Finite Group Databasebeta

← #14572863

Subgroups — #14572863

Order 2432.

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

normal subgroups only

This group has 994 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
1C22×D4×D19C211yesmaximal, characteristic, complemented
2C2×#10597360C212yesmaximal, complemented
3#11927057C211yesmaximal, characteristic, complemented
4#11926694C211yesmaximal, characteristic, complemented
5#11926693C212yesmaximal, complemented
6#11926680C211yesmaximal, characteristic, complemented
7#11926679C212yesmaximal, complemented
8#11926678C211yesmaximal, characteristic, complemented
9#11926547C212yesmaximal, complemented
10#11926506C211yesmaximal, characteristic, complemented
11C19×#450C211yesmaximal, characteristic, complemented
12C24×D19—21no—
13C22×D4×C19C2211yescharacteristic
14C22×C22⋊D19—21no—
15C2×#64545C2211yescharacteristic, complemented
16C2×D4×D19—28no—
17C2×D4×D19—21no—
18C2×D4×D19—21no—
19C2×D4×D19C2212yes—
20C2×D4×D19C2212yes—
21C22×D76C2211yescharacteristic
22C22×C4×D19C2211yescharacteristic
23C2×SD16×C19C2212yescomplemented
24C19×C22⋊Q8C2211yescharacteristic, complemented
25#10597392C2211yescharacteristic, complemented
26C2×#64527C2212yescomplemented
27C2×#64525C2212yescomplemented
28#10597376C2211yescharacteristic, complemented
29#10597360—28no—
30C2×D152C2212yescomplemented
31C2×#64515C2212yescomplemented
32#10597341C2211yescharacteristic, complemented
33#10597340—21no—
34#10597339—21no—
35#10597338C2211yescharacteristic, complemented
36#10597328—21no—
37(C22⋊D19)⋊C4—21no—
38C19×#102C2212yescomplemented
39C19×C22⋊C8C2211yescharacteristic, complemented
40#10597289C2212yescomplemented
41C22⋊(C19⋊C8)C2211yescharacteristic, complemented
42#10597278C2212yescomplemented
43(C2×D19)⋊C8C2212yescomplemented
44#10597266C2212yescomplemented
45C24×C19—21no—
46C23×D19—28no—
47C23×D19—21no—
48C23×D19—22no—
49C23×D19—22no—
50C23×D19—44no—
51C23×D19—44no—
52C23×D19D411yescharacteristic
53C2×Q8×C19C2311yescharacteristic, complemented
54C2×D4×C19—24no—
55C2×D4×C19—21no—
56C2×D4×C19C2312yes—
57C22×C4×C19C2311yescharacteristic
58C2×C22⋊D19—28no—
59C2×C22⋊D19—21no—
60C2×C22⋊D19—22no—
61C2×C22⋊D19—22no—
62C22×Dic19D411yescharacteristic
63#64545—24no—
64D4×D19—28no—
65D4×D19—28no—
66D4×D19—24no—
67D4×D19—24no—
68D4×D19—24no—
69D4×D19D418yescomplemented
70C2×D76—21no—
71C2×D76—24no—
72C2×D76—21no—
73C2×D76—21no—
74C2×D76C2312yes—
75C2×D76C2311yescharacteristic, complemented
76C2×C4×D19—24no—
77C2×C4×D19—21no—
78C2×C4×D19D411yescharacteristic
79C2×C4×D19D411yescharacteristic
80C2×C4×D19C2311yescharacteristic
81C2×C4×D19C2311yescharacteristic
82SD16×C19—24no—
83C2×C8×C19C2312yescomplemented
84C4⋊C4×C19—21no—
85C4⋊C4×C19C2311yescharacteristic, complemented
86C22⋊C4×C19—21no—
87#64527—24no—
88#64525—24no—
89(C2×D19)⋊C4—21no—
90(C2×D19)⋊C4—21no—
91(C2×D19)⋊C4—21no—
92(C2×D19)⋊C4—21no—
93C4⋊Dic19C2311yescharacteristic, complemented
94Dic19⋊C4—21no—
95C4×Dic19—21no—
96C2×C19⋊C8C2312yescomplemented
97D152—24no—
98#64515—24no—
99C23×C19—24no—
100C23×C19—22no—
101C23×C19—42no—
102C23×C19—42no—
103C23×C19C2×D411yescharacteristic
104C22×D19—22no—
105C22×D19—22no—
106C22×D19—22no—
107C22×D19—24no—
108C22×D19—28no—
109C22×D19—22no—
110C22×D19—28no—
111C22×D19—21no—
112C22×D19—432no—
113C22×D19—44no—
114C22×D19—44no—
115C22×D19—44no—
116C22×D19—42no—
117C22×D19—42no—
118C22×D19—44no—
119C22×D19C2×D411yescharacteristic
120C22×D19C2×D411yescharacteristic
121Q8×C19—22no—
122D4×C19—24no—
123D4×C19—22no—
124D4×C19C2×D414yes—
125C2×C4×C19—22no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19C2×D411yescharacteristic
129C2×C4×C19C2411yescharacteristic
130C22⋊D19—28no—
131C22⋊D19—28no—
132C22⋊D19—42no—
133C2×Dic19—22no—
134C2×Dic19—21no—
135C2×Dic19C2×D411yescharacteristic
136C2×Dic19C2×D411yescharacteristic
137D76—24no—
138D76—22no—
139D76—22no—
140D76—42no—
141D76—42no—
142D76C2×D414yes—
143C4×D19—22no—
144C4×D19—22no—
145C4×D19—22no—
146C4×D19—42no—
147C4×D19C2×D414yes—
148C8×C19—22no—
149C19⋊C8—22no—
150#3003—191nomaximal, Sylow
151C22×C19—21no—
152C22×C19—21no—
153C22×C19—24no—
154C22×C19—48no—
155C22×C19—42no—
156C22×C19—42no—
157C22×C19AGL(1,ℤ/8)12yescomplemented
158C22×C19C22×D411yescharacteristic
159C2×D19—28no—
160C2×D19—21no—
161C2×D19—21no—
162C2×D19—21no—
163C2×D19—21no—
164C2×D19—24no—
165C2×D19—416no—
166C2×D19—416no—
167C2×D19—48no—
168C2×D19—42no—
169C2×D19—42no—
170C2×D19—41no—
171C2×D19—41no—
172C2×D19—41no—
173C2×D19#12012yes—
174C2×D19AGL(1,ℤ/8)12yescomplemented
175C4×C19—21no—
176C4×C19—41no—
177C4×C19—41no—
178C4×C19C22×D412yes—
179Dic19—21no—
180Dic19—41no—
181Dic19#12012yes—
182C23×D4—191no—
183C2×AGL(1,ℤ/8)—192no—
184#525—191no—
185#450—192no—
186#450—191no—
187#450D1911yescharacteristic, complemented
188#447—191no—
189#447—192no—
190#447—191no—
191#418—192no—
192#407—191no—
193C2×C19—22no—
194C2×C19—44no—
195C2×C19C2×#12011yescharacteristic
196C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
197C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
198D19—22no—
199D19—22no—
200D19—44no—
201D19—81no—
202C25—381no—
203C2×#41—191no—
204C22×D4—192no—
205C22×D4—192no—
206C22×D4—191no—
207C22×D4—381no—
208C22×D4—381no—
209C22×D4—381no—
210C22×D4—388no—
211C22×D4C2×D1911yescharacteristic
212C23×C4—191no—
213AGL(1,ℤ/8)—388no—
214C2×SD16—192no—
215C2×SD16C2×D1912yescomplemented
216C2×D8—192no—
217C2×D8—192no—
218C2×M16—192no—
219#123—381no—
220C22⋊Q8—191no—
221C22⋊Q8C2×D1911yescharacteristic, complemented
222#121—191no—
223#121—191no—
224#120—381no—
225C4×D4—381no—
226C4×D4—381no—
227#117—191no—
228#102—192no—
229#102—192no—
230#102—192no—
231#102C2×D1912yescomplemented
232C22⋊C8—191no—
233C22⋊C8—192no—
234C22⋊C8C2×D1911yescharacteristic, complemented
235C19#300311yescharacteristic, complemented, Sylow
236C24—21no—
237C24—191no—
238C24—382no—
239C24—382no—
240C24—388no—
241C24—381no—
242C24—764no—
243C24—764no—
244#41—384no—
245C2×Q8C22×D1911yescharacteristic, complemented
246C2×D4—24no—
247C2×D4—21no—
248C2×D4—198no—
249C2×D4—192no—
250C2×D4—191no—
251C2×D4—384no—
252C2×D4—381no—
253C2×D4—381no—
254C2×D4—384no—
255C2×D4—382no—
256C2×D4—382no—
257C2×D4—384no—
258C2×D4—388no—
259C2×D4—388no—
260C2×D4—388no—
261C2×D4—384no—
262C2×D4—381no—
263C2×D4—381no—
264C2×D4C22×D1912yes—
265C22×C4—191no—
266C22×C4—191no—
267C22×C4—191no—
268C22×C4—191no—
269C22×C4—191no—
270C22×C4—384no—
271C22×C4—381no—
272C22×C4C22×D1911yescharacteristic
273SD16—24no—
274SD16—384no—
275D8—384no—
276D8—384no—
277M16—384no—
278C2×C8—192no—
279C2×C8C22×D1912yescomplemented
280C4⋊C4—21no—
281C4⋊C4—191no—
282C4⋊C4—381no—
283C4⋊C4C22×D1911yescharacteristic, complemented
284C22⋊C4—21no—
285C22⋊C4—381no—
286C22⋊C4—381no—
287C22⋊C4—381no—
288C22⋊C4—381no—
289C42—381no—
290C23—24no—
291C23—22no—
292C23—42no—
293C23—42no—
294C23—191no—
295C23—191no—
296C23—382no—
297C23—382no—
298C23—388no—
299C23—384no—
300C23—388no—
301C23—382no—
302C23—382no—
303C23—381no—
304C23—762no—
305C23—764no—
306C23—7632no—
307C23—764no—
308C23—764no—
309C23—764no—
310C23—762no—
311C23D4×D1911yescharacteristic
312Q8—22no—
313D4—24no—
314D4—22no—
315D4—194no—
316D4—384no—
317D4—388no—
318D4—388no—
319D4—382no—
320D4—382no—
321D4—762no—
322D4—762no—
323D4—762no—
324D4D4×D1914yes—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—191no—
329C2×C4—194no—
330C2×C4—191no—
331C2×C4—382no—
332C2×C4—382no—
333C2×C4—382no—
334C2×C4—382no—
335C2×C4—381no—
336C2×C4—762no—
337C2×C4D4×D1911yescharacteristic
338C2×C4C23×D1911yescharacteristic
339C8—22no—
340C8—382no—
341C22—21no—
342C22—21no—
343C22—24no—
344C22—48no—
345C22—42no—
346C22—42no—
347C22—192no—
348C22—192no—
349C22—388no—
350C22—381no—
351C22—381no—
352C22—381no—
353C22—381no—
354C22—384no—
355C22—768no—
356C22—7616no—
357C22—7616no—
358C22—762no—
359C22—762no—
360C22—761no—
361C22—761no—
362C22—761no—
363C22#1059736012yescomplemented
364C22C2×D4×D1911yescharacteristic
365C4—21no—
366C4—41no—
367C4—41no—
368C4—192no—
369C4—381no—
370C4—761no—
371C4C2×D4×D1912yes—
372C2—22no—
373C2—44no—
374C2—382no—
375C2—382no—
376C2—764no—
377C2—1521no—
378C2#120×D1911yescharacteristic
379C2AGL(1,ℤ/8)×D1911yescharacteristic
380C2C2×#1059736011yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#450C2
socleC22×C19C22×D4
hypercenter#450D19
hypocenterC19#3003
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C22×D4×D19C2semidirect
2. C2×#10597360C2semidirect
3. #11927057C2semidirect
4. #11926694C2semidirect
5. #11926693C2semidirect
6. #11926680C2semidirect
7. #11926679C2semidirect
8. #11926678C2semidirect
9. #11926547C2semidirect
10. #11926506C2semidirect
11. C19×#450C2semidirect
15. C2×#64545C22semidirect
23. C2×SD16×C19C22semidirect
24. C19×C22⋊Q8C22semidirect
25. #10597392C22semidirect
26. C2×#64527C22semidirect
27. C2×#64525C22semidirect
28. #10597376C22semidirect
30. C2×D152C22semidirect
31. C2×#64515C22semidirect
32. #10597341C22semidirect
35. #10597338C22semidirect
38. C19×#102C22semidirect
39. C19×C22⋊C8C22semidirect
40. #10597289C22semidirect
41. C22⋊(C19⋊C8)C22semidirect
42. #10597278C22semidirect
43. (C2×D19)⋊C8C22semidirect
44. #10597266C22semidirect
53. C2×Q8×C19C23semidirect
69. D4×D19D4semidirect
75. C2×D76C23semidirect
83. C2×C8×C19C23semidirect
85. C4⋊C4×C19C23semidirect
93. C4⋊Dic19C23semidirect
96. C2×C19⋊C8C23semidirect
157. C22×C19AGL(1,ℤ/8)semidirect
174. C2×D19AGL(1,ℤ/8)semidirect
187. #450D19semidirect
215. C2×SD16C2×D19semidirect
221. C22⋊Q8C2×D19semidirect
231. #102C2×D19semidirect
234. C22⋊C8C2×D19semidirect
235. C19#3003semidirect
245. C2×Q8C22×D19semidirect
279. C2×C8C22×D19semidirect
283. C4⋊C4C22×D19semidirect
363. C22#10597360semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D192
C2×#105973602
#119270572
#119266942
#119266932
#119266802
#119266792
#119266782
#119265472
#119265062
C19×#4502
#300319