Finite Group Databasebeta

← #14571914

Subgroups — #14571914

Order 2432.

1224 conjugacy classes of subgroups; only the 201 normal subgroups are shown.

normal subgroups only

This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 201 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×C4×D19C211yesmaximal, characteristic, complemented
2C2×#10597384C212yesmaximal, complemented
3C2×#10597383C212yesmaximal, complemented
4#11926424C212yesmaximal, complemented
5#11926420C214yesmaximal, complemented
6#11926404C211yesmaximal, characteristic, complemented
7#11926401C212yesmaximal, complemented
8C2×C19×#121C211yesmaximal, characteristic, complemented
9C24×D19C2211yescharacteristic
10C22×D4×C19C2212yes—
11C22×D4×C19C2211yescharacteristic, complemented
12C23×C4×C19C2211yescharacteristic
13C22×C22⋊D19C2214yes—
14C23×Dic19C2211yescharacteristic
15C22×C4×D19—24no—
16C22×C4×D19—28no—
17C22×C4×D19C2212yes—
18C22×C4×D19C2212yes—
19C19×#121—24no—
20C2×C4⋊C4×C19C2211yescharacteristic, complemented
21C2×C22⋊C4×C19C2212yescomplemented
22C2×C22⋊Dic19C2212yes—
23C2×C22⋊Dic19C2214yescomplemented
24#10597384—28no—
25#10597383—28no—
26C2×(C2×D19)⋊C4C2214yes—
27C2×C4⋊Dic19C2212yescomplemented
28C19⋊#95C2214yescomplemented
29C19⋊#95C2212yescomplemented
30C24×C19C2312yes—
31C24×C19C2311yescharacteristic
32C23×D19—22no—
33C23×D19—22no—
34C23×D19—24no—
35C23×D19—24no—
36C23×D19D414yescomplemented
37C23×D19C2312yes—
38C2×D4×C19—24no—
39C2×D4×C19—24no—
40C2×D4×C19—24no—
41C2×D4×C19—24no—
42C2×D4×C19—22no—
43C22×C4×C19—24no—
44C22×C4×C19D414yescomplemented
45C22×C4×C19C2312yes—
46C22×C4×C19C2311yescharacteristic
47C22×C4×C19C2311yescharacteristic
48C2×C22⋊D19—28no—
49C2×C22⋊D19—28no—
50C2×C22⋊D19—28no—
51C22×Dic19—22no—
52C22×Dic19—24no—
53C22×Dic19C2314yes—
54C22×Dic19C2312yes—
55C2×C4×D19—232no—
56C2×C4×D19—24no—
57C2×C4×D19—24no—
58C2×C4×D19—24no—
59C2×C4×D19—24no—
60C2×C4×D19—24no—
61C2×C4×D19D418yescomplemented
62C4⋊C4×C19—22no—
63C22⋊C4×C19—24no—
64C22⋊Dic19—24no—
65C22⋊Dic19—28no—
66(C2×D19)⋊C4—28no—
67C4⋊Dic19—24no—
68C23×C19—22no—
69C23×C19—22no—
70C23×C19—24no—
71C23×C19—22no—
72C23×C19—22no—
73C23×C19—24no—
74C23×C19—22no—
75C23×C19C2×D412yes—
76C23×C19C2×D412yes—
77C23×C19#4112yes—
78C23×C19C2411yescharacteristic
79C22×D19—28no—
80C22×D19—216no—
81C22×D19—28no—
82C22×D19—28no—
83C22×D19—22no—
84C22×D19—22no—
85C22×D19—22no—
86C22×D19—22no—
87C22×D19—216no—
88C22×D19C2×D414yes—
89C22×D19C2×D414yes—
90C22×D19#4114yes—
91D4×C19—48no—
92D4×C19—44no—
93C2×C4×C19—22no—
94C2×C4×C19—28no—
95C2×C4×C19—22no—
96C2×C4×C19—22no—
97C2×C4×C19—22no—
98C2×C4×C19C2×D414yes—
99C2×C4×C19C2×D412yes—
100C2×C4×C19C2×D412yes—
101C22⋊D19—416no—
102C2×Dic19—28no—
103C2×Dic19—22no—
104C2×Dic19—22no—
105C2×Dic19—24no—
106C2×Dic19—24no—
107C2×Dic19—24no—
108C2×Dic19C2×D414yes—
109C4×D19—216no—
110C4×D19—216no—
111#2847—191nomaximal, Sylow
112C22×C19—22no—
113C22×C19—24no—
114C22×C19—22no—
115C22×C19—24no—
116C22×C19—42no—
117C22×C19—44no—
118C22×C19—42no—
119C22×C19—42no—
120C22×C19—44no—
121C22×C19#12114yescomplemented
122C22×C19C22×D412yes—
123C22×C19C22×D411yescharacteristic
124C22×C19C22×D411yescharacteristic
125C22×C19C2×#4111yescharacteristic
126C22×C19C2×#4112yes—
127C2×D19—232no—
128C2×D19—24no—
129C2×D19—24no—
130C2×D19—24no—
131C2×D19—24no—
132C2×D19—24no—
133C2×D19—24no—
134C2×D19#12118yescomplemented
135C4×C19—22no—
136C4×C19—42no—
137C4×C19#12014yescomplemented
138Dic19—24no—
139Dic19—44no—
140C24×C4—191no—
141C2×#121—192no—
142C2×#121D1911yescharacteristic, complemented
143C2×#120—192no—
144#386—192no—
145#386—194no—
146#380—191no—
147#380—192no—
148C2×C19—24no—
149C2×C19—82no—
150C2×C19C2×#12011yescharacteristic
151C2×C19C2×#12112yes—
152C2×C19C2×#12111yescharacteristic
153C2×C19#52511yescharacteristic
154C2×C19#52512yes—
155D19—28no—
156C25—191no—
157C22×D4—194no—
158C22×D4C2×D1912yes—
159C22×D4C2×D1911yescharacteristic, complemented
160C23×C4—192no—
161C23×C4—191no—
162C23×C4—192no—
163C23×C4—388no—
164C23×C4—384no—
165C23×C4C2×D1911yescharacteristic
166#121—24no—
167#121—388no—
168#120—388no—
169C2×C4⋊C4—192no—
170C2×C4⋊C4C2×D1911yescharacteristic, complemented
171C2×C22⋊C4—192no—
172C2×C22⋊C4—194no—
173C2×C22⋊C4—194no—
174C2×C22⋊C4C2×D1912yescomplemented
175#95—194no—
176#95—192no—
177C19#284711yescharacteristic, complemented, Sylow
178C24—192no—
179C24—194no—
180C24—384no—
181C24—384no—
182C24—382no—
183C24—382no—
184C24C22×D1912yes—
185C24C22×D1911yescharacteristic
186C2×D4—24no—
187C2×D4—24no—
188C2×D4—24no—
189C2×D4—24no—
190C2×D4—22no—
191C2×D4—388no—
192C2×D4—388no—
193C2×D4—388no—
194C22×C4—24no—
195C22×C4—192no—
196C22×C4—198no—
197C22×C4—194no—
198C22×C4—384no—
199C22×C4—384no—
200C22×C4—3832no—
201C22×C4—384no—
202C22×C4—382no—
203C22×C4—384no—
204C22×C4—384no—
205C22×C4—384no—
206C22×C4C22⋊D1914yescomplemented
207C22×C4C22×D1912yes—
208C22×C4C22×D1911yescharacteristic
209C22×C4C22×D1911yescharacteristic
210C4⋊C4—22no—
211C4⋊C4—384no—
212C22⋊C4—24no—
213C22⋊C4—388no—
214C22⋊C4—388no—
215C22⋊C4—384no—
216C23—22no—
217C23—22no—
218C23—24no—
219C23—22no—
220C23—22no—
221C23—24no—
222C23—22no—
223C23—194no—
224C23—194no—
225C23—194no—
226C23—3816no—
227C23—388no—
228C23—388no—
229C23—3816no—
230C23—388no—
231C23—382no—
232C23—382no—
233C23—382no—
234C23—382no—
235C23D4×D1912yes—
236C23#6454312yes—
237C23C2×C22⋊D1912yes—
238C23C23×D1911yescharacteristic
239D4—48no—
240D4—44no—
241D4—7616no—
242C2×C4—22no—
243C2×C4—28no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—194no—
248C2×C4—3816no—
249C2×C4—388no—
250C2×C4—382no—
251C2×C4—382no—
252C2×C4—3816no—
253C2×C4—384no—
254C2×C4—384no—
255C2×C4—384no—
256C2×C4D4×D1914yes—
257C2×C4C2×C22⋊D1912yes—
258C2×C4C2×C22⋊D1912yes—
259C22—22no—
260C22—24no—
261C22—22no—
262C22—24no—
263C22—42no—
264C22—44no—
265C22—42no—
266C22—44no—
267C22—42no—
268C22—198no—
269C22—3832no—
270C22—384no—
271C22—384no—
272C22—384no—
273C22—384no—
274C22—384no—
275C22—384no—
276C22#1059738414yescomplemented
277C22C2×D4×D1912yes—
278C22C2×D4×D1911yescharacteristic
279C22C2×#6454311yescharacteristic
280C22#41×D1912yes—
281C22C22×C22⋊D1911yescharacteristic
282C4—22no—
283C4—42no—
284C4—384no—
285C4—764no—
286C4#1059738314yescomplemented
287C2—24no—
288C2—82no—
289C2—388no—
290C2C2×#1059738311yescharacteristic
291C2#121×D1912yes—
292C2C2×#1059738411yescharacteristic
293C2#1192705111yescharacteristic
294C2#1192705412yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#121C2
hypercenterC2×#121D19
hypocenterC19#2847
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C23×C4×D19C2semidirect
2. C2×#10597384C2semidirect
3. C2×#10597383C2semidirect
4. #11926424C2semidirect
5. #11926420C2semidirect
6. #11926404C2semidirect
7. #11926401C2semidirect
8. C2×C19×#121C2semidirect
11. C22×D4×C19C22semidirect
20. C2×C4⋊C4×C19C22semidirect
21. C2×C22⋊C4×C19C22semidirect
23. C2×C22⋊Dic19C22semidirect
27. C2×C4⋊Dic19C22semidirect
28. C19⋊#95C22semidirect
29. C19⋊#95C22semidirect
36. C23×D19D4semidirect
44. C22×C4×C19D4semidirect
61. C2×C4×D19D4semidirect
121. C22×C19#121semidirect
134. C2×D19#121semidirect
137. C4×C19#120semidirect
142. C2×#121D19semidirect
159. C22×D4C2×D19semidirect
170. C2×C4⋊C4C2×D19semidirect
174. C2×C22⋊C4C2×D19semidirect
177. C19#2847semidirect
206. C22×C4C22⋊D19semidirect
276. C22#10597384semidirect
286. C4#10597383semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D192
C2×#105973842
C2×#105973832
#119264242
#119264202
#119264042
#119264012
C2×C19×#1212
#284719