Finite Group Databasebeta

← #14575649

Subgroups — #14575649

Order 2432.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927228C211yesmaximal, characteristic, complemented
2D4×C22⋊D19C211yesmaximal, characteristic
3#11926907C211yesmaximal, characteristic, complemented
4#11926869C211yesmaximal, characteristic, complemented
5#11926856C211yesmaximal, characteristic, complemented
6#11926846C211yesmaximal, characteristic, complemented
7#11926792C211yesmaximal, characteristic, complemented
8#11926770C211yesmaximal, characteristic, complemented
9#11926742C211yesmaximal, characteristic, complemented
10#11926693C211yesmaximal, characteristic, complemented
11#11926645C211yesmaximal, characteristic, complemented
12#11926618C211yesmaximal, characteristic, complemented
13#11926549C211yesmaximal, characteristic, complemented
14#102×D19C211yesmaximal, characteristic, complemented
15C19×#450C211yesmaximal, characteristic, complemented
16C22×D4×C19C2211yescharacteristic
17C22×C22⋊D19—21no—
18C2×D4×D19C2211yescharacteristic
19C2×SD16×C19C2211yescharacteristic
20C2×SD16×C19C2211yescharacteristic, complemented
21C19×C22⋊Q8C2211yescharacteristic, complemented
22#10597399—21no—
23#10597392C2211yescharacteristic, complemented
24Q8×Dic19C2211yescharacteristic, complemented
25C2×#64527C2211yescharacteristic, complemented
26#10597386C2211yescharacteristic
27#10597385—21no—
28#10597384C2211yescharacteristic
29#10597383—21no—
30D4×Dic19C2211yescharacteristic
31#10597376C2211yescharacteristic
32C4×C22⋊D19C2211yescharacteristic
33#10597372C2211yescharacteristic, complemented
34C2×#64520C2211yescharacteristic, complemented
35C2×C8×D19C2211yescharacteristic, complemented
36#10597338—21no—
37C4⋊C4×D19C2211yescharacteristic, complemented
38#10597336C2211yescharacteristic, complemented
39#10597335—21no—
40#10597329—21no—
41#10597325—21no—
42C19×#102C2211yescharacteristic
43C19×#102C2211yescharacteristic, complemented
44C19×C22⋊C8C2211yescharacteristic, complemented
45#10597292C2211yescharacteristic, complemented
46#10597289C2211yescharacteristic
47#10597289C2211yescharacteristic
48#10597289C2211yescharacteristic, complemented
49#10597289C2211yescharacteristic, complemented
50#10597278C2211yescharacteristic, complemented
51#10597278C2211yescharacteristic, complemented
52(C2×D19)⋊C8C2211yescharacteristic, complemented
53#10597275C2211yescharacteristic, complemented
54#10597274C2211yescharacteristic, complemented
55#10597272C2211yescharacteristic, complemented
56Dic19⋊C8C2211yescharacteristic, complemented
57#10597266C2211yescharacteristic, complemented
58#10597264C2211yescharacteristic, complemented
59C24×C19—21no—
60C23×D19—21no—
61C2×Q8×C19C2311yescharacteristic
62C2×D4×C19—22no—
63C2×D4×C19—21no—
64C2×D4×C19—41no—
65C2×D4×C19C2311yescharacteristic
66C2×D4×C19C2311yescharacteristic
67C22×C4×C19C2311yescharacteristic
68C2×C22⋊D19—21no—
69C2×C22⋊D19—21no—
70C2×C22⋊D19—21no—
71C2×C22⋊D19—21no—
72C2×C22⋊D19—21no—
73C2×C22⋊D19—44no—
74C2×C22⋊D19D411yescharacteristic
75C22×Dic19—21no—
76D4×D19—22no—
77D4×D19—41no—
78C2×D76C2311yescharacteristic
79C2×C4×D19—21no—
80C2×C4×D19C2311yescharacteristic
81SD16×C19—22no—
82SD16×C19—41no—
83C2×C8×C19C2311yescharacteristic
84C2×C8×C19C2311yescharacteristic
85C4⋊C4×C19—21no—
86C4⋊C4×C19C2311yescharacteristic
87C22⋊C4×C19—21no—
88C22⋊Dic19—21no—
89C22⋊Dic19—21no—
90C22⋊Dic19—21no—
91C22⋊Dic19D411yescharacteristic
92#64527—41no—
93(C2×D19)⋊C4—21no—
94(C2×D19)⋊C4—21no—
95(C2×D19)⋊C4D411yescharacteristic
96C4⋊Dic19—21no—
97C4⋊Dic19—21no—
98C4⋊Dic19C2311yescharacteristic
99C4⋊Dic19C2311yescharacteristic
100C4⋊Dic19C2311yescharacteristic
101Dic19⋊C4—21no—
102Dic19⋊C4—21no—
103Dic19⋊C4—21no—
104Dic19⋊C4D411yescharacteristic
105C4×Dic19—21no—
106C4×Dic19—21no—
107C4×Dic19C2311yescharacteristic
108#64520—41no—
109C2×C19⋊C8C2311yescharacteristic
110C2×C19⋊C8C2311yescharacteristic
111C8×D19—41no—
112C23×C19—21no—
113C23×C19—21no—
114C23×C19—42no—
115C23×C19—42no—
116C23×C19—81no—
117C23×C19C2×D411yescharacteristic
118C22×D19—21no—
119C22×D19—42no—
120C22×D19—42no—
121C22×D19—81no—
122C22×D19C2×D411yescharacteristic
123Q8×C19—21no—
124Q8×C19—21no—
125D4×C19—21no—
126D4×C19—21no—
127D4×C19—21no—
128D4×C19—42no—
129D4×C19#4112yes—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19C2×D411yescharacteristic
135C2×C4×C19C2411yescharacteristic
136C22⋊D19—22no—
137C22⋊D19—42no—
138C22⋊D19—42no—
139C22⋊D19—42no—
140C22⋊D19—42no—
141C22⋊D19—81no—
142C2×Dic19—21no—
143C2×Dic19—21no—
144C2×Dic19—21no—
145C2×Dic19—42no—
146C2×Dic19C2×D411yescharacteristic
147C2×Dic19C2×D411yescharacteristic
148C2×Dic19C2×D411yescharacteristic
149D76—21no—
150D76—21no—
151C4×D19—21no—
152C4×D19—21no—
153C4×D19—42no—
154C8×C19—21no—
155C8×C19—21no—
156C19⋊C8—21no—
157C19⋊C8—21no—
158#3310—191nomaximal, Sylow
159C22×C19—22no—
160C22×C19—21no—
161C22×C19—21no—
162C22×C19—21no—
163C22×C19—41no—
164C22×C19—41no—
165C22×C19—41no—
166C22×C19—41no—
167C22×C19—41no—
168C22×C19—84no—
169C22×C19C22×D411yescharacteristic
170C2×D19—21no—
171C2×D19—21no—
172C2×D19—41no—
173C2×D19—41no—
174C2×D19—41no—
175C2×D19—84no—
176C2×D19AGL(1,ℤ/8)12yes—
177C4×C19—21no—
178C4×C19—41no—
179C4×C19—41no—
180C4×C19C2×#4111yescharacteristic
181C4×C19H(5,𝔽2)11yescharacteristic
182Dic19—21no—
183Dic19—21no—
184Dic19—21no—
185Dic19—41no—
186Dic19—41no—
187Dic19—41no—
188#552—191no—
189D42—191no—
190#490—191no—
191#482—191no—
192#480—191no—
193#478—191no—
194#468—191no—
195#465—191no—
196#460—191no—
197#450—191no—
198#450D1911yescharacteristic, complemented
199#440—191no—
200#435—191no—
201#418—191no—
202C2×#102—191no—
203C2×C19—42no—
204C2×C19—41no—
205C2×C19—81no—
206C2×C19#54611yescharacteristic
207C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
208C2×C19#57711yescharacteristic
209D19—22no—
210D19—81no—
211C22×D4—191no—
212C22×D4—381no—
213C22×D4C2×D1911yescharacteristic
214C2×SD16—191no—
215C2×SD16C2×D1911yescharacteristic
216C2×SD16C2×D1911yescharacteristic, complemented
217C2×M16—191no—
218C22×C8—191no—
219#127—191no—
220#126—381no—
221#125—191no—
222#125—381no—
223#123—381no—
224C22⋊Q8—191no—
225C22⋊Q8C2×D1911yescharacteristic, complemented
226#121—191no—
227#121—191no—
228#121—381no—
229#120—381no—
230#120—381no—
231C4×Q8—191no—
232C4×D4—191no—
233C4×D4—191no—
234#117—191no—
235#117—381no—
236C2×C4⋊C4—191no—
237#107—191no—
238#107—191no—
239#106—191no—
240C4⋊C8—191no—
241#103—191no—
242#102—191no—
243#102—191no—
244#102—191no—
245#102—191no—
246#102—191no—
247#102—191no—
248#102—191no—
249#102C2×D1911yescharacteristic
250#102C2×D1911yescharacteristic, complemented
251C22⋊C8—191no—
252C22⋊C8C2×D1911yescharacteristic, complemented
253#97—191no—
254C19#331011yescharacteristic, complemented, Sylow
255C24—21no—
256C24—381no—
257C2×Q8C22×D1911yescharacteristic
258C2×D4—22no—
259C2×D4—21no—
260C2×D4—41no—
261C2×D4—191no—
262C2×D4—191no—
263C2×D4—381no—
264C2×D4—381no—
265C2×D4—381no—
266C2×D4—382no—
267C2×D4—381no—
268C2×D4—381no—
269C2×D4—761no—
270C2×D4—764no—
271C2×D4C22×D1911yescharacteristic
272C2×D4C22×D1911yescharacteristic
273C22×C4—191no—
274C22×C4—381no—
275C22×C4—381no—
276C22×C4C22×D1911yescharacteristic
277SD16—22no—
278SD16—41no—
279SD16—761no—
280M16—761no—
281C2×C8—191no—
282C2×C8—191no—
283C2×C8—761no—
284C2×C8C22×D1911yescharacteristic
285C2×C8C22×D1911yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—191no—
288C4⋊C4—191no—
289C4⋊C4—191no—
290C4⋊C4—191no—
291C4⋊C4—381no—
292C4⋊C4—381no—
293C4⋊C4—381no—
294C4⋊C4—381no—
295C4⋊C4—381no—
296C4⋊C4C22×D1911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—191no—
299C22⋊C4—191no—
300C22⋊C4—381no—
301C22⋊C4—381no—
302C22⋊C4—381no—
303C22⋊C4—381no—
304C22⋊C4—381no—
305C42—191no—
306C42—381no—
307C42—381no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—191no—
314C23—381no—
315C23—762no—
316C23—762no—
317C23—1521no—
318C23D4×D1911yescharacteristic
319Q8—21no—
320Q8—21no—
321D4—21no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—382no—
326D4—381no—
327D4—381no—
328D4—762no—
329D4—762no—
330D4—762no—
331D4—762no—
332D4—1521no—
333D4#6454312yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—191no—
339C2×C4—191no—
340C2×C4—191no—
341C2×C4—381no—
342C2×C4—381no—
343C2×C4—381no—
344C2×C4—381no—
345C2×C4—381no—
346C2×C4—762no—
347C2×C4—762no—
348C2×C4D4×D1911yescharacteristic
349C2×C4C23×D1911yescharacteristic
350C8—21no—
351C8—21no—
352C8—381no—
353C8—381no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—84no—
364C22—192no—
365C22—381no—
366C22—381no—
367C22—761no—
368C22—761no—
369C22—761no—
370C22—1524no—
371C22C2×D4×D1911yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—381no—
376C4—381no—
377C4—381no—
378C4—761no—
379C4—761no—
380C4—761no—
381C4C2×#6454311yescharacteristic
382C4#1059743011yescharacteristic
383C2—41no—
384C2—42no—
385C2—81no—
386C2—382no—
387C2—1521no—
388C2#1192718111yescharacteristic
389C2AGL(1,ℤ/8)×D1911yescharacteristic
390C2#1192735011yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#450C2
socleC22×C19C22×D4
prime radicalD4×C22⋊D19C2
hypercenter#450D19
hypocenterC19#3310
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. #11927228C2semidirect
3. #11926907C2semidirect
4. #11926869C2semidirect
5. #11926856C2semidirect
6. #11926846C2semidirect
7. #11926792C2semidirect
8. #11926770C2semidirect
9. #11926742C2semidirect
10. #11926693C2semidirect
11. #11926645C2semidirect
12. #11926618C2semidirect
13. #11926549C2semidirect
14. #102×D19C2semidirect
15. C19×#450C2semidirect
20. C2×SD16×C19C22semidirect
21. C19×C22⋊Q8C22semidirect
23. #10597392C22semidirect
24. Q8×Dic19C22semidirect
25. C2×#64527C22semidirect
33. #10597372C22semidirect
34. C2×#64520C22semidirect
35. C2×C8×D19C22semidirect
37. C4⋊C4×D19C22semidirect
38. #10597336C22semidirect
43. C19×#102C22semidirect
44. C19×C22⋊C8C22semidirect
45. #10597292C22semidirect
48. #10597289C22semidirect
49. #10597289C22semidirect
50. #10597278C22semidirect
51. #10597278C22semidirect
52. (C2×D19)⋊C8C22semidirect
53. #10597275C22semidirect
54. #10597274C22semidirect
55. #10597272C22semidirect
56. Dic19⋊C8C22semidirect
57. #10597266C22semidirect
58. #10597264C22semidirect
198. #450D19semidirect
216. C2×SD16C2×D19semidirect
225. C22⋊Q8C2×D19semidirect
250. #102C2×D19semidirect
252. C22⋊C8C2×D19semidirect
254. C19#3310semidirect

Maximal subgroups

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

subgroupindex
#119272282
D4×C22⋊D192
#119269072
#119268692
#119268562
#119268462
#119267922
#119267702
#119267422
#119266932
#119266452
#119266182
#119265492
#102×D192
C19×#4502
#331019