Finite Group Databasebeta

← #14569855

Subgroups — #14569855

Order 2432.

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

normal subgroups only

This group has 796 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×#10597393C212yesmaximal, complemented
2C2×#10597328C212yesmaximal, complemented
3#11926462C212yesmaximal, complemented
4#11926454C212yesmaximal, complemented
5#11926453C211yesmaximal, characteristic, complemented
6#11926444C212yesmaximal, complemented
7#11926433C212yesmaximal, complemented
8#11926399C211yesmaximal, characteristic, complemented
9C19×#393C211yesmaximal, characteristic, complemented
10C24×D19C2211yescharacteristic
11C22×Q8×C19C2211yescharacteristic, complemented
12C22×C22⋊D19C2212yes—
13C22×D76C2212yes—
14C22×D76C2212yes—
15C22×D76C2211yescharacteristic, complemented
16C2×C22⋊C4×C19C2212yes—
17C2×C22⋊C4×C19C2211yescharacteristic
18C2×C22⋊Dic19C2211yescharacteristic
19#10597393—28no—
20C2×(C2×D19)⋊C4C2212yes—
21C2×(C2×D19)⋊C4C2212yes—
22C2×(C2×D19)⋊C4C2212yes—
23C2×(C2×D19)⋊C4C2212yes—
24C2×(C2×D19)⋊C4C2212yescomplemented
25C2×(C2×D19)⋊C4C2212yescomplemented
26C2×(C2×D19)⋊C4C2212yescomplemented
27C2×Dic19⋊C4C2212yescomplemented
28C2×C4×Dic19C2212yescomplemented
29#10597328—28no—
30C19×#95C2212yescomplemented
31C19×#95C2211yescharacteristic, complemented
32C19⋊#95C2211yescharacteristic, complemented
33C24×C19C2311yescharacteristic
34C23×D19—22no—
35C23×D19—24no—
36C23×D19—42no—
37C23×D19—41no—
38C23×D19—41no—
39C23×D19C2312yes—
40C23×D19C2312yes—
41C2×Q8×C19—24no—
42C2×Q8×C19—41no—
43C22×C4×C19C2312yes—
44C22×C4×C19C2311yescharacteristic
45C22×C4×C19C2311yescharacteristic
46C22×C4×C19C2312yes—
47C2×C22⋊D19—24no—
48C2×C22⋊D19—24no—
49C2×C22⋊D19—42no—
50C22×Dic19C2312yes—
51C22×Dic19C2312yes—
52C2×D76—24no—
53C2×D76—24no—
54C2×D76—24no—
55C2×D76—42no—
56C2×D76—42no—
57C2×D76—42no—
58C2×D76—42no—
59C2×D76—41no—
60C22⋊C4×C19—24no—
61C22⋊C4×C19—41no—
62C22⋊Dic19—41no—
63(C2×D19)⋊C4—24no—
64(C2×D19)⋊C4—24no—
65(C2×D19)⋊C4—24no—
66(C2×D19)⋊C4—24no—
67(C2×D19)⋊C4—42no—
68(C2×D19)⋊C4—42no—
69(C2×D19)⋊C4D418yescomplemented
70Dic19⋊C4—42no—
71C4×Dic19—24no—
72C23×C19—22no—
73C23×C19—21no—
74C23×C19—21no—
75C23×C19—22no—
76C23×C19#4112yes—
77C23×C19C2411yescharacteristic
78C22×D19—22no—
79C22×D19—22no—
80C22×D19—22no—
81C22×D19—22no—
82C22×D19—22no—
83C22×D19—22no—
84C22×D19—22no—
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—
97Q8×C19—44no—
98C2×C4×C19—22no—
99C2×C4×C19—22no—
100C2×C4×C19—22no—
101C2×C4×C19—22no—
102C2×C4×C19—22no—
103C2×C4×C19—22no—
104C2×C4×C19—22no—
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19C2×D414yes—
108C22⋊D19—48no—
109C2×Dic19—22no—
110C2×Dic19—22no—
111C2×Dic19—22no—
112C2×Dic19—22no—
113C2×Dic19—22no—
114C2×Dic19C2×D414yes—
115D76—48no—
116D76—48no—
117D76—44no—
118#2670—191nomaximal, Sylow
119C22×C19—22no—
120C22×C19—24no—
121C22×C19—42no—
122C22×C19—41no—
123C22×C19—41no—
124C22×C19C22×D412yes—
125C22×C19C2×#4111yescharacteristic
126C22×C19H(5,𝔽2)11yescharacteristic
127C22×C19H(5,𝔽2)11yescharacteristic
128C22×C19H(5,𝔽2)12yes—
129C2×D19—24no—
130C2×D19—24no—
131C2×D19—24no—
132C2×D19—416no—
133C2×D19—42no—
134C2×D19—42no—
135C2×D19—42no—
136C2×D19—42no—
137C2×D19—42no—
138C2×D19—42no—
139C2×D19—42no—
140C2×D19—42no—
141C2×D19—42no—
142C2×D19—42no—
143C2×D19—42no—
144C4×C19—24no—
145C4×C19—42no—
146C4×C19—41no—
147C4×C19—41no—
148Dic19—24no—
149Dic19—42no—
150C2×#124—192no—
151C2×#120—192no—
152#394—192no—
153#393D1911yescharacteristic, complemented
154#392—191no—
155#392—192no—
156#390—192no—
157#388—192no—
158#379—191no—
159C2×C19—42no—
160C2×C19#53512yes—
161C2×C19#53811yescharacteristic
162C2×C19D4211yescharacteristic
163C2×C19#54612yes—
164C2×C19H(3,𝔽4)11yescharacteristic
165D19—44no—
166D19—82no—
167C25—191no—
168C22×Q8C2×D1911yescharacteristic, complemented
169C22×D4—192no—
170C22×D4—192no—
171C22×D4—192no—
172C22×D4—191no—
173#124—388no—
174#120—388no—
175C2×C4⋊C4—192no—
176C2×C22⋊C4—192no—
177C2×C22⋊C4—192no—
178C2×C22⋊C4—192no—
179C2×C22⋊C4—192no—
180C2×C22⋊C4—192no—
181C2×C22⋊C4—191no—
182C2×C22⋊C4—192no—
183C2×C22⋊C4—192no—
184C2×C22⋊C4C2×D1912yes—
185C2×C22⋊C4C2×D1911yescharacteristic
186C2×C42—192no—
187#95—191no—
188#95C2×D1912yescomplemented
189#95C2×D1911yescharacteristic, complemented
190C19#267011yescharacteristic, complemented, Sylow
191C24—192no—
192C24—192no—
193C24—384no—
194C24—382no—
195C24—761no—
196C24—761no—
197C24—762no—
198C24C22×D1911yescharacteristic
199C2×Q8—24no—
200C2×Q8—41no—
201C2×D4—384no—
202C2×D4—384no—
203C2×D4—384no—
204C2×D4—384no—
205C2×D4—384no—
206C2×D4—762no—
207C2×D4—761no—
208C2×D4—762no—
209C2×D4—762no—
210C2×D4—762no—
211C2×D4—762no—
212C22×C4—192no—
213C22×C4—192no—
214C22×C4C22×D1911yescharacteristic
215C22×C4C22×D1912yes—
216C22×C4C22×D1911yescharacteristic
217C22×C4C22×D1912yes—
218C4⋊C4—762no—
219C22⋊C4—24no—
220C22⋊C4—41no—
221C22⋊C4—198no—
222C22⋊C4—384no—
223C22⋊C4—384no—
224C22⋊C4—384no—
225C22⋊C4—384no—
226C22⋊C4—762no—
227C22⋊C4—762no—
228C22⋊C4—761no—
229C42—384no—
230C23—22no—
231C23—21no—
232C23—21no—
233C23—22no—
234C23—194no—
235C23—382no—
236C23—382no—
237C23—382no—
238C23—382no—
239C23—382no—
240C23—382no—
241C23—382no—
242C23—382no—
243C23—382no—
244C23—382no—
245C23—382no—
246C23—382no—
247C23—382no—
248C23—768no—
249C23—764no—
250C23—764no—
251C23—768no—
252C23—764no—
253C23#6454512yes—
254C23C23×D1911yescharacteristic
255Q8—44no—
256D4—768no—
257D4—768no—
258D4—764no—
259D4—768no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—194no—
270C2×C4—382no—
271C2×C4—382no—
272C2×C4—382no—
273C2×C4—382no—
274C2×C4—382no—
275C2×C4D4×D1914yes—
276C22—22no—
277C22—24no—
278C22—42no—
279C22—41no—
280C22—41no—
281C22—384no—
282C22—384no—
283C22—384no—
284C22—7616no—
285C22—762no—
286C22—762no—
287C22—762no—
288C22—762no—
289C22—762no—
290C22—762no—
291C22—762no—
292C22—762no—
293C22—762no—
294C22—762no—
295C22—762no—
296C22C2×D4×D1912yes—
297C22#1059743011yescharacteristic
298C22C2×#6454511yescharacteristic
299C22#1059743511yescharacteristic
300C22#1059743512yes—
301C4—24no—
302C4—42no—
303C4—41no—
304C4—41no—
305C4—384no—
306C4—762no—
307C2—42no—
308C2—764no—
309C2—1522no—
310C2#1192711212yes—
311C2#1192713411yescharacteristic
312C2#1192717611yescharacteristic
313C2#1192718512yes—
314C2#1192728611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#393C2
hypercenter#393D19
hypocenterC19#2670
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#10597393C2semidirect
2. C2×#10597328C2semidirect
3. #11926462C2semidirect
4. #11926454C2semidirect
5. #11926453C2semidirect
6. #11926444C2semidirect
7. #11926433C2semidirect
8. #11926399C2semidirect
9. C19×#393C2semidirect
11. C22×Q8×C19C22semidirect
15. C22×D76C22semidirect
24. C2×(C2×D19)⋊C4C22semidirect
25. C2×(C2×D19)⋊C4C22semidirect
26. C2×(C2×D19)⋊C4C22semidirect
27. C2×Dic19⋊C4C22semidirect
28. C2×C4×Dic19C22semidirect
30. C19×#95C22semidirect
31. C19×#95C22semidirect
32. C19⋊#95C22semidirect
69. (C2×D19)⋊C4D4semidirect
153. #393D19semidirect
168. C22×Q8C2×D19semidirect
188. #95C2×D19semidirect
189. #95C2×D19semidirect
190. C19#2670semidirect

Maximal subgroups

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

subgroupindex
C2×#105973932
C2×#105973282
#119264622
#119264542
#119264532
#119264442
#119264332
#119263992
C19×#3932
#267019