Finite Group Databasebeta

← #14575238

Subgroups — #14575238

Order 2432.

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

normal subgroups only

This group has 546 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×#10597360C212yesmaximal, complemented
2#11927197C211yesmaximal, characteristic, complemented
3D4×D76C211yesmaximal, characteristic, complemented
4#11926918C211yesmaximal, characteristic, complemented
5#11926793C212yesmaximal, complemented
6#11926740C211yesmaximal, characteristic, complemented
7#11926693C212yesmaximal, complemented
8#11926692C212yesmaximal, complemented
9C4×#64525C211yesmaximal, characteristic, complemented
10#11926621C211yesmaximal, characteristic, complemented
11C19×#461C211yesmaximal, characteristic, complemented
12C2×#64545C2212yescomplemented
13C2×D4×D19C2212yes—
14C22×D76—21no—
15C2×SD16×C19C2212yes—
16C19×C4⋊Q8C2211yescharacteristic, complemented
17C4×D4×C19C2211yescharacteristic
18#10597392C2212yescomplemented
19C2×#64527C2212yescomplemented
20C2×#64527C2212yescomplemented
21C2×#64525C2211yescharacteristic
22#10597376—21no—
23#10597360—28no—
24C2×D152C2212yescomplemented
25C2×#64515C2212yescomplemented
26#10597341—21no—
27#10597341C2212yes—
28#10597340—22no—
29C4⋊C4×D19—21no—
30#10597328—22no—
31#10597320C2211yescharacteristic
32C4×D76C2211yescharacteristic
33C4×D76C2211yescharacteristic, complemented
34C19×C4⋊C8C2211yescharacteristic, complemented
35C19×#103C2212yescomplemented
36#10597289C2211yescharacteristic
37#10597278C2212yescomplemented
38(C2×D19)⋊C8C2212yescomplemented
39#10597266C2211yescharacteristic, complemented
40#10597264C2211yescharacteristic, complemented
41C4×C19⋊C8C2211yescharacteristic, complemented
42C23×D19—22no—
43C2×Q8×C19C2312yes—
44C2×D4×C19C2311yescharacteristic
45C22×C4×C19—21no—
46C2×C22⋊D19—22no—
47#64545—24no—
48#64545—42no—
49D4×D19—24no—
50D4×D19—42no—
51C2×D76—22no—
52C2×D76—22no—
53C2×D76—21no—
54C2×D76—21no—
55C2×D76—44no—
56C2×D76D411yescharacteristic
57C2×D76C2312yes—
58C2×D76C2311yescharacteristic
59C2×C4×D19—21no—
60C2×C4×D19—22no—
61C2×C4×D19C2312yes—
62SD16×C19—24no—
63C2×C8×C19C2312yes—
64C4⋊C4×C19—21no—
65C4⋊C4×C19—21no—
66C4⋊C4×C19C2311yescharacteristic
67C22⋊C4×C19—21no—
68C42×C19C2311yescharacteristic
69#64527—24no—
70#64527—42no—
71#64525D414yescomplemented
72(C2×D19)⋊C4—22no—
73(C2×D19)⋊C4—21no—
74(C2×D19)⋊C4—22no—
75(C2×D19)⋊C4D412yes—
76C4⋊Dic19D411yescharacteristic
77C4⋊Dic19C2311yescharacteristic
78Dic19⋊C4—22no—
79C2×C19⋊C8C2311yescharacteristic
80C2×C19⋊C8C2311yescharacteristic
81D152—24no—
82#64515—24no—
83C23×C19—21no—
84C22×D19—21no—
85C22×D19—22no—
86C22×D19—44no—
87C22×D19—44no—
88C22×D19—82no—
89C22×D19C2×D412yes—
90Q8×C19—22no—
91Q8×C19—22no—
92D4×C19—21no—
93D4×C19C2×D412yes—
94C2×C4×C19—22no—
95C2×C4×C19—21no—
96C2×C4×C19—42no—
97C2×C4×C19C2×D411yescharacteristic
98C2×C4×C19C2×D411yescharacteristic
99C2×C4×C19C2411yescharacteristic
100C22⋊D19—44no—
101C2×Dic19—21no—
102C2×Dic19C2×D412yes—
103D76—22no—
104D76—22no—
105D76—21no—
106D76—22no—
107D76—44no—
108D76—44no—
109D76—42no—
110D76—81no—
111D76C2×D412yescomplemented
112C4×D19—22no—
113C4×D19—22no—
114C4×D19—44no—
115C4×D19—42no—
116C8×C19—22no—
117C19⋊C8—21no—
118C19⋊C8C2×D412yescomplemented
119#3272—191nomaximal, Sylow
120C22×C19—22no—
121C22×C19—41no—
122C22×C19—41no—
123C22×C19C22×D411yescharacteristic
124C2×D19—22no—
125C2×D19—22no—
126C2×D19—22no—
127C2×D19—22no—
128C2×D19—41no—
129C2×D19—41no—
130C2×D19—42no—
131C2×D19—42no—
132C2×D19—42no—
133C2×D19—88no—
134C4×C19—21no—
135C4×C19—42no—
136C4×C19—41no—
137C4×C19AGL(1,ℤ/8)12yescomplemented
138C4×C19C22×D411yescharacteristic
139C4×C19H(5,𝔽2)11yescharacteristic
140Dic19—22no—
141Dic19—41no—
142C2×AGL(1,ℤ/8)—192no—
143#547—191no—
144D42—191no—
145#492—191no—
146#468—192no—
147#461D1911yescharacteristic, complemented
148#459—191no—
149#450—192no—
150#449—192no—
151C4×D8—191no—
152#436—191no—
153C2×C19—42no—
154C2×C19D4211yescharacteristic
155C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
156C2×C19#57711yescharacteristic
157D19—42no—
158D19—42no—
159D19—82no—
160C2×#41—192no—
161C22×D4—192no—
162C22×D4—381no—
163AGL(1,ℤ/8)—388no—
164C2×SD16—192no—
165C2×SD16—192no—
166C2×SD16C2×D1912yes—
167C2×D8—191no—
168C2×D8—192no—
169C2×M16—192no—
170C4⋊Q8C2×D1911yescharacteristic, complemented
171#127—191no—
172#123—382no—
173C22⋊Q8—192no—
174#121—192no—
175#121—381no—
176#121—381no—
177#120—382no—
178C4×D4—191no—
179C4×D4—191no—
180C4×D4C2×D1911yescharacteristic
181C2×C4⋊C4—381no—
182#107—191no—
183C4⋊C8C2×D1911yescharacteristic, complemented
184#103C2×D1912yescomplemented
185#102—191no—
186#102—192no—
187#102—191no—
188C22⋊C8—192no—
189C4×C8—191no—
190C19#327211yescharacteristic, complemented, Sylow
191C24—382no—
192#41—384no—
193#41—762no—
194C2×Q8C22×D1912yes—
195C2×D4—191no—
196C2×D4—191no—
197C2×D4—192no—
198C2×D4—382no—
199C2×D4—382no—
200C2×D4—382no—
201C2×D4—384no—
202C2×D4—381no—
203C2×D4—381no—
204C2×D4—764no—
205C2×D4—762no—
206C2×D4C22×D1911yescharacteristic
207C22×C4—21no—
208C22×C4—192no—
209C22×C4—382no—
210C22×C4—381no—
211SD16—24no—
212SD16—384no—
213SD16—762no—
214D8—194no—
215D8—384no—
216M16—384no—
217C2×C8—191no—
218C2×C8—191no—
219C2×C8C22×D1912yes—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—191no—
223C4⋊C4—191no—
224C4⋊C4—382no—
225C4⋊C4C22×D1911yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—192no—
228C22⋊C4—382no—
229C22⋊C4—382no—
230C22⋊C4—381no—
231C42C22×D1911yescharacteristic
232C23—21no—
233C23—192no—
234C23—381no—
235C23—382no—
236C23—764no—
237C23—764no—
238C23—1522no—
239Q8—22no—
240Q8—22no—
241D4—21no—
242D4—192no—
243D4—382no—
244D4—381no—
245D4—382no—
246D4—382no—
247D4—764no—
248D4—764no—
249D4—764no—
250D4—762no—
251D4—1521no—
252D4D4×D1912yes—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—192no—
257C2×C4—382no—
258C2×C4—382no—
259C2×C4—381no—
260C2×C4—764no—
261C2×C4—762no—
262C2×C4D4×D1911yescharacteristic
263C2×C4D4×D1911yescharacteristic
264C2×C4C23×D1911yescharacteristic
265C8—22no—
266C8—192no—
267C8—381no—
268C22—22no—
269C22—41no—
270C22—41no—
271C22—382no—
272C22—382no—
273C22—382no—
274C22—382no—
275C22—761no—
276C22—761no—
277C22—762no—
278C22—762no—
279C22—762no—
280C22—1528no—
281C22C2×D4×D1911yescharacteristic
282C4—21no—
283C4—41no—
284C4—42no—
285C4—382no—
286C4—761no—
287C4#1059736012yescomplemented
288C4C2×D4×D1911yescharacteristic
289C4#1059743511yescharacteristic
290C2—42no—
291C2—762no—
292C2—762no—
293C2—1522no—
294C2#1192717811yescharacteristic
295C2C2×#1059736011yescharacteristic
296C2#1192735311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#461C2
socleC22×C19C22×D4
hypercenter#461D19
hypocenterC19#3272
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×#10597360C2semidirect
2. #11927197C2semidirect
3. D4×D76C2semidirect
4. #11926918C2semidirect
5. #11926793C2semidirect
6. #11926740C2semidirect
7. #11926693C2semidirect
8. #11926692C2semidirect
9. C4×#64525C2semidirect
10. #11926621C2semidirect
11. C19×#461C2semidirect
12. C2×#64545C22semidirect
16. C19×C4⋊Q8C22semidirect
18. #10597392C22semidirect
19. C2×#64527C22semidirect
20. C2×#64527C22semidirect
24. C2×D152C22semidirect
25. C2×#64515C22semidirect
33. C4×D76C22semidirect
34. C19×C4⋊C8C22semidirect
35. C19×#103C22semidirect
37. #10597278C22semidirect
38. (C2×D19)⋊C8C22semidirect
39. #10597266C22semidirect
40. #10597264C22semidirect
41. C4×C19⋊C8C22semidirect
71. #64525D4semidirect
111. D76C2×D4semidirect
118. C19⋊C8C2×D4semidirect
137. C4×C19AGL(1,ℤ/8)semidirect
147. #461D19semidirect
170. C4⋊Q8C2×D19semidirect
183. C4⋊C8C2×D19semidirect
184. #103C2×D19semidirect
190. C19#3272semidirect
287. C4#10597360semidirect

Maximal subgroups

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

subgroupindex
C2×#105973602
#119271972
D4×D762
#119269182
#119267932
#119267402
#119266932
#119266922
C4×#645252
#119266212
C19×#4612
#327219