Finite Group Databasebeta

← #14575475

Subgroups — #14575475

Order 2432.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927235C211yesmaximal, characteristic, complemented
2#11927189C211yesmaximal, characteristic
3#11926899C211yesmaximal, characteristic, complemented
4#11926876C211yesmaximal, characteristic, complemented
5#11926870C211yesmaximal, characteristic, complemented
6#11926844C211yesmaximal, characteristic, complemented
7#11926784C211yesmaximal, characteristic, complemented
8#11926776C211yesmaximal, characteristic, complemented
9#11926766C211yesmaximal, characteristic, complemented
10#11926703C211yesmaximal, characteristic, complemented
11#11926693C211yesmaximal, characteristic, complemented
12C8×D76C211yesmaximal, characteristic, complemented
13#11926537C211yesmaximal, characteristic, complemented
14#102×D19C211yesmaximal, characteristic, complemented
15C4×SD16×C19C211yesmaximal, characteristic, complemented
16C2×#64543C2211yescharacteristic
17C2×D4×D19C2211yescharacteristic
18C2×SD16×C19C2211yescharacteristic
19C4×Q8×C19C2211yescharacteristic, complemented
20C4×D4×C19C2211yescharacteristic
21#10597392C2211yescharacteristic
22#10597392C2211yescharacteristic, complemented
23C2×#64528C2211yescharacteristic, complemented
24C2×#64527C2211yescharacteristic
25#10597376—21no—
26C2×(C2×D19)⋊C4—21no—
27C2×C8×D19C2211yescharacteristic
28C2×C8×D19C2211yescharacteristic, complemented
29#10597343C2211yescharacteristic
30#10597341C2211yescharacteristic
31#10597340—21no—
32#10597338C2211yescharacteristic, complemented
33C4⋊C4×D19C2211yescharacteristic
34#10597335—21no—
35#10597332—21no—
36#10597328—21no—
37#10597322—21no—
38#10597321C2211yescharacteristic
39C4×D76C2211yescharacteristic
40#10597318—21no—
41#10597316C2211yescharacteristic, complemented
42C19×#106C2211yescharacteristic, complemented
43C19×#103C2211yescharacteristic, complemented
44C19×#102C2211yescharacteristic
45C4×C8×C19C2211yescharacteristic, complemented
46#10597289C2211yescharacteristic
47#10597289C2211yescharacteristic
48#10597278C2211yescharacteristic
49#10597278C2211yescharacteristic
50(C2×D19)⋊C8C2211yescharacteristic
51(C2×D19)⋊C8C2211yescharacteristic, complemented
52#10597273C2211yescharacteristic, complemented
53#10597273C2211yescharacteristic, complemented
54#10597267C2211yescharacteristic, complemented
55#10597266C2211yescharacteristic
56#10597265C2211yescharacteristic, complemented
57#10597264C2211yescharacteristic, complemented
58C4⋊(C19⋊C8)C2211yescharacteristic, complemented
59C23×D19—21no—
60C2×Q8×C19C2311yescharacteristic
61C2×D4×C19C2311yescharacteristic
62C22×C4×C19—21no—
63C2×C22⋊D19—21no—
64C2×C22⋊D19—21no—
65C22×Dic19—21no—
66#64543—22no—
67#64543—41no—
68D4×D19—22no—
69D4×D19—41no—
70C2×D76—21no—
71C2×D76D411yescharacteristic
72C2×D76C2311yescharacteristic
73C2×C4×D19—21no—
74C2×C4×D19C2311yescharacteristic
75C2×C4×D19C2311yescharacteristic
76C2×Dic38C2311yescharacteristic
77SD16×C19—22no—
78C2×C8×C19C2311yescharacteristic
79C2×C8×C19C2311yescharacteristic
80C4⋊C4×C19—21no—
81C4⋊C4×C19C2311yescharacteristic
82C4⋊C4×C19C2311yescharacteristic
83C22⋊C4×C19—21no—
84C42×C19—21no—
85C42×C19C2311yescharacteristic
86#64528—41no—
87#64527—41no—
88(C2×D19)⋊C4—21no—
89(C2×D19)⋊C4—21no—
90(C2×D19)⋊C4—21no—
91(C2×D19)⋊C4—21no—
92(C2×D19)⋊C4—21no—
93(C2×D19)⋊C4—21no—
94(C2×D19)⋊C4—21no—
95(C2×D19)⋊C4D411yescharacteristic
96(C2×D19)⋊C4D411yescharacteristic
97C4⋊Dic19—21no—
98C4⋊Dic19D411yescharacteristic
99C4⋊Dic19C2311yescharacteristic
100C4⋊Dic19C2311yescharacteristic
101Dic19⋊C4—21no—
102Dic19⋊C4—21no—
103Dic19⋊C4—21no—
104Dic19⋊C4—21no—
105Dic19⋊C4—21no—
106C4×Dic19—21no—
107C2×C19⋊C8C2311yescharacteristic
108C2×C19⋊C8C2311yescharacteristic
109C8×D19—41no—
110C8×D19—41no—
111C23×C19—21no—
112C22×D19—21no—
113C22×D19—42no—
114C22×D19—42no—
115C22×D19—81no—
116C22×D19C2×D411yescharacteristic
117C22×D19C2×D411yescharacteristic
118Q8×C19—21no—
119Q8×C19—21no—
120D4×C19—21no—
121D4×C19#4112yes—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—81no—
126C2×C4×C19C2×D411yescharacteristic
127C2×C4×C19C2×D411yescharacteristic
128C2×C4×C19C2411yescharacteristic
129C22⋊D19—42no—
130C22⋊D19—42no—
131C2×Dic19—21no—
132C2×Dic19—21no—
133C2×Dic19—21no—
134C2×Dic19—42no—
135C2×Dic19C2×D411yescharacteristic
136C2×Dic19C2×D411yescharacteristic
137D76—22no—
138D76—21no—
139D76—21no—
140D76—81no—
141C4×D19—21no—
142C4×D19—21no—
143C4×D19—21no—
144C4×D19—21no—
145C4×D19—42no—
146Dic38—21no—
147Dic38—21no—
148C8×C19—21no—
149C8×C19—21no—
150C19⋊C8—21no—
151C19⋊C8—21no—
152#3296—191nomaximal, Sylow
153C22×C19—22no—
154C22×C19—41no—
155C22×C19—41no—
156C22×C19C22×D411yescharacteristic
157C2×D19—21no—
158C2×D19—21no—
159C2×D19—21no—
160C2×D19—21no—
161C2×D19—21no—
162C2×D19—41no—
163C2×D19—41no—
164C2×D19—41no—
165C2×D19—84no—
166C2×D19#13512yes—
167C4×C19—21no—
168C4×C19—21no—
169C4×C19—41no—
170C4×C19—41no—
171C4×C19—41no—
172C4×C19C2×#4111yescharacteristic
173C4×C19H(5,𝔽2)11yescharacteristic
174Dic19—21no—
175Dic19—21no—
176Dic19—41no—
177Dic19—41no—
178Dic19—41no—
179#552—191no—
180#546—191no—
181#488—191no—
182#483—191no—
183#482—191no—
184#478—191no—
185#467—191no—
186#465—191no—
187#464—191no—
188#452—191no—
189#450—191no—
190C4×SD16D1911yescharacteristic, complemented
191C8×D4—191no—
192#416—191no—
193C2×#102—191no—
194C2×C19—42no—
195C2×C19#54611yescharacteristic
196C2×C19C2×#13511yescharacteristic
197C2×C19#57711yescharacteristic
198D19—22no—
199D19—41no—
200D19—81no—
201C2×#41—191no—
202C22×D4—191no—
203C2×Q16—191no—
204C2×SD16—191no—
205C2×SD16C2×D1911yescharacteristic
206C22×C8—191no—
207C22×C8—191no—
208#126—381no—
209#125—191no—
210#125—381no—
211#124—191no—
212#123—381no—
213#123—381no—
214C22⋊Q8—191no—
215C22⋊Q8—191no—
216C22⋊Q8—191no—
217#121—191no—
218#121—381no—
219#120—381no—
220C4×Q8C2×D1911yescharacteristic, complemented
221C4×D4—191no—
222C4×D4C2×D1911yescharacteristic
223#117—191no—
224#117—381no—
225C2×C4⋊C4—191no—
226C2×C22⋊C4—381no—
227#107—191no—
228#106—191no—
229#106C2×D1911yescharacteristic, complemented
230C4⋊C8—191no—
231#103—191no—
232#103—191no—
233#103—191no—
234#103C2×D1911yescharacteristic, complemented
235#102—191no—
236#102—191no—
237#102—191no—
238#102—191no—
239#102—191no—
240#102C2×D1911yescharacteristic
241C22⋊C8—191no—
242C22⋊C8—191no—
243C4×C8C2×D1911yescharacteristic, complemented
244C19#329611yescharacteristic, complemented, Sylow
245C24—381no—
246#41—382no—
247#41—761no—
248C2×Q8—191no—
249C2×Q8C22×D1911yescharacteristic
250C2×D4—191no—
251C2×D4—191no—
252C2×D4—381no—
253C2×D4—381no—
254C2×D4—382no—
255C2×D4—381no—
256C2×D4—761no—
257C2×D4C22×D1911yescharacteristic
258C22×C4—21no—
259C22×C4—191no—
260C22×C4—191no—
261C22×C4—381no—
262C22×C4—381no—
263Q16—761no—
264SD16—22no—
265SD16—761no—
266C2×C8—191no—
267C2×C8—191no—
268C2×C8—761no—
269C2×C8—761no—
270C2×C8C22×D1911yescharacteristic
271C2×C8C22×D1911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—191no—
274C4⋊C4—191no—
275C4⋊C4—191no—
276C4⋊C4—381no—
277C4⋊C4—381no—
278C4⋊C4—381no—
279C4⋊C4—381no—
280C4⋊C4—381no—
281C4⋊C4—381no—
282C4⋊C4C22×D1911yescharacteristic
283C4⋊C4C22×D1911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—191no—
286C22⋊C4—191no—
287C22⋊C4—381no—
288C22⋊C4—381no—
289C22⋊C4—381no—
290C22⋊C4—381no—
291C22⋊C4—381no—
292C22⋊C4—381no—
293C22⋊C4—381no—
294C42—21no—
295C42—381no—
296C42C22×D1911yescharacteristic
297C23—21no—
298C23—191no—
299C23—191no—
300C23—381no—
301C23—762no—
302C23—762no—
303C23—1521no—
304Q8—21no—
305Q8—21no—
306Q8—381no—
307Q8—381no—
308D4—21no—
309D4—382no—
310D4—381no—
311D4—381no—
312D4—762no—
313D4—762no—
314D4—1521no—
315D4#6454112yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—191no—
321C2×C4—191no—
322C2×C4—381no—
323C2×C4—381no—
324C2×C4—381no—
325C2×C4—381no—
326C2×C4—381no—
327C2×C4—381no—
328C2×C4—381no—
329C2×C4—762no—
330C2×C4—762no—
331C2×C4D4×D1911yescharacteristic
332C2×C4D4×D1911yescharacteristic
333C2×C4C23×D1911yescharacteristic
334C8—21no—
335C8—21no—
336C8—381no—
337C8—381no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—192no—
342C22—381no—
343C22—381no—
344C22—381no—
345C22—381no—
346C22—381no—
347C22—761no—
348C22—761no—
349C22—761no—
350C22—1524no—
351C22C2×D4×D1911yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—381no—
358C4—381no—
359C4—761no—
360C4—761no—
361C4—761no—
362C4C2×#6454111yescharacteristic
363C4#1059743511yescharacteristic
364C2—42no—
365C2—382no—
366C2—761no—
367C2—1521no—
368C2#1192719011yescharacteristic
369C2#135×D1911yescharacteristic
370C2#1192735011yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC4×SD16×C19C2
socleC22×C19C22×D4
prime radical#11927189C2
hypercenterC4×SD16D19
hypocenterC19#3296
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #11927235C2semidirect
3. #11926899C2semidirect
4. #11926876C2semidirect
5. #11926870C2semidirect
6. #11926844C2semidirect
7. #11926784C2semidirect
8. #11926776C2semidirect
9. #11926766C2semidirect
10. #11926703C2semidirect
11. #11926693C2semidirect
12. C8×D76C2semidirect
13. #11926537C2semidirect
14. #102×D19C2semidirect
15. C4×SD16×C19C2semidirect
19. C4×Q8×C19C22semidirect
22. #10597392C22semidirect
23. C2×#64528C22semidirect
28. C2×C8×D19C22semidirect
32. #10597338C22semidirect
41. #10597316C22semidirect
42. C19×#106C22semidirect
43. C19×#103C22semidirect
45. C4×C8×C19C22semidirect
51. (C2×D19)⋊C8C22semidirect
52. #10597273C22semidirect
53. #10597273C22semidirect
54. #10597267C22semidirect
56. #10597265C22semidirect
57. #10597264C22semidirect
58. C4⋊(C19⋊C8)C22semidirect
190. C4×SD16D19semidirect
220. C4×Q8C2×D19semidirect
229. #106C2×D19semidirect
234. #103C2×D19semidirect
243. C4×C8C2×D19semidirect
244. C19#3296semidirect

Maximal subgroups

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

subgroupindex
#119272352
#119271892
#119268992
#119268762
#119268702
#119268442
#119267842
#119267762
#119267662
#119267032
#119266932
C8×D762
#119265372
#102×D192
C4×SD16×C192
#329619