Finite Group Databasebeta

← #14569837

Subgroups — #14569837

Order 2432.

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

normal subgroups only

This group has 816 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×#10597385C212yesmaximal, complemented
2C2×#10597383C212yesmaximal, complemented
3#11926480C211yesmaximal, characteristic, complemented
4#11926473C212yesmaximal, complemented
5#11926460C212yesmaximal, complemented
6#11926424C212yesmaximal, complemented
7#11926421C212yesmaximal, complemented
8#11926399C211yesmaximal, characteristic, complemented
9C19×#392C211yesmaximal, characteristic, complemented
10C24×D19C2211yescharacteristic
11C22×D4×C19C2212yes—
12C22×D4×C19C2211yescharacteristic, complemented
13C22×C22⋊D19C2212yes—
14C22×C22⋊D19C2212yes—
15C23×Dic19C2212yescomplemented
16C2×C22⋊C4×C19C2211yescharacteristic
17C2×C22⋊C4×C19C2212yescomplemented
18C2×C22⋊Dic19C2212yes—
19C2×C22⋊Dic19C2211yescharacteristic
20C2×C22⋊Dic19C2212yescomplemented
21#10597385—28no—
22#10597383—28no—
23C2×(C2×D19)⋊C4C2212yes—
24C2×(C2×D19)⋊C4C2212yes—
25C2×(C2×D19)⋊C4C2212yes—
26C2×(C2×D19)⋊C4C2212yes—
27C2×C4⋊Dic19C2211yescharacteristic, complemented
28C2×Dic19⋊C4C2212yescomplemented
29C19×#95C2211yescharacteristic, complemented
30C19⋊#95C2211yescharacteristic, complemented
31C19⋊#95C2212yescomplemented
32C19⋊#95C2212yescomplemented
33C24×C19C2312yes—
34C24×C19C2311yescharacteristic
35C23×D19—22no—
36C23×D19—24no—
37C23×D19—42no—
38C23×D19—41no—
39C23×D19—41no—
40C23×D19C2312yes—
41C2×D4×C19—24no—
42C2×D4×C19—24no—
43C2×D4×C19—24no—
44C2×D4×C19—42no—
45C2×D4×C19—41no—
46C22×C4×C19C2311yescharacteristic
47C22×C4×C19C2311yescharacteristic
48C22×C4×C19C2312yes—
49C2×C22⋊D19—24no—
50C2×C22⋊D19—24no—
51C2×C22⋊D19—42no—
52C2×C22⋊D19—42no—
53C2×C22⋊D19—42no—
54C2×C22⋊D19D418yescomplemented
55C22×Dic19—24no—
56C22×Dic19—42no—
57C22×Dic19—42no—
58C22×Dic19C2312yes—
59C22×Dic19C2312yes—
60C22×Dic19C2312yes—
61C22⋊C4×C19—41no—
62C22⋊C4×C19—42no—
63C22⋊Dic19—24no—
64C22⋊Dic19—24no—
65C22⋊Dic19—41no—
66(C2×D19)⋊C4—24no—
67(C2×D19)⋊C4—24no—
68(C2×D19)⋊C4—24no—
69(C2×D19)⋊C4—42no—
70C4⋊Dic19—41no—
71Dic19⋊C4—24no—
72C23×C19—22no—
73C23×C19—22no—
74C23×C19—22no—
75C23×C19—21no—
76C23×C19—22no—
77C23×C19—21no—
78C23×C19—22no—
79C23×C19—22no—
80C23×C19—22no—
81C23×C19—22no—
82C23×C19C2×D414yes—
83C23×C19#4112yes—
84C23×C19C2411yescharacteristic
85C22×D19—22no—
86C22×D19—22no—
87C22×D19—22no—
88C22×D19—22no—
89C22×D19—22no—
90C22×D19—22no—
91C22×D19—44no—
92C22×D19—48no—
93C22×D19—48no—
94C22×D19—44no—
95C22×D19—44no—
96C22×D19C2×D414yes—
97D4×C19—44no—
98D4×C19—48no—
99C2×C4×C19—22no—
100C2×C4×C19—22no—
101C2×C4×C19—22no—
102C2×C4×C19—21no—
103C2×C4×C19—22no—
104C2×C4×C19—21no—
105C2×C4×C19—22no—
106C22⋊D19—48no—
107C22⋊D19—48no—
108C2×Dic19—22no—
109C2×Dic19—22no—
110C2×Dic19—22no—
111C2×Dic19—22no—
112C2×Dic19—22no—
113C2×Dic19—22no—
114C2×Dic19—22no—
115C2×Dic19—22no—
116C2×Dic19—48no—
117C2×Dic19C2×D414yes—
118#2668—191nomaximal, Sylow
119C22×C19—24no—
120C22×C19—22no—
121C22×C19—24no—
122C22×C19—24no—
123C22×C19—24no—
124C22×C19—42no—
125C22×C19—42no—
126C22×C19—42no—
127C22×C19—41no—
128C22×C19—42no—
129C22×C19—41no—
130C22×C19—42no—
131C22×C19C22×D412yes—
132C22×C19C2×#4111yescharacteristic
133C22×C19H(5,𝔽2)12yes—
134C22×C19H(5,𝔽2)11yescharacteristic
135C22×C19H(5,𝔽2)11yescharacteristic
136C2×D19—24no—
137C2×D19—24no—
138C2×D19—24no—
139C2×D19—416no—
140C2×D19—42no—
141C2×D19—42no—
142C2×D19—42no—
143C2×D19—42no—
144C4×C19—41no—
145C4×C19—42no—
146C4×C19—41no—
147Dic19—24no—
148Dic19—42no—
149Dic19—42no—
150C2×#121—192no—
151C2×#120—192no—
152#399—191no—
153#397—192no—
154#394—192no—
155#392D1911yescharacteristic, complemented
156#386—192no—
157#386—192no—
158#379—191no—
159C2×C19—42no—
160C2×C19—44no—
161C2×C19#53412yes—
162C2×C19#53811yescharacteristic
163C2×C19D4211yescharacteristic
164C2×C19#54612yes—
165C2×C19#56011yescharacteristic
166D19—44no—
167C25—191no—
168C22×D4—192no—
169C22×D4—192no—
170C22×D4C2×D1912yes—
171C22×D4C2×D1911yescharacteristic, complemented
172C23×C4—192no—
173#121—388no—
174#120—388no—
175C2×C4⋊C4—192no—
176C2×C4⋊C4—191no—
177C2×C22⋊C4—192no—
178C2×C22⋊C4—192no—
179C2×C22⋊C4—192no—
180C2×C22⋊C4—192no—
181C2×C22⋊C4—192no—
182C2×C22⋊C4—191no—
183C2×C22⋊C4—192no—
184C2×C22⋊C4C2×D1911yescharacteristic
185C2×C22⋊C4C2×D1912yescomplemented
186#95—192no—
187#95—191no—
188#95—192no—
189#95C2×D1911yescharacteristic, complemented
190C19#266811yescharacteristic, complemented, Sylow
191C24—192no—
192C24—384no—
193C24—382no—
194C24—761no—
195C24—762no—
196C24—761no—
197C24C22×D1912yes—
198C24C22×D1911yescharacteristic
199C2×D4—24no—
200C2×D4—24no—
201C2×D4—24no—
202C2×D4—42no—
203C2×D4—41no—
204C2×D4—198no—
205C2×D4—384no—
206C2×D4—384no—
207C2×D4—762no—
208C2×D4—762no—
209C2×D4—762no—
210C22×C4—192no—
211C22×C4—192no—
212C22×C4—192no—
213C22×C4—384no—
214C22×C4—762no—
215C22×C4—762no—
216C22×C4C22×D1912yes—
217C22×C4C22×D1911yescharacteristic
218C22×C4C22×D1911yescharacteristic
219C4⋊C4—384no—
220C4⋊C4—761no—
221C22⋊C4—41no—
222C22⋊C4—42no—
223C22⋊C4—384no—
224C22⋊C4—384no—
225C22⋊C4—384no—
226C22⋊C4—384no—
227C22⋊C4—384no—
228C22⋊C4—762no—
229C22⋊C4—761no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23—21no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—21no—
239C23—22no—
240C23—194no—
241C23—382no—
242C23—382no—
243C23—382no—
244C23—382no—
245C23—382no—
246C23—382no—
247C23—768no—
248C23—764no—
249C23—764no—
250C23—768no—
251C23—764no—
252C23D4×D1914yes—
253C23#6454312yes—
254C23C23×D1911yescharacteristic
255D4—44no—
256D4—48no—
257D4—768no—
258D4—768no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—194no—
267C2×C4—382no—
268C2×C4—382no—
269C2×C4—382no—
270C2×C4—382no—
271C2×C4—382no—
272C2×C4—382no—
273C2×C4—382no—
274C2×C4—382no—
275C2×C4—768no—
276C22—24no—
277C22—22no—
278C22—24no—
279C22—24no—
280C22—24no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—41no—
285C22—42no—
286C22—41no—
287C22—42no—
288C22—384no—
289C22—384no—
290C22—384no—
291C22—7616no—
292C22—762no—
293C22—762no—
294C22—762no—
295C22—762no—
296C22C2×D4×D1912yes—
297C22C2×#6454311yescharacteristic
298C22#1059743012yes—
299C22#1059743011yescharacteristic
300C22#1059743511yescharacteristic
301C4—41no—
302C4—42no—
303C4—41no—
304C4—384no—
305C4—762no—
306C4—762no—
307C2—42no—
308C2—44no—
309C2—764no—
310C2#1192710212yes—
311C2#1192713111yescharacteristic
312C2#1192717611yescharacteristic
313C2#1192718112yes—
314C2#1192728111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#392C2
hypercenter#392D19
hypocenterC19#2668
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#10597385C2semidirect
2. C2×#10597383C2semidirect
3. #11926480C2semidirect
4. #11926473C2semidirect
5. #11926460C2semidirect
6. #11926424C2semidirect
7. #11926421C2semidirect
8. #11926399C2semidirect
9. C19×#392C2semidirect
12. C22×D4×C19C22semidirect
15. C23×Dic19C22semidirect
17. C2×C22⋊C4×C19C22semidirect
20. C2×C22⋊Dic19C22semidirect
27. C2×C4⋊Dic19C22semidirect
28. C2×Dic19⋊C4C22semidirect
29. C19×#95C22semidirect
30. C19⋊#95C22semidirect
31. C19⋊#95C22semidirect
32. C19⋊#95C22semidirect
54. C2×C22⋊D19D4semidirect
155. #392D19semidirect
171. C22×D4C2×D19semidirect
185. C2×C22⋊C4C2×D19semidirect
189. #95C2×D19semidirect
190. C19#2668semidirect

Maximal subgroups

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

subgroupindex
C2×#105973852
C2×#105973832
#119264802
#119264732
#119264602
#119264242
#119264212
#119263992
C19×#3922
#266819