Finite Group Databasebeta

← #14567912

Subgroups — #14567912

Order 2432.

700 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 141 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×C22⋊C4×D19C212yesmaximal
2#11926472C212yesmaximal, complemented
3#11926469C211yesmaximal, characteristic, complemented
4#11926418C212yesmaximal, complemented
5#11926415C212yesmaximal, complemented
6#11926406C212yesmaximal, complemented
7#11926406C212yesmaximal, complemented
8#11926399C211yesmaximal, characteristic
9C19×#397C211yesmaximal, characteristic, complemented
10C24×D19C2211yescharacteristic
11C22×C4×D19C2212yes—
12C22×C4×D19C2212yes—
13C2×C4⋊C4×C19C2211yescharacteristic, complemented
14C2×C22⋊C4×C19C2212yes—
15C2×C22⋊C4×C19C2211yescharacteristic
16C2×C22⋊Dic19C2212yes—
17C2×C22⋊Dic19C2211yescharacteristic
18C2×(C2×D19)⋊C4C2212yes—
19C2×(C2×D19)⋊C4C2212yes—
20C2×(C2×D19)⋊C4C2212yes—
21C2×(C2×D19)⋊C4C2212yes—
22C2×C4⋊Dic19C2211yescharacteristic, complemented
23C2×Dic19⋊C4C2212yescomplemented
24C22⋊C4×D19—28no—
25C19×#95C2211yescharacteristic, complemented
26C19×#95C2212yescomplemented
27C19⋊#95C2211yescharacteristic, complemented
28C19⋊#95C2212yescomplemented
29C19⋊#95C2212yescomplemented
30C19⋊#95C2212yescomplemented
31C19⋊#95C2212yescomplemented
32C24×C19C2311yescharacteristic
33C23×D19—24no—
34C23×D19—24no—
35C23×D19—41no—
36C23×D19—41no—
37C23×D19D414yes—
38C23×D19C2312yes—
39C22×C4×C19C2312yes—
40C22×C4×C19C2311yescharacteristic
41C22×C4×C19C2312yes—
42C22×C4×C19C2311yescharacteristic
43C22×Dic19C2312yes—
44C22×Dic19C2312yes—
45C22×Dic19C2312yes—
46C2×C4×D19—24no—
47C2×C4×D19—24no—
48C2×C4×D19—24no—
49C2×C4×D19—24no—
50C2×C4×D19—42no—
51C2×C4×D19—42no—
52C4⋊C4×C19—41no—
53C22⋊C4×C19—24no—
54C22⋊C4×C19—41no—
55C22⋊Dic19—24no—
56C22⋊Dic19—41no—
57(C2×D19)⋊C4—24no—
58(C2×D19)⋊C4—24no—
59(C2×D19)⋊C4—24no—
60(C2×D19)⋊C4—24no—
61C4⋊Dic19—41no—
62Dic19⋊C4—42no—
63C23×C19—22no—
64C23×C19—22no—
65C23×C19—21no—
66C23×C19—21no—
67C23×C19C2×D412yes—
68C23×C19C2411yescharacteristic
69C22×D19—22no—
70C22×D19—22no—
71C22×D19—22no—
72C22×D19—22no—
73C22×D19—216no—
74C22×D19—44no—
75C22×D19—48no—
76C22×D19—44no—
77C22×D19—44no—
78C22×D19C2×D414yes—
79C22×D19#4114yes—
80C22×D19#4114yes—
81C2×C4×C19—22no—
82C2×C4×C19—22no—
83C2×C4×C19—22no—
84C2×C4×C19—22no—
85C2×C4×C19—22no—
86C2×C4×C19—22no—
87C2×C4×C19—22no—
88C2×C4×C19—21no—
89C2×C4×C19—21no—
90C2×C4×C19—22no—
91C2×Dic19—22no—
92C2×Dic19—22no—
93C2×Dic19—22no—
94C2×Dic19—22no—
95C2×Dic19—22no—
96C2×Dic19—22no—
97C2×Dic19—22no—
98C2×Dic19—22no—
99C2×Dic19—22no—
100C4×D19—48no—
101C4×D19—48no—
102#2483—191nomaximal, Sylow
103C22×C19—24no—
104C22×C19—22no—
105C22×C19—42no—
106C22×C19—41no—
107C22×C19—41no—
108C22×C19C22×D411yescharacteristic
109C22×C19C2×#4112yes—
110C22×C19C2×#4112yes—
111C22×C19H(5,𝔽2)11yescharacteristic
112C22×C19H(5,𝔽2)11yescharacteristic
113C2×D19—24no—
114C2×D19—24no—
115C2×D19—24no—
116C2×D19—24no—
117C2×D19—24no—
118C2×D19—24no—
119C2×D19—416no—
120C2×D19#12318yes—
121C4×C19—42no—
122C4×C19—42no—
123C4×C19—41no—
124C4×C19—41no—
125Dic19—42no—
126Dic19—42no—
127Dic19—42no—
128C22×C22⋊C4—192no—
129#397—191no—
130#397—192no—
131#397D1911yescharacteristic, complemented
132#385—192no—
133#385—192no—
134#381—192no—
135#381—192no—
136#379—191no—
137C2×C19—42no—
138C2×C19C2×#12312yes—
139C2×C19#53411yescharacteristic
140C2×C19#55112yes—
141C2×C19#55111yescharacteristic
142C2×C19#55111yescharacteristic
143D19—28no—
144C25—191no—
145C23×C4—192no—
146C23×C4—192no—
147C2×C4⋊C4—192no—
148C2×C4⋊C4—191no—
149C2×C4⋊C4C2×D1911yescharacteristic, complemented
150C2×C22⋊C4—192no—
151C2×C22⋊C4—192no—
152C2×C22⋊C4—192no—
153C2×C22⋊C4—192no—
154C2×C22⋊C4—192no—
155C2×C22⋊C4—191no—
156C2×C22⋊C4—388no—
157C2×C22⋊C4C2×D1912yes—
158C2×C22⋊C4C2×D1911yescharacteristic
159#95—191no—
160#95—192no—
161#95—192no—
162#95—192no—
163#95—192no—
164#95C2×D1911yescharacteristic, complemented
165#95C2×D1912yescomplemented
166C19#248311yescharacteristic, complemented, Sylow
167C24—192no—
168C24—194no—
169C24—384no—
170C24—384no—
171C24—761no—
172C24—761no—
173C24C22×D1911yescharacteristic
174C22×C4—192no—
175C22×C4—192no—
176C22×C4—192no—
177C22×C4—384no—
178C22×C4—384no—
179C22×C4—384no—
180C22×C4—384no—
181C22×C4—762no—
182C22×C4—762no—
183C22×C4C22×D1912yes—
184C22×C4C22×D1911yescharacteristic
185C22×C4C22×D1911yescharacteristic
186C22×C4C22×D1912yes—
187C4⋊C4—41no—
188C4⋊C4—762no—
189C4⋊C4—761no—
190C22⋊C4—24no—
191C22⋊C4—41no—
192C22⋊C4—384no—
193C22⋊C4—384no—
194C22⋊C4—384no—
195C22⋊C4—384no—
196C22⋊C4—384no—
197C22⋊C4—761no—
198C23—21no—
199C23—22no—
200C23—22no—
201C23—21no—
202C23—194no—
203C23—194no—
204C23—194no—
205C23—3816no—
206C23—382no—
207C23—382no—
208C23—382no—
209C23—382no—
210C23—764no—
211C23—768no—
212C23—764no—
213C23—764no—
214C23D4×D1912yes—
215C23C23×D1911yescharacteristic
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—382no—
227C2×C4—382no—
228C2×C4—382no—
229C2×C4—382no—
230C2×C4—382no—
231C2×C4—382no—
232C2×C4—382no—
233C2×C4—382no—
234C2×C4—382no—
235C2×C4—768no—
236C2×C4—768no—
237C22—24no—
238C22—22no—
239C22—42no—
240C22—41no—
241C22—41no—
242C22—198no—
243C22—384no—
244C22—384no—
245C22—384no—
246C22—384no—
247C22—384no—
248C22—384no—
249C22—7616no—
250C22C2×D4×D1911yescharacteristic
251C22#1059743011yescharacteristic
252C22#41×D1912yes—
253C22#41×D1912yes—
254C22#1059743511yescharacteristic
255C4—42no—
256C4—42no—
257C4—41no—
258C4—41no—
259C4—762no—
260C4—762no—
261C4—762no—
262C2—42no—
263C2—388no—
264C2#123×D1912yes—
265C2#1192710211yescharacteristic
266C2#1192721912yes—
267C2#1192722211yescharacteristic
268C2#1192722411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#397C2
prime radicalC24×D19C22
hypercenter#397D19
hypocenterC19#2483
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #11926472C2semidirect
3. #11926469C2semidirect
4. #11926418C2semidirect
5. #11926415C2semidirect
6. #11926406C2semidirect
7. #11926406C2semidirect
9. C19×#397C2semidirect
13. C2×C4⋊C4×C19C22semidirect
22. C2×C4⋊Dic19C22semidirect
23. C2×Dic19⋊C4C22semidirect
25. C19×#95C22semidirect
26. C19×#95C22semidirect
27. C19⋊#95C22semidirect
28. C19⋊#95C22semidirect
29. C19⋊#95C22semidirect
30. C19⋊#95C22semidirect
31. C19⋊#95C22semidirect
131. #397D19semidirect
149. C2×C4⋊C4C2×D19semidirect
164. #95C2×D19semidirect
165. #95C2×D19semidirect
166. C19#2483semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D192
#119264722
#119264692
#119264182
#119264152
#119264062
#119263992
C19×#3972
#248319