1494no—
172C2×C22⋊Q8—1494no—
173C2×#121—1494no—
174C22×Q8—1492no—
175C22×D4—1494no—
176C22×D4—1492no—
177C23×C4—1494no—
178#125—1494no—
179#125—1492no—
180#125—1491no—
181#125C2×D14911yescharacteristic, complemented
182#124—1492no—
183#124—1492no—
184#124—1494no—
185#124—1494no—
186#124—1492no—
187#124C2×D14912yescomplemented
188#123—1494no—
189#123—1494no—
190#123—1494no—
191#123—1494no—
192#123—1494no—
193#123—1494no—
194#123—1494no—
195#123C2×D14914yescomplemented
196C22⋊Q8—1494no—
197C22⋊Q8—1494no—
198C22⋊Q8—1494no—
199C22⋊Q8—1494no—
200C22⋊Q8—1494no—
201C22⋊Q8—1494no—
202C22⋊Q8—1494no—
203C22⋊Q8C2×D14914yescomplemented
204#121—1494no—
205#121—1494no—
206#121—1494no—
207#121—1494no—
208#121—1494no—
209#121—1494no—
210#121—1494no—
211#121C2×D14914yescomplemented
212C2×C4⋊C4—1494no—
213C2×C4⋊C4—1494no—
214C2×C4⋊C4—1492no—
215C2×C22⋊C4—1494no—
216C2×C22⋊C4—1494no—
217C2×C22⋊C4—1494no—
218C2×C42—1491no—
219C24—1494no—
220C2×Q8—5964no—
221C2×Q8—1494no—
222C2×Q8—1492no—
223C2×Q8C22×D14912yes—
224C2×D4—5968no—
225C2×D4—5964no—
226C2×D4—1494no—
227C2×D4—1494no—
228C2×D4—1494no—
229C2×D4—1494no—
230C2×D4—1492no—
231C2×D4C22×D14914yes—
232C2×D4C22×D14912yes—
233C22×C4—5968no—
234C22×C4—1491no—
235C22×C4—1492no—
236C22×C4—1494no—
237C22×C4—1494no—
238C22×C4—1494no—
239C22×C4—1494no—
240C22×C4—1494no—
241C22×C4C22×D14914yes—
242C4⋊C4—1494no—
243C4⋊C4—1494no—
244C4⋊C4—1494no—
245C4⋊C4—1494no—
246C4⋊C4—1494no—
247C4⋊C4—1494no—
248C4⋊C4—1494no—
249C4⋊C4—1492no—
250C4⋊C4C22×D14914yes—
251C4⋊C4C22×D14914yes—
252C4⋊C4C22×D14912yes—
253C22⋊C4—1494no—
254C22⋊C4—1494no—
255C22⋊C4—1494no—
256C22⋊C4—1494no—
257C22⋊C4—1494no—
258C22⋊C4—1494no—
259C22⋊C4—1494no—
260C22⋊C4—1494no—
261C22⋊C4—1494no—
262C22⋊C4C22×D14914yes—
263C22⋊C4C22×D14914yes—
264C22⋊C4C22×D14914yes—
265C42—1492no—
266C42—1491no—
267C42C22×D14911yescharacteristic
268C23—2988no—
269C23—2988no—
270C23—2988no—
271C23—1494no—
272C23—1491no—
273C23C23×D14914yes—
274Q8—42no—
275Q8—5964no—
276Q8—5962no—
277D4—44no—
278D4—42no—
279D4—5964no—
280D4—5962no—
281D4—5964no—
282D4—5964no—
283D4—5964no—
284C2×C4—44no—
285C2×C4—2988no—
286C2×C4—2988no—
287C2×C4—2982no—
288C2×C4—2984no—
289C2×C4—5964no—
290C2×C4—5964no—
291C2×C4—5964no—
292C2×C4—1491no—
293C2×C4—1492no—
294C2×C4—1494no—
295C2×C4—1494no—
296C2×C4C23×D14911yescharacteristic
297C2×C4C23×D14912yes—
298C2×C4C23×D14914yes—
299C2×C4C23×D14914yes—
300C22—24no—
301C22—24no—
302C22—24no—
303C22—2984no—
304C22—2984no—
305C22—2984no—
306C22—59616no—
307C22—1494no—
308C22—1492no—
309C22C24×D14911yescharacteristic
310C4—24no—
311C4—24no—
312C4—22no—
313C4—21no—
314C4—2984no—
315C4—2984no—
316C4—2982no—
317C4—2981no—
318C2—44no—
319C2—5964no—
320C2—1494no—
321C2H(5,𝔽2)×D14912yes—
322C22−1+4×D14911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D149
commutator, socle, cosocleC22×C149C25
Fitting#562×C149C2
hypercenter#562D149
hypocenterC149C2×#562
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #23750373C2semidirect
2. #23750372C2semidirect
3. #23750371C2semidirect
4. #23750370C2semidirect
5. #23750369C2semidirect
6. #125×D149C2semidirect
7. #124×D149C2semidirect
8. #123×D149C2semidirect
9. C22⋊Q8×D149C2semidirect
10. #121×D149C2semidirect
11. #562×C149C2semidirect
16. #18011903C22semidirect
17. #18011902C22semidirect
18. #18011901C22semidirect
19. #18011900C22semidirect
20. #18011899C22semidirect
21. #18011898C22semidirect
22. #18011897C22semidirect
23. #18011897C22semidirect
24. #18011896C22semidirect
25. #18011896C22semidirect
26. #18011895C22semidirect
27. #18011894C22semidirect
28. #18011893C22semidirect
29. #18011893C22semidirect
30. #18011892C22semidirect
31. #18011891C22semidirect
32. #18011890C22semidirect
33. #18011889C22semidirect
34. #18011889C22semidirect
35. #18011888C22semidirect
36. #18011888C22semidirect
37. #18011887C22semidirect
38. #18011886C22semidirect
39. #18011885C22semidirect
40. #18011884C22semidirect
41. #18011884C22semidirect
42. #18011883C22semidirect
43. #18011883C22semidirect
44. #18011882C22semidirect
52. #125×C149C22semidirect
53. #124×C149C22semidirect
54. #123×C149C22semidirect
55. C22⋊Q8×C149C22semidirect
56. #121×C149C22semidirect
160. D149#562direct (N × H)
161. C149C2×#562semidirect
168. #562D149direct (N × H)
181. #125C2×D149semidirect
187. #124C2×D149semidirect
195. #123C2×D149semidirect
203. C22⋊Q8C2×D149semidirect
211. #121C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237503732
#237503722
#237503712
#237503702
#237503692
#125×D1492
#124×D1492
#123×D1492
C22⋊Q8×D1492
#121×D1492
#562×C1492
C2×#562149