Finite Group Databasebeta

← #14566992

Subgroups — #14566992

Order 2432.

1232 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 189 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
1C23×D76C211yesmaximal, characteristic, complemented
2C2×#10597341C212yesmaximal, complemented
3C2×#10597328C212yesmaximal, complemented
4C2×C4×C22⋊D19C211yesmaximal, characteristic, complemented
5#11926462C212yesmaximal, complemented
6#11926454C212yesmaximal, complemented
7#11926445C212yesmaximal, complemented
8#11926399C212yesmaximal, complemented
9C19×#380C211yesmaximal, characteristic, complemented
10C24×D19C2212yes—
11C23×C4×C19C2211yescharacteristic
12C22×C22⋊D19C2211yescharacteristic
13C22×D76—24no—
14C22×D76—28no—
15C22×D76C2212yes—
16C22×D76C2212yes—
17C22×D76C2214yescomplemented
18C22×C4×D19C2211yescharacteristic, complemented
19C2×C4⋊C4×C19C2212yescomplemented
20C2×C22⋊C4×C19C2212yes—
21C2×C22⋊Dic19C2211yescharacteristic
22C4×C22⋊D19—24no—
23C2×(C2×D19)⋊C4C2214yescomplemented
24C2×(C2×D19)⋊C4C2214yescomplemented
25C2×(C2×D19)⋊C4C2211yescharacteristic, complemented
26C2×(C2×D19)⋊C4C2214yescomplemented
27C2×Dic19⋊C4C2211yescharacteristic, complemented
28C2×C4×Dic19C2211yescharacteristic, complemented
29#10597341—28no—
30#10597328—28no—
31C19×#95C2212yescomplemented
32C24×C19C2311yescharacteristic
33C23×D19—24no—
34C23×D19—28no—
35C23×D19—24no—
36C23×D19—24no—
37C23×D19—44no—
38C23×D19C2314yes—
39C23×D19C2311yescharacteristic
40C22×C4×C19—24no—
41C22×C4×C19D414yescomplemented
42C22×C4×C19C2314yes—
43C22×C4×C19C2311yescharacteristic
44C22×C4×C19C2311yescharacteristic
45C2×C22⋊D19—22no—
46C2×C22⋊D19—22no—
47C2×C22⋊D19D414yescomplemented
48C22×Dic19C2311yescharacteristic
49C22×Dic19C2311yescharacteristic
50C22×Dic19C2311yescharacteristic
51C2×D76—232no—
52C2×D76—28no—
53C2×D76—24no—
54C2×D76—24no—
55C2×D76—24no—
56C2×D76—28no—
57C2×D76—28no—
58C2×D76—44no—
59C2×D76D418yescomplemented
60C2×C4×D19—24no—
61C2×C4×D19—22no—
62C4⋊C4×C19—24no—
63C22⋊C4×C19—24no—
64C22⋊Dic19—22no—
65(C2×D19)⋊C4—28no—
66(C2×D19)⋊C4—22no—
67(C2×D19)⋊C4—28no—
68(C2×D19)⋊C4—44no—
69Dic19⋊C4—22no—
70C4×Dic19—22no—
71C23×C19—22no—
72C23×C19—22no—
73C23×C19C2×D412yes—
74C23×C19C2×D412yes—
75C23×C19#4112yes—
76C23×C19C2411yescharacteristic
77C22×D19—216no—
78C22×D19—21no—
79C22×D19—24no—
80C22×D19—22no—
81C22×D19—24no—
82C22×D19—24no—
83C22×D19—21no—
84C22×D19—24no—
85C22×D19—24no—
86C22×D19—22no—
87C22×D19—24no—
88C22×D19—416no—
89C22×D19—416no—
90C22×D19—48no—
91C22×D19—48no—
92C22×D19C2×D418yes—
93C22×D19C2×D412yescomplemented
94C2×C4×C19—22no—
95C2×C4×C19—28no—
96C2×C4×C19—24no—
97C2×C4×C19—24no—
98C2×C4×C19—24no—
99C2×C4×C19C2×D412yes—
100C2×C4×C19C2×D412yes—
101C2×C4×C19C2×D414yes—
102C22⋊D19—28no—
103C2×Dic19—21no—
104C2×Dic19—21no—
105C2×Dic19—21no—
106C2×Dic19—21no—
107C2×Dic19—22no—
108C2×Dic19—22no—
109C2×Dic19C2×D412yescomplemented
110D76—216no—
111D76—216no—
112D76—416no—
113C4×D19—44no—
114#2408—191nomaximal, Sylow
115C22×C19—22no—
116C22×C19—22no—
117C22×C19—24no—
118C22×C19—24no—
119C22×C19#12114yescomplemented
120C22×C19C22×D411yescharacteristic
121C22×C19C22×D412yes—
122C22×C19C22×D411yescharacteristic
123C22×C19C2×#4111yescharacteristic
124C22×C19H(5,𝔽2)12yes—
125C2×D19—28no—
126C2×D19—22no—
127C2×D19—24no—
128C2×D19—28no—
129C2×D19—28no—
130C2×D19—432no—
131C2×D19—41no—
132C2×D19—44no—
133C2×D19—41no—
134C2×D19—44no—
135C2×D19—44no—
136C2×D19—42no—
137C2×D19—44no—
138C4×C19—22no—
139C4×C19—44no—
140C4×C19#12014yescomplemented
141Dic19—22no—
142Dic19—41no—
143Dic19—41no—
144C23×D4—191no—
145C2×#121—192no—
146C2×#120—192no—
147C2×C4×D4—191no—
148#394—192no—
149#392—192no—
150#390—192no—
151#380D1911yescharacteristic, complemented
152#379—192no—
153C2×C19—24no—
154C2×C19C2×#12011yescharacteristic
155C2×C19C2×#12111yescharacteristic
156C2×C19#53511yescharacteristic
157C2×C19D4212yes—
158C2×C19#54612yes—
159D19—42no—
160D19—48no—
161C25—192no—
162C22×D4—191no—
163C22×D4—192no—
164C22×D4—192no—
165C22×D4—194no—
166C22×D4—388no—
167C22×D4—384no—
168C23×C4—191no—
169C23×C4C2×D1911yescharacteristic
170#121—388no—
171#120—388no—
172C4×D4—384no—
173C2×C4⋊C4—191no—
174C2×C4⋊C4C2×D1912yescomplemented
175C2×C22⋊C4—191no—
176C2×C22⋊C4—191no—
177C2×C22⋊C4—194no—
178C2×C22⋊C4—194no—
179C2×C22⋊C4—194no—
180C2×C22⋊C4C2×D1912yes—
181C2×C42—191no—
182#95C2×D1912yescomplemented
183C19#240811yescharacteristic, complemented, Sylow
184C24—194no—
185C24—191no—
186C24—388no—
187C24—384no—
188C24—384no—
189C24—384no—
190C24—764no—
191C24C22×D1911yescharacteristic
192C2×D4—194no—
193C2×D4—198no—
194C2×D4—388no—
195C2×D4—3832no—
196C2×D4—388no—
197C2×D4—388no—
198C2×D4—382no—
199C2×D4—382no—
200C2×D4—384no—
201C2×D4—384no—
202C2×D4—384no—
203C2×D4—764no—
204C22×C4—24no—
205C22×C4—191no—
206C22×C4—191no—
207C22×C4—191no—
208C22×C4—382no—
209C22×C4—384no—
210C22×C4D7614yescomplemented
211C22×C4C22×D1914yes—
212C22×C4C22×D1911yescharacteristic
213C22×C4C22×D1911yescharacteristic
214C4⋊C4—24no—
215C4⋊C4—382no—
216C22⋊C4—24no—
217C22⋊C4—388no—
218C22⋊C4—388no—
219C22⋊C4—382no—
220C22⋊C4—382no—
221C22⋊C4—764no—
222C42—382no—
223C23—22no—
224C23—22no—
225C23—198no—
226C23—192no—
227C23—3816no—
228C23—381no—
229C23—384no—
230C23—384no—
231C23—382no—
232C23—384no—
233C23—381no—
234C23—384no—
235C23—384no—
236C23—382no—
237C23—384no—
238C23—7616no—
239C23—7616no—
240C23—768no—
241C23—768no—
242C23C2×D7612yes—
243C23D4×D1912yes—
244C23#6454512yes—
245C23C23×D1911yescharacteristic
246D4—3816no—
247D4—388no—
248D4—3816no—
249D4—7616no—
250C2×C4—22no—
251C2×C4—28no—
252C2×C4—24no—
253C2×C4—24no—
254C2×C4—24no—
255C2×C4—192no—
256C2×C4—381no—
257C2×C4—381no—
258C2×C4—381no—
259C2×C4—381no—
260C2×C4—382no—
261C2×C4—382no—
262C2×C4—764no—
263C2×C4C2×D7612yes—
264C2×C4C2×D7612yes—
265C2×C4D4×D1914yes—
266C22—22no—
267C22—24no—
268C22—24no—
269C22—22no—
270C22—384no—
271C22—388no—
272C22—388no—
273C22—388no—
274C22—382no—
275C22—7632no—
276C22—764no—
277C22—761no—
278C22—764no—
279C22—764no—
280C22—762no—
281C22—761no—
282C22—764no—
283C22#1059734114yescomplemented
284C22C22×D7611yescharacteristic
285C22C2×D4×D1911yescharacteristic
286C22C2×D4×D1912yes—
287C22C2×#6454511yescharacteristic
288C22#1059743512yes—
289C4—22no—
290C4—44no—
291C4—382no—
292C4—761no—
293C4—761no—
294C4#1059732814yescomplemented
295C2—24no—
296C2—768no—
297C2—762no—
298C2C2×#1059732811yescharacteristic
299C2C2×#1059734111yescharacteristic
300C2#1192711311yescharacteristic
301C2#1192717812yes—
302C2#1192718512yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#380C2
hypercenter#380D19
hypocenterC19#2408
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C23×D76C2semidirect
2. C2×#10597341C2semidirect
3. C2×#10597328C2semidirect
4. C2×C4×C22⋊D19C2semidirect
5. #11926462C2semidirect
6. #11926454C2semidirect
7. #11926445C2semidirect
8. #11926399C2semidirect
9. C19×#380C2semidirect
17. C22×D76C22semidirect
18. C22×C4×D19C22semidirect
19. C2×C4⋊C4×C19C22semidirect
23. C2×(C2×D19)⋊C4C22semidirect
24. C2×(C2×D19)⋊C4C22semidirect
25. C2×(C2×D19)⋊C4C22semidirect
26. C2×(C2×D19)⋊C4C22semidirect
27. C2×Dic19⋊C4C22semidirect
28. C2×C4×Dic19C22semidirect
31. C19×#95C22semidirect
41. C22×C4×C19D4semidirect
47. C2×C22⋊D19D4semidirect
59. C2×D76D4semidirect
93. C22×D19C2×D4semidirect
109. C2×Dic19C2×D4semidirect
119. C22×C19#121semidirect
140. C4×C19#120semidirect
151. #380D19semidirect
174. C2×C4⋊C4C2×D19semidirect
182. #95C2×D19semidirect
183. C19#2408semidirect
210. C22×C4D76semidirect
283. C22#10597341semidirect
294. C4#10597328semidirect

Maximal subgroups

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

subgroupindex
C23×D762
C2×#105973412
C2×#105973282
C2×C4×C22⋊D192
#119264622
#119264542
#119264452
#119263992
C19×#3802
#240819