Finite Group Databasebeta

← #14570670

Subgroups — #14570670

Order 2432.

552 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#11926480C211yesmaximal, characteristic, complemented
2#11926471C212yesmaximal, complemented
3#11926466C212yesmaximal, complemented
4#11926437C212yesmaximal, complemented
5#11926436C212yesmaximal, complemented
6#11926433C212yesmaximal, complemented
7#11926399C211yesmaximal, characteristic
8#11926399C212yesmaximal
9C19×#397C211yesmaximal, characteristic, complemented
10C24×D19C2211yescharacteristic
11C2×C4⋊C4×C19C2211yescharacteristic, complemented
12C2×C22⋊C4×C19C2212yes—
13C2×C22⋊C4×C19C2211yescharacteristic
14C2×C22⋊Dic19C2211yescharacteristic
15C2×C22⋊Dic19C2212yes—
16C2×(C2×D19)⋊C4C2212yes—
17C2×(C2×D19)⋊C4C2212yes—
18C2×(C2×D19)⋊C4C2212yes—
19C2×(C2×D19)⋊C4C2212yes—
20C2×(C2×D19)⋊C4C2212yes—
21C2×(C2×D19)⋊C4C2212yes—
22C2×C4⋊Dic19C2211yescharacteristic, complemented
23C2×C4⋊Dic19C2212yescomplemented
24C2×Dic19⋊C4C2212yescomplemented
25C2×C4×Dic19C2212yescomplemented
26C19×#95C2211yescharacteristic, complemented
27C19×#95C2212yescomplemented
28C19⋊#95C2212yescomplemented
29C19⋊#95C2212yescomplemented
30C19⋊#95C2211yescharacteristic, complemented
31C24×C19C2311yescharacteristic
32C23×D19—22no—
33C23×D19—24no—
34C23×D19—41no—
35C23×D19—42no—
36C23×D19—41no—
37C23×D19C2312yes—
38C22×C4×C19C2312yes—
39C22×C4×C19C2311yescharacteristic
40C22×C4×C19C2312yes—
41C22×C4×C19C2311yescharacteristic
42C22×Dic19C2312yes—
43C22×Dic19C2312yes—
44C22×Dic19C2312yes—
45C4⋊C4×C19—41no—
46C22⋊C4×C19—24no—
47C22⋊C4×C19—41no—
48C22⋊Dic19—42no—
49C22⋊Dic19—41no—
50(C2×D19)⋊C4—24no—
51(C2×D19)⋊C4—24no—
52(C2×D19)⋊C4—42no—
53(C2×D19)⋊C4—42no—
54(C2×D19)⋊C4—42no—
55(C2×D19)⋊C4—42no—
56C4⋊Dic19—41no—
57C4⋊Dic19—42no—
58Dic19⋊C4—42no—
59C4×Dic19—42no—
60C23×C19—22no—
61C23×C19—21no—
62C23×C19—22no—
63C23×C19—21no—
64C23×C19#4112yes—
65C23×C19C2411yescharacteristic
66C22×D19—22no—
67C22×D19—22no—
68C22×D19—22no—
69C22×D19—22no—
70C22×D19—22no—
71C22×D19—22no—
72C22×D19—44no—
73C22×D19—48no—
74C22×D19—48no—
75C22×D19—44no—
76C22×D19—44no—
77C22×D19#4114yes—
78C2×C4×C19—22no—
79C2×C4×C19—22no—
80C2×C4×C19—22no—
81C2×C4×C19—22no—
82C2×C4×C19—22no—
83C2×C4×C19—22no—
84C2×C4×C19—22no—
85C2×C4×C19—21no—
86C2×C4×C19—22no—
87C2×C4×C19—21no—
88C2×Dic19—22no—
89C2×Dic19—22no—
90C2×Dic19—22no—
91C2×Dic19—22no—
92C2×Dic19—22no—
93C2×Dic19—22no—
94C2×Dic19—22no—
95C2×Dic19—22no—
96C2×Dic19—22no—
97#2735—191nomaximal, Sylow
98C22×C19—22no—
99C22×C19—24no—
100C22×C19—42no—
101C22×C19—41no—
102C22×C19—41no—
103C22×C19C2×#4111yescharacteristic
104C22×C19C2×#4112yes—
105C22×C19H(5,𝔽2)11yescharacteristic
106C22×C19H(5,𝔽2)11yescharacteristic
107C22×C19H(5,𝔽2)12yes—
108C2×D19—24no—
109C2×D19—24no—
110C2×D19—24no—
111C2×D19—416no—
112C2×D19—42no—
113C2×D19—42no—
114C2×D19—42no—
115C2×D19—42no—
116C4×C19—42no—
117C4×C19—42no—
118C4×C19—41no—
119C4×C19—41no—
120Dic19—42no—
121Dic19—42no—
122Dic19—42no—
123#399—191no—
124#397—192no—
125#397D1911yescharacteristic, complemented
126#396—192no—
127#388—192no—
128#388—192no—
129#388—192no—
130#379—191no—
131#379—192no—
132C2×C19—42no—
133C2×C19#53811yescharacteristic
134C2×C19#53812yes—
135C2×C19#55112yes—
136C2×C19#55111yescharacteristic
137C2×C19#56011yescharacteristic
138D19—44no—
139C25—191no—
140C2×C4⋊C4—191no—
141C2×C4⋊C4—192no—
142C2×C4⋊C4—192no—
143C2×C4⋊C4C2×D1911yescharacteristic, complemented
144C2×C22⋊C4—192no—
145C2×C22⋊C4—192no—
146C2×C22⋊C4—191no—
147C2×C22⋊C4—192no—
148C2×C22⋊C4—192no—
149C2×C22⋊C4—192no—
150C2×C22⋊C4—192no—
151C2×C22⋊C4—192no—
152C2×C22⋊C4C2×D1912yes—
153C2×C22⋊C4C2×D1911yescharacteristic
154C2×C42—192no—
155#95—192no—
156#95—192no—
157#95—191no—
158#95C2×D1911yescharacteristic, complemented
159#95C2×D1912yescomplemented
160C19#273511yescharacteristic, complemented, Sylow
161C24—192no—
162C24—384no—
163C24—382no—
164C24—761no—
165C24—762no—
166C24—761no—
167C24C22×D1911yescharacteristic
168C22×C4—192no—
169C22×C4—192no—
170C22×C4—192no—
171C22×C4C22×D1912yes—
172C22×C4C22×D1911yescharacteristic
173C22×C4C22×D1912yes—
174C22×C4C22×D1911yescharacteristic
175C4⋊C4—41no—
176C4⋊C4—762no—
177C4⋊C4—761no—
178C4⋊C4—762no—
179C22⋊C4—24no—
180C22⋊C4—41no—
181C22⋊C4—384no—
182C22⋊C4—384no—
183C22⋊C4—762no—
184C22⋊C4—762no—
185C22⋊C4—762no—
186C22⋊C4—762no—
187C22⋊C4—762no—
188C22⋊C4—761no—
189C42—762no—
190C23—21no—
191C23—22no—
192C23—21no—
193C23—22no—
194C23—194no—
195C23—382no—
196C23—382no—
197C23—382no—
198C23—382no—
199C23—382no—
200C23—382no—
201C23—768no—
202C23—764no—
203C23—764no—
204C23—768no—
205C23—764no—
206C23#6454312yes—
207C23C23×D1911yescharacteristic
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—382no—
219C2×C4—382no—
220C2×C4—382no—
221C2×C4—382no—
222C2×C4—382no—
223C2×C4—382no—
224C2×C4—382no—
225C2×C4—382no—
226C2×C4—382no—
227C22—22no—
228C22—24no—
229C22—42no—
230C22—41no—
231C22—41no—
232C22—384no—
233C22—384no—
234C22—384no—
235C22—7616no—
236C22—762no—
237C22—762no—
238C22—762no—
239C22—762no—
240C22C2×#6454311yescharacteristic
241C22#1059743011yescharacteristic
242C22#41×D1912yes—
243C22#1059743511yescharacteristic
244C22#1059743512yes—
245C4—42no—
246C4—42no—
247C4—41no—
248C4—41no—
249C4—762no—
250C4—762no—
251C4—762no—
252C2—42no—
253C2—764no—
254C2#1192713111yescharacteristic
255C2#1192713312yes—
256C2#1192721712yes—
257C2#1192722411yescharacteristic
258C2#1192728411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#397C2
prime radicalC24×D19C22
hypercenter#397D19
hypocenterC19#2735
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #11926480C2semidirect
2. #11926471C2semidirect
3. #11926466C2semidirect
4. #11926437C2semidirect
5. #11926436C2semidirect
6. #11926433C2semidirect
9. C19×#397C2semidirect
11. C2×C4⋊C4×C19C22semidirect
22. C2×C4⋊Dic19C22semidirect
23. C2×C4⋊Dic19C22semidirect
24. C2×Dic19⋊C4C22semidirect
25. C2×C4×Dic19C22semidirect
26. C19×#95C22semidirect
27. C19×#95C22semidirect
28. C19⋊#95C22semidirect
29. C19⋊#95C22semidirect
30. C19⋊#95C22semidirect
125. #397D19semidirect
143. C2×C4⋊C4C2×D19semidirect
158. #95C2×D19semidirect
159. #95C2×D19semidirect
160. C19#2735semidirect

Maximal subgroups

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

subgroupindex
#119264802
#119264712
#119264662
#119264372
#119264362
#119264332
#119263992
C19×#3972
#273519