Finite Group Databasebeta

← #14567910

Subgroups — #14567910

Order 2432.

672 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 139 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×#10597338C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D19C211yesmaximal, characteristic
3#11926479C211yesmaximal, characteristic, complemented
4#11926471C211yesmaximal, characteristic, complemented
5#11926469C211yesmaximal, characteristic, complemented
6#11926438C212yesmaximal, complemented
7#11926434C212yesmaximal, complemented
8#11926415C212yesmaximal, complemented
9#11926406C211yesmaximal, characteristic, complemented
10#11926399C212yesmaximal
11C19×#399C211yesmaximal, characteristic, complemented
12C24×D19C2211yescharacteristic
13C22×C4×D19C2211yescharacteristic
14C22×C4×D19C2211yescharacteristic
15C2×C4⋊C4×C19C2211yescharacteristic, complemented
16C2×C4⋊C4×C19C2212yescomplemented
17C2×C22⋊C4×C19C2211yescharacteristic
18C2×C22⋊C4×C19C2212yes—
19C2×C22⋊Dic19C2212yes—
20C2×C22⋊Dic19C2211yescharacteristic
21C2×(C2×D19)⋊C4C2212yes—
22C2×(C2×D19)⋊C4C2212yes—
23C2×(C2×D19)⋊C4C2212yes—
24C2×(C2×D19)⋊C4C2211yescharacteristic
25C2×(C2×D19)⋊C4C2211yescharacteristic
26C2×(C2×D19)⋊C4C2212yes—
27C2×C4⋊Dic19C2211yescharacteristic, complemented
28C2×Dic19⋊C4C2212yescomplemented
29C2×C4×Dic19C2212yescomplemented
30#10597338—24no—
31C22⋊C4×D19—24no—
32C19×#95C2211yescharacteristic, complemented
33C19⋊#95C2212yescomplemented
34C19⋊#95C2211yescharacteristic, complemented
35C19⋊#95C2212yescomplemented
36C19⋊#95C2212yescomplemented
37C24×C19C2311yescharacteristic
38C23×D19—22no—
39C23×D19—22no—
40C23×D19—22no—
41C23×D19—24no—
42C23×D19—42no—
43C23×D19C2311yescharacteristic
44C23×D19C2311yescharacteristic
45C22×C4×C19C2311yescharacteristic
46C22×C4×C19C2312yes—
47C22×C4×C19C2312yes—
48C22×C4×C19C2311yescharacteristic
49C22×Dic19C2311yescharacteristic
50C22×Dic19C2312yes—
51C22×Dic19C2312yes—
52C22×Dic19C2311yescharacteristic
53C2×C4×D19—24no—
54C2×C4×D19—22no—
55C2×C4×D19—42no—
56C2×C4×D19D414yes—
57C4⋊C4×C19—22no—
58C4⋊C4×C19—42no—
59C22⋊C4×C19—22no—
60C22⋊C4×C19—42no—
61C22⋊Dic19—24no—
62C22⋊Dic19—22no—
63(C2×D19)⋊C4—24no—
64(C2×D19)⋊C4—24no—
65(C2×D19)⋊C4—24no—
66(C2×D19)⋊C4—22no—
67(C2×D19)⋊C4—22no—
68(C2×D19)⋊C4—42no—
69C4⋊Dic19—22no—
70Dic19⋊C4—42no—
71C4×Dic19—24no—
72C23×C19—21no—
73C23×C19—21no—
74C23×C19—22no—
75C23×C19—22no—
76C23×C19#4112yes—
77C23×C19C2411yescharacteristic
78C22×D19—21no—
79C22×D19—21no—
80C22×D19—22no—
81C22×D19—28no—
82C22×D19—21no—
83C22×D19—21no—
84C22×D19—22no—
85C22×D19—22no—
86C22×D19—48no—
87C22×D19—48no—
88C22×D19—44no—
89C22×D19—44no—
90C22×D19C2×D412yes—
91C22×D19#4112yes—
92C22×D19#4114yes—
93C2×C4×C19—22no—
94C2×C4×C19—22no—
95C2×C4×C19—21no—
96C2×C4×C19—22no—
97C2×C4×C19—22no—
98C2×C4×C19—22no—
99C2×C4×C19—22no—
100C2×C4×C19—22no—
101C2×C4×C19—22no—
102C2×C4×C19C2×D412yes—
103C2×Dic19—22no—
104C2×Dic19—22no—
105C2×Dic19—21no—
106C2×Dic19—22no—
107C2×Dic19—22no—
108C2×Dic19—22no—
109C2×Dic19—22no—
110C2×Dic19—22no—
111C2×Dic19—22no—
112C2×Dic19C2×D412yes—
113C4×D19—28no—
114C4×D19—44no—
115#2482—191nomaximal, Sylow
116C22×C19—22no—
117C22×C19—24no—
118C22×C19—41no—
119C22×C19—41no—
120C22×C19—42no—
121C22×C19C22×D411yescharacteristic
122C22×C19C2×#4111yescharacteristic
123C22×C19C2×#4112yes—
124C22×C19C2×#4111yescharacteristic
125C22×C19H(5,𝔽2)12yes—
126C2×D19—22no—
127C2×D19—22no—
128C2×D19—24no—
129C2×D19—24no—
130C2×D19—22no—
131C2×D19—24no—
132C2×D19—416no—
133C2×D19—41no—
134C2×D19—41no—
135C2×D19—42no—
136C2×D19#12314yes—
137C4×C19—22no—
138C4×C19—41no—
139C4×C19—42no—
140C4×C19—42no—
141Dic19—22no—
142Dic19—42no—
143Dic19—41no—
144Dic19—42no—
145C2×#117—191no—
146C22×C22⋊C4—191no—
147#399—191no—
148#399D1911yescharacteristic, complemented
149#397—191no—
150#397—191no—
151#388—192no—
152#388—192no—
153#385—192no—
154#381—191no—
155#379—192no—
156C2×C19—42no—
157C2×C19C2×#12311yescharacteristic
158C2×C19#52511yescharacteristic
159C2×C19#53511yescharacteristic
160C2×C19#55112yes—
161C2×C19#55112yes—
162D19—24no—
163D19—42no—
164C25—191no—
165C23×C4—191no—
166C23×C4—191no—
167#117—384no—
168C2×C4⋊C4—191no—
169C2×C4⋊C4—192no—
170C2×C4⋊C4C2×D1911yescharacteristic, complemented
171C2×C4⋊C4C2×D1912yescomplemented
172C2×C22⋊C4—191no—
173C2×C22⋊C4—192no—
174C2×C22⋊C4—191no—
175C2×C22⋊C4—191no—
176C2×C22⋊C4—192no—
177C2×C22⋊C4—192no—
178C2×C22⋊C4—192no—
179C2×C22⋊C4—192no—
180C2×C22⋊C4—384no—
181C2×C22⋊C4C2×D1911yescharacteristic
182C2×C22⋊C4C2×D1912yes—
183C2×C42—192no—
184#95—192no—
185#95—191no—
186#95—192no—
187#95—192no—
188#95C2×D1911yescharacteristic, complemented
189C19#248211yescharacteristic, complemented, Sylow
190C24—191no—
191C24—191no—
192C24—382no—
193C24—382no—
194C24—384no—
195C24—382no—
196C24—762no—
197C24C22×D1911yescharacteristic
198C22×C4—191no—
199C22×C4—194no—
200C22×C4—192no—
201C22×C4—192no—
202C22×C4—191no—
203C22×C4—384no—
204C22×C4—382no—
205C22×C4—762no—
206C22×C4C22×D1912yes—
207C22×C4C22×D1911yescharacteristic
208C22×C4C22×D1912yes—
209C22×C4C22×D1911yescharacteristic
210C4⋊C4—22no—
211C4⋊C4—42no—
212C4⋊C4—382no—
213C4⋊C4—762no—
214C22⋊C4—22no—
215C22⋊C4—42no—
216C22⋊C4—382no—
217C22⋊C4—384no—
218C22⋊C4—384no—
219C22⋊C4—384no—
220C22⋊C4—382no—
221C22⋊C4—384no—
222C22⋊C4—382no—
223C22⋊C4—762no—
224C42—384no—
225C23—21no—
226C23—22no—
227C23—21no—
228C23—22no—
229C23—192no—
230C23—194no—
231C23—192no—
232C23—388no—
233C23—382no—
234C23—381no—
235C23—381no—
236C23—381no—
237C23—382no—
238C23—381no—
239C23—382no—
240C23—768no—
241C23—764no—
242C23—768no—
243C23—764no—
244C23#6454512yes—
245C23C23×D1911yescharacteristic
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—192no—
256C2×C4—388no—
257C2×C4—382no—
258C2×C4—382no—
259C2×C4—381no—
260C2×C4—382no—
261C2×C4—382no—
262C2×C4—382no—
263C2×C4—382no—
264C2×C4—382no—
265C2×C4—382no—
266C2×C4—764no—
267C2×C4D4×D1912yes—
268C22—22no—
269C22—24no—
270C22—41no—
271C22—41no—
272C22—42no—
273C22—194no—
274C22—382no—
275C22—382no—
276C22—384no—
277C22—384no—
278C22—382no—
279C22—384no—
280C22—7616no—
281C22—761no—
282C22—761no—
283C22—762no—
284C22C2×D4×D1911yescharacteristic
285C22#1059743012yes—
286C22C2×#6454511yescharacteristic
287C22#41×D1912yes—
288C22#41×D1911yescharacteristic
289C4—22no—
290C4—41no—
291C4—42no—
292C4—42no—
293C4—382no—
294C4—762no—
295C4—761no—
296C4—762no—
297C2—42no—
298C2—384no—
299C2—762no—
300C2#123×D1911yescharacteristic
301C2#1192705711yescharacteristic
302C2#1192710711yescharacteristic
303C2#1192722112yes—
304C2#1192722212yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#399C2
prime radicalC24×D19C22
hypercenter#399D19
hypocenterC19#2482
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#10597338C2semidirect
3. #11926479C2semidirect
4. #11926471C2semidirect
5. #11926469C2semidirect
6. #11926438C2semidirect
7. #11926434C2semidirect
8. #11926415C2semidirect
9. #11926406C2semidirect
11. C19×#399C2semidirect
15. C2×C4⋊C4×C19C22semidirect
16. C2×C4⋊C4×C19C22semidirect
27. C2×C4⋊Dic19C22semidirect
28. C2×Dic19⋊C4C22semidirect
29. C2×C4×Dic19C22semidirect
32. C19×#95C22semidirect
33. C19⋊#95C22semidirect
34. C19⋊#95C22semidirect
35. C19⋊#95C22semidirect
36. C19⋊#95C22semidirect
148. #399D19semidirect
170. C2×C4⋊C4C2×D19semidirect
171. C2×C4⋊C4C2×D19semidirect
188. #95C2×D19semidirect
189. C19#2482semidirect

Maximal subgroups

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

subgroupindex
C2×#105973382
C2×C22⋊C4×D192
#119264792
#119264712
#119264692
#119264382
#119264342
#119264152
#119264062
#119263992
C19×#3992
#248219