Finite Group Databasebeta

← #14575235

Subgroups — #14575235

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×#10597395C212yesmaximal, complemented
2D4×D76C211yesmaximal, characteristic, complemented
3#11926918C211yesmaximal, characteristic, complemented
4#11926792C212yesmaximal, complemented
5#11926746C211yesmaximal, characteristic, complemented
6#11926739C211yesmaximal, characteristic, complemented
7#11926694C212yesmaximal, complemented
8#11926689C212yesmaximal, complemented
9C4×#64525C211yesmaximal, characteristic, complemented
10#11926622C211yesmaximal, characteristic, complemented
11C19×#547C211yesmaximal, characteristic, complemented
12C2×#41×C19C2212yescomplemented
13C2×D4×D19—21no—
14C22×D76C2212yes—
15C19×C4⋊Q8C2211yescharacteristic, complemented
16C19×#123—22no—
17C19×C22⋊Q8C2212yescomplemented
18C19×#121—21no—
19C4×D4×C19C2211yescharacteristic
20C4×D4×C19C2211yescharacteristic, complemented
21C2×C4⋊C4×C19—21no—
22#10597395—28no—
23C2×#64527C2212yes—
24C2×#64527C2212yescomplemented
25C2×#64527C2212yescomplemented
26C2×#64525C2211yescharacteristic
27C2×#64525C2212yescomplemented
28#10597376C2212yes—
29C2×#64520C2212yescomplemented
30#10597341—21no—
31#10597328—22no—
32#10597320C2211yescharacteristic
33C4×D76C2211yescharacteristic
34#10597292C2212yescomplemented
35#10597289C2211yescharacteristic, complemented
36C22⋊(C19⋊C8)C2212yescomplemented
37#10597266C2211yescharacteristic
38#10597266C2212yescomplemented
39#10597264C2211yescharacteristic, complemented
40C4⋊(C19⋊C8)C2211yescharacteristic, complemented
41C4×C19⋊C8C2211yescharacteristic, complemented
42C23×D19—22no—
43#41×C19—24no—
44#41×C19—42no—
45C2×Q8×C19C2312yes—
46C2×D4×C19—22no—
47C2×D4×C19D411yescharacteristic
48C2×D4×C19C2311yescharacteristic
49C22×C4×C19—21no—
50C22×C4×C19—22no—
51C22×C4×C19C2312yes—
52C2×C22⋊D19—22no—
53D4×D19—44no—
54C2×D76—24no—
55C2×D76—22no—
56C2×D76—21no—
57C2×D76—21no—
58C2×D76—42no—
59C2×D76C2312yes—
60C2×D76C2311yescharacteristic
61C2×C4×D19—21no—
62C4⋊C4×C19—21no—
63C4⋊C4×C19—22no—
64C4⋊C4×C19—21no—
65C4⋊C4×C19D411yescharacteristic
66C4⋊C4×C19C2311yescharacteristic
67C22⋊C4×C19—22no—
68C22⋊C4×C19—21no—
69C22⋊C4×C19D412yes—
70C42×C19C2311yescharacteristic
71#64527—24no—
72#64527—24no—
73#64527—42no—
74#64525—24no—
75#64525D414yescomplemented
76(C2×D19)⋊C4—22no—
77(C2×D19)⋊C4—21no—
78C4⋊Dic19C2311yescharacteristic
79#64520—24no—
80C2×C19⋊C8C2312yes—
81C2×C19⋊C8C2311yescharacteristic
82C2×C19⋊C8C2311yescharacteristic
83C23×C19—21no—
84C23×C19C2×D412yes—
85C22×D19—21no—
86C22×D19—22no—
87C22×D19—44no—
88C22×D19—44no—
89C22×D19—82no—
90Q8×C19—22no—
91Q8×C19—22no—
92D4×C19—22no—
93D4×C19—21no—
94D4×C19—44no—
95D4×C19C2×D412yescomplemented
96C2×C4×C19—22no—
97C2×C4×C19—22no—
98C2×C4×C19—21no—
99C2×C4×C19—22no—
100C2×C4×C19—44no—
101C2×C4×C19—42no—
102C2×C4×C19C2×D411yescharacteristic
103C2×C4×C19C2×D412yes—
104C2×C4×C19C2×D411yescharacteristic
105C2×C4×C19C2411yescharacteristic
106C22⋊D19—44no—
107C2×Dic19—21no—
108D76—22no—
109D76—21no—
110D76—22no—
111D76—44no—
112D76—42no—
113D76—81no—
114D76C2×D412yes—
115C4×D19—42no—
116C19⋊C8—22no—
117C19⋊C8—21no—
118C19⋊C8C2×D412yescomplemented
119#3272—191nomaximal, Sylow
120C22×C19—22no—
121C22×C19—22no—
122C22×C19—22no—
123C22×C19—22no—
124C22×C19—41no—
125C22×C19—41no—
126C22×C19C22×D411yescharacteristic
127C2×D19—22no—
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×C19—42no—
137C4×C19—41no—
138C4×C19AGL(1,ℤ/8)12yescomplemented
139C4×C19C22×D411yescharacteristic
140C4×C19H(5,𝔽2)11yescharacteristic
141Dic19—41no—
142C2×AGL(1,ℤ/8)—192no—
143#547D1911yescharacteristic, complemented
144D42—191no—
145#492—191no—
146#468—192no—
147#461—191no—
148#459—191no—
149#450—192no—
150#449—192no—
151C4×D8—191no—
152#436—191no—
153C2×C19—42no—
154C2×C19—42no—
155C2×C19D4211yescharacteristic
156C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
157C2×C19#57711yescharacteristic
158D19—42no—
159D19—82no—
160C2×#41C2×D1912yescomplemented
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×M16—192no—
170C4⋊Q8C2×D1911yescharacteristic, complemented
171#127—191no—
172#123—22no—
173C22⋊Q8C2×D1912yescomplemented
174#121—21no—
175#121—192no—
176#121—381no—
177#120—382no—
178C4×D4—191no—
179C4×D4C2×D1911yescharacteristic
180C4×D4C2×D1911yescharacteristic, complemented
181C2×C4⋊C4—21no—
182#107—191no—
183C4⋊C8—191no—
184#103—192no—
185#102—191no—
186#102—191no—
187#102—192no—
188C22⋊C8—192no—
189C4×C8—191no—
190C19#327211yescharacteristic, complemented, Sylow
191C24—382no—
192#41—24no—
193#41—42no—
194C2×Q8C22×D1912yes—
195C2×D4—22no—
196C2×D4—191no—
197C2×D4—192no—
198C2×D4—384no—
199C2×D4—382no—
200C2×D4—382no—
201C2×D4—381no—
202C2×D4—381no—
203C2×D4—762no—
204C2×D4—764no—
205C2×D4C22⋊D1911yescharacteristic
206C2×D4C22×D1911yescharacteristic
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—381no—
210C22×C4C22×D1912yes—
211SD16—384no—
212SD16—384no—
213SD16—762no—
214D8—194no—
215D8—384no—
216M16—384no—
217C2×C8—191no—
218C2×C8—191no—
219C2×C8—192no—
220C4⋊C4—21no—
221C4⋊C4—22no—
222C4⋊C4—21no—
223C4⋊C4—191no—
224C4⋊C4C22⋊D1911yescharacteristic
225C4⋊C4C22×D1911yescharacteristic
226C22⋊C4—22no—
227C22⋊C4—21no—
228C22⋊C4—381no—
229C22⋊C4—382no—
230C22⋊C4C22⋊D1912yes—
231C42C22×D1911yescharacteristic
232C23—21no—
233C23—381no—
234C23—382no—
235C23—764no—
236C23—764no—
237C23—1522no—
238C23C2×C22⋊D1912yes—
239Q8—22no—
240Q8—22no—
241D4—22no—
242D4—21no—
243D4—44no—
244D4—192no—
245D4—382no—
246D4—381no—
247D4—382no—
248D4—764no—
249D4—764no—
250D4—762no—
251D4—1521no—
252D4D4×D1912yescomplemented
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—44no—
258C2×C4—42no—
259C2×C4—381no—
260C2×C4—762no—
261C2×C4C2×C22⋊D1911yescharacteristic
262C2×C4C2×C22⋊D1912yes—
263C2×C4C2×C22⋊D1911yescharacteristic
264C2×C4C23×D1911yescharacteristic
265C8—192no—
266C8—382no—
267C8—381no—
268C22—22no—
269C22—22no—
270C22—22no—
271C22—22no—
272C22—41no—
273C22—41no—
274C22—382no—
275C22—761no—
276C22—761no—
277C22—762no—
278C22—762no—
279C22—762no—
280C22—1528no—
281C22C22×C22⋊D1911yescharacteristic
282C4—21no—
283C4—22no—
284C4—41no—
285C4—42no—
286C4—761no—
287C4#1059739512yescomplemented
288C4C2×D4×D1911yescharacteristic
289C4#1059743011yescharacteristic
290C2—42no—
291C2—42no—
292C2—762no—
293C2—1522no—
294C2D4×C22⋊D1911yescharacteristic
295C2C2×#1059739511yescharacteristic
296C2#1192735211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#547C2
socleC22×C19C22×D4
hypercenter#547D19
hypocenterC19#3272
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C2×#10597395C2semidirect
2. D4×D76C2semidirect
3. #11926918C2semidirect
4. #11926792C2semidirect
5. #11926746C2semidirect
6. #11926739C2semidirect
7. #11926694C2semidirect
8. #11926689C2semidirect
9. C4×#64525C2semidirect
10. #11926622C2semidirect
11. C19×#547C2semidirect
12. C2×#41×C19C22semidirect
15. C19×C4⋊Q8C22semidirect
17. C19×C22⋊Q8C22semidirect
20. C4×D4×C19C22semidirect
24. C2×#64527C22semidirect
25. C2×#64527C22semidirect
27. C2×#64525C22semidirect
29. C2×#64520C22semidirect
34. #10597292C22semidirect
35. #10597289C22semidirect
36. C22⋊(C19⋊C8)C22semidirect
38. #10597266C22semidirect
39. #10597264C22semidirect
40. C4⋊(C19⋊C8)C22semidirect
41. C4×C19⋊C8C22semidirect
75. #64525D4semidirect
95. D4×C19C2×D4semidirect
118. C19⋊C8C2×D4semidirect
138. C4×C19AGL(1,ℤ/8)semidirect
143. #547D19semidirect
160. C2×#41C2×D19semidirect
170. C4⋊Q8C2×D19semidirect
173. C22⋊Q8C2×D19semidirect
180. C4×D4C2×D19semidirect
190. C19#3272semidirect
252. D4D4×D19semidirect
287. C4#10597395semidirect

Maximal subgroups

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

subgroupindex
C2×#105973952
D4×D762
#119269182
#119267922
#119267462
#119267392
#119266942
#119266892
C4×#645252
#119266222
C19×#5472
#327219