Finite Group Databasebeta

← #34056306

Subgroups — #34056306

Order 19072.

556 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011938C212yesmaximal, complemented
2#23750297C211yesmaximal, characteristic, complemented
3#23750260C211yesmaximal, characteristic, complemented
4#23750001C211yesmaximal, characteristic, complemented
5#23749877C212yesmaximal, complemented
6#23749821C211yesmaximal, characteristic, complemented
7#23749769C212yesmaximal, complemented
8#23749760C212yesmaximal, complemented
9C4×#14558723C211yesmaximal, characteristic, complemented
10#23749702C211yesmaximal, characteristic, complemented
11#460×C149C211yesmaximal, characteristic, complemented
12C2×#14558737C2212yescomplemented
13C2×D4×D149—21no—
14C2×D4×D149C2212yes—
15#18011938—28no—
16C2×#14558723C2211yescharacteristic
17C2×D1192C2212yes—
18C2×#14558721C2212yescomplemented
19C2×#14558721C2212yescomplemented
20C2×#14558719C2212yescomplemented
21#18011908—21no—
22#18011908C2211yescharacteristic, complemented
23#18011886—22no—
24#18011886C2212yescomplemented
25#18011882—21no—
26#18011882C2212yes—
27#18011879—22no—
28C4×D596—21no—
29C4×D596C2211yescharacteristic
30C4×D596C2211yescharacteristic
31#18011842C2211yescharacteristic, complemented
32#18011835C2211yescharacteristic, complemented
33#18011833C2212yescomplemented
34#18011831C2211yescharacteristic
35#18011823C2212yescomplemented
36C4×#11924746C2211yescharacteristic, complemented
37C2×SD16×C149C2212yescomplemented
38#127×C149C2211yescharacteristic
39C4×Q8×C149C2211yescharacteristic, complemented
40C4⋊C8×C149C2211yescharacteristic, complemented
41#102×C149C2212yescomplemented
42C23×D149—22no—
43#14558737—24no—
44#14558737—42no—
45C2×D596—22no—
46C2×D596—22no—
47C2×D596—21no—
48C2×D596—21no—
49C2×D596D411yescharacteristic
50C2×D596C2312yes—
51C2×D596C2311yescharacteristic
52C2×C22⋊D149—22no—
53C2×C22⋊D149—22no—
54D4×D149—24no—
55D4×D149—42no—
56D4×D149—44no—
57C2×C4×D149—22no—
58C2×C4×D149—21no—
59C2×C4×D149C2312yes—
60#14558723D414yescomplemented
61D1192—24no—
62#14558721—24no—
63#14558721—42no—
64#14558719—24no—
65C2×#11924746C2311yescharacteristic
66C2×#11924746C2311yescharacteristic
67C4⋊Dic149D411yescharacteristic
68C4⋊Dic149C2311yescharacteristic
69C22⋊Dic149—22no—
70#14558713—22no—
71#14558713—21no—
72#14558713D412yes—
73C2×Q8×C149C2311yescharacteristic
74C2×D4×C149—21no—
75C2×D4×C149—21no—
76C2×D4×C149C2312yes—
77SD16×C149—24no—
78C2×C8×C149C2312yes—
79C4⋊C4×C149—21no—
80C4⋊C4×C149C2311yescharacteristic
81C42×C149—21no—
82C42×C149C2311yescharacteristic
83C22×D149—21no—
84C22×D149—22no—
85C22×D149—44no—
86C22×D149—44no—
87C22×D149—82no—
88C22×D149C2×D412yes—
89D596—22no—
90D596—22no—
91D596—21no—
92D596—22no—
93D596—44no—
94D596—42no—
95D596—81no—
96D596—82no—
97D596C2×D412yes—
98C22⋊D149—44no—
99C22⋊D149—44no—
100C2×Dic149—21no—
101C2×Dic149C2×D412yes—
102C4×D149—22no—
103C4×D149—22no—
104C4×D149—44no—
105C4×D149—42no—
106#11924746—21no—
107#11924746C2×D412yescomplemented
108C23×C149—22no—
109Q8×C149—21no—
110Q8×C149C2×D412yescomplemented
111D4×C149—22no—
112D4×C149—22no—
113D4×C149—42no—
114D4×C149—81no—
115C2×C4×C149—21no—
116C2×C4×C149—21no—
117C2×C4×C149C2×D411yescharacteristic
118C2×C4×C149C2×D411yescharacteristic
119C2×C4×C149C2411yescharacteristic
120C8×C149—22no—
121C22×C149—42no—
122C22×C149—42no—
123C22×C149—42no—
124C22×C149C22×D411yescharacteristic
125C2×D149—22no—
126C2×D149—22no—
127C2×D149—22no—
128C2×D149—22no—
129C2×D149—41no—
130C2×D149—41no—
131C2×D149—42no—
132C2×D149—42no—
133C2×D149—42no—
134C2×D149—88no—
135C4×C149—22no—
136C4×C149—21no—
137C4×C149—41no—
138C4×C149AGL(1,ℤ/8)12yescomplemented
139C4×C149C22×D411yescharacteristic
140C4×C149H(5,𝔽2)11yescharacteristic
141Dic149—22no—
142Dic149—41no—
143C2×C149—82no—
144C2×C149D4211yescharacteristic
145C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
146C2×C149#57611yescharacteristic
147D149—42no—
148D149—42no—
149D149—82no—
150C149#327411yescharacteristic, complemented, Sylow
151#3274—1491nomaximal, Sylow
152C2×AGL(1,ℤ/8)—1492no—
153#550—1491no—
154D42—1491no—
155#493—1491no—
156#469—1492no—
157#460D14911yescharacteristic, complemented
158#459—1491no—
159#449—1492no—
160#447—1492no—
161C4×SD16—1491no—
162#436—1491no—
163C2×#41—1492no—
164C22×D4—2981no—
165C22×D4—1492no—
166AGL(1,ℤ/8)—2988no—
167C2×SD16—1491no—
168C2×SD16C2×D14912yescomplemented
169C2×D8—1492no—
170C2×D8—1492no—
171C2×D8—1492no—
172C2×M16—1492no—
173#127—2981no—
174#127—1491no—
175#127C2×D14911yescharacteristic
176#121—2981no—
177#121—2982no—
178#121—1492no—
179#121—1492no—
180#120—2982no—
181C4×Q8C2×D14911yescharacteristic, complemented
182C4×D4—2981no—
183C4×D4—1491no—
184C4×D4—1491no—
185#106—1491no—
186C4⋊C8C2×D14911yescharacteristic, complemented
187#103—1491no—
188#102—1492no—
189#102—1491no—
190#102C2×D14912yescomplemented
191C22⋊C8—1492no—
192C4×C8—1491no—
193C24—2982no—
194#41—2984no—
195#41—5962no—
196C2×Q8C22×D14911yescharacteristic
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—2982no—
200C2×D4—2982no—
201C2×D4—2984no—
202C2×D4—2982no—
203C2×D4—2982no—
204C2×D4—2981no—
205C2×D4—2981no—
206C2×D4—5962no—
207C2×D4—5964no—
208C2×D4—1491no—
209C2×D4—1492no—
210C2×D4—1491no—
211C2×D4C22×D14912yes—
212C22×C4—2982no—
213C22×C4—2981no—
214C22×C4—1492no—
215SD16—24no—
216SD16—1494no—
217D8—2984no—
218D8—2984no—
219D8—5962no—
220M16—2984no—
221C2×C8—1491no—
222C2×C8—1491no—
223C2×C8C22×D14912yes—
224C4⋊C4—21no—
225C4⋊C4—1491no—
226C4⋊C4—1491no—
227C4⋊C4C22×D14911yescharacteristic
228C22⋊C4—2982no—
229C22⋊C4—2982no—
230C22⋊C4—2981no—
231C22⋊C4—1492no—
232C42—21no—
233C42C22×D14911yescharacteristic
234C23—22no—
235C23—2981no—
236C23—2982no—
237C23—5964no—
238C23—5964no—
239C23—1492no—
240C23—11922no—
241Q8—21no—
242Q8D4×D14912yescomplemented
243D4—22no—
244D4—22no—
245D4—42no—
246D4—81no—
247D4—2982no—
248D4—2982no—
249D4—2981no—
250D4—2982no—
251D4—5964no—
252D4—5964no—
253D4—5964no—
254D4—5962no—
255D4—1492no—
256D4—11921no—
257D4—11922no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—2982no—
261C2×C4—2982no—
262C2×C4—2981no—
263C2×C4—5964no—
264C2×C4—5962no—
265C2×C4—1492no—
266C2×C4D4×D14911yescharacteristic
267C2×C4D4×D14911yescharacteristic
268C2×C4C23×D14911yescharacteristic
269C8—22no—
270C8—2981no—
271C8—1492no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22—2982no—
276C22—2982no—
277C22—2982no—
278C22—2982no—
279C22—5961no—
280C22—5961no—
281C22—5962no—
282C22—5962no—
283C22—5962no—
284C22—11928no—
285C22C2×D4×D14911yescharacteristic
286C4—21no—
287C4—22no—
288C4—41no—
289C4—2982no—
290C4—5961no—
291C4#1801193812yescomplemented
292C4C2×D4×D14911yescharacteristic
293C4#1801195711yescharacteristic
294C2—82no—
295C2—5962no—
296C2—5962no—
297C2—11922no—
298C2#2375025911yescharacteristic
299C2C2×#1801193811yescharacteristic
300C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#460×C149C2
socleC22×C149C22×D4
hypercenter#460D149
hypocenterC149#3274
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×#18011938C2semidirect
2. #23750297C2semidirect
3. #23750260C2semidirect
4. #23750001C2semidirect
5. #23749877C2semidirect
6. #23749821C2semidirect
7. #23749769C2semidirect
8. #23749760C2semidirect
9. C4×#14558723C2semidirect
10. #23749702C2semidirect
11. #460×C149C2semidirect
12. C2×#14558737C22semidirect
18. C2×#14558721C22semidirect
19. C2×#14558721C22semidirect
20. C2×#14558719C22semidirect
22. #18011908C22semidirect
24. #18011886C22semidirect
31. #18011842C22semidirect
32. #18011835C22semidirect
33. #18011833C22semidirect
35. #18011823C22semidirect
36. C4×#11924746C22semidirect
37. C2×SD16×C149C22semidirect
39. C4×Q8×C149C22semidirect
40. C4⋊C8×C149C22semidirect
41. #102×C149C22semidirect
60. #14558723D4semidirect
107. #11924746C2×D4semidirect
110. Q8×C149C2×D4semidirect
138. C4×C149AGL(1,ℤ/8)semidirect
150. C149#3274semidirect
157. #460D149semidirect
168. C2×SD16C2×D149semidirect
181. C4×Q8C2×D149semidirect
186. C4⋊C8C2×D149semidirect
190. #102C2×D149semidirect
242. Q8D4×D149semidirect
291. C4#18011938semidirect

Maximal subgroups

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

subgroupindex
C2×#180119382
#237502972
#237502602
#237500012
#237498772
#237498212
#237497692
#237497602
C4×#145587232
#237497022
#460×C1492
#3274149