Finite Group Databasebeta

← #14569346

Subgroups — #14569346

Order 2432.

1134 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 153 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×D19C211yesmaximal, characteristic, complemented
2C2×#10597329C211yesmaximal, characteristic, complemented
3C2×#10597383C212yesmaximal, complemented
4#11926462C211yesmaximal, characteristic, complemented
5#11926460C212yesmaximal, complemented
6#11926458C211yesmaximal, characteristic, complemented
7#11926453C211yesmaximal, characteristic, complemented
8#11926452C212yesmaximal, complemented
9#11926406C211yesmaximal, characteristic, complemented
10#11926399C212yesmaximal, complemented
11C19×#392C211yesmaximal, characteristic, complemented
12C24×D19C2212yes—
13C22×D4×C19C2211yescharacteristic
14C22×D4×C19C2212yescomplemented
15C22×C22⋊D19C2211yescharacteristic
16C22×C22⋊D19C2212yes—
17C22×C22⋊D19C2212yescomplemented
18C2×D4×D19—28no—
19C2×D4×D19—24no—
20C22×D76C2211yescharacteristic
21C22×C4×D19C2211yescharacteristic
22C2×C22⋊C4×C19C2211yescharacteristic, complemented
23C2×C22⋊C4×C19C2212yescomplemented
24C2×C22⋊Dic19C2211yescharacteristic, complemented
25C2×C22⋊Dic19C2212yescomplemented
26C2×C22⋊Dic19C2212yescomplemented
27#10597383—28no—
28C2×(C2×D19)⋊C4C2211yescharacteristic
29C2×(C2×D19)⋊C4C2212yes—
30C2×(C2×D19)⋊C4C2212yescomplemented
31C2×(C2×D19)⋊C4C2212yescomplemented
32C2×(C2×D19)⋊C4C2212yescomplemented
33C2×C4⋊Dic19C2211yescharacteristic, complemented
34C2×Dic19⋊C4C2211yescharacteristic, complemented
35#10597329—24no—
36C19×#95C2211yescharacteristic, complemented
37C19⋊#95C2212yescomplemented
38C19⋊#95C2211yescharacteristic, complemented
39C24×C19C2311yescharacteristic
40C24×C19C2312yes—
41C23×D19—24no—
42C23×D19—24no—
43C23×D19—42no—
44C23×D19—42no—
45C23×D19—42no—
46C23×D19—42no—
47C23×D19D418yescomplemented
48C23×D19C2312yes—
49C23×D19C2311yescharacteristic
50C2×D4×C19—24no—
51C2×D4×C19—24no—
52C2×D4×C19—22no—
53C2×D4×C19—42no—
54C2×D4×C19—42no—
55C22×C4×C19C2311yescharacteristic
56C22×C4×C19C2312yes—
57C22×C4×C19C2311yescharacteristic
58C2×C22⋊D19—24no—
59C2×C22⋊D19—24no—
60C2×C22⋊D19—24no—
61C2×C22⋊D19—24no—
62C2×C22⋊D19—22no—
63C2×C22⋊D19—24no—
64C2×C22⋊D19—42no—
65C2×C22⋊D19—42no—
66C22×Dic19C2311yescharacteristic
67C22×Dic19C2311yescharacteristic
68C22×Dic19C2312yes—
69C22×Dic19C2311yescharacteristic
70D4×D19—232no—
71C2×D76—24no—
72C2×D76—22no—
73C2×C4×D19—24no—
74C2×C4×D19D414yescomplemented
75C22⋊C4×C19—22no—
76C22⋊C4×C19—42no—
77C22⋊Dic19—24no—
78C22⋊Dic19—22no—
79C22⋊Dic19—42no—
80(C2×D19)⋊C4—24no—
81(C2×D19)⋊C4—24no—
82(C2×D19)⋊C4—22no—
83(C2×D19)⋊C4—42no—
84(C2×D19)⋊C4—42no—
85C4⋊Dic19—22no—
86Dic19⋊C4—22no—
87C23×C19—22no—
88C23×C19—22no—
89C23×C19—22no—
90C23×C19—22no—
91C23×C19—22no—
92C23×C19—22no—
93C23×C19—21no—
94C23×C19—22no—
95C23×C19—21no—
96C23×C19—22no—
97C23×C19—21no—
98C23×C19C2×D414yes—
99C23×C19C2411yescharacteristic
100C22×D19—22no—
101C22×D19—21no—
102C22×D19—21no—
103C22×D19—22no—
104C22×D19—22no—
105C22×D19—22no—
106C22×D19—22no—
107C22×D19—22no—
108C22×D19—22no—
109C22×D19—216no—
110C22×D19—48no—
111C22×D19—48no—
112C22×D19—48no—
113C22×D19—48no—
114C22×D19—48no—
115C22×D19—48no—
116C22×D19C2×D414yes—
117C22×D19C2×D414yes—
118C22×D19C2×D412yes—
119D4×C19—28no—
120D4×C19—48no—
121C2×C4×C19—22no—
122C2×C4×C19—21no—
123C2×C4×C19—22no—
124C2×C4×C19—22no—
125C2×C4×C19—22no—
126C2×C4×C19—22no—
127C2×C4×C19C2×D412yes—
128C22⋊D19—216no—
129C22⋊D19—48no—
130C22⋊D19—44no—
131C2×Dic19—22no—
132C2×Dic19—21no—
133C2×Dic19—21no—
134C2×Dic19—22no—
135C2×Dic19—22no—
136C2×Dic19—21no—
137C2×Dic19—22no—
138C2×Dic19—21no—
139C2×Dic19—22no—
140C2×Dic19C2×D412yes—
141D76—28no—
142C4×D19—28no—
143#2613—191nomaximal, Sylow
144C22×C19—24no—
145C22×C19—24no—
146C22×C19—24no—
147C22×C19—42no—
148C22×C19—42no—
149C22×C19—42no—
150C22×C19—42no—
151C22×C19—41no—
152C22×C19—42no—
153C22×C19—42no—
154C22×C19—41no—
155C22×C19—41no—
156C22×C19C22×D412yes—
157C22×C19C22×D411yescharacteristic
158C22×C19H(5,𝔽2)12yes—
159C22×C19H(5,𝔽2)11yescharacteristic
160C22×C19H(5,𝔽2)11yescharacteristic
161C2×D19—24no—
162C2×D19—24no—
163C2×D19—22no—
164C2×D19—22no—
165C2×D19—24no—
166C2×D19—24no—
167C2×D19—24no—
168C2×D19—432no—
169C2×D19—42no—
170C2×D19—42no—
171C2×D19—42no—
172C2×D19—42no—
173C2×D19#12014yes—
174C4×C19—22no—
175C4×C19—42no—
176C4×C19—41no—
177Dic19—22no—
178Dic19—41no—
179Dic19—42no—
180Dic19—41no—
181C23×D4—191no—
182C2×#123—191no—
183C2×#120—192no—
184#394—191no—
185#394—192no—
186#394—191no—
187#392—192no—
188#392—191no—
189#392D1911yescharacteristic, complemented
190#381—191no—
191#379—192no—
192C2×C19—44no—
193C2×C19—81no—
194C2×C19C2×#12011yescharacteristic
195C2×C19#53412yes—
196C2×C19#53412yes—
197C2×C19#53511yescharacteristic
198C2×C19#53511yescharacteristic
199D19—24no—
200D19—44no—
201C25—192no—
202C22×D4—191no—
203C22×D4—192no—
204C22×D4—192no—
205C22×D4—191no—
206C22×D4—384no—
207C22×D4—388no—
208C22×D4C2×D1911yescharacteristic
209C22×D4C2×D1912yescomplemented
210C23×C4—191no—
211#123—384no—
212#120—388no—
213C2×C4⋊C4—191no—
214C2×C4⋊C4—191no—
215C2×C22⋊C4—192no—
216C2×C22⋊C4—191no—
217C2×C22⋊C4—192no—
218C2×C22⋊C4—192no—
219C2×C22⋊C4—191no—
220C2×C22⋊C4—192no—
221C2×C22⋊C4—192no—
222C2×C22⋊C4—192no—
223C2×C22⋊C4C2×D1911yescharacteristic, complemented
224C2×C22⋊C4C2×D1912yescomplemented
225#95—192no—
226#95—191no—
227#95C2×D1911yescharacteristic, complemented
228C19#261311yescharacteristic, complemented, Sylow
229C24—191no—
230C24—192no—
231C24—198no—
232C24—384no—
233C24—384no—
234C24—762no—
235C24—762no—
236C24—762no—
237C24—762no—
238C24C22×D1911yescharacteristic
239C24C22×D1912yes—
240C2×D4—24no—
241C2×D4—24no—
242C2×D4—22no—
243C2×D4—42no—
244C2×D4—42no—
245C2×D4—384no—
246C2×D4—384no—
247C2×D4—3832no—
248C2×D4—384no—
249C2×D4—384no—
250C2×D4—384no—
251C2×D4—384no—
252C2×D4—382no—
253C2×D4—382no—
254C2×D4—762no—
255C2×D4—762no—
256C22×C4—191no—
257C22×C4—194no—
258C22×C4—192no—
259C22×C4—191no—
260C22×C4—191no—
261C22×C4—384no—
262C22×C4C22×D1912yes—
263C22×C4C22×D1911yescharacteristic
264C22×C4C22×D1911yescharacteristic
265C4⋊C4—382no—
266C4⋊C4—382no—
267C22⋊C4—22no—
268C22⋊C4—42no—
269C22⋊C4—384no—
270C22⋊C4—384no—
271C22⋊C4—382no—
272C22⋊C4—382no—
273C22⋊C4—384no—
274C22⋊C4—762no—
275C22⋊C4—762no—
276C22⋊C4—762no—
277C23—22no—
278C23—22no—
279C23—22no—
280C23—22no—
281C23—22no—
282C23—22no—
283C23—21no—
284C23—22no—
285C23—21no—
286C23—22no—
287C23—21no—
288C23—192no—
289C23—194no—
290C23—194no—
291C23—3816no—
292C23—382no—
293C23—381no—
294C23—381no—
295C23—382no—
296C23—382no—
297C23—382no—
298C23—382no—
299C23—382no—
300C23—382no—
301C23—768no—
302C23—768no—
303C23—768no—
304C23—768no—
305C23—768no—
306C23—768no—
307C23D4×D1914yes—
308C23C23×D1911yescharacteristic
309D4—28no—
310D4—48no—
311D4—388no—
312D4—3816no—
313D4—764no—
314D4—768no—
315C2×C4—22no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—192no—
322C2×C4—388no—
323C2×C4—382no—
324C2×C4—381no—
325C2×C4—382no—
326C2×C4—382no—
327C2×C4—381no—
328C2×C4—381no—
329C2×C4—382no—
330C2×C4—381no—
331C2×C4—382no—
332C2×C4D4×D1912yes—
333C22—24no—
334C22—24no—
335C22—24no—
336C22—42no—
337C22—42no—
338C22—42no—
339C22—42no—
340C22—42no—
341C22—42no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—194no—
346C22—384no—
347C22—384no—
348C22—382no—
349C22—382no—
350C22—384no—
351C22—384no—
352C22—384no—
353C22—7632no—
354C22—762no—
355C22—762no—
356C22—762no—
357C22—762no—
358C22C2×D4×D1912yes—
359C22C2×D4×D1911yescharacteristic
360C22#1059743012yes—
361C22#1059743011yescharacteristic
362C22#1059743511yescharacteristic
363C4—22no—
364C4—42no—
365C4—41no—
366C4—382no—
367C4—762no—
368C4—761no—
369C4—761no—
370C2—44no—
371C2—81no—
372C2—384no—
373C2—764no—
374C2#120×D1911yescharacteristic
375C2#1192710212yes—
376C2#1192710412yes—
377C2#1192710711yescharacteristic
378C2#1192711011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#392C2
hypercenter#392D19
hypocenterC19#2613
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×#10597329C2semidirect
3. C2×#10597383C2semidirect
4. #11926462C2semidirect
5. #11926460C2semidirect
6. #11926458C2semidirect
7. #11926453C2semidirect
8. #11926452C2semidirect
9. #11926406C2semidirect
10. #11926399C2semidirect
11. C19×#392C2semidirect
14. C22×D4×C19C22semidirect
17. C22×C22⋊D19C22semidirect
22. C2×C22⋊C4×C19C22semidirect
23. C2×C22⋊C4×C19C22semidirect
24. C2×C22⋊Dic19C22semidirect
25. C2×C22⋊Dic19C22semidirect
26. C2×C22⋊Dic19C22semidirect
30. C2×(C2×D19)⋊C4C22semidirect
31. C2×(C2×D19)⋊C4C22semidirect
32. C2×(C2×D19)⋊C4C22semidirect
33. C2×C4⋊Dic19C22semidirect
34. C2×Dic19⋊C4C22semidirect
36. C19×#95C22semidirect
37. C19⋊#95C22semidirect
38. C19⋊#95C22semidirect
47. C23×D19D4semidirect
74. C2×C4×D19D4semidirect
189. #392D19semidirect
209. C22×D4C2×D19semidirect
223. C2×C22⋊C4C2×D19semidirect
224. C2×C22⋊C4C2×D19semidirect
227. #95C2×D19semidirect
228. C19#2613semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D192
C2×#105973292
C2×#105973832
#119264622
#119264602
#119264582
#119264532
#119264522
#119264062
#119263992
C19×#3922
#261319