Finite Group Databasebeta

← #34056287

Subgroups — #34056287

Order 19072.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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×#18011937C212yesmaximal, complemented
2#23750280C211yesmaximal, characteristic, complemented
3#23749997C211yesmaximal, characteristic, complemented
4#23749869C212yesmaximal, complemented
5#23749830C211yesmaximal, characteristic, complemented
6#23749817C211yesmaximal, characteristic, complemented
7#23749776C212yesmaximal, complemented
8#23749768C212yesmaximal, complemented
9C4×#14558721C211yesmaximal, characteristic, complemented
10#23749703C211yesmaximal, characteristic, complemented
11D42×C149C211yesmaximal, characteristic, complemented
12C2×#14558736C2212yescomplemented
13#18011937—28no—
14C2×#14558724C2212yes—
15C2×#14558724C2212yescomplemented
16C2×#14558724C2212yescomplemented
17C2×#14558721C2211yescharacteristic
18C2×#14558721C2212yescomplemented
19C2×#14558720C2212yescomplemented
20#18011911C2211yescharacteristic, complemented
21#18011893—22no—
22#18011890C2212yescomplemented
23#18011882—21no—
24C4×D596C2211yescharacteristic, complemented
25C4⋊C4×D149—21no—
26#18011844C2211yescharacteristic, complemented
27C4⋊#11924746C2211yescharacteristic, complemented
28#18011834C2212yescomplemented
29#18011832C2211yescharacteristic
30#18011832C2212yescomplemented
31#18011831C2211yescharacteristic, complemented
32C22⋊#11924746C2212yescomplemented
33C4×#11924746C2211yescharacteristic, complemented
34C22×D4×C149—21no—
35C22×D4×C149C2212yes—
36#127×C149C2211yescharacteristic
37#121×C149—21no—
38#121×C149C2212yes—
39#120×C149—22no—
40C4×D4×C149C2211yescharacteristic
41C4×D4×C149C2211yescharacteristic
42#14558736—24no—
43#14558736—42no—
44C2×Dic298C2312yes—
45C2×D596C2311yescharacteristic
46C2×C22⋊D149—22no—
47C2×C4×D149—22no—
48C2×C4×D149—21no—
49#14558724—24no—
50#14558724—24no—
51#14558724—42no—
52#14558721—24no—
53#14558721D414yescomplemented
54#14558720—24no—
55C2×#11924746C2312yes—
56C2×#11924746C2311yescharacteristic
57C2×#11924746C2311yescharacteristic
58C4⋊Dic149—21no—
59C4⋊Dic149—21no—
60C4⋊Dic149C2311yescharacteristic
61#14558715—22no—
62C22⋊Dic149—22no—
63#14558713—21no—
64C24×C149—22no—
65C2×D4×C149—24no—
66C2×D4×C149—22no—
67C2×D4×C149—22no—
68C2×D4×C149—21no—
69C2×D4×C149—21no—
70C2×D4×C149—42no—
71C2×D4×C149—44no—
72C2×D4×C149D411yescharacteristic
73C2×D4×C149C2312yes—
74C2×D4×C149C2311yescharacteristic
75C22×C4×C149—21no—
76C22×C4×C149C2312yes—
77C4⋊C4×C149D411yescharacteristic
78C4⋊C4×C149C2311yescharacteristic
79C22⋊C4×C149—21no—
80C22⋊C4×C149—22no—
81C22⋊C4×C149D412yes—
82C42×C149C2311yescharacteristic
83C22×D149—21no—
84Dic298—22no—
85Dic298—22no—
86D596—21no—
87D596C2×D412yescomplemented
88C22⋊D149—44no—
89C2×Dic149—22no—
90C2×Dic149—21no—
91C4×D149—44no—
92C4×D149—42no—
93#11924746—22no—
94#11924746—21no—
95#11924746C2×D412yescomplemented
96C23×C149—21no—
97C23×C149—22no—
98C23×C149—44no—
99C23×C149—44no—
100C23×C149—82no—
101C23×C149C2×D412yes—
102D4×C149—22no—
103D4×C149—22no—
104D4×C149—21no—
105D4×C149—22no—
106D4×C149—44no—
107D4×C149—44no—
108D4×C149—42no—
109D4×C149—81no—
110D4×C149C2×D412yes—
111C2×C4×C149—22no—
112C2×C4×C149—22no—
113C2×C4×C149—21no—
114C2×C4×C149—42no—
115C2×C4×C149C2×D412yes—
116C2×C4×C149C2×D411yescharacteristic
117C2×C4×C149C2×D411yescharacteristic
118C2×C4×C149C2411yescharacteristic
119C22×C149—22no—
120C22×C149—22no—
121C22×C149—22no—
122C22×C149—22no—
123C22×C149—41no—
124C22×C149—41no—
125C22×C149—42no—
126C22×C149—42no—
127C22×C149—42no—
128C22×C149—88no—
129C22×C149C22×D411yescharacteristic
130C2×D149—22no—
131C2×D149—41no—
132C2×D149—41no—
133C4×C149—22no—
134C4×C149—21no—
135C4×C149—41no—
136C4×C149AGL(1,ℤ/8)12yescomplemented
137C4×C149C22×D411yescharacteristic
138C4×C149H(5,𝔽2)11yescharacteristic
139Dic149—42no—
140Dic149—41no—
141C2×C149—42no—
142C2×C149—42no—
143C2×C149—82no—
144C2×C149D4211yescharacteristic
145C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
146C2×C149#57711yescharacteristic
147D149—42no—
148C149#327211yescharacteristic, complemented, Sylow
149#3272—1491nomaximal, Sylow
150C2×AGL(1,ℤ/8)—1492no—
151#547—1491no—
152D42D14911yescharacteristic, complemented
153#492—1491no—
154#468—1492no—
155#461—1491no—
156#459—1491no—
157#450—1492no—
158#449—1492no—
159C4×D8—1491no—
160#436—1491no—
161C2×#41—1492no—
162C22×D4—21no—
163C22×D4C2×D14912yes—
164AGL(1,ℤ/8)—2988no—
165C2×SD16—1492no—
166C2×SD16—1492no—
167C2×SD16—1492no—
168C2×D8—1492no—
169C2×D8—1491no—
170C2×M16—1492no—
171C4⋊Q8—1491no—
172#127C2×D14911yescharacteristic
173#123—2982no—
174C22⋊Q8—1492no—
175#121—21no—
176#121—2981no—
177#121C2×D14912yes—
178#120—22no—
179C4×D4—1491no—
180C4×D4C2×D14911yescharacteristic
181C4×D4C2×D14911yescharacteristic
182C2×C4⋊C4—2981no—
183#107—1491no—
184C4⋊C8—1491no—
185#103—1492no—
186#102—1491no—
187#102—1492no—
188#102—1491no—
189C22⋊C8—1492no—
190C4×C8—1491no—
191C24—22no—
192#41—2984no—
193#41—5962no—
194C2×Q8—1492no—
195C2×D4—24no—
196C2×D4—22no—
197C2×D4—22no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—42no—
201C2×D4—44no—
202C2×D4—2982no—
203C2×D4—1491no—
204C2×D4C22⋊D14911yescharacteristic
205C2×D4C22×D14912yes—
206C2×D4C22×D14911yescharacteristic
207C22×C4—21no—
208C22×C4—2981no—
209C22×C4—2982no—
210C22×C4C22×D14912yes—
211SD16—2984no—
212SD16—2984no—
213SD16—5962no—
214D8—2984no—
215D8—1494no—
216M16—2984no—
217C2×C8—1491no—
218C2×C8—1492no—
219C2×C8—1491no—
220C4⋊C4—2981no—
221C4⋊C4—2982no—
222C4⋊C4—2981no—
223C4⋊C4—1491no—
224C4⋊C4C22⋊D14911yescharacteristic
225C4⋊C4C22×D14911yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—22no—
228C22⋊C4—2982no—
229C22⋊C4—2981no—
230C22⋊C4C22⋊D14912yes—
231C42C22×D14911yescharacteristic
232C23—21no—
233C23—22no—
234C23—44no—
235C23—44no—
236C23—82no—
237C23—2981no—
238C23C2×C22⋊D14912yes—
239Q8—2982no—
240Q8—2982no—
241D4—22no—
242D4—22no—
243D4—21no—
244D4—22no—
245D4—44no—
246D4—44no—
247D4—42no—
248D4—81no—
249D4—2981no—
250D4—5964no—
251D4—1492no—
252D4D4×D14912yes—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—2981no—
258C2×C4—2982no—
259C2×C4—5964no—
260C2×C4—5962no—
261C2×C4C2×C22⋊D14911yescharacteristic
262C2×C4C2×C22⋊D14912yes—
263C2×C4C2×C22⋊D14911yescharacteristic
264C2×C4C23×D14911yescharacteristic
265C8—2982no—
266C8—2981no—
267C8—1492no—
268C22—22no—
269C22—22no—
270C22—22no—
271C22—22no—
272C22—41no—
273C22—41no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—88no—
278C22—2982no—
279C22—5961no—
280C22—5961no—
281C22C22×C22⋊D14911yescharacteristic
282C4—21no—
283C4—22no—
284C4—41no—
285C4—5961no—
286C4—5962no—
287C4#1801193712yescomplemented
288C4C2×D4×D14911yescharacteristic
289C4#1801195611yescharacteristic
290C2—42no—
291C2—42no—
292C2—82no—
293C2—5962no—
294C2D4×C22⋊D14911yescharacteristic
295C2C2×#1801193711yescharacteristic
296C2#2375043611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingD42×C149C2
socleC22×C149C22×D4
hypercenterD42D149
hypocenterC149#3272
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#18011937C2semidirect
2. #23750280C2semidirect
3. #23749997C2semidirect
4. #23749869C2semidirect
5. #23749830C2semidirect
6. #23749817C2semidirect
7. #23749776C2semidirect
8. #23749768C2semidirect
9. C4×#14558721C2semidirect
10. #23749703C2semidirect
11. D42×C149C2semidirect
12. C2×#14558736C22semidirect
15. C2×#14558724C22semidirect
16. C2×#14558724C22semidirect
18. C2×#14558721C22semidirect
19. C2×#14558720C22semidirect
20. #18011911C22semidirect
22. #18011890C22semidirect
24. C4×D596C22semidirect
26. #18011844C22semidirect
27. C4⋊#11924746C22semidirect
28. #18011834C22semidirect
30. #18011832C22semidirect
31. #18011831C22semidirect
32. C22⋊#11924746C22semidirect
33. C4×#11924746C22semidirect
53. #14558721D4semidirect
87. D596C2×D4semidirect
95. #11924746C2×D4semidirect
136. C4×C149AGL(1,ℤ/8)semidirect
148. C149#3272semidirect
152. D42D149semidirect
287. C4#18011937semidirect

Maximal subgroups

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

subgroupindex
C2×#180119372
#237502802
#237499972
#237498692
#237498302
#237498172
#237497762
#237497682
C4×#145587212
#237497032
D42×C1492
#3272149