Finite Group Databasebeta

← #14567295

Subgroups — #14567295

Order 2432.

780 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 161 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×#10597392C212yesmaximal, complemented
2C2×C22⋊C4×D19C212yesmaximal
3#11926480C211yesmaximal, characteristic, complemented
4#11926467C212yesmaximal, complemented
5#11926418C212yesmaximal, complemented
6#11926418C212yesmaximal, complemented
7#11926403C212yesmaximal, complemented
8#11926399C211yesmaximal, characteristic
9C19×#393C211yesmaximal, characteristic, complemented
10C24×D19C2211yescharacteristic
11C22×Q8×C19C2211yescharacteristic, complemented
12C22×C4×D19C2212yes—
13C22×C4×D19C2212yes—
14C2×C22⋊C4×C19C2212yes—
15C2×C22⋊C4×C19C2211yescharacteristic
16C2×C22⋊Dic19C2212yes—
17C2×C22⋊Dic19C2211yescharacteristic
18#10597392—28no—
19C2×(C2×D19)⋊C4C2212yes—
20C2×(C2×D19)⋊C4C2212yes—
21C2×(C2×D19)⋊C4C2212yes—
22C2×(C2×D19)⋊C4C2212yes—
23C2×C4⋊Dic19C2212yescomplemented
24C2×C4⋊Dic19C2211yescharacteristic, complemented
25C2×Dic19⋊C4C2212yescomplemented
26C2×Dic19⋊C4C2212yescomplemented
27C2×Dic19⋊C4C2212yescomplemented
28C22⋊C4×D19—28no—
29C19×#95C2211yescharacteristic, complemented
30C19×#95C2212yescomplemented
31C19⋊#95C2212yescomplemented
32C19⋊#95C2211yescharacteristic, complemented
33C24×C19C2311yescharacteristic
34C23×D19—24no—
35C23×D19—24no—
36C23×D19—41no—
37C23×D19—41no—
38C23×D19Q814yescomplemented
39C23×D19C2312yes—
40C2×Q8×C19—24no—
41C2×Q8×C19—41no—
42C22×C4×C19C2312yes—
43C22×C4×C19C2311yescharacteristic
44C22×C4×C19C2311yescharacteristic
45C22×C4×C19C2312yes—
46C22×Dic19C2312yes—
47C22×Dic19C2312yes—
48C22×Dic19C2312yes—
49C2×C4×D19—24no—
50C2×C4×D19—24no—
51C2×C4×D19—24no—
52C2×C4×D19—24no—
53C2×C4×D19—42no—
54C2×C4×D19—42no—
55C22⋊C4×C19—24no—
56C22⋊C4×C19—41no—
57C22⋊Dic19—24no—
58C22⋊Dic19—41no—
59(C2×D19)⋊C4—24no—
60(C2×D19)⋊C4—24no—
61(C2×D19)⋊C4—24no—
62(C2×D19)⋊C4D418yes—
63C4⋊Dic19—24no—
64C4⋊Dic19—41no—
65Dic19⋊C4—24no—
66Dic19⋊C4—24no—
67Dic19⋊C4—42no—
68C23×C19—22no—
69C23×C19—22no—
70C23×C19—21no—
71C23×C19—21no—
72C23×C19C2×Q812yes—
73C23×C19C2411yescharacteristic
74C22×D19—22no—
75C22×D19—22no—
76C22×D19—22no—
77C22×D19—22no—
78C22×D19—216no—
79C22×D19—44no—
80C22×D19—44no—
81C22×D19—48no—
82C22×D19—44no—
83C22×D19C2×D414yes—
84C22×D19C2×Q814yes—
85C22×D19#4114yes—
86Q8×C19—44no—
87C2×C4×C19—22no—
88C2×C4×C19—22no—
89C2×C4×C19—22no—
90C2×C4×C19—22no—
91C2×C4×C19—22no—
92C2×C4×C19—22no—
93C2×C4×C19—22no—
94C2×C4×C19—21no—
95C2×C4×C19—21no—
96C2×C4×C19C2×D414yes—
97C2×Dic19—22no—
98C2×Dic19—22no—
99C2×Dic19—22no—
100C2×Dic19—22no—
101C2×Dic19—22no—
102C2×Dic19—22no—
103C2×Dic19—22no—
104C2×Dic19—22no—
105C2×Dic19C2×D414yes—
106C4×D19—48no—
107C4×D19—48no—
108#2437—191nomaximal, Sylow
109C22×C19—24no—
110C22×C19—22no—
111C22×C19—41no—
112C22×C19—42no—
113C22×C19—41no—
114C22×C19C22×D412yes—
115C22×C19C22×Q811yescharacteristic
116C22×C19C2×#4112yes—
117C22×C19H(5,𝔽2)11yescharacteristic
118C22×C19H(5,𝔽2)11yescharacteristic
119C2×D19—24no—
120C2×D19—24no—
121C2×D19—24no—
122C2×D19—24no—
123C2×D19—24no—
124C2×D19—24no—
125C2×D19—416no—
126C2×D19C22⋊Q818yescomplemented
127C4×C19—24no—
128C4×C19—41no—
129C4×C19—42no—
130C4×C19—41no—
131Dic19—24no—
132Dic19—42no—
133Dic19—42no—
134C2×C22⋊Q8—192no—
135C22×C22⋊C4—192no—
136#399—191no—
137#396—192no—
138#393D1911yescharacteristic, complemented
139#385—192no—
140#385—192no—
141#380—192no—
142#379—191no—
143C2×C19—42no—
144C2×C19C2×C22⋊Q812yes—
145C2×C19#54311yescharacteristic
146C2×C19D4211yescharacteristic
147C2×C19#54612yes—
148C2×C19#55111yescharacteristic
149D19—28no—
150C25—191no—
151C22×Q8C2×D1911yescharacteristic, complemented
152C23×C4—192no—
153C23×C4—192no—
154C22⋊Q8—388no—
155C2×C4⋊C4—192no—
156C2×C4⋊C4—192no—
157C2×C4⋊C4—192no—
158C2×C4⋊C4—192no—
159C2×C4⋊C4—191no—
160C2×C22⋊C4—192no—
161C2×C22⋊C4—192no—
162C2×C22⋊C4—192no—
163C2×C22⋊C4—192no—
164C2×C22⋊C4—192no—
165C2×C22⋊C4—191no—
166C2×C22⋊C4—388no—
167C2×C22⋊C4C2×D1912yes—
168C2×C22⋊C4C2×D1911yescharacteristic
169#95—192no—
170#95—191no—
171#95C2×D1911yescharacteristic, complemented
172#95C2×D1912yescomplemented
173C19#243711yescharacteristic, complemented, Sylow
174C24—192no—
175C24—194no—
176C24—384no—
177C24—384no—
178C24—761no—
179C24—761no—
180C24C22×D1911yescharacteristic
181C2×Q8—24no—
182C2×Q8—41no—
183C22×C4—192no—
184C22×C4—192no—
185C22×C4—192no—
186C22×C4—384no—
187C22×C4—384no—
188C22×C4—384no—
189C22×C4—384no—
190C22×C4—762no—
191C22×C4—762no—
192C22×C4C22×D1911yescharacteristic
193C22×C4C22×D1912yes—
194C22×C4C22×D1911yescharacteristic
195C22×C4C22×D1912yes—
196C4⋊C4—384no—
197C4⋊C4—384no—
198C4⋊C4—384no—
199C4⋊C4—762no—
200C4⋊C4—761no—
201C22⋊C4—24no—
202C22⋊C4—41no—
203C22⋊C4—198no—
204C22⋊C4—384no—
205C22⋊C4—384no—
206C22⋊C4—384no—
207C22⋊C4—384no—
208C22⋊C4—761no—
209C23—22no—
210C23—21no—
211C23—22no—
212C23—21no—
213C23—194no—
214C23—194no—
215C23—194no—
216C23—3816no—
217C23—382no—
218C23—382no—
219C23—382no—
220C23—382no—
221C23—764no—
222C23—764no—
223C23—768no—
224C23—764no—
225C23Q8×D1912yes—
226C23C23×D1911yescharacteristic
227Q8—44no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—194no—
238C2×C4—382no—
239C2×C4—382no—
240C2×C4—382no—
241C2×C4—382no—
242C2×C4—382no—
243C2×C4—382no—
244C2×C4—382no—
245C2×C4—382no—
246C2×C4—768no—
247C2×C4—768no—
248C2×C4D4×D1914yes—
249C22—22no—
250C22—24no—
251C22—41no—
252C22—42no—
253C22—41no—
254C22—198no—
255C22—384no—
256C22—384no—
257C22—384no—
258C22—384no—
259C22—384no—
260C22—384no—
261C22—7616no—
262C22C2×D4×D1912yes—
263C22#1059743011yescharacteristic
264C22C2×Q8×D1911yescharacteristic
265C22#41×D1912yes—
266C22#1059743511yescharacteristic
267C4—24no—
268C4—41no—
269C4—42no—
270C4—41no—
271C4—384no—
272C4—762no—
273C4—762no—
274C2—42no—
275C2—388no—
276C2C22⋊Q8×D1912yes—
277C2#1192716911yescharacteristic
278C2#1192717611yescharacteristic
279C2#1192718712yes—
280C2#1192722411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#393C2
prime radicalC24×D19C22
hypercenter#393D19
hypocenterC19#2437
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#10597392C2semidirect
3. #11926480C2semidirect
4. #11926467C2semidirect
5. #11926418C2semidirect
6. #11926418C2semidirect
7. #11926403C2semidirect
9. C19×#393C2semidirect
11. C22×Q8×C19C22semidirect
23. C2×C4⋊Dic19C22semidirect
24. C2×C4⋊Dic19C22semidirect
25. C2×Dic19⋊C4C22semidirect
26. C2×Dic19⋊C4C22semidirect
27. C2×Dic19⋊C4C22semidirect
29. C19×#95C22semidirect
30. C19×#95C22semidirect
31. C19⋊#95C22semidirect
32. C19⋊#95C22semidirect
38. C23×D19Q8semidirect
126. C2×D19C22⋊Q8semidirect
138. #393D19semidirect
151. C22×Q8C2×D19semidirect
171. #95C2×D19semidirect
172. #95C2×D19semidirect
173. C19#2437semidirect

Maximal subgroups

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

subgroupindex
C2×#105973922
C2×C22⋊C4×D192
#119264802
#119264672
#119264182
#119264032
#119263992
C19×#3932
#243719