Finite Group Databasebeta

← #14575237

Subgroups — #14575237

Order 2432.

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×#10597354C212yesmaximal, complemented
2#11927199C211yesmaximal, characteristic, complemented
3D4×D76C211yesmaximal, characteristic, complemented
4#11926917C211yesmaximal, characteristic, complemented
5#11926790C212yesmaximal, complemented
6#11926750C211yesmaximal, characteristic, complemented
7#11926740C211yesmaximal, characteristic, complemented
8#11926697C212yesmaximal, complemented
9#11926691C212yesmaximal, complemented
10C4×D152C211yesmaximal, characteristic, complemented
11C19×#436C211yesmaximal, characteristic, complemented
12C2×D4×D19—21no—
13C2×#64541C2212yescomplemented
14C22×D76C2212yes—
15C2×M16×C19C2212yescomplemented
16C4×D4×C19C2211yescharacteristic
17#10597384—21no—
18#10597376C2212yes—
19#10597370C2212yescomplemented
20#10597354—28no—
21C2×D152C2211yescharacteristic
22C2×D152C2212yescomplemented
23C2×#64516C2212yes—
24C2×#64516C2212yescomplemented
25C2×#64516C2212yescomplemented
26#10597341—21no—
27C4⋊C4×D19—21no—
28#10597329—22no—
29#10597328—22no—
30#10597320C2211yescharacteristic
31C4×D76C2211yescharacteristic
32C4×D76C2211yescharacteristic, complemented
33#10597315C2211yescharacteristic, complemented
34C19×C4⋊C8C2211yescharacteristic, complemented
35C19×C22⋊C8C2212yescomplemented
36C4×C8×C19C2211yescharacteristic, complemented
37#10597278C2211yescharacteristic
38#10597278C2212yescomplemented
39#10597278C2211yescharacteristic, complemented
40#10597275C2211yescharacteristic, complemented
41#10597273C2212yescomplemented
42C23×D19—22no—
43C2×D4×C19D411yescharacteristic
44C22×C4×C19C2312yes—
45C2×C22⋊D19—22no—
46C2×C22⋊D19—22no—
47D4×D19—44no—
48#64541—24no—
49#64541—42no—
50C2×D76—24no—
51C2×D76—22no—
52C2×D76—21no—
53C2×D76—21no—
54C2×D76—42no—
55C2×D76C2312yes—
56C2×D76C2311yescharacteristic
57C2×D76C2311yescharacteristic
58C2×C4×D19—21no—
59C2×C4×D19—22no—
60C2×C4×D19—21no—
61C2×Dic38C2312yes—
62M16×C19—24no—
63C2×C8×C19C2312yes—
64C2×C8×C19C2311yescharacteristic
65C2×C8×C19C2311yescharacteristic
66C4⋊C4×C19D411yescharacteristic
67C22⋊C4×C19D412yes—
68C42×C19C2311yescharacteristic
69C22⋊Dic19—22no—
70(C2×D19)⋊C4—22no—
71(C2×D19)⋊C4—21no—
72(C2×D19)⋊C4—21no—
73C4⋊Dic19—21no—
74C4⋊Dic19—21no—
75C4⋊Dic19C2311yescharacteristic
76C4⋊Dic19C2311yescharacteristic
77Dic19⋊C4—22no—
78D152—24no—
79D152D414yescomplemented
80#64516—24no—
81#64516—24no—
82#64516—42no—
83C23×C19C2×D412yes—
84C22×D19—21no—
85C22×D19—21no—
86C22×D19—22no—
87C22×D19—44no—
88C22×D19—44no—
89C22×D19—82no—
90D4×C19—22no—
91C2×C4×C19—22no—
92C2×C4×C19—22no—
93C2×C4×C19C2×D412yes—
94C2×C4×C19C2×D411yescharacteristic
95C2×C4×C19C2×D411yescharacteristic
96C2×C4×C19C2411yescharacteristic
97C22⋊D19—44no—
98C22⋊D19—44no—
99C2×Dic19—21no—
100C2×Dic19—22no—
101C2×Dic19—21no—
102D76—22no—
103D76—21no—
104D76—21no—
105D76—22no—
106D76—44no—
107D76—42no—
108D76—81no—
109D76C2×D412yes—
110D76C2×D412yescomplemented
111C4×D19—44no—
112C4×D19—42no—
113C4×D19—42no—
114Dic38—22no—
115Dic38—22no—
116C8×C19—22no—
117C8×C19—21no—
118C8×C19C2×D412yescomplemented
119#3272—191nomaximal, Sylow
120C22×C19—22no—
121C22×C19—22no—
122C22×C19—22no—
123C22×C19C22×D411yescharacteristic
124C2×D19—22no—
125C2×D19—22no—
126C2×D19—41no—
127C2×D19—41no—
128C2×D19—41no—
129C2×D19—41no—
130C2×D19—42no—
131C2×D19—42no—
132C2×D19—42no—
133C2×D19—88no—
134C4×C19—22no—
135C4×C19—21no—
136C4×C19AGL(1,ℤ/8)12yescomplemented
137C4×C19C22×D411yescharacteristic
138C4×C19H(5,𝔽2)11yescharacteristic
139Dic19—42no—
140Dic19—41no—
141Dic19—41no—
142C2×AGL(1,ℤ/8)—192no—
143#547—191no—
144D42—191no—
145#492—191no—
146#468—192no—
147#461—191no—
148#459—191no—
149#450—192no—
150#449—192no—
151C4×D8—191no—
152#436D1911yescharacteristic, complemented
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×SD16—192no—
167C2×D8—191no—
168C2×D8—192no—
169C2×M16C2×D1912yescomplemented
170C4⋊Q8—191no—
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#103—192no—
185#102—191no—
186#102—191no—
187#102—192no—
188C22⋊C8C2×D1912yescomplemented
189C4×C8C2×D1911yescharacteristic, complemented
190C19#327211yescharacteristic, complemented, Sylow
191C24—382no—
192#41—384no—
193#41—762no—
194C2×Q8—192no—
195C2×D4—191no—
196C2×D4—191no—
197C2×D4—192no—
198C2×D4—384no—
199C2×D4—382no—
200C2×D4—382no—
201C2×D4—382no—
202C2×D4—381no—
203C2×D4—381no—
204C2×D4—762no—
205C2×D4—764no—
206C2×D4D7611yescharacteristic
207C22×C4—381no—
208C22×C4—382no—
209C22×C4—381no—
210C22×C4C22×D1912yes—
211SD16—384no—
212SD16—384no—
213SD16—762no—
214D8—194no—
215D8—384no—
216M16—24no—
217C2×C8C22×D1911yescharacteristic
218C2×C8C22×D1912yes—
219C2×C8C22×D1911yescharacteristic
220C4⋊C4—191no—
221C4⋊C4—191no—
222C4⋊C4—382no—
223C4⋊C4—381no—
224C4⋊C4—381no—
225C4⋊C4D7611yescharacteristic
226C22⋊C4—382no—
227C22⋊C4—381no—
228C22⋊C4—381no—
229C22⋊C4—382no—
230C22⋊C4D7612yes—
231C42C22×D1911yescharacteristic
232C23—381no—
233C23—381no—
234C23—382no—
235C23—764no—
236C23—764no—
237C23—1522no—
238C23C2×D7612yes—
239Q8—382no—
240Q8—382no—
241D4—22no—
242D4—192no—
243D4—192no—
244D4—382no—
245D4—381no—
246D4—381no—
247D4—382no—
248D4—764no—
249D4—764no—
250D4—764no—
251D4—762no—
252D4—1521no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—381no—
256C2×C4—381no—
257C2×C4—382no—
258C2×C4—764no—
259C2×C4—762no—
260C2×C4—762no—
261C2×C4C2×D7611yescharacteristic
262C2×C4C2×D7612yes—
263C2×C4C2×D7611yescharacteristic
264C2×C4C23×D1911yescharacteristic
265C8—22no—
266C8—21no—
267C8D4×D1912yescomplemented
268C22—22no—
269C22—22no—
270C22—22no—
271C22—382no—
272C22—382no—
273C22—761no—
274C22—761no—
275C22—761no—
276C22—761no—
277C22—762no—
278C22—762no—
279C22—762no—
280C22—1528no—
281C22C22×D7611yescharacteristic
282C4—21no—
283C4—22no—
284C4—761no—
285C4—761no—
286C4—762no—
287C4#1059735412yescomplemented
288C4C2×D4×D1911yescharacteristic
289C4#1059743511yescharacteristic
290C2—42no—
291C2—762no—
292C2—762no—
293C2—1522no—
294C2D4×D7611yescharacteristic
295C2C2×#1059735411yescharacteristic
296C2#1192735611yescharacteristic
subgroupG/H
centerC22C22×D76
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#436C2
socleC22×C19C22×D4
hypercenter#436D19
hypocenterC19#3272
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#10597354C2semidirect
2. #11927199C2semidirect
3. D4×D76C2semidirect
4. #11926917C2semidirect
5. #11926790C2semidirect
6. #11926750C2semidirect
7. #11926740C2semidirect
8. #11926697C2semidirect
9. #11926691C2semidirect
10. C4×D152C2semidirect
11. C19×#436C2semidirect
13. C2×#64541C22semidirect
15. C2×M16×C19C22semidirect
19. #10597370C22semidirect
22. C2×D152C22semidirect
24. C2×#64516C22semidirect
25. C2×#64516C22semidirect
32. C4×D76C22semidirect
33. #10597315C22semidirect
34. C19×C4⋊C8C22semidirect
35. C19×C22⋊C8C22semidirect
36. C4×C8×C19C22semidirect
38. #10597278C22semidirect
39. #10597278C22semidirect
40. #10597275C22semidirect
41. #10597273C22semidirect
79. D152D4semidirect
110. D76C2×D4semidirect
118. C8×C19C2×D4semidirect
136. C4×C19AGL(1,ℤ/8)semidirect
152. #436D19semidirect
169. C2×M16C2×D19semidirect
183. C4⋊C8C2×D19semidirect
188. C22⋊C8C2×D19semidirect
189. C4×C8C2×D19semidirect
190. C19#3272semidirect
267. C8D4×D19semidirect
287. C4#10597354semidirect

Maximal subgroups

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

subgroupindex
C2×#105973542
#119271992
D4×D762
#119269172
#119267902
#119267502
#119267402
#119266972
#119266912
C4×D1522
C19×#4362
#327219