Finite Group Databasebeta

← #14569439

Subgroups — #14569439

Order 2432.

668 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 143 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×#10597392C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D19C211yesmaximal, characteristic
3#11926481C211yesmaximal, characteristic, complemented
4#11926480C211yesmaximal, characteristic, complemented
5#11926468C212yesmaximal, complemented
6#11926467C212yesmaximal, complemented
7#11926455C211yesmaximal, characteristic, complemented
8#11926418C212yesmaximal, complemented
9#11926403C211yesmaximal, characteristic, complemented
10#11926399C212yesmaximal
11C19×#393C211yesmaximal, characteristic, complemented
12C24×D19C2211yescharacteristic
13C22×Q8×C19C2211yescharacteristic, complemented
14C22×C4×D19C2211yescharacteristic
15C22×C4×D19C2211yescharacteristic
16C2×C22⋊C4×C19C2211yescharacteristic
17C2×C22⋊C4×C19C2212yes—
18C2×C22⋊Dic19C2211yescharacteristic
19C2×C22⋊Dic19C2212yes—
20#10597392—24no—
21C2×(C2×D19)⋊C4C2212yes—
22C2×(C2×D19)⋊C4C2212yes—
23C2×(C2×D19)⋊C4C2211yescharacteristic
24C2×(C2×D19)⋊C4C2211yescharacteristic
25C2×(C2×D19)⋊C4C2212yes—
26C2×(C2×D19)⋊C4C2212yes—
27C2×C4⋊Dic19C2211yescharacteristic, complemented
28C2×C4⋊Dic19C2212yescomplemented
29C2×Dic19⋊C4C2212yescomplemented
30C2×Dic19⋊C4C2212yescomplemented
31C2×Dic19⋊C4C2212yescomplemented
32C22⋊C4×D19—24no—
33C19×#95C2211yescharacteristic, complemented
34C19×#95C2212yescomplemented
35C19⋊#95C2211yescharacteristic, complemented
36C19⋊#95C2212yescomplemented
37C24×C19C2311yescharacteristic
38C23×D19—22no—
39C23×D19—22no—
40C23×D19—42no—
41C23×D19—42no—
42C23×D19Q814yescomplemented
43C23×D19C2311yescharacteristic
44C23×D19C2311yescharacteristic
45C2×Q8×C19—22no—
46C2×Q8×C19—42no—
47C22×C4×C19C2311yescharacteristic
48C22×C4×C19C2312yes—
49C22×C4×C19C2312yes—
50C22×C4×C19C2311yescharacteristic
51C22×Dic19C2311yescharacteristic
52C22×Dic19C2312yes—
53C22×Dic19C2312yes—
54C22×Dic19C2311yescharacteristic
55C2×C4×D19—22no—
56C2×C4×D19—42no—
57C2×C4×D19—42no—
58C2×C4×D19D414yes—
59C22⋊C4×C19—22no—
60C22⋊C4×C19—42no—
61C22⋊Dic19—22no—
62C22⋊Dic19—42no—
63(C2×D19)⋊C4—24no—
64(C2×D19)⋊C4—24no—
65(C2×D19)⋊C4—22no—
66(C2×D19)⋊C4—22no—
67(C2×D19)⋊C4—42no—
68(C2×D19)⋊C4—42no—
69C4⋊Dic19—22no—
70C4⋊Dic19—42no—
71Dic19⋊C4—24no—
72Dic19⋊C4—42no—
73Dic19⋊C4—42no—
74C23×C19—21no—
75C23×C19—21no—
76C23×C19—22no—
77C23×C19—22no—
78C23×C19C2×Q812yes—
79C23×C19C2411yescharacteristic
80C22×D19—22no—
81C22×D19—22no—
82C22×D19—21no—
83C22×D19—21no—
84C22×D19—22no—
85C22×D19—22no—
86C22×D19—28no—
87C22×D19—48no—
88C22×D19—44no—
89C22×D19—44no—
90C22×D19—48no—
91C22×D19C2×D412yes—
92C22×D19C2×Q812yes—
93C22×D19C2×Q812yes—
94C22×D19#4112yes—
95Q8×C19—44no—
96C2×C4×C19—22no—
97C2×C4×C19—22no—
98C2×C4×C19—21no—
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×C19C2×D412yes—
106C2×Dic19—22no—
107C2×Dic19—22no—
108C2×Dic19—21no—
109C2×Dic19—22no—
110C2×Dic19—22no—
111C2×Dic19—22no—
112C2×Dic19—22no—
113C2×Dic19—22no—
114C2×Dic19—22no—
115C2×Dic19C2×D412yes—
116C4×D19—44no—
117C4×D19—44no—
118#2626—191nomaximal, Sylow
119C22×C19—22no—
120C22×C19—24no—
121C22×C19—41no—
122C22×C19—41no—
123C22×C19—42no—
124C22×C19C22×D411yescharacteristic
125C22×C19C22×Q811yescharacteristic
126C22×C19C2×#4111yescharacteristic
127C22×C19H(5,𝔽2)12yes—
128C22×C19H(5,𝔽2)12yes—
129C2×D19—22no—
130C2×D19—22no—
131C2×D19—24no—
132C2×D19—24no—
133C2×D19—22no—
134C2×D19—24no—
135C2×D19—416no—
136C2×D19—41no—
137C2×D19—41no—
138C2×D19—42no—
139C2×D19C22⋊Q814yes—
140C4×C19—22no—
141C4×C19—42no—
142C4×C19—41no—
143C4×C19—42no—
144Dic19—22no—
145Dic19—41no—
146Dic19—42no—
147Dic19—42no—
148C2×C22⋊Q8—191no—
149C22×C22⋊C4—191no—
150#399—191no—
151#399—191no—
152#396—192no—
153#396—192no—
154#393—191no—
155#393D1911yescharacteristic, complemented
156#385—192no—
157#380—191no—
158#379—192no—
159C2×C19—42no—
160C2×C19C2×C22⋊Q811yescharacteristic
161C2×C19#53411yescharacteristic
162C2×C19#53511yescharacteristic
163C2×C19#53812yes—
164C2×C19#54312yes—
165D19—24no—
166D19—42no—
167C25—191no—
168C22×Q8C2×D1911yescharacteristic, complemented
169C23×C4—191no—
170C23×C4—191no—
171C22⋊Q8—384no—
172C2×C4⋊C4—192no—
173C2×C4⋊C4—191no—
174C2×C4⋊C4—192no—
175C2×C4⋊C4—192no—
176C2×C4⋊C4—192no—
177C2×C22⋊C4—191no—
178C2×C22⋊C4—191no—
179C2×C22⋊C4—191no—
180C2×C22⋊C4—192no—
181C2×C22⋊C4—192no—
182C2×C22⋊C4—192no—
183C2×C22⋊C4—192no—
184C2×C22⋊C4—192no—
185C2×C22⋊C4—384no—
186C2×C22⋊C4C2×D1911yescharacteristic
187C2×C22⋊C4C2×D1912yes—
188#95—191no—
189#95—192no—
190#95C2×D1911yescharacteristic, complemented
191#95C2×D1912yescomplemented
192C19#262611yescharacteristic, complemented, Sylow
193C24—191no—
194C24—191no—
195C24—194no—
196C24—382no—
197C24—382no—
198C24—762no—
199C24—762no—
200C24C22×D1911yescharacteristic
201C2×Q8—22no—
202C2×Q8—42no—
203C22×C4—191no—
204C22×C4—194no—
205C22×C4—192no—
206C22×C4—191no—
207C22×C4—192no—
208C22×C4—382no—
209C22×C4—762no—
210C22×C4—762no—
211C22×C4C22×D1912yes—
212C22×C4C22×D1912yes—
213C22×C4C22×D1911yescharacteristic
214C22×C4C22×D1911yescharacteristic
215C4⋊C4—384no—
216C4⋊C4—382no—
217C4⋊C4—762no—
218C4⋊C4—762no—
219C4⋊C4—762no—
220C22⋊C4—22no—
221C22⋊C4—42no—
222C22⋊C4—382no—
223C22⋊C4—384no—
224C22⋊C4—384no—
225C22⋊C4—382no—
226C22⋊C4—382no—
227C22⋊C4—762no—
228C22⋊C4—762no—
229C22⋊C4—762no—
230C23—21no—
231C23—22no—
232C23—21no—
233C23—22no—
234C23—192no—
235C23—192no—
236C23—192no—
237C23—192no—
238C23—388no—
239C23—382no—
240C23—382no—
241C23—381no—
242C23—382no—
243C23—381no—
244C23—382no—
245C23—768no—
246C23—764no—
247C23—764no—
248C23—768no—
249C23Q8×D1912yes—
250C23C23×D1911yescharacteristic
251Q8—44no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—192no—
262C2×C4—382no—
263C2×C4—381no—
264C2×C4—382no—
265C2×C4—382no—
266C2×C4—382no—
267C2×C4—382no—
268C2×C4—382no—
269C2×C4—382no—
270C2×C4—382no—
271C2×C4—764no—
272C2×C4—764no—
273C2×C4D4×D1912yes—
274C22—24no—
275C22—22no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—194no—
280C22—382no—
281C22—382no—
282C22—384no—
283C22—384no—
284C22—384no—
285C22—382no—
286C22—7616no—
287C22—761no—
288C22—761no—
289C22—762no—
290C22C2×D4×D1911yescharacteristic
291C22#1059743012yes—
292C22C2×Q8×D1911yescharacteristic
293C22#41×D1911yescharacteristic
294C22#1059743512yes—
295C4—22no—
296C4—42no—
297C4—41no—
298C4—42no—
299C4—382no—
300C4—761no—
301C4—762no—
302C4—762no—
303C2—42no—
304C2—384no—
305C2—762no—
306C2C22⋊Q8×D1911yescharacteristic
307C2#1192710411yescharacteristic
308C2#1192711211yescharacteristic
309C2#1192712812yes—
310C2#1192716912yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#393C2
prime radicalC24×D19C22
hypercenter#393D19
hypocenterC19#2626
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#10597392C2semidirect
3. #11926481C2semidirect
4. #11926480C2semidirect
5. #11926468C2semidirect
6. #11926467C2semidirect
7. #11926455C2semidirect
8. #11926418C2semidirect
9. #11926403C2semidirect
11. C19×#393C2semidirect
13. C22×Q8×C19C22semidirect
27. C2×C4⋊Dic19C22semidirect
28. C2×C4⋊Dic19C22semidirect
29. C2×Dic19⋊C4C22semidirect
30. C2×Dic19⋊C4C22semidirect
31. C2×Dic19⋊C4C22semidirect
33. C19×#95C22semidirect
34. C19×#95C22semidirect
35. C19⋊#95C22semidirect
36. C19⋊#95C22semidirect
42. C23×D19Q8semidirect
155. #393D19semidirect
168. C22×Q8C2×D19semidirect
190. #95C2×D19semidirect
191. #95C2×D19semidirect
192. C19#2626semidirect

Maximal subgroups

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

subgroupindex
C2×#105973922
C2×C22⋊C4×D192
#119264812
#119264802
#119264682
#119264672
#119264552
#119264182
#119264032
#119263992
C19×#3932
#262619