Finite Group Databasebeta

← #14569444

Subgroups — #14569444

Order 2432.

668 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 157 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×#10597324C211yesmaximal, characteristic, complemented
2C22×C22⋊Dic19C211yesmaximal, characteristic
3#11926480C212yesmaximal, complemented
4#11926467C212yesmaximal, complemented
5#11926467C212yesmaximal, complemented
6#11926456C212yesmaximal, complemented
7#11926419C211yesmaximal, characteristic, complemented
8#11926416C211yesmaximal, characteristic, complemented
9#11926402C211yesmaximal, characteristic, complemented
10#11926400C211yesmaximal, characteristic
11C19×#379C211yesmaximal, characteristic
12C25×C19C2211yescharacteristic
13C23×Dic19C2211yescharacteristic
14C23×Dic19C2211yescharacteristic
15C22×Dic38C2211yescharacteristic, complemented
16C2×C22⋊C4×C19C2211yescharacteristic
17C2×C22⋊C4×C19C2211yescharacteristic
18C2×C22⋊C4×C19C2212yes—
19C2×C22⋊C4×C19C2212yes—
20C2×C22⋊Dic19—24no—
21C2×C22⋊Dic19C2211yescharacteristic
22C2×C22⋊Dic19C2211yescharacteristic
23C2×C22⋊Dic19C2212yes—
24C2×C22⋊Dic19C2212yes—
25C2×C22⋊Dic19C2212yes—
26C2×C22⋊Dic19C2212yes—
27C2×C4⋊Dic19C2211yescharacteristic, complemented
28C2×C4⋊Dic19C2212yescomplemented
29C2×Dic19⋊C4C2211yescharacteristic, complemented
30C2×Dic19⋊C4C2211yescharacteristic, complemented
31C2×Dic19⋊C4C2212yescomplemented
32C2×Dic19⋊C4C2212yescomplemented
33#10597324—24no—
34C19⋊#95C2212yescomplemented
35C19⋊#95C2212yescomplemented
36C19⋊#95C2212yescomplemented
37C24×C19—22no—
38C24×C19—22no—
39C24×C19—42no—
40C24×C19—42no—
41C24×C19Q814yescomplemented
42C24×C19C2312yes—
43C24×C19C2311yescharacteristic
44C22×C4×C19C2311yescharacteristic
45C22×C4×C19C2312yes—
46C22×C4×C19C2311yescharacteristic
47C22×Dic19—22no—
48C22×Dic19—42no—
49C22×Dic19—42no—
50C22×Dic19D414yes—
51C22×Dic19C2311yescharacteristic
52C22×Dic19C2312yes—
53C22×Dic19C2311yescharacteristic
54C22×Dic19C2312yes—
55C22×Dic19C2311yescharacteristic
56C22×Dic19C2311yescharacteristic
57C2×Dic38—22no—
58C2×Dic38—42no—
59C22⋊C4×C19—22no—
60C22⋊C4×C19—22no—
61C22⋊C4×C19—42no—
62C22⋊C4×C19—42no—
63C22⋊Dic19—22no—
64C22⋊Dic19—22no—
65C22⋊Dic19—24no—
66C22⋊Dic19—24no—
67C22⋊Dic19—42no—
68C22⋊Dic19—42no—
69C4⋊Dic19—22no—
70C4⋊Dic19—42no—
71Dic19⋊C4—22no—
72Dic19⋊C4—22no—
73Dic19⋊C4—42no—
74Dic19⋊C4—42no—
75C23×C19—22no—
76C23×C19—22no—
77C23×C19—28no—
78C23×C19—22no—
79C23×C19—22no—
80C23×C19—22no—
81C23×C19—22no—
82C23×C19—22no—
83C23×C19—22no—
84C23×C19—48no—
85C23×C19—44no—
86C23×C19—44no—
87C23×C19—48no—
88C23×C19C2×D412yes—
89C23×C19C2×Q814yes—
90C23×C19C2×Q812yes—
91C23×C19#4112yes—
92C23×C19C2411yescharacteristic
93C2×C4×C19—21no—
94C2×C4×C19—21no—
95C2×C4×C19—22no—
96C2×C4×C19—22no—
97C2×C4×C19—22no—
98C2×C4×C19—22no—
99C2×C4×C19—22no—
100C2×Dic19—22no—
101C2×Dic19—22no—
102C2×Dic19—21no—
103C2×Dic19—21no—
104C2×Dic19—22no—
105C2×Dic19—22no—
106C2×Dic19—22no—
107C2×Dic19—22no—
108C2×Dic19—22no—
109C2×Dic19—22no—
110C2×Dic19—22no—
111C2×Dic19—22no—
112C2×Dic19—44no—
113C2×Dic19—44no—
114C2×Dic19C2×D412yes—
115C2×Dic19C2×D412yes—
116Dic38—44no—
117#2626—191nomaximal, Sylow
118C22×C19—22no—
119C22×C19—22no—
120C22×C19—24no—
121C22×C19—24no—
122C22×C19—24no—
123C22×C19—24no—
124C22×C19—24no—
125C22×C19—416no—
126C22×C19—42no—
127C22×C19—42no—
128C22×C19—42no—
129C22×C19—42no—
130C22×C19C22⋊Q814yes—
131C22×C19C22×D411yescharacteristic
132C22×C19C22×Q811yescharacteristic
133C22×C19C2×#4111yescharacteristic
134C22×C19H(5,𝔽2)12yes—
135C22×C19H(5,𝔽2)12yes—
136C4×C19—41no—
137C4×C19—41no—
138C4×C19—42no—
139Dic19—22no—
140Dic19—22no—
141Dic19—41no—
142Dic19—41no—
143Dic19—42no—
144Dic19—42no—
145C2×C22⋊Q8—191no—
146C22×C22⋊C4—191no—
147#399—192no—
148#396—192no—
149#396—192no—
150#393—192no—
151#385—191no—
152#385—191no—
153#380—191no—
154#379—191no—
155#379D1911yescharacteristic
156C2×C19—24no—
157C2×C19—44no—
158C2×C19C2×C22⋊Q811yescharacteristic
159C2×C19#53411yescharacteristic
160C2×C19#53511yescharacteristic
161C2×C19#53812yes—
162C2×C19#54312yes—
163C25C2×D1911yescharacteristic
164C22×Q8—191no—
165C23×C4—191no—
166C23×C4—191no—
167C22⋊Q8—384no—
168C2×C4⋊C4—191no—
169C2×C4⋊C4—191no—
170C2×C4⋊C4—191no—
171C2×C4⋊C4—192no—
172C2×C4⋊C4—192no—
173C2×C4⋊C4—192no—
174C2×C22⋊C4—192no—
175C2×C22⋊C4—192no—
176C2×C22⋊C4—191no—
177C2×C22⋊C4—191no—
178C2×C22⋊C4—192no—
179C2×C22⋊C4—192no—
180C2×C22⋊C4—384no—
181C2×C22⋊C4C2×D1911yescharacteristic
182C2×C22⋊C4C2×D1911yescharacteristic
183C2×C22⋊C4C2×D1912yes—
184C2×C22⋊C4C2×D1912yes—
185#95—192no—
186#95—192no—
187#95—192no—
188C19#262611yescharacteristic, complemented, Sylow
189C24—22no—
190C24—22no—
191C24—42no—
192C24—42no—
193C24Dic3814yescomplemented
194C24C22×D1912yes—
195C24C22×D1911yescharacteristic
196C2×Q8—382no—
197C2×Q8—762no—
198C22×C4—191no—
199C22×C4—191no—
200C22×C4—194no—
201C22×C4—192no—
202C22×C4—191no—
203C22×C4—192no—
204C22×C4—191no—
205C22×C4—382no—
206C22×C4—762no—
207C22×C4—762no—
208C22×C4C22×D1912yes—
209C22×C4C22×D1911yescharacteristic
210C22×C4C22×D1911yescharacteristic
211C4⋊C4—382no—
212C4⋊C4—382no—
213C4⋊C4—382no—
214C4⋊C4—762no—
215C4⋊C4—762no—
216C4⋊C4—762no—
217C22⋊C4—22no—
218C22⋊C4—22no—
219C22⋊C4—42no—
220C22⋊C4—42no—
221C22⋊C4—384no—
222C22⋊C4—384no—
223C22⋊C4—382no—
224C22⋊C4—382no—
225C22⋊C4—762no—
226C22⋊C4—762no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23—22no—
235C23—28no—
236C23—48no—
237C23—44no—
238C23—44no—
239C23—48no—
240C23C2×Dic3814yes—
241C23C2×Dic3812yes—
242C23D4×D1912yes—
243C23#6454312yes—
244C23C23×D1911yescharacteristic
245Q8—764no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—192no—
254C2×C4—192no—
255C2×C4—382no—
256C2×C4—382no—
257C2×C4—382no—
258C2×C4—381no—
259C2×C4—381no—
260C2×C4—382no—
261C2×C4—382no—
262C2×C4—382no—
263C2×C4—382no—
264C2×C4—382no—
265C2×C4—382no—
266C2×C4—382no—
267C2×C4—764no—
268C2×C4—764no—
269C22—22no—
270C22—22no—
271C22—24no—
272C22—24no—
273C22—24no—
274C22—24no—
275C22—24no—
276C22—416no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22#1059732414yes—
282C22C22×Dic3811yescharacteristic
283C22C2×D4×D1911yescharacteristic
284C22C2×#6454311yescharacteristic
285C22#1059743012yes—
286C22#1059743012yes—
287C4—41no—
288C4—41no—
289C4—42no—
290C4—382no—
291C4—382no—
292C4—761no—
293C4—762no—
294C4—761no—
295C4—762no—
296C2—24no—
297C2—44no—
298C2C2×#1059732411yescharacteristic
299C2#1192710411yescharacteristic
300C2#1192710911yescharacteristic
301C2#1192712912yes—
302C2#1192717012yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#379C2
prime radicalC25×C19C22
hypercenter#379D19
hypocenterC19#2626
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#10597324C2semidirect
3. #11926480C2semidirect
4. #11926467C2semidirect
5. #11926467C2semidirect
6. #11926456C2semidirect
7. #11926419C2semidirect
8. #11926416C2semidirect
9. #11926402C2semidirect
15. C22×Dic38C22semidirect
27. C2×C4⋊Dic19C22semidirect
28. C2×C4⋊Dic19C22semidirect
29. C2×Dic19⋊C4C22semidirect
30. C2×Dic19⋊C4C22semidirect
31. C2×Dic19⋊C4C22semidirect
32. C2×Dic19⋊C4C22semidirect
34. C19⋊#95C22semidirect
35. C19⋊#95C22semidirect
36. C19⋊#95C22semidirect
41. C24×C19Q8semidirect
188. C19#2626semidirect
193. C24Dic38semidirect

Maximal subgroups

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

subgroupindex
C2×#105973242
C22×C22⋊Dic192
#119264802
#119264672
#119264562
#119264192
#119264162
#119264022
#119264002
C19×#3792
#262619