Finite Group Databasebeta

← #14569350

Subgroups — #14569350

Order 2432.

1134 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 165 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×C22⋊D19C211yesmaximal, characteristic, complemented
2C2×#10597332C211yesmaximal, characteristic, complemented
3C2×#10597328C211yesmaximal, characteristic, complemented
4C2×#10597399C211yesmaximal, characteristic, complemented
5#11926460C214yesmaximal, complemented
6#11926453C214yesmaximal, complemented
7#11926405C211yesmaximal, characteristic, complemented
8#11926399C211yesmaximal, characteristic, complemented
9C19×#379C211yesmaximal, characteristic, complemented
10C25×C19C2211yescharacteristic
11C24×D19C2211yescharacteristic
12C22×C22⋊D19—24no—
13C22×C22⋊D19—24no—
14C22×C22⋊D19—24no—
15C22×C22⋊D19C2211yescharacteristic
16C22×C22⋊D19C2214yes—
17C22×C22⋊D19C2212yescomplemented
18C23×Dic19C2211yescharacteristic
19C22×D76C2212yescomplemented
20C2×C22⋊C4×C19C2211yescharacteristic
21C2×C22⋊C4×C19C2211yescharacteristic
22C2×C22⋊C4×C19C2214yescomplemented
23#10597399—24no—
24C2×C22⋊Dic19C2211yescharacteristic
25C2×C22⋊Dic19C2212yescomplemented
26C2×(C2×D19)⋊C4C2212yescomplemented
27C2×(C2×D19)⋊C4C2212yescomplemented
28C2×(C2×D19)⋊C4C2214yescomplemented
29C2×C4⋊Dic19C2212yescomplemented
30#10597332—24no—
31#10597328—24no—
32C19⋊#95C2214yescomplemented
33C24×C19—22no—
34C24×C19—22no—
35C24×C19—44no—
36C24×C19D414yescomplemented
37C24×C19C2312yes—
38C24×C19C2311yescharacteristic
39C23×D19—22no—
40C23×D19—22no—
41C23×D19—44no—
42C23×D19D414yescomplemented
43C23×D19C2311yescharacteristic
44C23×D19C2312yes—
45C22×C4×C19C2312yes—
46C22×C4×C19C2312yes—
47C2×C22⋊D19—232no—
48C2×C22⋊D19—28no—
49C2×C22⋊D19—28no—
50C2×C22⋊D19—22no—
51C2×C22⋊D19—24no—
52C2×C22⋊D19—22no—
53C2×C22⋊D19—22no—
54C2×C22⋊D19—28no—
55C2×C22⋊D19—44no—
56C22×Dic19—22no—
57C22×Dic19—22no—
58C22×Dic19D414yescomplemented
59C22×Dic19C2312yes—
60C22×Dic19C2311yescharacteristic
61C22×Dic19C2312yes—
62C2×D76—24no—
63C2×D76—44no—
64C22⋊C4×C19—22no—
65C22⋊C4×C19—22no—
66C22⋊C4×C19—44no—
67C22⋊Dic19—22no—
68C22⋊Dic19—24no—
69(C2×D19)⋊C4—24no—
70(C2×D19)⋊C4—24no—
71(C2×D19)⋊C4—44no—
72C4⋊Dic19—24no—
73C23×C19—24no—
74C23×C19—28no—
75C23×C19—22no—
76C23×C19—22no—
77C23×C19—24no—
78C23×C19—24no—
79C23×C19—48no—
80C23×C19—48no—
81C23×C19—48no—
82C23×C19C2×D414yes—
83C23×C19C2×D412yes—
84C23×C19C2×D412yes—
85C23×C19C2×D412yes—
86C23×C19C2411yescharacteristic
87C22×D19—28no—
88C22×D19—22no—
89C22×D19—22no—
90C22×D19—24no—
91C22×D19—24no—
92C22×D19—21no—
93C22×D19—21no—
94C22×D19—21no—
95C22×D19—24no—
96C22×D19—48no—
97C22×D19—48no—
98C22×D19—48no—
99C22×D19C2×D414yes—
100C2×C4×C19—22no—
101C2×C4×C19—22no—
102C2×C4×C19—24no—
103C2×C4×C19—24no—
104C22⋊D19—232no—
105C22⋊D19—48no—
106C22⋊D19—44no—
107C2×Dic19—28no—
108C2×Dic19—22no—
109C2×Dic19—22no—
110C2×Dic19—21no—
111C2×Dic19—21no—
112C2×Dic19—21no—
113C2×Dic19—22no—
114C2×Dic19—24no—
115C2×Dic19C2×D414yes—
116D76—48no—
117#2613—191nomaximal, Sylow
118C22×C19—24no—
119C22×C19—24no—
120C22×C19—24no—
121C22×C19—24no—
122C22×C19—24no—
123C22×C19—24no—
124C22×C19—416no—
125C22×C19—44no—
126C22×C19—44no—
127C22×C19#12014yes—
128C22×C19C22×D411yescharacteristic
129C22×C19C22×D411yescharacteristic
130C22×C19C22×D411yescharacteristic
131C22×C19H(5,𝔽2)14yes—
132C2×D19—24no—
133C2×D19—24no—
134C2×D19—24no—
135C2×D19—416no—
136C2×D19—44no—
137C2×D19—44no—
138C2×D19—41no—
139C2×D19—42no—
140C2×D19—42no—
141C2×D19—42no—
142C4×C19—42no—
143C4×C19—42no—
144Dic19—24no—
145Dic19—41no—
146Dic19—42no—
147C23×D4—191no—
148C2×#123—191no—
149C2×#120—191no—
150C2×#120—191no—
151#394—194no—
152#392—194no—
153#381—191no—
154#379—191no—
155#379D1911yescharacteristic, complemented
156C2×C19—24no—
157C2×C19—44no—
158C2×C19C2×#12011yescharacteristic
159C2×C19#53412yes—
160C2×C19#53412yes—
161C2×C19#53512yes—
162D19—44no—
163D19—81no—
164C25—191no—
165C25C2×D1911yescharacteristic
166C22×D4—191no—
167C22×D4—194no—
168C22×D4—192no—
169C22×D4—192no—
170C22×D4—384no—
171C22×D4—384no—
172C22×D4—384no—
173C23×C4—191no—
174#123—384no—
175#120—384no—
176#120—384no—
177C2×C4⋊C4—192no—
178C2×C22⋊C4—191no—
179C2×C22⋊C4—192no—
180C2×C22⋊C4—192no—
181C2×C22⋊C4—192no—
182C2×C22⋊C4—194no—
183C2×C22⋊C4C2×D1911yescharacteristic
184C2×C22⋊C4C2×D1911yescharacteristic
185C2×C22⋊C4C2×D1914yescomplemented
186#95—194no—
187C19#261311yescharacteristic, complemented, Sylow
188C24—22no—
189C24—22no—
190C24—44no—
191C24—192no—
192C24—194no—
193C24—191no—
194C24—382no—
195C24—382no—
196C24—764no—
197C24D7614yescomplemented
198C24C22×D1912yes—
199C24C22×D1911yescharacteristic
200C2×D4—384no—
201C2×D4—388no—
202C2×D4—388no—
203C2×D4—3832no—
204C2×D4—388no—
205C2×D4—384no—
206C2×D4—382no—
207C2×D4—382no—
208C2×D4—382no—
209C2×D4—764no—
210C2×D4—764no—
211C22×C4—194no—
212C22×C4—192no—
213C22×C4—192no—
214C22×C4—191no—
215C22×C4—382no—
216C22×C4—382no—
217C22×C4C22×D1912yes—
218C22×C4C22×D1912yes—
219C4⋊C4—384no—
220C22⋊C4—22no—
221C22⋊C4—22no—
222C22⋊C4—44no—
223C22⋊C4—384no—
224C22⋊C4—384no—
225C22⋊C4—384no—
226C22⋊C4—382no—
227C22⋊C4—764no—
228C23—24no—
229C23—22no—
230C23—22no—
231C23—24no—
232C23—24no—
233C23—28no—
234C23—48no—
235C23—48no—
236C23—48no—
237C23—194no—
238C23—382no—
239C23—382no—
240C23—384no—
241C23—384no—
242C23—388no—
243C23—381no—
244C23—381no—
245C23—381no—
246C23—384no—
247C23—768no—
248C23—768no—
249C23—768no—
250C23C2×D7614yes—
251C23C2×D7612yes—
252C23D4×D1912yes—
253C23D4×D1912yes—
254C23C23×D1911yescharacteristic
255D4—3832no—
256D4—768no—
257D4—768no—
258D4—764no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—24no—
262C2×C4—24no—
263C2×C4—194no—
264C2×C4—382no—
265C2×C4—382no—
266C2×C4—388no—
267C2×C4—382no—
268C2×C4—381no—
269C2×C4—381no—
270C2×C4—381no—
271C2×C4—384no—
272C22—24no—
273C22—24no—
274C22—24no—
275C22—24no—
276C22—24no—
277C22—24no—
278C22—416no—
279C22—44no—
280C22—44no—
281C22—384no—
282C22—384no—
283C22—384no—
284C22—7616no—
285C22—764no—
286C22—764no—
287C22—762no—
288C22—762no—
289C22—762no—
290C22—761no—
291C22#1059732814yes—
292C22C22×D7611yescharacteristic
293C22C2×D4×D1911yescharacteristic
294C22C2×D4×D1911yescharacteristic
295C22#1059743014yes—
296C4—42no—
297C4—42no—
298C4—384no—
299C4—762no—
300C4—761no—
301C2—24no—
302C2—44no—
303C2—764no—
304C2—1521no—
305C2C2×#1059732811yescharacteristic
306C2#1192710412yes—
307C2#1192710612yes—
308C2#1192710912yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#379C2
hypercenter#379D19
hypocenterC19#2613
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D19C2semidirect
2. C2×#10597332C2semidirect
3. C2×#10597328C2semidirect
4. C2×#10597399C2semidirect
5. #11926460C2semidirect
6. #11926453C2semidirect
7. #11926405C2semidirect
8. #11926399C2semidirect
9. C19×#379C2semidirect
17. C22×C22⋊D19C22semidirect
19. C22×D76C22semidirect
22. C2×C22⋊C4×C19C22semidirect
25. C2×C22⋊Dic19C22semidirect
26. C2×(C2×D19)⋊C4C22semidirect
27. C2×(C2×D19)⋊C4C22semidirect
28. C2×(C2×D19)⋊C4C22semidirect
29. C2×C4⋊Dic19C22semidirect
32. C19⋊#95C22semidirect
36. C24×C19D4semidirect
42. C23×D19D4semidirect
58. C22×Dic19D4semidirect
155. #379D19semidirect
185. C2×C22⋊C4C2×D19semidirect
187. C19#2613semidirect
197. C24D76semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊D192
C2×#105973322
C2×#105973282
C2×#105973992
#119264602
#119264532
#119264052
#119263992
C19×#3792
#261319