Finite Group Databasebeta

← #14575601

Subgroups — #14575601

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#11927199C211yesmaximal, characteristic, complemented
2#11927189C211yesmaximal, characteristic, complemented
3#11926904C211yesmaximal, characteristic, complemented
4#11926876C211yesmaximal, characteristic, complemented
5#11926864C211yesmaximal, characteristic, complemented
6#11926834C211yesmaximal, characteristic, complemented
7#11926796C211yesmaximal, characteristic, complemented
8#11926772C211yesmaximal, characteristic, complemented
9#11926759C211yesmaximal, characteristic, complemented
10#11926686C211yesmaximal, characteristic, complemented
11#11926676C211yesmaximal, characteristic, complemented
12#11926617C211yesmaximal, characteristic, complemented
13#11926542C211yesmaximal, characteristic, complemented
14#102×D19C211yesmaximal, characteristic, complemented
15C19×#442C211yesmaximal, characteristic, complemented
16C2×#64543C2211yescharacteristic
17C2×D4×D19C2211yescharacteristic
18C2×#64541—21no—
19C2×D8×C19C2211yescharacteristic
20C4×D4×C19C2211yescharacteristic
21C4×D4×C19C2211yescharacteristic, complemented
22#10597384C2211yescharacteristic
23#10597384C2211yescharacteristic, complemented
24C2×#64526C2211yescharacteristic, complemented
25C2×#64525C2211yescharacteristic
26#10597376—21no—
27C2×(C2×D19)⋊C4—21no—
28#10597370—21no—
29C2×#64515C2211yescharacteristic, complemented
30C2×C8×D19C2211yescharacteristic
31#10597343C2211yescharacteristic
32#10597341C2211yescharacteristic
33C4⋊C4×D19C2211yescharacteristic
34C4⋊C4×D19C2211yescharacteristic, complemented
35#10597332—21no—
36#10597329—21no—
37#10597329—21no—
38#10597328—21no—
39#10597321C2211yescharacteristic
40C4×D76C2211yescharacteristic
41#10597315C2211yescharacteristic, complemented
42C19×#106C2211yescharacteristic, complemented
43C19×#102C2211yescharacteristic
44C19×#102C2211yescharacteristic, complemented
45C19×#97C2211yescharacteristic, 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#10597265C2211yescharacteristic, complemented
58C4⋊(C19⋊C8)C2211yescharacteristic, complemented
59C23×D19—21no—
60C2×D4×C19C2311yescharacteristic
61C2×D4×C19C2311yescharacteristic
62C22×C4×C19—21no—
63C22×C4×C19—21no—
64C2×C22⋊D19—21no—
65C2×C22⋊D19—21no—
66C2×C22⋊D19—21no—
67C2×C22⋊D19—21no—
68C22×Dic19—21no—
69#64543—22no—
70#64543—41no—
71D4×D19—22no—
72D4×D19—41no—
73#64541—44no—
74C2×D76—21no—
75C2×D76D411yescharacteristic
76C2×D76C2311yescharacteristic
77C2×C4×D19—21no—
78C2×C4×D19—21no—
79C2×C4×D19C2311yescharacteristic
80C2×C4×D19C2311yescharacteristic
81C2×Dic38—21no—
82C2×Dic38C2311yescharacteristic
83D8×C19—22no—
84C2×C8×C19C2311yescharacteristic
85C2×C8×C19C2311yescharacteristic
86C4⋊C4×C19C2311yescharacteristic
87C4⋊C4×C19C2311yescharacteristic
88C22⋊C4×C19—21no—
89C22⋊C4×C19—21no—
90C42×C19C2311yescharacteristic
91C22⋊Dic19—21no—
92C22⋊Dic19—21no—
93#64526—41no—
94#64525—41no—
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⋊Dic19—21no—
102C4⋊Dic19—21no—
103C4⋊Dic19D411yescharacteristic
104C4⋊Dic19C2311yescharacteristic
105C4⋊Dic19C2311yescharacteristic
106Dic19⋊C4—21no—
107Dic19⋊C4—21no—
108C2×C19⋊C8C2311yescharacteristic
109C2×C19⋊C8C2311yescharacteristic
110#64515—41no—
111C8×D19—41no—
112C23×C19—21no—
113C23×C19—21no—
114C22×D19—21no—
115C22×D19—42no—
116C22×D19—42no—
117C22×D19—81no—
118C22×D19C2×D411yescharacteristic
119C22×D19C2×D411yescharacteristic
120D4×C19—21no—
121D4×C19—21no—
122D4×C19—21no—
123D4×C19#4112yescomplemented
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—42no—
127C2×C4×C19—81no—
128C2×C4×C19C2×D411yescharacteristic
129C2×C4×C19C2×D411yescharacteristic
130C2×C4×C19C2411yescharacteristic
131C22⋊D19—42no—
132C22⋊D19—42no—
133C22⋊D19—42no—
134C22⋊D19—42no—
135C2×Dic19—21no—
136C2×Dic19—21no—
137C2×Dic19—21no—
138C2×Dic19—42no—
139C2×Dic19C2×D411yescharacteristic
140C2×Dic19C2×D411yescharacteristic
141D76—22no—
142D76—21no—
143D76—21no—
144D76—81no—
145C4×D19—21no—
146C4×D19—21no—
147C4×D19—21no—
148C4×D19—21no—
149C4×D19—42no—
150C4×D19—42no—
151Dic38—21no—
152Dic38—21no—
153Dic38—42no—
154C8×C19—21no—
155C8×C19—21no—
156C19⋊C8—21no—
157C19⋊C8—21no—
158#3306—191nomaximal, Sylow
159C22×C19—22no—
160C22×C19—41no—
161C22×C19—41no—
162C22×C19—41no—
163C22×C19—41no—
164C22×C19—41no—
165C22×C19C22×D411yescharacteristic
166C2×D19—21no—
167C2×D19—21no—
168C2×D19—21no—
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—21no—
178C4×C19—41no—
179C4×C19—41no—
180C4×C19C2×#4111yescharacteristic
181C4×C19H(5,𝔽2)11yescharacteristic
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#449—191no—
197#447—191no—
198#442D1911yescharacteristic, complemented
199#435—191no—
200#417—191no—
201C2×#102—191no—
202C2×C19—42no—
203C2×C19—81no—
204C2×C19#54611yescharacteristic
205C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
206C2×C19#57711yescharacteristic
207D19—22no—
208D19—41no—
209D19—81no—
210C2×#41—191no—
211C2×#41—381no—
212C22×D4—191no—
213C2×SD16—191no—
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—191no—
228#121—381no—
229#120—381no—
230C4×D4—191no—
231C4×D4C2×D1911yescharacteristic
232C4×D4C2×D1911yescharacteristic, complemented
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#103—191no—
243#102—191no—
244#102—191no—
245#102—191no—
246#102—191no—
247#102—191no—
248#102C2×D1911yescharacteristic
249#102C2×D1911yescharacteristic, complemented
250C22⋊C8—191no—
251C22⋊C8—191no—
252#97C2×D1911yescharacteristic, complemented
253C19#330611yescharacteristic, complemented, Sylow
254C24—381no—
255#41—382no—
256#41—764no—
257#41—761no—
258C2×Q8—191no—
259C2×Q8—381no—
260C2×D4—191no—
261C2×D4—191no—
262C2×D4—381no—
263C2×D4—381no—
264C2×D4—382no—
265C2×D4—381no—
266C2×D4—381no—
267C2×D4—381no—
268C2×D4—761no—
269C2×D4C22×D1911yescharacteristic
270C2×D4C22×D1911yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—191no—
274C22×C4—191no—
275C22×C4—381no—
276C22×C4—381no—
277C22×C4—381no—
278SD16—761no—
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—381no—
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—21no—
309C23—191no—
310C23—191no—
311C23—381no—
312C23—762no—
313C23—762no—
314C23—1521no—
315Q8—381no—
316Q8—381no—
317Q8—762no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—382no—
322D4—381no—
323D4—381no—
324D4—762no—
325D4—762no—
326D4—762no—
327D4—762no—
328D4—1521no—
329D4#6454112yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—81no—
334C2×C4—191no—
335C2×C4—191no—
336C2×C4—381no—
337C2×C4—381no—
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×C4D4×D1911yescharacteristic
347C2×C4D4×D1911yescharacteristic
348C2×C4C23×D1911yescharacteristic
349C8—21no—
350C8—21no—
351C8—381no—
352C8—381no—
353C22—22no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—192no—
360C22—381no—
361C22—381no—
362C22—381no—
363C22—381no—
364C22—381no—
365C22—761no—
366C22—761no—
367C22—761no—
368C22—1524no—
369C22C2×D4×D1911yescharacteristic
370C4—21no—
371C4—21no—
372C4—41no—
373C4—41no—
374C4—381no—
375C4—381no—
376C4—761no—
377C4—761no—
378C4—761no—
379C4C2×#6454111yescharacteristic
380C4#1059743511yescharacteristic
381C2—42no—
382C2—81no—
383C2—382no—
384C2—761no—
385C2—1521no—
386C2#1192719011yescharacteristic
387C2AGL(1,ℤ/8)×D1911yescharacteristic
388C2#1192735411yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#442C2
socleC22×C19C22×D4
hypercenter#442D19
hypocenterC19#3306
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #11927199C2semidirect
2. #11927189C2semidirect
3. #11926904C2semidirect
4. #11926876C2semidirect
5. #11926864C2semidirect
6. #11926834C2semidirect
7. #11926796C2semidirect
8. #11926772C2semidirect
9. #11926759C2semidirect
10. #11926686C2semidirect
11. #11926676C2semidirect
12. #11926617C2semidirect
13. #11926542C2semidirect
14. #102×D19C2semidirect
15. C19×#442C2semidirect
21. C4×D4×C19C22semidirect
23. #10597384C22semidirect
24. C2×#64526C22semidirect
29. C2×#64515C22semidirect
34. C4⋊C4×D19C22semidirect
41. #10597315C22semidirect
42. C19×#106C22semidirect
44. C19×#102C22semidirect
45. C19×#97C22semidirect
51. (C2×D19)⋊C8C22semidirect
52. #10597273C22semidirect
53. #10597273C22semidirect
54. #10597267C22semidirect
56. #10597265C22semidirect
57. #10597265C22semidirect
58. C4⋊(C19⋊C8)C22semidirect
123. D4×C19#41semidirect
198. #442D19semidirect
232. C4×D4C2×D19semidirect
238. #106C2×D19semidirect
249. #102C2×D19semidirect
252. #97C2×D19semidirect
253. C19#3306semidirect
329. D4#64541semidirect

Maximal subgroups

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

subgroupindex
#119271992
#119271892
#119269042
#119268762
#119268642
#119268342
#119267962
#119267722
#119267592
#119266862
#119266762
#119266172
#119265422
#102×D192
C19×#4422
#330619