Finite Group Databasebeta

← #14567301

Subgroups — #14567301

Order 2432.

780 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 181 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×#10597324C212yesmaximal, complemented
2C22×C22⋊Dic19C212yesmaximal
3#11926480C211yesmaximal, characteristic, complemented
4#11926467C212yesmaximal, complemented
5#11926456C211yesmaximal, characteristic, complemented
6#11926419C212yesmaximal, complemented
7#11926416C212yesmaximal, complemented
8#11926402C212yesmaximal, complemented
9C19×#379C211yesmaximal, characteristic
10C25×C19C2211yescharacteristic
11C23×Dic19C2212yes—
12C23×Dic19C2212yes—
13C22×Dic38C2211yescharacteristic, complemented
14C2×C22⋊C4×C19C2212yes—
15C2×C22⋊C4×C19C2212yes—
16C2×C22⋊C4×C19C2211yescharacteristic
17C2×C22⋊C4×C19C2211yescharacteristic
18C2×C22⋊Dic19—28no—
19C2×C22⋊Dic19C2212yes—
20C2×C22⋊Dic19C2212yes—
21C2×C22⋊Dic19C2212yes—
22C2×C22⋊Dic19C2212yes—
23C2×C4⋊Dic19C2212yescomplemented
24C2×C4⋊Dic19C2211yescharacteristic, complemented
25C2×Dic19⋊C4C2212yescomplemented
26C2×Dic19⋊C4C2212yescomplemented
27C2×Dic19⋊C4C2212yescomplemented
28#10597324—28no—
29C19⋊#95C2211yescharacteristic, complemented
30C19⋊#95C2212yescomplemented
31C19⋊#95C2211yescharacteristic, complemented
32C19⋊#95C2212yescomplemented
33C24×C19—24no—
34C24×C19—24no—
35C24×C19—41no—
36C24×C19—41no—
37C24×C19Q814yescomplemented
38C24×C19C2311yescharacteristic
39C24×C19C2312yes—
40C22×C4×C19C2311yescharacteristic
41C22×C4×C19C2311yescharacteristic
42C22×C4×C19C2312yes—
43C22×Dic19—24no—
44C22×Dic19—24no—
45C22×Dic19—24no—
46C22×Dic19—24no—
47C22×Dic19—42no—
48C22×Dic19—42no—
49C22×Dic19C2312yes—
50C22×Dic19C2312yes—
51C22×Dic19C2312yes—
52C22×Dic19C2312yes—
53C2×Dic38—24no—
54C2×Dic38—41no—
55C22⋊C4×C19—24no—
56C22⋊C4×C19—24no—
57C22⋊C4×C19—41no—
58C22⋊C4×C19—41no—
59C22⋊Dic19—24no—
60C22⋊Dic19—24no—
61C22⋊Dic19—24no—
62C22⋊Dic19D418yes—
63C4⋊Dic19—24no—
64C4⋊Dic19—41no—
65Dic19⋊C4—24no—
66Dic19⋊C4—24no—
67Dic19⋊C4—42no—
68C23×C19—22no—
69C23×C19—22no—
70C23×C19—22no—
71C23×C19—22no—
72C23×C19—216no—
73C23×C19—22no—
74C23×C19—22no—
75C23×C19—21no—
76C23×C19—21no—
77C23×C19—44no—
78C23×C19—44no—
79C23×C19—48no—
80C23×C19—44no—
81C23×C19C2×D414yes—
82C23×C19C2×Q812yes—
83C23×C19C2×Q814yes—
84C23×C19#4114yes—
85C23×C19C2411yescharacteristic
86C2×C4×C19—22no—
87C2×C4×C19—22no—
88C2×C4×C19—22no—
89C2×C4×C19—22no—
90C2×C4×C19—22no—
91C2×C4×C19—21no—
92C2×C4×C19—21no—
93C2×Dic19—22no—
94C2×Dic19—22no—
95C2×Dic19—22no—
96C2×Dic19—22no—
97C2×Dic19—22no—
98C2×Dic19—22no—
99C2×Dic19—22no—
100C2×Dic19—22no—
101C2×Dic19—22no—
102C2×Dic19—22no—
103C2×Dic19—48no—
104C2×Dic19—48no—
105C2×Dic19C2×D414yes—
106C2×Dic19C2×D414yes—
107Dic38—44no—
108#2437—191nomaximal, Sylow
109C22×C19—24no—
110C22×C19—24no—
111C22×C19—24no—
112C22×C19—24no—
113C22×C19—24no—
114C22×C19—24no—
115C22×C19—24no—
116C22×C19—22no—
117C22×C19—416no—
118C22×C19—41no—
119C22×C19—42no—
120C22×C19—41no—
121C22×C19C22⋊Q818yescomplemented
122C22×C19C22×D412yes—
123C22×C19C22×Q811yescharacteristic
124C22×C19C2×#4112yes—
125C22×C19H(5,𝔽2)11yescharacteristic
126C22×C19H(5,𝔽2)11yescharacteristic
127C4×C19—41no—
128C4×C19—42no—
129C4×C19—41no—
130Dic19—24no—
131Dic19—24no—
132Dic19—42no—
133Dic19—42no—
134C2×C22⋊Q8—192no—
135C22×C22⋊C4—192no—
136#399—191no—
137#396—192no—
138#393—191no—
139#385—192no—
140#385—192no—
141#380—192no—
142#379D1911yescharacteristic
143C2×C19—28no—
144C2×C19—42no—
145C2×C19C2×C22⋊Q812yes—
146C2×C19#54311yescharacteristic
147C2×C19D4211yescharacteristic
148C2×C19#54612yes—
149C2×C19#55111yescharacteristic
150C25C2×D1911yescharacteristic
151C22×Q8—191no—
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—388no—
165C2×C22⋊C4C2×D1912yes—
166C2×C22⋊C4C2×D1912yes—
167C2×C22⋊C4C2×D1911yescharacteristic
168C2×C22⋊C4C2×D1911yescharacteristic
169#95—191no—
170#95—192no—
171#95—192no—
172#95—191no—
173C19#243711yescharacteristic, complemented, Sylow
174C24—24no—
175C24—24no—
176C24—41no—
177C24—41no—
178C24Dic3814yescomplemented
179C24C22×D1911yescharacteristic
180C24C22×D1912yes—
181C2×Q8—384no—
182C2×Q8—761no—
183C22×C4—192no—
184C22×C4—192no—
185C22×C4—192no—
186C22×C4—192no—
187C22×C4—384no—
188C22×C4—384no—
189C22×C4—384no—
190C22×C4—384no—
191C22×C4—762no—
192C22×C4—762no—
193C22×C4C22×D1911yescharacteristic
194C22×C4C22×D1912yes—
195C22×C4C22×D1911yescharacteristic
196C4⋊C4—384no—
197C4⋊C4—384no—
198C4⋊C4—384no—
199C4⋊C4—762no—
200C4⋊C4—761no—
201C22⋊C4—24no—
202C22⋊C4—24no—
203C22⋊C4—41no—
204C22⋊C4—41no—
205C22⋊C4—198no—
206C22⋊C4—384no—
207C22⋊C4—384no—
208C22⋊C4—384no—
209C23—22no—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—22no—
214C23—22no—
215C23—21no—
216C23—21no—
217C23—216no—
218C23—44no—
219C23—44no—
220C23—48no—
221C23—44no—
222C23C2×Dic3812yes—
223C23C2×Dic3814yes—
224C23D4×D1914yes—
225C23#6454314yes—
226C23C23×D1911yescharacteristic
227Q8—764no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—194no—
236C2×C4—194no—
237C2×C4—382no—
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—382no—
247C2×C4—768no—
248C2×C4—768no—
249C22—24no—
250C22—24no—
251C22—24no—
252C22—24no—
253C22—24no—
254C22—24no—
255C22—24no—
256C22—22no—
257C22—416no—
258C22—41no—
259C22—42no—
260C22—41no—
261C22#1059732418yescomplemented
262C22C22×Dic3811yescharacteristic
263C22C2×D4×D1912yes—
264C22C2×#6454312yes—
265C22#1059743011yescharacteristic
266C22#1059743011yescharacteristic
267C4—41no—
268C4—42no—
269C4—41no—
270C4—384no—
271C4—384no—
272C4—762no—
273C4—762no—
274C2—28no—
275C2—42no—
276C2C2×#1059732412yes—
277C2#1192717011yescharacteristic
278C2#1192717611yescharacteristic
279C2#1192718112yes—
280C2#1192722511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#379C2
prime radicalC25×C19C22
hypercenter#379D19
hypocenterC19#2437
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#10597324C2semidirect
3. #11926480C2semidirect
4. #11926467C2semidirect
5. #11926456C2semidirect
6. #11926419C2semidirect
7. #11926416C2semidirect
8. #11926402C2semidirect
13. C22×Dic38C22semidirect
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
37. C24×C19Q8semidirect
121. C22×C19C22⋊Q8semidirect
173. C19#2437semidirect
178. C24Dic38semidirect
261. C22#10597324semidirect

Maximal subgroups

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

subgroupindex
C2×#105973242
C22×C22⋊Dic192
#119264802
#119264672
#119264562
#119264192
#119264162
#119264022
C19×#3792
#243719