Finite Group Databasebeta

← #14575589

Subgroups — #14575589

Order 2432.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927194C211yesmaximal, characteristic, complemented
2#11927182C211yesmaximal, characteristic, complemented
3#11926905C211yesmaximal, characteristic, complemented
4#11926873C211yesmaximal, characteristic, complemented
5#11926863C211yesmaximal, characteristic, complemented
6#11926832C211yesmaximal, characteristic, complemented
7#11926795C211yesmaximal, characteristic, complemented
8#11926770C211yesmaximal, characteristic, complemented
9#11926761C211yesmaximal, characteristic, complemented
10#11926676C211yesmaximal, characteristic, complemented
11#11926656C211yesmaximal, characteristic, complemented
12#11926618C211yesmaximal, characteristic, complemented
13#11926545C211yesmaximal, characteristic, complemented
14#102×D19C211yesmaximal, characteristic, complemented
15C19×#449C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C2×#64543—21no—
18C2×D4×D19C2211yescharacteristic
19C2×SD16×C19C2211yescharacteristic, complemented
20C2×D8×C19C2211yescharacteristic
21C19×#121C2211yescharacteristic, complemented
22#10597393C2211yescharacteristic
23#10597392C2211yescharacteristic
24#10597385—21no—
25#10597384C2211yescharacteristic
26#10597383—21no—
27#10597381—21no—
28D4×Dic19C2211yescharacteristic
29D4×Dic19C2211yescharacteristic, complemented
30C2×#64525C2211yescharacteristic
31#10597376C2211yescharacteristic
32#10597375—21no—
33C4×C22⋊D19C2211yescharacteristic
34C2×(C2×D19)⋊C4—21no—
35C2×C4⋊Dic19C2211yescharacteristic, complemented
36C2×#64520C2211yescharacteristic, complemented
37C2×C8×D19C2211yescharacteristic
38C4⋊C4×D19C2211yescharacteristic
39#10597334C2211yescharacteristic, complemented
40#10597329—21no—
41#10597324—21no—
42C19×#103C2211yescharacteristic, complemented
43C19×#102C2211yescharacteristic
44C19×C22⋊C8C2211yescharacteristic, complemented
45#10597292C2211yescharacteristic, complemented
46#10597292C2211yescharacteristic, complemented
47#10597289C2211yescharacteristic
48#10597289C2211yescharacteristic
49#10597289C2211yescharacteristic, complemented
50#10597278C2211yescharacteristic
51#10597278C2211yescharacteristic
52(C2×D19)⋊C8C2211yescharacteristic
53#10597274C2211yescharacteristic, complemented
54#10597274C2211yescharacteristic, complemented
55#10597272C2211yescharacteristic, complemented
56Dic19⋊C8C2211yescharacteristic, complemented
57#10597266C2211yescharacteristic
58#10597265C2211yescharacteristic, complemented
59C23×D19—21no—
60#41×C19—22no—
61#41×C19—41no—
62C2×Q8×C19C2311yescharacteristic
63C2×D4×C19—21no—
64C2×D4×C19—21no—
65C2×D4×C19C2311yescharacteristic
66C2×D4×C19C2311yescharacteristic
67C22×C4×C19—21no—
68C22×C4×C19C2311yescharacteristic
69C2×C22⋊D19—21no—
70C2×C22⋊D19—21no—
71C2×C22⋊D19—21no—
72C2×C22⋊D19D411yescharacteristic
73C22×Dic19—21no—
74C22×Dic19—21no—
75C22×Dic19—21no—
76#64543—44no—
77D4×D19—22no—
78D4×D19—41no—
79C2×D76C2311yescharacteristic
80C2×C4×D19—21no—
81C2×C4×D19C2311yescharacteristic
82C2×Dic38—21no—
83SD16×C19—41no—
84D8×C19—22no—
85C2×C8×C19C2311yescharacteristic
86C2×C8×C19C2311yescharacteristic
87C4⋊C4×C19C2311yescharacteristic
88C22⋊C4×C19—21no—
89C22⋊Dic19—21no—
90C22⋊Dic19—21no—
91C22⋊Dic19—21no—
92C22⋊Dic19D411yescharacteristic
93#64525—41no—
94(C2×D19)⋊C4—21no—
95(C2×D19)⋊C4—21no—
96(C2×D19)⋊C4—21no—
97(C2×D19)⋊C4—21no—
98(C2×D19)⋊C4D411yescharacteristic
99C4⋊Dic19—21no—
100C4⋊Dic19C2311yescharacteristic
101C4⋊Dic19C2311yescharacteristic
102C4⋊Dic19C2311yescharacteristic
103Dic19⋊C4—21no—
104Dic19⋊C4—21no—
105Dic19⋊C4—21no—
106Dic19⋊C4D411yescharacteristic
107C4×Dic19C2311yescharacteristic
108#64520—41no—
109C2×C19⋊C8C2311yescharacteristic
110C2×C19⋊C8C2311yescharacteristic
111C8×D19—41no—
112C23×C19—21no—
113C23×C19—21no—
114C23×C19C2×D411yescharacteristic
115C22×D19—21no—
116C22×D19—42no—
117C22×D19—42no—
118C22×D19—81no—
119C22×D19C2×D411yescharacteristic
120Q8×C19—21no—
121Q8×C19—21no—
122D4×C19—21no—
123D4×C19—21no—
124D4×C19—21no—
125D4×C19—42no—
126D4×C19—42no—
127D4×C19#4112yescomplemented
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—42no—
133C2×C4×C19C2×D411yescharacteristic
134C2×C4×C19C2411yescharacteristic
135C22⋊D19—22no—
136C22⋊D19—42no—
137C22⋊D19—42no—
138C22⋊D19—81no—
139C2×Dic19—21no—
140C2×Dic19—21no—
141C2×Dic19—21no—
142C2×Dic19—42no—
143C2×Dic19—42no—
144C2×Dic19—81no—
145C2×Dic19C2×D411yescharacteristic
146C2×Dic19C2×D411yescharacteristic
147C2×Dic19C2×D411yescharacteristic
148D76—21no—
149D76—21no—
150C4×D19—21no—
151C4×D19—21no—
152C4×D19—42no—
153Dic38—42no—
154C8×C19—21no—
155C8×C19—21no—
156C19⋊C8—21no—
157C19⋊C8—21no—
158#3306—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×C19C22×D411yescharacteristic
169C2×D19—21no—
170C2×D19—21no—
171C2×D19—41no—
172C2×D19—41no—
173C2×D19—41no—
174C2×D19—84no—
175C2×D19AGL(1,ℤ/8)12yes—
176C4×C19—21no—
177C4×C19—41no—
178C4×C19—41no—
179C4×C19C2×#4111yescharacteristic
180C4×C19H(5,𝔽2)11yescharacteristic
181Dic19—21no—
182Dic19—21no—
183Dic19—21no—
184Dic19—41no—
185Dic19—41no—
186Dic19—41no—
187#547—191no—
188#546—191no—
189#489—191no—
190#483—191no—
191#481—191no—
192#476—191no—
193#469—191no—
194#465—191no—
195#463—191no—
196#449D1911yescharacteristic, complemented
197#447—191no—
198#442—191no—
199#435—191no—
200#417—191no—
201C2×#102—191no—
202C2×C19—42no—
203C2×C19—41no—
204C2×C19—81no—
205C2×C19#54611yescharacteristic
206C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
207C2×C19#57711yescharacteristic
208D19—22no—
209D19—81no—
210C2×#41—381no—
211C2×#41C2×D1911yescharacteristic
212C22×D4—191no—
213C2×SD16C2×D1911yescharacteristic, complemented
214C2×D8—191no—
215C2×D8C2×D1911yescharacteristic
216C2×M16—191no—
217C22×C8—191no—
218C4⋊Q8—191no—
219#124—191no—
220#123—381no—
221#123—381no—
222#123—381no—
223C22⋊Q8—191no—
224C22⋊Q8—381no—
225#121—191no—
226#121—191no—
227#121—381no—
228#121C2×D1911yescharacteristic, complemented
229#120—381no—
230C4×D4—191no—
231C4×D4—191no—
232C4×D4—191no—
233C2×C4⋊C4—191no—
234C2×C4⋊C4—191no—
235C2×C22⋊C4—381no—
236#106—191no—
237#106—191no—
238#106—191no—
239C4⋊C8—191no—
240#103—191no—
241#103—191no—
242#103C2×D1911yescharacteristic, complemented
243#102—191no—
244#102—191no—
245#102—191no—
246#102—191no—
247#102—191no—
248#102—191no—
249#102C2×D1911yescharacteristic
250C22⋊C8—191no—
251C22⋊C8C2×D1911yescharacteristic, complemented
252#97—191no—
253C19#330611yescharacteristic, complemented, Sylow
254C24—381no—
255#41—22no—
256#41—41no—
257#41—764no—
258C2×Q8—381no—
259C2×Q8C22×D1911yescharacteristic
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—191no—
263C2×D4—191no—
264C2×D4—381no—
265C2×D4—382no—
266C2×D4—381no—
267C2×D4—381no—
268C2×D4—761no—
269C2×D4C22×D1911yescharacteristic
270C2×D4C22×D1911yescharacteristic
271C22×C4—21no—
272C22×C4—191no—
273C22×C4—381no—
274C22×C4—381no—
275C22×C4—381no—
276C22×C4—381no—
277C22×C4C22×D1911yescharacteristic
278SD16—41no—
279D8—22no—
280D8—761no—
281M16—761no—
282C2×C8—191no—
283C2×C8—191no—
284C2×C8—761no—
285C2×C8C22×D1911yescharacteristic
286C2×C8C22×D1911yescharacteristic
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⋊C4C22×D1911yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—191no—
298C22⋊C4—191no—
299C22⋊C4—381no—
300C22⋊C4—381no—
301C22⋊C4—381no—
302C22⋊C4—381no—
303C22⋊C4—381no—
304C22⋊C4—381no—
305C22⋊C4—381no—
306C42—191no—
307C23—21no—
308C23—21no—
309C23—191no—
310C23—381no—
311C23—762no—
312C23—762no—
313C23—1521no—
314C23D4×D1911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—762no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—42no—
323D4—382no—
324D4—381no—
325D4—381no—
326D4—762no—
327D4—762no—
328D4—1521no—
329D4#6454312yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—191no—
336C2×C4—191no—
337C2×C4—191no—
338C2×C4—381no—
339C2×C4—381no—
340C2×C4—381no—
341C2×C4—381no—
342C2×C4—381no—
343C2×C4—762no—
344C2×C4—762no—
345C2×C4—762no—
346C2×C4—1521no—
347C2×C4D4×D1911yescharacteristic
348C2×C4C23×D1911yescharacteristic
349C8—21no—
350C8—21no—
351C8—381no—
352C8—381no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—192no—
363C22—381no—
364C22—381no—
365C22—761no—
366C22—761no—
367C22—761no—
368C22—1524no—
369C22C2×D4×D1911yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—381no—
374C4—381no—
375C4—381no—
376C4—761no—
377C4—761no—
378C4—761no—
379C4C2×#6454311yescharacteristic
380C4#1059743011yescharacteristic
381C2—41no—
382C2—42no—
383C2—81no—
384C2—382no—
385C2—1521no—
386C2#1192718111yescharacteristic
387C2AGL(1,ℤ/8)×D1911yescharacteristic
388C2#1192735111yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#449C2
socleC22×C19C22×D4
hypercenter#449D19
hypocenterC19#3306
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #11927194C2semidirect
2. #11927182C2semidirect
3. #11926905C2semidirect
4. #11926873C2semidirect
5. #11926863C2semidirect
6. #11926832C2semidirect
7. #11926795C2semidirect
8. #11926770C2semidirect
9. #11926761C2semidirect
10. #11926676C2semidirect
11. #11926656C2semidirect
12. #11926618C2semidirect
13. #11926545C2semidirect
14. #102×D19C2semidirect
15. C19×#449C2semidirect
19. C2×SD16×C19C22semidirect
21. C19×#121C22semidirect
29. D4×Dic19C22semidirect
35. C2×C4⋊Dic19C22semidirect
36. C2×#64520C22semidirect
39. #10597334C22semidirect
42. C19×#103C22semidirect
44. C19×C22⋊C8C22semidirect
45. #10597292C22semidirect
46. #10597292C22semidirect
49. #10597289C22semidirect
53. #10597274C22semidirect
54. #10597274C22semidirect
55. #10597272C22semidirect
56. Dic19⋊C8C22semidirect
58. #10597265C22semidirect
127. D4×C19#41semidirect
196. #449D19semidirect
213. C2×SD16C2×D19semidirect
228. #121C2×D19semidirect
242. #103C2×D19semidirect
251. C22⋊C8C2×D19semidirect
253. C19#3306semidirect
329. D4#64543semidirect

Maximal subgroups

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

subgroupindex
#119271942
#119271822
#119269052
#119268732
#119268632
#119268322
#119267952
#119267702
#119267612
#119266762
#119266562
#119266182
#119265452
#102×D192
C19×#4492
#330619