Finite Group Databasebeta

← #14575602

Subgroups — #14575602

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#11927185C211yesmaximal, characteristic, complemented
3#11926905C211yesmaximal, characteristic, complemented
4#11926872C211yesmaximal, characteristic, complemented
5#11926864C211yesmaximal, characteristic, complemented
6#11926833C211yesmaximal, characteristic, complemented
7#11926796C211yesmaximal, characteristic, complemented
8#11926761C211yesmaximal, characteristic, complemented
9#11926688C211yesmaximal, characteristic, complemented
10#11926677C211yesmaximal, characteristic, complemented
11#11926653C211yesmaximal, characteristic, complemented
12#11926615C211yesmaximal, characteristic, complemented
13#11926544C211yesmaximal, characteristic, complemented
14C2×#10597278C211yesmaximal, characteristic, complemented
15C19×#465C211yesmaximal, characteristic, complemented
16C2×#64545C2211yescharacteristic
17C2×#64543—21no—
18C22×D76C2211yescharacteristic
19C2×SD16×C19C2211yescharacteristic, complemented
20C22×C8×C19C2211yescharacteristic
21C19×C22⋊Q8C2211yescharacteristic
22C19×#121C2211yescharacteristic
23#10597393C2211yescharacteristic
24#10597384C2211yescharacteristic, complemented
25#10597381—21no—
26D4×Dic19C2211yescharacteristic, complemented
27C2×#64525C2211yescharacteristic
28C2×#64525C2211yescharacteristic
29C4×C22⋊D19C2211yescharacteristic
30C2×C4⋊Dic19C2211yescharacteristic
31C2×#64515C2211yescharacteristic, complemented
32#10597341—21no—
33#10597341C2211yescharacteristic
34#10597340—21no—
35#10597339C2211yescharacteristic
36C4⋊C4×D19C2211yescharacteristic, complemented
37#10597334C2211yescharacteristic, complemented
38#10597329—21no—
39#10597328—21no—
40C22⋊C4×D19—21no—
41#10597324—21no—
42C19×#106C2211yescharacteristic, complemented
43C19×#103C2211yescharacteristic, complemented
44C19×#102C2211yescharacteristic, complemented
45#10597292C2211yescharacteristic, complemented
46#10597292C2211yescharacteristic, complemented
47C22⋊(C19⋊C8)C2211yescharacteristic
48#10597278C2211yescharacteristic
49#10597278C2211yescharacteristic
50#10597278C2211yescharacteristic
51#10597278C2211yescharacteristic
52(C2×D19)⋊C8C2211yescharacteristic, complemented
53#10597272C2211yescharacteristic, complemented
54Dic19⋊C8C2211yescharacteristic, complemented
55#10597266C2211yescharacteristic
56#10597266C2211yescharacteristic
57#10597265C2211yescharacteristic, complemented
58#10597265C2211yescharacteristic, complemented
59C23×D19—21no—
60C2×Q8×C19C2311yescharacteristic
61C2×D4×C19—21no—
62C2×D4×C19C2311yescharacteristic
63C22×C4×C19C2311yescharacteristic
64C2×C22⋊D19—21no—
65C2×C22⋊D19D411yescharacteristic
66C22×Dic19—21no—
67C22×Dic19—21no—
68#64545—22no—
69#64545—41no—
70#64543—44no—
71C2×D76—22no—
72C2×D76—21no—
73C2×D76—21no—
74C2×D76—21no—
75C2×D76—41no—
76C2×D76C2311yescharacteristic
77C2×D76C2311yescharacteristic
78C2×C4×D19—21no—
79C2×C4×D19—21no—
80C2×C4×D19—21no—
81C2×C4×D19C2311yescharacteristic
82C2×Dic38—21no—
83SD16×C19—41no—
84C2×C8×C19—41no—
85C2×C8×C19C2311yescharacteristic
86C2×C8×C19C2311yescharacteristic
87C4⋊C4×C19—21no—
88C4⋊C4×C19C2311yescharacteristic
89C4⋊C4×C19C2311yescharacteristic
90C22⋊C4×C19—21no—
91C22⋊C4×C19—21no—
92C22⋊Dic19—21no—
93C22⋊Dic19—21no—
94C22⋊Dic19D411yescharacteristic
95#64525—22no—
96#64525—41no—
97(C2×D19)⋊C4—21no—
98(C2×D19)⋊C4—21no—
99(C2×D19)⋊C4—21no—
100(C2×D19)⋊C4—21no—
101(C2×D19)⋊C4D411yescharacteristic
102C4⋊Dic19—21no—
103C4⋊Dic19C2311yescharacteristic
104C4⋊Dic19C2311yescharacteristic
105Dic19⋊C4—21no—
106Dic19⋊C4—21no—
107Dic19⋊C4D411yescharacteristic
108C4×Dic19C2311yescharacteristic
109C2×C19⋊C8C2311yescharacteristic
110C2×C19⋊C8C2311yescharacteristic
111#64515—41no—
112C23×C19—21no—
113C23×C19C2×D411yescharacteristic
114C22×D19—21no—
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—42no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19C2×D411yescharacteristic
131C2×C4×C19C2411yescharacteristic
132C22⋊D19—22no—
133C22⋊D19—42no—
134C2×Dic19—21no—
135C2×Dic19—21no—
136C2×Dic19—42no—
137C2×Dic19—42no—
138C2×Dic19C2×D411yescharacteristic
139C2×Dic19C2×D411yescharacteristic
140C2×Dic19C2×D411yescharacteristic
141D76—21no—
142D76—21no—
143D76—21no—
144D76—42no—
145D76—42no—
146D76—81no—
147D76#4112yescomplemented
148C4×D19—21no—
149C4×D19—21no—
150C4×D19—42no—
151C4×D19—42no—
152C4×D19—81no—
153Dic38—42no—
154C8×C19—21no—
155C8×C19—21no—
156C19⋊C8—21no—
157C19⋊C8—21no—
158#3306—191nomaximal, Sylow
159C22×C19—21no—
160C22×C19—21no—
161C22×C19—41no—
162C22×C19—41no—
163C22×C19—41no—
164C22×C19AGL(1,ℤ/8)12yes—
165C22×C19C22×D411yescharacteristic
166C2×D19—21no—
167C2×D19—22no—
168C2×D19—21no—
169C2×D19—21no—
170C2×D19—41no—
171C2×D19—41no—
172C2×D19—41no—
173C2×D19—41no—
174C2×D19—41no—
175C2×D19—84no—
176C4×C19—21no—
177C4×C19—41no—
178C4×C19—41no—
179C4×C19—41no—
180C4×C19C2×#4111yescharacteristic
181C4×C19H(5,𝔽2)11yescharacteristic
182Dic19—21no—
183Dic19—21no—
184Dic19—21no—
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#465D1911yescharacteristic, complemented
195#463—191no—
196#449—191no—
197#447—191no—
198#442—191no—
199#435—191no—
200#417—191no—
201C2×#102—191no—
202C2×C19—22no—
203C2×C19—81no—
204C2×C19#54611yescharacteristic
205C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
206C2×C19#57711yescharacteristic
207D19—41no—
208D19—42no—
209D19—81no—
210C2×#41—191no—
211C2×#41—381no—
212C22×D4—191no—
213C2×SD16C2×D1911yescharacteristic, complemented
214C2×D8—191no—
215C2×D8—191no—
216C2×M16—191no—
217C22×C8C2×D1911yescharacteristic
218C4⋊Q8—191no—
219#124—191no—
220#123—381no—
221#123—381no—
222#123—381no—
223C22⋊Q8—381no—
224C22⋊Q8C2×D1911yescharacteristic
225#121—191no—
226#121—191no—
227#121—381no—
228#121C2×D1911yescharacteristic
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#106C2×D1911yescharacteristic, complemented
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, complemented
250C22⋊C8—191no—
251C22⋊C8—191no—
252#97—191no—
253C19#330611yescharacteristic, complemented, Sylow
254C24—381no—
255#41—382no—
256#41—761no—
257#41—764no—
258C2×Q8—381no—
259C2×Q8C22×D1911yescharacteristic
260C2×D4—21no—
261C2×D4—191no—
262C2×D4—191no—
263C2×D4—191no—
264C2×D4—382no—
265C2×D4—381no—
266C2×D4—381no—
267C2×D4—381no—
268C2×D4—381no—
269C2×D4—761no—
270C2×D4C22×D1911yescharacteristic
271C22×C4—191no—
272C22×C4—381no—
273C22×C4—381no—
274C22×C4—381no—
275C22×C4—381no—
276C22×C4—381no—
277C22×C4C22×D1911yescharacteristic
278SD16—41no—
279D8—382no—
280D8—761no—
281M16—761no—
282C2×C8—41no—
283C2×C8—191no—
284C2×C8—191no—
285C2×C8C22×D1911yescharacteristic
286C2×C8C22×D1911yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—191no—
289C4⋊C4—191no—
290C4⋊C4—191no—
291C4⋊C4—381no—
292C4⋊C4—381no—
293C4⋊C4—381no—
294C4⋊C4C22×D1911yescharacteristic
295C4⋊C4C22×D1911yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—191no—
299C22⋊C4—191no—
300C22⋊C4—381no—
301C22⋊C4—381no—
302C22⋊C4—381no—
303C22⋊C4—381no—
304C22⋊C4—381no—
305C22⋊C4—381no—
306C42—191no—
307C23—21no—
308C23—191no—
309C23—381no—
310C23—381no—
311C23—762no—
312C23—762no—
313C23—1521no—
314C23D4×D1911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—762no—
318D4—21no—
319D4—21no—
320D4—42no—
321D4—192no—
322D4—382no—
323D4—381no—
324D4—381no—
325D4—381no—
326D4—762no—
327D4—762no—
328D4—762no—
329D4—1521no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—191no—
336C2×C4—191no—
337C2×C4—191no—
338C2×C4—381no—
339C2×C4—381no—
340C2×C4—381no—
341C2×C4—381no—
342C2×C4—762no—
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—41no—
356C22—41no—
357C22—41no—
358C22—381no—
359C22—381no—
360C22—381no—
361C22—382no—
362C22—761no—
363C22—761no—
364C22—761no—
365C22—761no—
366C22—761no—
367C22—1524no—
368C22#1059736012yes—
369C22C2×D4×D1911yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—381no—
375C4—381no—
376C4—381no—
377C4—761no—
378C4—761no—
379C4#1059743011yescharacteristic
380C4#41×D1911yescharacteristic
381C2—22no—
382C2—81no—
383C2—761no—
384C2—762no—
385C2—1521no—
386C2#1192718311yescharacteristic
387C2C2×#1059736011yescharacteristic
388C2#1192735111yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#465C2
socleC22×C19C22×D4
hypercenter#465D19
hypocenterC19#3306
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #11927194C2semidirect
2. #11927185C2semidirect
3. #11926905C2semidirect
4. #11926872C2semidirect
5. #11926864C2semidirect
6. #11926833C2semidirect
7. #11926796C2semidirect
8. #11926761C2semidirect
9. #11926688C2semidirect
10. #11926677C2semidirect
11. #11926653C2semidirect
12. #11926615C2semidirect
13. #11926544C2semidirect
14. C2×#10597278C2semidirect
15. C19×#465C2semidirect
19. C2×SD16×C19C22semidirect
24. #10597384C22semidirect
26. D4×Dic19C22semidirect
31. C2×#64515C22semidirect
36. C4⋊C4×D19C22semidirect
37. #10597334C22semidirect
42. C19×#106C22semidirect
43. C19×#103C22semidirect
44. C19×#102C22semidirect
45. #10597292C22semidirect
46. #10597292C22semidirect
52. (C2×D19)⋊C8C22semidirect
53. #10597272C22semidirect
54. Dic19⋊C8C22semidirect
57. #10597265C22semidirect
58. #10597265C22semidirect
147. D76#41semidirect
194. #465D19semidirect
213. C2×SD16C2×D19semidirect
238. #106C2×D19semidirect
242. #103C2×D19semidirect
249. #102C2×D19semidirect
253. C19#3306semidirect

Maximal subgroups

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

subgroupindex
#119271942
#119271852
#119269052
#119268722
#119268642
#119268332
#119267962
#119267612
#119266882
#119266772
#119266532
#119266152
#119265442
C2×#105972782
C19×#4652
#330619