Finite Group Databasebeta

← #14570681

Subgroups — #14570681

Order 2432.

560 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 125 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#11926472C212yesmaximal, complemented
2#11926469C211yesmaximal, characteristic, complemented
3#11926456C211yesmaximal, characteristic, complemented
4#11926456C212yesmaximal, complemented
5#11926438C212yesmaximal, complemented
6#11926437C212yesmaximal, complemented
7#11926432C212yesmaximal, complemented
8#11926400C212yesmaximal
9C19×#379C211yesmaximal, characteristic
10C25×C19C2211yescharacteristic
11C22×Dic38C2211yescharacteristic, complemented
12C2×C22⋊C4×C19C2212yes—
13C2×C22⋊C4×C19C2211yescharacteristic
14C2×C22⋊C4×C19C2212yes—
15C2×C22⋊C4×C19C2211yescharacteristic
16C2×C22⋊Dic19C2212yes—
17C2×C22⋊Dic19C2212yes—
18C2×C22⋊Dic19C2212yes—
19C2×C22⋊Dic19C2212yes—
20C2×C22⋊Dic19C2212yes—
21C2×C22⋊Dic19C2212yes—
22C2×C4⋊Dic19C2211yescharacteristic, complemented
23C2×Dic19⋊C4C2212yescomplemented
24C2×C4×Dic19C2212yescomplemented
25C19⋊#95C2212yescomplemented
26C19⋊#95C2212yescomplemented
27C19⋊#95C2212yescomplemented
28C19⋊#95C2211yescharacteristic, complemented
29C19⋊#95C2212yescomplemented
30C19⋊#95C2211yescharacteristic, complemented
31C24×C19—22no—
32C24×C19—24no—
33C24×C19—42no—
34C24×C19—41no—
35C24×C19—41no—
36C24×C19C2311yescharacteristic
37C24×C19C2312yes—
38C22×C4×C19C2311yescharacteristic
39C22×C4×C19C2311yescharacteristic
40C22×C4×C19C2312yes—
41C22×Dic19C2312yes—
42C22×Dic19C2312yes—
43C22×Dic19C2312yes—
44C22×Dic19C2312yes—
45C2×Dic38—42no—
46C2×Dic38—41no—
47C22⋊C4×C19—24no—
48C22⋊C4×C19—41no—
49C22⋊C4×C19—42no—
50C22⋊C4×C19—41no—
51C22⋊Dic19—24no—
52C22⋊Dic19—24no—
53C22⋊Dic19—42no—
54C22⋊Dic19—42no—
55C22⋊Dic19—42no—
56C22⋊Dic19—42no—
57C4⋊Dic19—41no—
58Dic19⋊C4—42no—
59C4×Dic19—42no—
60C23×C19—22no—
61C23×C19—22no—
62C23×C19—22no—
63C23×C19—22no—
64C23×C19—22no—
65C23×C19—22no—
66C23×C19—22no—
67C23×C19—21no—
68C23×C19—21no—
69C23×C19—22no—
70C23×C19—48no—
71C23×C19—44no—
72C23×C19—48no—
73C23×C19—44no—
74C23×C19—44no—
75C23×C19#4112yes—
76C23×C19#4114yes—
77C23×C19C2411yescharacteristic
78C2×C4×C19—22no—
79C2×C4×C19—22no—
80C2×C4×C19—22no—
81C2×C4×C19—22no—
82C2×C4×C19—21no—
83C2×C4×C19—22no—
84C2×C4×C19—21no—
85C2×Dic19—22no—
86C2×Dic19—22no—
87C2×Dic19—22no—
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—
97Dic38—44no—
98#2736—191nomaximal, Sylow
99C22×C19—24no—
100C22×C19—22no—
101C22×C19—24no—
102C22×C19—24no—
103C22×C19—24no—
104C22×C19—416no—
105C22×C19—42no—
106C22×C19—42no—
107C22×C19—42no—
108C22×C19—42no—
109C22×C19—41no—
110C22×C19—42no—
111C22×C19—41no—
112C22×C19C2×#4111yescharacteristic
113C22×C19C2×#4112yes—
114C22×C19H(5,𝔽2)11yescharacteristic
115C22×C19H(5,𝔽2)12yes—
116C22×C19H(5,𝔽2)11yescharacteristic
117C4×C19—42no—
118C4×C19—41no—
119C4×C19—41no—
120Dic19—42no—
121Dic19—42no—
122Dic19—42no—
123Dic19—42no—
124#397—191no—
125#397—192no—
126#393—191no—
127#393—192no—
128#388—192no—
129#388—192no—
130#388—192no—
131#379—192no—
132#379D1911yescharacteristic
133C2×C19—44no—
134C2×C19—42no—
135C2×C19#53812yes—
136C2×C19#53811yescharacteristic
137C2×C19#55112yes—
138C2×C19#55111yescharacteristic
139C2×C19H(3,𝔽4)11yescharacteristic
140C25C2×D1911yescharacteristic
141C22×Q8—191no—
142C2×C4⋊C4—192no—
143C2×C4⋊C4—191no—
144C2×C22⋊C4—192no—
145C2×C22⋊C4—192no—
146C2×C22⋊C4—192no—
147C2×C22⋊C4—192no—
148C2×C22⋊C4—192no—
149C2×C22⋊C4—192no—
150C2×C22⋊C4C2×D1912yes—
151C2×C22⋊C4C2×D1911yescharacteristic
152C2×C22⋊C4C2×D1912yes—
153C2×C22⋊C4C2×D1911yescharacteristic
154C2×C42—192no—
155#95—192no—
156#95—191no—
157#95—192no—
158#95—192no—
159#95—192no—
160#95—191no—
161C19#273611yescharacteristic, complemented, Sylow
162C24—22no—
163C24—24no—
164C24—41no—
165C24—42no—
166C24—41no—
167C24C22×D1911yescharacteristic
168C24C22×D1912yes—
169C2×Q8—762no—
170C2×Q8—761no—
171C22×C4—192no—
172C22×C4—192no—
173C22×C4—192no—
174C22×C4—192no—
175C22×C4C22×D1911yescharacteristic
176C22×C4C22×D1911yescharacteristic
177C22×C4C22×D1912yes—
178C4⋊C4—762no—
179C4⋊C4—761no—
180C22⋊C4—24no—
181C22⋊C4—41no—
182C22⋊C4—42no—
183C22⋊C4—41no—
184C22⋊C4—384no—
185C22⋊C4—384no—
186C22⋊C4—762no—
187C22⋊C4—762no—
188C22⋊C4—762no—
189C22⋊C4—762no—
190C42—762no—
191C23—22no—
192C23—22no—
193C23—22no—
194C23—21no—
195C23—21no—
196C23—22no—
197C23—22no—
198C23—22no—
199C23—22no—
200C23—22no—
201C23—48no—
202C23—44no—
203C23—48no—
204C23—44no—
205C23—44no—
206C23#6454112yes—
207C23#6454314yes—
208C23C23×D1911yescharacteristic
209Q8—764no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—382no—
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—
227C2×C4—382no—
228C2×C4—382no—
229C22—24no—
230C22—22no—
231C22—24no—
232C22—24no—
233C22—24no—
234C22—416no—
235C22—42no—
236C22—42no—
237C22—42no—
238C22—42no—
239C22—41no—
240C22—42no—
241C22—41no—
242C22C2×#6454111yescharacteristic
243C22C2×#6454312yes—
244C22#1059743011yescharacteristic
245C22#1059743012yes—
246C22#1059743011yescharacteristic
247C4—42no—
248C4—41no—
249C4—41no—
250C4—762no—
251C4—762no—
252C4—762no—
253C4—762no—
254C2—44no—
255C2—42no—
256C2#1192712912yes—
257C2#1192713211yescharacteristic
258C2#1192722012yes—
259C2#1192722511yescharacteristic
260C2#1192728711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#379C2
prime radicalC25×C19C22
hypercenter#379D19
hypocenterC19#2736
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #11926472C2semidirect
2. #11926469C2semidirect
3. #11926456C2semidirect
4. #11926456C2semidirect
5. #11926438C2semidirect
6. #11926437C2semidirect
7. #11926432C2semidirect
11. C22×Dic38C22semidirect
22. C2×C4⋊Dic19C22semidirect
23. C2×Dic19⋊C4C22semidirect
24. C2×C4×Dic19C22semidirect
25. C19⋊#95C22semidirect
26. C19⋊#95C22semidirect
27. C19⋊#95C22semidirect
28. C19⋊#95C22semidirect
29. C19⋊#95C22semidirect
30. C19⋊#95C22semidirect
161. C19#2736semidirect

Maximal subgroups

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

subgroupindex
#119264722
#119264692
#119264562
#119264382
#119264372
#119264322
#119264002
C19×#3792
#273619