Finite Group Databasebeta

← #14574636

Subgroups — #14574636

Order 2432.

400 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927098C211yesmaximal, characteristic, complemented
2#124×D19C211yesmaximal, characteristic
3#11926937C211yesmaximal, characteristic, complemented
4#11926935C211yesmaximal, characteristic, complemented
5#11926905C211yesmaximal, characteristic, complemented
6#11926902C211yesmaximal, characteristic, complemented
7#11926767C211yesmaximal, characteristic, complemented
8#11926766C211yesmaximal, characteristic, complemented
9#11926763C211yesmaximal, characteristic, complemented
10#11926701C211yesmaximal, characteristic, complemented
11#11926698C211yesmaximal, characteristic, complemented
12#11926696C211yesmaximal, characteristic
13#11926693C211yesmaximal, characteristic
14#11926600C211yesmaximal, characteristic, complemented
15C19×#464C211yesmaximal, characteristic, complemented
16C2×Q8×D19C2211yescharacteristic
17C2×D4×D19C2211yescharacteristic
18C2×Q16×C19C2211yescharacteristic, complemented
19C2×SD16×C19C2211yescharacteristic
20C19×#124C2211yescharacteristic
21C4×Q8×C19C2211yescharacteristic, complemented
22#10597393C2211yescharacteristic
23#10597392C2211yescharacteristic
24#10597390C2211yescharacteristic, complemented
25C2×#64528C2211yescharacteristic, complemented
26C2×#64528C2211yescharacteristic, complemented
27C2×#64527C2211yescharacteristic
28#10597382C2211yescharacteristic
29C2×#64526C2211yescharacteristic
30C2×Dic76C2211yescharacteristic, complemented
31C2×#64516C2211yescharacteristic
32#10597343C2211yescharacteristic
33#10597342—21no—
34#10597335—21no—
35#10597334C2211yescharacteristic, complemented
36#10597331—21no—
37#10597331—21no—
38C22⋊C4×D19—21no—
39C22⋊C4×D19—21no—
40#10597321C2211yescharacteristic
41#10597318—21no—
42C42×D19C2211yescharacteristic
43C4×Dic38—21no—
44C4×Dic38C2211yescharacteristic, complemented
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×Q8×C19C2311yescharacteristic
62C2×D4×C19C2311yescharacteristic
63C2×C22⋊D19—21no—
64Q8×D19—41no—
65Q8×D19—41no—
66D4×D19—41no—
67D4×D19—41no—
68C2×D76C2311yescharacteristic
69C2×C4×D19—21no—
70C2×C4×D19D411yescharacteristic
71C2×C4×D19D411yescharacteristic
72C2×C4×D19C2311yescharacteristic
73C2×Dic38—21no—
74C2×Dic38—21no—
75C2×Dic38C2311yescharacteristic
76C2×Dic38C2311yescharacteristic
77Q16×C19—41no—
78SD16×C19—41no—
79C2×C8×C19C2311yescharacteristic
80C2×C8×C19C2311yescharacteristic
81C4⋊C4×C19—21no—
82C4⋊C4×C19C2311yescharacteristic
83C22⋊C4×C19—21no—
84C22⋊C4×C19—21no—
85C42×C19—21no—
86C42×C19C2311yescharacteristic
87C22⋊Dic19—21no—
88C22⋊Dic19—21no—
89#64528—41no—
90#64528—41no—
91#64527—41no—
92#64526—41no—
93(C2×D19)⋊C4—21no—
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—
99C4⋊Dic19—21no—
100C4⋊Dic19C2311yescharacteristic
101Dic19⋊C4—21no—
102Dic19⋊C4—21no—
103Dic19⋊C4—21no—
104Dic19⋊C4—21no—
105Dic19⋊C4—21no—
106C4×Dic19—21no—
107C4×Dic19D411yescharacteristic
108C4×Dic19D411yescharacteristic
109C4×Dic19C2311yescharacteristic
110C2×C19⋊C8C2311yescharacteristic
111C2×C19⋊C8C2311yescharacteristic
112Dic76—41no—
113#64516—41no—
114C23×C19—21no—
115C22×D19—21no—
116C22×D19—42no—
117C22×D19—42no—
118C22×D19—42no—
119C22×D19C2×D411yescharacteristic
120Q8×C19—21no—
121Q8×C19—21no—
122Q8×C19—21no—
123Q8×C19—21no—
124D4×C19—21no—
125D4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19C2×D411yescharacteristic
130C2×C4×C19C2×D411yescharacteristic
131C2×C4×C19C2411yescharacteristic
132C22⋊D19—42no—
133C2×Dic19—21no—
134C2×Dic19—21no—
135C2×Dic19—21no—
136C2×Dic19C2×D411yescharacteristic
137C2×Dic19C2×D411yescharacteristic
138C2×Dic19C2×D411yescharacteristic
139D76—21no—
140D76—21no—
141C4×D19—22no—
142C4×D19—21no—
143C4×D19—21no—
144C4×D19—41no—
145C4×D19—42no—
146Dic38—21no—
147Dic38—21no—
148Dic38—21no—
149Dic38—21no—
150Dic38—42no—
151Dic38—42no—
152C8×C19—21no—
153C8×C19—21no—
154C19⋊C8—21no—
155C19⋊C8—21no—
156#3215—191nomaximal, Sylow
157C22×C19—41no—
158C22×C19—41no—
159C22×C19—41no—
160C22×C19C22×D411yescharacteristic
161C2×D19—21no—
162C2×D19—21no—
163C2×D19—41no—
164C2×D19—41no—
165C2×D19—41no—
166C2×D19—84no—
167C2×D19#13712yes—
168C4×C19—21no—
169C4×C19—21no—
170C4×C19—41no—
171C4×C19—41no—
172C4×C19—41no—
173C4×C19H(5,𝔽2)11yescharacteristic
174C4×C19H(5,𝔽2)11yescharacteristic
175Dic19—21no—
176Dic19—21no—
177Dic19—21no—
178Dic19—41no—
179Dic19—41no—
180Dic19—41no—
181#533—191no—
182C2×#124—191no—
183#497—191no—
184#497—191no—
185#489—191no—
186#489—191no—
187#464—191no—
188#464—191no—
189#464—191no—
190#464D1911yescharacteristic, complemented
191#451—191no—
192#451—191no—
193#450—191no—
194#450—191no—
195#432—191no—
196C2×C19—81no—
197C2×C19#53511yescharacteristic
198C2×C19C2×#13711yescharacteristic
199C2×C19#57511yescharacteristic
200D19—22no—
201D19—81no—
202C22×Q8—191no—
203C22×D4—191no—
204C2×Q16—191no—
205C2×Q16—191no—
206C2×Q16—191no—
207C2×Q16C2×D1911yescharacteristic, complemented
208C2×SD16—191no—
209C2×SD16—191no—
210C2×SD16—191no—
211C2×SD16C2×D1911yescharacteristic
212C4⋊Q8—191no—
213C4⋊Q8—191no—
214#125—381no—
215#124—191no—
216#124—191no—
217#124—191no—
218#124—381no—
219#124—381no—
220#124C2×D1911yescharacteristic
221C22⋊Q8—191no—
222C22⋊Q8—191no—
223C22⋊Q8—381no—
224C4×Q8—191no—
225C4×Q8—381no—
226C4×Q8C2×D1911yescharacteristic, complemented
227#117—381no—
228C2×C22⋊C4—381no—
229C2×C22⋊C4—381no—
230C2×C42—191no—
231C4⋊C8—191no—
232C4⋊C8C2×D1911yescharacteristic, complemented
233#103—191no—
234#103—191no—
235#103—191no—
236#103C2×D1911yescharacteristic, complemented
237#102—191no—
238#102—191no—
239#102—191no—
240#102C2×D1911yescharacteristic
241C22⋊C8—191no—
242C22⋊C8—191no—
243#97—191no—
244#97—191no—
245C19#321511yescharacteristic, complemented, Sylow
246C24—381no—
247C2×Q8—191no—
248C2×Q8—191no—
249C2×Q8—381no—
250C2×Q8—381no—
251C2×Q8—761no—
252C2×Q8—761no—
253C2×Q8C22×D1911yescharacteristic
254C2×Q8C22×D1911yescharacteristic
255C2×D4—191no—
256C2×D4—381no—
257C2×D4—761no—
258C2×D4—761no—
259C2×D4C22×D1911yescharacteristic
260C22×C4—191no—
261C22×C4—191no—
262C22×C4—191no—
263C22×C4—381no—
264Q16—41no—
265Q16—761no—
266Q16—761no—
267Q16—761no—
268SD16—41no—
269SD16—761no—
270SD16—761no—
271SD16—761no—
272C2×C8—191no—
273C2×C8—191no—
274C2×C8C22×D1911yescharacteristic
275C2×C8C22×D1911yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—191no—
278C4⋊C4—381no—
279C4⋊C4—381no—
280C4⋊C4—381no—
281C4⋊C4—381no—
282C4⋊C4—381no—
283C4⋊C4—381no—
284C4⋊C4C22×D1911yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—381no—
288C22⋊C4—381no—
289C22⋊C4—381no—
290C22⋊C4—381no—
291C22⋊C4—381no—
292C22⋊C4—381no—
293C22⋊C4—381no—
294C22⋊C4—381no—
295C42—21no—
296C42—191no—
297C42—191no—
298C42—191no—
299C42—381no—
300C42C22×D1911yescharacteristic
301C23—21no—
302C23—191no—
303C23—381no—
304C23—762no—
305C23—762no—
306C23—762no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—381no—
312Q8—381no—
313Q8—381no—
314Q8—381no—
315Q8—762no—
316Q8—762no—
317D4—21no—
318D4—21no—
319D4—381no—
320D4—381no—
321D4—762no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—191no—
326C2×C4—191no—
327C2×C4—191no—
328C2×C4—382no—
329C2×C4—381no—
330C2×C4—381no—
331C2×C4—381no—
332C2×C4—381no—
333C2×C4—381no—
334C2×C4—761no—
335C2×C4—762no—
336C2×C4D4×D1911yescharacteristic
337C2×C4D4×D1911yescharacteristic
338C2×C4C23×D1911yescharacteristic
339C8—21no—
340C8—21no—
341C8—381no—
342C8—381no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—192no—
347C22—381no—
348C22—381no—
349C22—761no—
350C22—761no—
351C22—761no—
352C22—1524no—
353C22C2×D4×D1911yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—381no—
360C4—381no—
361C4—381no—
362C4—761no—
363C4—761no—
364C4—761no—
365C4#1059743011yescharacteristic
366C4#1059743511yescharacteristic
367C2—81no—
368C2—382no—
369C2—1521no—
370C2#1192711011yescharacteristic
371C2#137×D1911yescharacteristic
372C2#1192734111yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#464C2
socleC22×C19C22×D4
prime radicalC2×D4×D19C22
hypercenter#464D19
hypocenterC19#3215
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #11927098C2semidirect
3. #11926937C2semidirect
4. #11926935C2semidirect
5. #11926905C2semidirect
6. #11926902C2semidirect
7. #11926767C2semidirect
8. #11926766C2semidirect
9. #11926763C2semidirect
10. #11926701C2semidirect
11. #11926698C2semidirect
14. #11926600C2semidirect
15. C19×#464C2semidirect
18. C2×Q16×C19C22semidirect
21. C4×Q8×C19C22semidirect
24. #10597390C22semidirect
25. C2×#64528C22semidirect
26. C2×#64528C22semidirect
30. C2×Dic76C22semidirect
35. #10597334C22semidirect
44. C4×Dic38C22semidirect
45. C19×C4⋊C8C22semidirect
46. C19×#103C22semidirect
48. #10597292C22semidirect
53. #10597273C22semidirect
54. #10597272C22semidirect
55. #10597272C22semidirect
56. #10597267C22semidirect
58. C4⋊(C19⋊C8)C22semidirect
190. #464D19semidirect
207. C2×Q16C2×D19semidirect
226. C4×Q8C2×D19semidirect
232. C4⋊C8C2×D19semidirect
236. #103C2×D19semidirect
245. C19#3215semidirect

Maximal subgroups

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

subgroupindex
#119270982
#124×D192
#119269372
#119269352
#119269052
#119269022
#119267672
#119267662
#119267632
#119267012
#119266982
#119266962
#119266932
#119266002
C19×#4642
#321519