Finite Group Databasebeta

← #14566944

Subgroups — #14566944

Order 2432.

1564 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1564 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C22×D4×D19C212yesmaximal, complemented
2C2×#10597328C212yesmaximal, complemented
3C2×#10597383C212yesmaximal, complemented
4#11926453C211yesmaximal, characteristic, complemented
5#11926452C212yesmaximal, complemented
6#11926422C212yesmaximal, complemented
7#11926420C212yesmaximal, complemented
8#11926399C211yesmaximal, characteristic, complemented
9C19×#392C211yesmaximal, characteristic, complemented
10C24×D19C2211yescharacteristic
11C24×D19C2212yescomplemented
12C22×D4×C19C2212yescomplemented
13C22×D4×C19C2211yescharacteristic, complemented
14C22×C22⋊D19C2212yes—
15C22×C22⋊D19C2212yescomplemented
16C22×C22⋊D19C2212yescomplemented
17C2×D4×D19—28no—
18C2×D4×D19—28no—
19C2×D4×D19—28no—
20C22×D76C2212yes—
21C22×D76C2211yescharacteristic, complemented
22C22×C4×D19C2212yescomplemented
23C2×C22⋊C4×C19C2212yescomplemented
24C2×C22⋊C4×C19C2211yescharacteristic, complemented
25C2×C22⋊Dic19C2212yescomplemented
26C2×C22⋊Dic19C2211yescharacteristic, complemented
27#10597383—28no—
28C2×(C2×D19)⋊C4C2212yescomplemented
29C2×(C2×D19)⋊C4C2212yescomplemented
30C2×(C2×D19)⋊C4C2212yescomplemented
31C2×(C2×D19)⋊C4C2212yescomplemented
32#10597328—28no—
33C19×#95C2211yescharacteristic, complemented
34C19⋊#95C2211yescharacteristic, complemented
35C19⋊#95C2212yescomplemented
36C24×C19C2311yescharacteristic
37C24×C19C2312yes—
38C23×D19—24no—
39C23×D19—24no—
40C23×D19—24no—
41C23×D19—24no—
42C23×D19—24no—
43C23×D19—24no—
44C23×D19—24no—
45C23×D19—41no—
46C23×D19—41no—
47C23×D19—42no—
48C23×D19—42no—
49C23×D19D414yescomplemented
50C23×D19C2312yes—
51C23×D19C2312yes—
52C2×D4×C19—24no—
53C2×D4×C19—24no—
54C2×D4×C19—24no—
55C2×D4×C19—24no—
56C2×D4×C19—41no—
57C22×C4×C19C2311yescharacteristic
58C22×C4×C19C2311yescharacteristic
59C22×C4×C19C2312yes—
60C2×C22⋊D19—24no—
61C2×C22⋊D19—24no—
62C2×C22⋊D19—24no—
63C2×C22⋊D19—24no—
64C2×C22⋊D19—24no—
65C2×C22⋊D19—24no—
66C2×C22⋊D19—24no—
67C2×C22⋊D19—42no—
68C2×C22⋊D19D418yescomplemented
69C22×Dic19C2312yes—
70C22×Dic19C2312yes—
71D4×D19—264no—
72C2×D76—24no—
73C2×D76—24no—
74C2×D76—24no—
75C2×D76—41no—
76C2×D76D418yescomplemented
77C2×C4×D19—24no—
78C2×C4×D19—24no—
79C2×C4×D19—24no—
80C22⋊C4×C19—24no—
81C22⋊C4×C19—41no—
82C22⋊Dic19—24no—
83C22⋊Dic19—41no—
84(C2×D19)⋊C4—24no—
85(C2×D19)⋊C4—24no—
86(C2×D19)⋊C4—24no—
87(C2×D19)⋊C4—24no—
88C23×C19—22no—
89C23×C19—22no—
90C23×C19—22no—
91C23×C19—22no—
92C23×C19—22no—
93C23×C19—22no—
94C23×C19—21no—
95C23×C19—21no—
96C23×C19—22no—
97C23×C19—22no—
98C23×C19C2×D412yes—
99C23×C19C2×D414yescomplemented
100C23×C19C2411yescharacteristic
101C22×D19—22no—
102C22×D19—22no—
103C22×D19—22no—
104C22×D19—22no—
105C22×D19—216no—
106C22×D19—22no—
107C22×D19—22no—
108C22×D19—22no—
109C22×D19—22no—
110C22×D19—22no—
111C22×D19—22no—
112C22×D19—216no—
113C22×D19—44no—
114C22×D19—44no—
115C22×D19—48no—
116C22×D19—44no—
117C22×D19—48no—
118C22×D19—48no—
119C22×D19—48no—
120C22×D19—48no—
121C22×D19—48no—
122C22×D19—48no—
123C22×D19C2×D414yes—
124C22×D19C2×D414yes—
125C22×D19C2×D414yes—
126C22×D19C2×D414yescomplemented
127D4×C19—216no—
128D4×C19—44no—
129C2×C4×C19—22no—
130C2×C4×C19—22no—
131C2×C4×C19—22no—
132C2×C4×C19—22no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19C2×D414yescomplemented
136C22⋊D19—216no—
137C22⋊D19—216no—
138C22⋊D19—48no—
139C2×Dic19—22no—
140C2×Dic19—22no—
141C2×Dic19—22no—
142C2×Dic19—22no—
143C2×Dic19—22no—
144C2×Dic19C2×D414yescomplemented
145D76—216no—
146D76—44no—
147C4×D19—216no—
148#2403—191nomaximal, Sylow
149C22×C19—24no—
150C22×C19—24no—
151C22×C19—22no—
152C22×C19—24no—
153C22×C19—24no—
154C22×C19—42no—
155C22×C19—42no—
156C22×C19—41no—
157C22×C19—42no—
158C22×C19—42no—
159C22×C19—42no—
160C22×C19—41no—
161C22×C19C22×D411yescharacteristic
162C22×C19C22×D412yes—
163C22×C19C22×D412yes—
164C22×C19H(5,𝔽2)11yescharacteristic
165C22×C19H(5,𝔽2)11yescharacteristic
166C2×D19—24no—
167C2×D19—24no—
168C2×D19—24no—
169C2×D19—24no—
170C2×D19—24no—
171C2×D19—24no—
172C2×D19—24no—
173C2×D19—24no—
174C2×D19—24no—
175C2×D19—416no—
176C2×D19—432no—
177C2×D19—42no—
178C2×D19—42no—
179C2×D19—42no—
180C2×D19—42no—
181C2×D19#12018yescomplemented
182C4×C19—24no—
183C4×C19—41no—
184C4×C19—41no—
185Dic19—24no—
186Dic19—42no—
187C23×D4—192no—
188C2×#120—192no—
189C2×#120—192no—
190#392—192no—
191#392—191no—
192#392D1911yescharacteristic, complemented
193#386—192no—
194#386—192no—
195#379—191no—
196C2×C19—42no—
197C2×C19—44no—
198C2×C19C2×#12012yes—
199C2×C19#53411yescharacteristic
200C2×C19D4211yescharacteristic
201C2×C19D4212yes—
202C2×C19D4211yescharacteristic
203D19—28no—
204D19—44no—
205C25—191no—
206C25—192no—
207C22×D4—192no—
208C22×D4—192no—
209C22×D4—192no—
210C22×D4—192no—
211C22×D4—191no—
212C22×D4—388no—
213C22×D4—388no—
214C22×D4—388no—
215C22×D4C2×D1912yescomplemented
216C22×D4C2×D1911yescharacteristic, complemented
217C23×C4—192no—
218#120—388no—
219#120—388no—
220C2×C22⋊C4—192no—
221C2×C22⋊C4—192no—
222C2×C22⋊C4—192no—
223C2×C22⋊C4—192no—
224C2×C22⋊C4—192no—
225C2×C22⋊C4—191no—
226C2×C22⋊C4C2×D1912yescomplemented
227C2×C22⋊C4C2×D1911yescharacteristic, complemented
228#95—191no—
229#95—192no—
230#95C2×D1911yescharacteristic, complemented
231C19#240311yescharacteristic, complemented, Sylow
232C24—192no—
233C24—192no—
234C24—194no—
235C24—384no—
236C24—384no—
237C24—384no—
238C24—384no—
239C24—384no—
240C24—384no—
241C24—384no—
242C24—761no—
243C24—762no—
244C24—761no—
245C24—762no—
246C24C22×D1911yescharacteristic
247C24C22×D1912yes—
248C2×D4—24no—
249C2×D4—24no—
250C2×D4—24no—
251C2×D4—24no—
252C2×D4—41no—
253C2×D4—198no—
254C2×D4—198no—
255C2×D4—384no—
256C2×D4—384no—
257C2×D4—384no—
258C2×D4—384no—
259C2×D4—3864no—
260C2×D4—384no—
261C2×D4—384no—
262C2×D4—384no—
263C2×D4—384no—
264C2×D4—384no—
265C2×D4—384no—
266C2×D4—761no—
267C2×D4—762no—
268C22×C4—192no—
269C22×C4—192no—
270C22×C4—384no—
271C22×C4—384no—
272C22×C4—384no—
273C22×C4C22×D1911yescharacteristic
274C22×C4C22×D1911yescharacteristic
275C22×C4C22×D1912yes—
276C22⋊C4—24no—
277C22⋊C4—41no—
278C22⋊C4—384no—
279C22⋊C4—384no—
280C22⋊C4—384no—
281C22⋊C4—384no—
282C22⋊C4—384no—
283C22⋊C4—761no—
284C23—22no—
285C23—22no—
286C23—22no—
287C23—22no—
288C23—22no—
289C23—22no—
290C23—21no—
291C23—22no—
292C23—21no—
293C23—22no—
294C23—194no—
295C23—194no—
296C23—194no—
297C23—194no—
298C23—3816no—
299C23—3816no—
300C23—382no—
301C23—382no—
302C23—382no—
303C23—382no—
304C23—382no—
305C23—382no—
306C23—382no—
307C23—382no—
308C23—382no—
309C23—382no—
310C23—764no—
311C23—768no—
312C23—768no—
313C23—768no—
314C23—764no—
315C23—768no—
316C23—768no—
317C23—764no—
318C23—768no—
319C23—768no—
320C23D4×D1912yes—
321C23D4×D1914yescomplemented
322C23C23×D1911yescharacteristic
323D4—216no—
324D4—44no—
325D4—3816no—
326D4—3816no—
327D4—3816no—
328D4—764no—
329D4—768no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—194no—
337C2×C4—3816no—
338C2×C4—382no—
339C2×C4—382no—
340C2×C4—382no—
341C2×C4—382no—
342C2×C4—382no—
343C2×C4D4×D1914yescomplemented
344C22—22no—
345C22—24no—
346C22—24no—
347C22—24no—
348C22—24no—
349C22—42no—
350C22—41no—
351C22—42no—
352C22—42no—
353C22—42no—
354C22—41no—
355C22—42no—
356C22—198no—
357C22—384no—
358C22—384no—
359C22—384no—
360C22—384no—
361C22—384no—
362C22—384no—
363C22—384no—
364C22—384no—
365C22—384no—
366C22—7616no—
367C22—7632no—
368C22—762no—
369C22—762no—
370C22—762no—
371C22—762no—
372C22C2×D4×D1911yescharacteristic
373C22C2×D4×D1912yes—
374C22C2×D4×D1912yes—
375C22#1059743011yescharacteristic
376C22#1059743511yescharacteristic
377C4—24no—
378C4—41no—
379C4—41no—
380C4—384no—
381C4—762no—
382C2—42no—
383C2—44no—
384C2—388no—
385C2—764no—
386C2#120×D1912yes—
387C2#1192710211yescharacteristic
388C2#1192717611yescharacteristic
389C2#1192717812yes—
390C2#1192717911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#392C2
hypercenter#392D19
hypocenterC19#2403
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×D19C2semidirect
2. C2×#10597328C2semidirect
3. C2×#10597383C2semidirect
4. #11926453C2semidirect
5. #11926452C2semidirect
6. #11926422C2semidirect
7. #11926420C2semidirect
8. #11926399C2semidirect
9. C19×#392C2semidirect
11. C24×D19C22semidirect
12. C22×D4×C19C22semidirect
13. C22×D4×C19C22semidirect
15. C22×C22⋊D19C22semidirect
16. C22×C22⋊D19C22semidirect
21. C22×D76C22semidirect
22. C22×C4×D19C22semidirect
23. C2×C22⋊C4×C19C22semidirect
24. C2×C22⋊C4×C19C22semidirect
25. C2×C22⋊Dic19C22semidirect
26. C2×C22⋊Dic19C22semidirect
28. C2×(C2×D19)⋊C4C22semidirect
29. C2×(C2×D19)⋊C4C22semidirect
30. C2×(C2×D19)⋊C4C22semidirect
31. C2×(C2×D19)⋊C4C22semidirect
33. C19×#95C22semidirect
34. C19⋊#95C22semidirect
35. C19⋊#95C22semidirect
49. C23×D19D4semidirect
68. C2×C22⋊D19D4semidirect
76. C2×D76D4semidirect
99. C23×C19C2×D4semidirect
126. C22×D19C2×D4semidirect
135. C2×C4×C19C2×D4semidirect
144. C2×Dic19C2×D4semidirect
181. C2×D19#120semidirect
192. #392D19semidirect
215. C22×D4C2×D19semidirect
216. C22×D4C2×D19semidirect
226. C2×C22⋊C4C2×D19semidirect
227. C2×C22⋊C4C2×D19semidirect
230. #95C2×D19semidirect
231. C19#2403semidirect
321. C23D4×D19semidirect
343. C2×C4D4×D19semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D192
C2×#105973282
C2×#105973832
#119264532
#119264522
#119264222
#119264202
#119263992
C19×#3922
#240319