Finite Group Databasebeta

← #14574620

Subgroups — #14574620

Order 2432.

444 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927091C211yesmaximal, characteristic, complemented
2#124×D19C211yesmaximal, characteristic, complemented
3#11926932C211yesmaximal, characteristic, complemented
4#11926930C211yesmaximal, characteristic, complemented
5#11926905C211yesmaximal, characteristic, complemented
6#11926902C211yesmaximal, characteristic, complemented
7#11926760C211yesmaximal, characteristic, complemented
8#11926759C211yesmaximal, characteristic, complemented
9#11926756C211yesmaximal, characteristic, complemented
10#11926684C211yesmaximal, characteristic, complemented
11#11926681C211yesmaximal, characteristic, complemented
12#11926679C211yesmaximal, characteristic, complemented
13#11926676C211yesmaximal, characteristic, complemented
14#11926600C211yesmaximal, characteristic, complemented
15C19×#463C211yesmaximal, characteristic, complemented
16C2×Q8×D19C2211yescharacteristic
17C2×D4×D19C2211yescharacteristic
18C2×#64541—21no—
19C2×SD16×C19C2211yescharacteristic, complemented
20C2×D8×C19C2211yescharacteristic
21C19×#124C2211yescharacteristic
22C4×D4×C19C2211yescharacteristic, complemented
23#10597393C2211yescharacteristic
24C2×#64527C2211yescharacteristic, complemented
25#10597386C2211yescharacteristic, complemented
26#10597384C2211yescharacteristic
27#10597382C2211yescharacteristic
28C2×#64526C2211yescharacteristic, complemented
29C2×#64525C2211yescharacteristic
30C2×#64525C2211yescharacteristic
31C4×C22⋊D19—21no—
32C2×D152C2211yescharacteristic
33C2×#64516C2211yescharacteristic, complemented
34#10597341C2211yescharacteristic
35#10597334C2211yescharacteristic, complemented
36#10597331—21no—
37#10597331—21no—
38#10597331—21no—
39#10597330—21no—
40C22⋊C4×D19—21no—
41C22⋊C4×D19—21no—
42#10597321C2211yescharacteristic
43C4×D76C2211yescharacteristic, complemented
44C42×D19C2211yescharacteristic
45C19×C4⋊C8C2211yescharacteristic, complemented
46C19×#103C2211yescharacteristic, complemented
47C19×#102C2211yescharacteristic
48#10597292C2211yescharacteristic, complemented
49#10597289C2211yescharacteristic
50#10597278C2211yescharacteristic
51(C2×D19)⋊C8C2211yescharacteristic
52(C2×D19)⋊C8C2211yescharacteristic
53#10597273C2211yescharacteristic, complemented
54#10597272C2211yescharacteristic, complemented
55#10597272C2211yescharacteristic, complemented
56#10597267C2211yescharacteristic, complemented
57#10597266C2211yescharacteristic
58C4⋊(C19⋊C8)C2211yescharacteristic, complemented
59C23×D19—21no—
60C2×Q8×C19C2311yescharacteristic
61C2×D4×C19C2311yescharacteristic
62C2×D4×C19C2311yescharacteristic
63C22×C4×C19—21no—
64C2×C22⋊D19—21no—
65C2×C22⋊D19—21no—
66C2×C22⋊D19—21no—
67C2×C22⋊D19—21no—
68Q8×D19—41no—
69Q8×D19—41no—
70D4×D19—41no—
71D4×D19—41no—
72#64541—44no—
73C2×D76—21no—
74C2×D76C2311yescharacteristic
75C2×D76C2311yescharacteristic
76C2×C4×D19—21no—
77C2×C4×D19—21no—
78C2×C4×D19D411yescharacteristic
79C2×C4×D19D411yescharacteristic
80C2×C4×D19C2311yescharacteristic
81C2×Dic38—21no—
82C2×Dic38—21no—
83C2×Dic38C2311yescharacteristic
84SD16×C19—41no—
85D8×C19—41no—
86C2×C8×C19C2311yescharacteristic
87C2×C8×C19C2311yescharacteristic
88C4⋊C4×C19C2311yescharacteristic
89C22⋊C4×C19—21no—
90C22⋊C4×C19—21no—
91C22⋊C4×C19—21no—
92C42×C19C2311yescharacteristic
93C22⋊Dic19—21no—
94C22⋊Dic19—21no—
95C22⋊Dic19—21no—
96#64527—41no—
97#64526—41no—
98#64525—41no—
99#64525—41no—
100(C2×D19)⋊C4—21no—
101(C2×D19)⋊C4—21no—
102(C2×D19)⋊C4—21no—
103(C2×D19)⋊C4—21no—
104(C2×D19)⋊C4—21no—
105(C2×D19)⋊C4—21no—
106C4⋊Dic19C2311yescharacteristic
107Dic19⋊C4—21no—
108C4×Dic19D411yescharacteristic
109C4×Dic19D411yescharacteristic
110C4×Dic19C2311yescharacteristic
111C2×C19⋊C8C2311yescharacteristic
112C2×C19⋊C8C2311yescharacteristic
113D152—41no—
114#64516—41no—
115C23×C19—21no—
116C23×C19—21no—
117C22×D19—21no—
118C22×D19—21no—
119C22×D19—42no—
120C22×D19—42no—
121C22×D19—42no—
122C22×D19C2×D411yescharacteristic
123Q8×C19—21no—
124Q8×C19—21no—
125D4×C19—21no—
126D4×C19—21no—
127D4×C19—21no—
128D4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—42no—
132C2×C4×C19C2×D411yescharacteristic
133C2×C4×C19C2×D411yescharacteristic
134C2×C4×C19C2411yescharacteristic
135C22⋊D19—42no—
136C22⋊D19—42no—
137C22⋊D19—42no—
138C22⋊D19—42no—
139C2×Dic19—21no—
140C2×Dic19—21no—
141C2×Dic19C2×D411yescharacteristic
142C2×Dic19C2×D411yescharacteristic
143C2×Dic19C2×D411yescharacteristic
144D76—21no—
145D76—21no—
146D76—21no—
147D76—21no—
148D76—42no—
149C4×D19—22no—
150C4×D19—21no—
151C4×D19—21no—
152C4×D19—41no—
153C4×D19—42no—
154C4×D19—42no—
155Dic38—21no—
156Dic38—21no—
157Dic38—42no—
158Dic38—42no—
159C8×C19—21no—
160C8×C19—21no—
161C19⋊C8—21no—
162C19⋊C8—21no—
163#3213—191nomaximal, Sylow
164C22×C19—41no—
165C22×C19—41no—
166C22×C19—41no—
167C22×C19—41no—
168C22×C19—41no—
169C22×C19—41no—
170C22×C19C22×D411yescharacteristic
171C2×D19—21no—
172C2×D19—21no—
173C2×D19—41no—
174C2×D19—41no—
175C2×D19—41no—
176C2×D19—41no—
177C2×D19—41no—
178C2×D19—41no—
179C2×D19—84no—
180C2×D19AGL(1,ℤ/8)12yes—
181C4×C19—21no—
182C4×C19—21no—
183C4×C19—41no—
184C4×C19—41no—
185C4×C19H(5,𝔽2)11yescharacteristic
186C4×C19H(5,𝔽2)11yescharacteristic
187Dic19—21no—
188Dic19—21no—
189Dic19—21no—
190Dic19—41no—
191Dic19—41no—
192#532—191no—
193C2×#124—191no—
194#496—191no—
195#496—191no—
196#489—191no—
197#489—191no—
198#463—191no—
199#463—191no—
200#463—191no—
201#463D1911yescharacteristic, complemented
202#448—191no—
203#448—191no—
204#447—191no—
205#447—191no—
206#432—191no—
207C2×C19—81no—
208C2×C19—81no—
209C2×C19#53511yescharacteristic
210C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
211C2×C19#57511yescharacteristic
212D19—22no—
213D19—81no—
214D19—81no—
215C2×#41—381no—
216C22×Q8—191no—
217C22×D4—191no—
218C2×SD16—191no—
219C2×SD16—191no—
220C2×SD16—191no—
221C2×SD16C2×D1911yescharacteristic, complemented
222C2×D8—191no—
223C2×D8—191no—
224C2×D8—191no—
225C2×D8C2×D1911yescharacteristic
226C4⋊Q8—191no—
227#127—191no—
228#124—191no—
229#124—191no—
230#124—191no—
231#124—381no—
232#124—381no—
233#124—381no—
234#124C2×D1911yescharacteristic
235#121—191no—
236#121—191no—
237#121—381no—
238C4×D4—191no—
239C4×D4—381no—
240C4×D4C2×D1911yescharacteristic, complemented
241C2×C22⋊C4—381no—
242C2×C22⋊C4—381no—
243C2×C42—191no—
244C4⋊C8—191no—
245C4⋊C8C2×D1911yescharacteristic, complemented
246#103—191no—
247#103—191no—
248#103—191no—
249#103C2×D1911yescharacteristic, complemented
250#102—191no—
251#102—191no—
252#102—191no—
253#102C2×D1911yescharacteristic
254C22⋊C8—191no—
255C22⋊C8—191no—
256#97—191no—
257#97—191no—
258C19#321311yescharacteristic, complemented, Sylow
259C24—381no—
260#41—764no—
261C2×Q8—191no—
262C2×Q8—381no—
263C2×Q8—381no—
264C2×Q8—761no—
265C2×Q8—761no—
266C2×Q8C22×D1911yescharacteristic
267C2×D4—191no—
268C2×D4—191no—
269C2×D4—381no—
270C2×D4—381no—
271C2×D4—381no—
272C2×D4—381no—
273C2×D4—381no—
274C2×D4—761no—
275C2×D4—761no—
276C2×D4C22×D1911yescharacteristic
277C2×D4C22×D1911yescharacteristic
278C22×C4—21no—
279C22×C4—191no—
280C22×C4—191no—
281C22×C4—191no—
282C22×C4—381no—
283C22×C4—381no—
284SD16—41no—
285SD16—761no—
286SD16—761no—
287SD16—761no—
288D8—41no—
289D8—761no—
290D8—761no—
291D8—761no—
292C2×C8—191no—
293C2×C8—191no—
294C2×C8C22×D1911yescharacteristic
295C2×C8C22×D1911yescharacteristic
296C4⋊C4—191no—
297C4⋊C4—381no—
298C4⋊C4C22×D1911yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—381no—
303C22⋊C4—381no—
304C22⋊C4—381no—
305C22⋊C4—381no—
306C22⋊C4—381no—
307C22⋊C4—381no—
308C22⋊C4—381no—
309C22⋊C4—381no—
310C22⋊C4—381no—
311C42—191no—
312C42—191no—
313C42—191no—
314C42C22×D1911yescharacteristic
315C23—21no—
316C23—21no—
317C23—191no—
318C23—381no—
319C23—381no—
320C23—762no—
321C23—762no—
322C23—762no—
323Q8—21no—
324Q8—21no—
325Q8—381no—
326Q8—381no—
327Q8—762no—
328Q8—762no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—381no—
334D4—381no—
335D4—381no—
336D4—381no—
337D4—762no—
338D4—762no—
339D4—762no—
340D4—762no—
341D4—762no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—191no—
346C2×C4—191no—
347C2×C4—191no—
348C2×C4—382no—
349C2×C4—381no—
350C2×C4—381no—
351C2×C4—381no—
352C2×C4—381no—
353C2×C4—761no—
354C2×C4—762no—
355C2×C4—762no—
356C2×C4D4×D1911yescharacteristic
357C2×C4D4×D1911yescharacteristic
358C2×C4C23×D1911yescharacteristic
359C8—21no—
360C8—21no—
361C8—381no—
362C8—381no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—192no—
370C22—381no—
371C22—381no—
372C22—761no—
373C22—761no—
374C22—761no—
375C22—761no—
376C22—761no—
377C22—761no—
378C22—1524no—
379C22C2×D4×D1911yescharacteristic
380C4—21no—
381C4—21no—
382C4—41no—
383C4—41no—
384C4—381no—
385C4—381no—
386C4—381no—
387C4—761no—
388C4—761no—
389C4#1059743011yescharacteristic
390C4#1059743511yescharacteristic
391C2—81no—
392C2—81no—
393C2—382no—
394C2—1521no—
395C2—1521no—
396C2#1192711011yescharacteristic
397C2AGL(1,ℤ/8)×D1911yescharacteristic
398C2#1192734111yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#463C2
socleC22×C19C22×D4
hypercenter#463D19
hypocenterC19#3213
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #11927091C2semidirect
2. #124×D19C2semidirect
3. #11926932C2semidirect
4. #11926930C2semidirect
5. #11926905C2semidirect
6. #11926902C2semidirect
7. #11926760C2semidirect
8. #11926759C2semidirect
9. #11926756C2semidirect
10. #11926684C2semidirect
11. #11926681C2semidirect
12. #11926679C2semidirect
13. #11926676C2semidirect
14. #11926600C2semidirect
15. C19×#463C2semidirect
19. C2×SD16×C19C22semidirect
22. C4×D4×C19C22semidirect
24. C2×#64527C22semidirect
25. #10597386C22semidirect
28. C2×#64526C22semidirect
33. C2×#64516C22semidirect
35. #10597334C22semidirect
43. C4×D76C22semidirect
45. C19×C4⋊C8C22semidirect
46. C19×#103C22semidirect
48. #10597292C22semidirect
53. #10597273C22semidirect
54. #10597272C22semidirect
55. #10597272C22semidirect
56. #10597267C22semidirect
58. C4⋊(C19⋊C8)C22semidirect
201. #463D19semidirect
221. C2×SD16C2×D19semidirect
240. C4×D4C2×D19semidirect
245. C4⋊C8C2×D19semidirect
249. #103C2×D19semidirect
258. C19#3213semidirect

Maximal subgroups

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

subgroupindex
#119270912
#124×D192
#119269322
#119269302
#119269052
#119269022
#119267602
#119267592
#119267562
#119266842
#119266812
#119266792
#119266762
#119266002
C19×#4632
#321319