Finite Group Databasebeta

← #14575595

Subgroups — #14575595

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#11927197C211yesmaximal, characteristic, complemented
2#11927187C211yesmaximal, characteristic, complemented
3#11926873C211yesmaximal, characteristic, complemented
4#11926861C211yesmaximal, characteristic, complemented
5#11926831C211yesmaximal, characteristic, complemented
6#11926796C211yesmaximal, characteristic, complemented
7#11926776C211yesmaximal, characteristic, complemented
8#11926756C211yesmaximal, characteristic, complemented
9#11926692C211yesmaximal, characteristic, complemented
10#11926679C211yesmaximal, characteristic, complemented
11#11926657C211yesmaximal, characteristic, complemented
12#11926617C211yesmaximal, characteristic, complemented
13#11926544C211yesmaximal, characteristic, complemented
14#102×D19C211yesmaximal, characteristic, complemented
15C19×#489C211yesmaximal, characteristic, complemented
16C2×#64545—21no—
17C2×#64545C2211yescharacteristic
18C2×D4×D19C2211yescharacteristic
19C19×C4⋊Q8C2211yescharacteristic, complemented
20C19×#124C2211yescharacteristic
21#10597392—21no—
22#10597392C2211yescharacteristic
23C2×#64527C2211yescharacteristic, complemented
24#10597384C2211yescharacteristic
25C2×#64525C2211yescharacteristic
26C2×D152C2211yescharacteristic
27C2×#64515C2211yescharacteristic, complemented
28C2×C8×D19C2211yescharacteristic
29#10597341C2211yescharacteristic
30#10597341C2211yescharacteristic, complemented
31#10597340—21no—
32#10597340—21no—
33C4⋊C4×D19C2211yescharacteristic
34C4⋊C4×D19C2211yescharacteristic, complemented
35#10597330—21no—
36#10597329—21no—
37#10597328—21no—
38C22⋊C4×D19—21no—
39C4×D76C2211yescharacteristic
40C4×D76C2211yescharacteristic
41C4×D76C2211yescharacteristic, complemented
42C19×#103C2211yescharacteristic, complemented
43C19×#103C2211yescharacteristic, complemented
44C19×#102C2211yescharacteristic
45C19×#102C2211yescharacteristic
46C19×#97C2211yescharacteristic, complemented
47#10597292C2211yescharacteristic, complemented
48#10597289C2211yescharacteristic
49#10597278C2211yescharacteristic
50#10597278C2211yescharacteristic, complemented
51(C2×D19)⋊C8C2211yescharacteristic
52(C2×D19)⋊C8C2211yescharacteristic, complemented
53#10597274C2211yescharacteristic, complemented
54#10597266C2211yescharacteristic
55#10597266C2211yescharacteristic
56#10597265C2211yescharacteristic, complemented
57#10597265C2211yescharacteristic, complemented
58C4⋊(C19⋊C8)C2211yescharacteristic, complemented
59C23×D19—21no—
60C2×Q8×C19—21no—
61C2×Q8×C19C2311yescharacteristic
62C2×D4×C19C2311yescharacteristic
63C2×C22⋊D19—21no—
64C2×C22⋊D19—21no—
65#64545—22no—
66#64545—41no—
67#64545—44no—
68D4×D19—22no—
69D4×D19—41no—
70C2×D76—21no—
71C2×D76—21no—
72C2×D76—21no—
73C2×D76D411yescharacteristic
74C2×D76C2311yescharacteristic
75C2×D76C2311yescharacteristic
76C2×C4×D19—21no—
77C2×C4×D19—21no—
78C2×C4×D19—21no—
79C2×C4×D19—21no—
80C2×C4×D19—21no—
81C2×C4×D19C2311yescharacteristic
82C2×C4×D19C2311yescharacteristic
83C2×C8×C19C2311yescharacteristic
84C2×C8×C19C2311yescharacteristic
85C4⋊C4×C19—21no—
86C4⋊C4×C19C2311yescharacteristic
87C4⋊C4×C19C2311yescharacteristic
88C22⋊C4×C19—21no—
89C22⋊C4×C19—21no—
90C42×C19C2311yescharacteristic
91C22⋊Dic19—21no—
92#64527—41no—
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)⋊C4—21no—
99(C2×D19)⋊C4D411yescharacteristic
100(C2×D19)⋊C4D411yescharacteristic
101C4⋊Dic19D411yescharacteristic
102C4⋊Dic19C2311yescharacteristic
103C4⋊Dic19C2311yescharacteristic
104Dic19⋊C4—21no—
105Dic19⋊C4—21no—
106Dic19⋊C4—21no—
107C2×C19⋊C8C2311yescharacteristic
108C2×C19⋊C8C2311yescharacteristic
109D152—22no—
110#64515—41no—
111C8×D19—41no—
112C23×C19—21no—
113C22×D19—21no—
114C22×D19—21no—
115C22×D19—42no—
116C22×D19—42no—
117C22×D19—81no—
118C22×D19C2×D411yescharacteristic
119C22×D19C2×D411yescharacteristic
120Q8×C19—21no—
121Q8×C19—21no—
122Q8×C19—42no—
123D4×C19—21no—
124D4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19C2×D411yescharacteristic
129C2×C4×C19C2×D411yescharacteristic
130C2×C4×C19C2411yescharacteristic
131C22⋊D19—42no—
132C22⋊D19—81no—
133C2×Dic19—21no—
134C2×Dic19—21no—
135C2×Dic19C2×D411yescharacteristic
136C2×Dic19C2×D411yescharacteristic
137D76—22no—
138D76—21no—
139D76—21no—
140D76—21no—
141D76—42no—
142D76—42no—
143D76—42no—
144D76#4112yescomplemented
145C4×D19—21no—
146C4×D19—21no—
147C4×D19—21no—
148C4×D19—21no—
149C4×D19—42no—
150C4×D19—42no—
151C4×D19—42no—
152C4×D19—42no—
153C4×D19—81no—
154C8×C19—21no—
155C8×C19—21no—
156C19⋊C8—21no—
157C19⋊C8—21no—
158#3306—191nomaximal, Sylow
159C22×C19—41no—
160C22×C19—41no—
161C22×C19—41no—
162C22×C19C22×D411yescharacteristic
163C2×D19—21no—
164C2×D19—21no—
165C2×D19—21no—
166C2×D19—22no—
167C2×D19—21no—
168C2×D19—21no—
169C2×D19—41no—
170C2×D19—41no—
171C2×D19—41no—
172C2×D19—41no—
173C2×D19—41no—
174C2×D19—84no—
175C2×D19AGL(1,ℤ/8)12yes—
176C4×C19—21no—
177C4×C19—21no—
178C4×C19—41no—
179C4×C19—41no—
180C4×C19—41no—
181C4×C19C2×#4111yescharacteristic
182C4×C19H(5,𝔽2)11yescharacteristic
183Dic19—21no—
184Dic19—21no—
185Dic19—41no—
186Dic19—41no—
187#547—191no—
188#546—191no—
189#489D1911yescharacteristic, complemented
190#483—191no—
191#481—191no—
192#476—191no—
193#469—191no—
194#465—191no—
195#463—191no—
196#449—191no—
197#447—191no—
198#442—191no—
199#435—191no—
200#417—191no—
201C2×#102—191no—
202C2×C19—81no—
203C2×C19#54611yescharacteristic
204C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
205C2×C19#57711yescharacteristic
206D19—22no—
207D19—41no—
208D19—42no—
209D19—81no—
210C2×#41—191no—
211C2×#41—381no—
212C22×D4—191no—
213C2×SD16—191no—
214C2×D8—191no—
215C2×D8—191no—
216C2×M16—191no—
217C22×C8—191no—
218C4⋊Q8C2×D1911yescharacteristic, complemented
219#124C2×D1911yescharacteristic
220#123—381no—
221#123—381no—
222#123—381no—
223C22⋊Q8—191no—
224C22⋊Q8—381no—
225#121—191no—
226#121—191no—
227#121—191no—
228#121—381no—
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#103C2×D1911yescharacteristic, complemented
242#103C2×D1911yescharacteristic, complemented
243#102—191no—
244#102—191no—
245#102—191no—
246#102—191no—
247#102—191no—
248#102C2×D1911yescharacteristic
249#102C2×D1911yescharacteristic
250C22⋊C8—191no—
251C22⋊C8—191no—
252#97C2×D1911yescharacteristic, complemented
253C19#330611yescharacteristic, complemented, Sylow
254C24—381no—
255#41—382no—
256#41—761no—
257#41—764no—
258C2×Q8—21no—
259C2×Q8C22×D1911yescharacteristic
260C2×D4—191no—
261C2×D4—191no—
262C2×D4—191no—
263C2×D4—381no—
264C2×D4—381no—
265C2×D4—381no—
266C2×D4—381no—
267C2×D4—382no—
268C2×D4—381no—
269C2×D4—761no—
270C2×D4C22×D1911yescharacteristic
271C22×C4—191no—
272C22×C4—191no—
273C22×C4—381no—
274C22×C4—381no—
275C22×C4—381no—
276C22×C4—381no—
277C22×C4—381no—
278SD16—761no—
279D8—382no—
280D8—761no—
281M16—761no—
282C2×C8—191no—
283C2×C8—191no—
284C2×C8—761no—
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—
306C42C22×D1911yescharacteristic
307C23—21no—
308C23—191no—
309C23—191no—
310C23—381no—
311C23—381no—
312C23—762no—
313C23—762no—
314C23—1521no—
315Q8—21no—
316Q8—21no—
317Q8—42no—
318D4—21no—
319D4—21no—
320D4—192no—
321D4—382no—
322D4—381no—
323D4—381no—
324D4—381no—
325D4—762no—
326D4—762no—
327D4—762no—
328D4—762no—
329D4—1521no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—191no—
334C2×C4—191no—
335C2×C4—381no—
336C2×C4—381no—
337C2×C4—381no—
338C2×C4—381no—
339C2×C4—381no—
340C2×C4—381no—
341C2×C4—762no—
342C2×C4—762no—
343C2×C4—762no—
344C2×C4—762no—
345C2×C4—1521no—
346C2×C4D4×D1911yescharacteristic
347C2×C4D4×D1911yescharacteristic
348C2×C4C23×D1911yescharacteristic
349C8—21no—
350C8—21no—
351C8—381no—
352C8—381no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—192no—
357C22—381no—
358C22—381no—
359C22—381no—
360C22—381no—
361C22—381no—
362C22—382no—
363C22—761no—
364C22—761no—
365C22—761no—
366C22—761no—
367C22—761no—
368C22—1524no—
369C22C2×D4×D1911yescharacteristic
370C4—21no—
371C4—21no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—381no—
376C4—381no—
377C4—761no—
378C4—761no—
379C4#41×D1911yescharacteristic
380C4#1059743511yescharacteristic
381C2—81no—
382C2—382no—
383C2—761no—
384C2—762no—
385C2—1521no—
386C2#1192718711yescharacteristic
387C2AGL(1,ℤ/8)×D1911yescharacteristic
388C2#1192735311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#489C2
socleC22×C19C22×D4
hypercenter#489D19
hypocenterC19#3306
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #11927197C2semidirect
2. #11927187C2semidirect
3. #11926873C2semidirect
4. #11926861C2semidirect
5. #11926831C2semidirect
6. #11926796C2semidirect
7. #11926776C2semidirect
8. #11926756C2semidirect
9. #11926692C2semidirect
10. #11926679C2semidirect
11. #11926657C2semidirect
12. #11926617C2semidirect
13. #11926544C2semidirect
14. #102×D19C2semidirect
15. C19×#489C2semidirect
19. C19×C4⋊Q8C22semidirect
23. C2×#64527C22semidirect
27. C2×#64515C22semidirect
30. #10597341C22semidirect
34. C4⋊C4×D19C22semidirect
41. C4×D76C22semidirect
42. C19×#103C22semidirect
43. C19×#103C22semidirect
46. C19×#97C22semidirect
47. #10597292C22semidirect
50. #10597278C22semidirect
52. (C2×D19)⋊C8C22semidirect
53. #10597274C22semidirect
56. #10597265C22semidirect
57. #10597265C22semidirect
58. C4⋊(C19⋊C8)C22semidirect
144. D76#41semidirect
189. #489D19semidirect
218. C4⋊Q8C2×D19semidirect
241. #103C2×D19semidirect
242. #103C2×D19semidirect
252. #97C2×D19semidirect
253. C19#3306semidirect

Maximal subgroups

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

subgroupindex
#119271972
#119271872
#119268732
#119268612
#119268312
#119267962
#119267762
#119267562
#119266922
#119266792
#119266572
#119266172
#119265442
#102×D192
C19×#4892
#330619