Finite Group Databasebeta

← #14574503

Subgroups — #14574503

Order 2432.

410 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927117C211yesmaximal, characteristic, complemented
2#11927110C211yesmaximal, characteristic
3#11926887C211yesmaximal, characteristic, complemented
4#11926884C211yesmaximal, characteristic, complemented
5#11926871C211yesmaximal, characteristic, complemented
6#11926866C211yesmaximal, characteristic, complemented
7#11926790C211yesmaximal, characteristic, complemented
8#11926775C211yesmaximal, characteristic, complemented
9#11926771C211yesmaximal, characteristic, complemented
10#11926696C211yesmaximal, characteristic, complemented
11#11926693C211yesmaximal, characteristic, complemented
12#11926684C211yesmaximal, characteristic, complemented
13#11926681C211yesmaximal, characteristic, complemented
14#11926512C211yesmaximal, characteristic, complemented
15C19×#468C211yesmaximal, characteristic, complemented
16C2×Q8×D19C2211yescharacteristic, complemented
17C2×D4×D19C2211yescharacteristic
18C2×#64541C2211yescharacteristic
19C2×SD16×C19C2211yescharacteristic
20C2×M16×C19C2211yescharacteristic, complemented
21C19×C22⋊Q8C2211yescharacteristic, complemented
22C19×#121C2211yescharacteristic
23#10597392C2211yescharacteristic
24C2×#64527C2211yescharacteristic
25#10597386—21no—
26#10597384C2211yescharacteristic
27#10597383—21no—
28C2×#64526C2211yescharacteristic
29#10597376C2211yescharacteristic
30#10597370C2211yescharacteristic, complemented
31C22×C19⋊C8C2211yescharacteristic, complemented
32C2×#64516C2211yescharacteristic
33#10597343C2211yescharacteristic
34#10597341C2211yescharacteristic
35#10597340—21no—
36#10597338C2211yescharacteristic
37#10597338C2211yescharacteristic, complemented
38#10597334—21no—
39#10597331—21no—
40#10597331—21no—
41#10597329—21no—
42#10597328—21no—
43C19×#107C2211yescharacteristic, complemented
44C19×#103C2211yescharacteristic, complemented
45C19×#102C2211yescharacteristic
46#10597292C2211yescharacteristic, complemented
47#10597289C2211yescharacteristic
48#10597278C2211yescharacteristic
49(C2×D19)⋊C8C2211yescharacteristic
50(C2×D19)⋊C8C2211yescharacteristic
51(C2×D19)⋊C8C2211yescharacteristic, complemented
52(C2×D19)⋊C8C2211yescharacteristic, complemented
53#10597275C2211yescharacteristic, complemented
54#10597273C2211yescharacteristic, complemented
55#10597267C2211yescharacteristic, complemented
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⋊D19—21no—
66C2×C22⋊D19—21no—
67C2×C22⋊D19D411yescharacteristic
68C2×C22⋊D19D411yescharacteristic
69Q8×D19—41no—
70Q8×D19—41no—
71D4×D19—41no—
72D4×D19—41no—
73#64541—41no—
74#64541—41no—
75C2×D76—21no—
76C2×D76D411yescharacteristic
77C2×D76C2311yescharacteristic
78C2×C4×D19—21no—
79C2×C4×D19C2311yescharacteristic
80C2×C4×D19C2311yescharacteristic
81C2×Dic38—21no—
82C2×Dic38D411yescharacteristic
83C2×Dic38C2311yescharacteristic
84SD16×C19—41no—
85M16×C19—41no—
86C2×C8×C19C2311yescharacteristic
87C2×C8×C19C2311yescharacteristic
88C4⋊C4×C19—21no—
89C4⋊C4×C19C2311yescharacteristic
90C4⋊C4×C19C2311yescharacteristic
91C22⋊C4×C19—21no—
92C22⋊C4×C19—21no—
93C22⋊Dic19—21no—
94C22⋊Dic19—21no—
95#64527—41no—
96#64526—41no—
97(C2×D19)⋊C4—21no—
98(C2×D19)⋊C4—21no—
99(C2×D19)⋊C4—21no—
100(C2×D19)⋊C4—21no—
101(C2×D19)⋊C4—21no—
102(C2×D19)⋊C4—21no—
103C4⋊Dic19—21no—
104C4⋊Dic19C2311yescharacteristic
105C4⋊Dic19C2311yescharacteristic
106Dic19⋊C4—21no—
107Dic19⋊C4—21no—
108C4×Dic19—21no—
109C4×Dic19—21no—
110C2×C19⋊C8—41no—
111C2×C19⋊C8C2311yescharacteristic
112C2×C19⋊C8C2311yescharacteristic
113#64516—41no—
114C23×C19—21no—
115C23×C19C2×D411yescharacteristic
116C22×D19—21no—
117C22×D19—42no—
118C22×D19—81no—
119C22×D19—81no—
120C22×D19C2×D411yescharacteristic
121C22×D19C2×D411yescharacteristic
122Q8×C19—21no—
123Q8×C19—21no—
124D4×C19—21no—
125D4×C19—21no—
126D4×C19—81no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19C2×D411yescharacteristic
133C2×C4×C19C2411yescharacteristic
134C22⋊D19—41no—
135C22⋊D19—41no—
136C22⋊D19—42no—
137C22⋊D19—81no—
138C22⋊D19—81no—
139C2×Dic19—21no—
140C2×Dic19—21no—
141C2×Dic19—21no—
142C2×Dic19C2×D411yescharacteristic
143C2×Dic19C2×D411yescharacteristic
144D76—21no—
145D76—21no—
146D76—41no—
147D76—81no—
148C4×D19—21no—
149C4×D19—21no—
150C4×D19—21no—
151C4×D19—21no—
152C4×D19—42no—
153Dic38—21no—
154Dic38—21no—
155Dic38—41no—
156Dic38—42no—
157C8×C19—21no—
158C8×C19—21no—
159C19⋊C8—21no—
160C19⋊C8—21no—
161#3200—191nomaximal, Sylow
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—21no—
165C22×C19—41no—
166C22×C19—41no—
167C22×C19—41no—
168C22×C19C22×D411yescharacteristic
169C2×D19—21no—
170C2×D19—21no—
171C2×D19—21no—
172C2×D19—21no—
173C2×D19—21no—
174C2×D19—21no—
175C2×D19—41no—
176C2×D19—41no—
177C2×D19—41no—
178C2×D19—84no—
179C4×C19—21no—
180C4×C19—41no—
181C4×C19—41no—
182C4×C19—41no—
183C4×C19H(5,𝔽2)11yescharacteristic
184C4×C19H(5,𝔽2)11yescharacteristic
185Dic19—21no—
186Dic19—21no—
187Dic19—41no—
188Dic19—41no—
189Dic19—41no—
190#536—191no—
191#535—191no—
192#485—191no—
193#485—191no—
194#482—191no—
195#482—191no—
196#468—191no—
197#468D1911yescharacteristic, complemented
198#465—191no—
199#465—191no—
200#450—191no—
201#450—191no—
202#448—191no—
203#448—191no—
204#408—191no—
205C2×C19—41no—
206C2×C19—81no—
207C2×C19#53411yescharacteristic
208C2×C19#57711yescharacteristic
209C2×C19#57711yescharacteristic
210D19—41no—
211D19—41no—
212D19—81no—
213C2×#41—191no—
214C22×Q8—191no—
215C22×D4—191no—
216C2×SD16—191no—
217C2×SD16—191no—
218C2×SD16—191no—
219C2×SD16C2×D1911yescharacteristic
220C2×M16C2×D1911yescharacteristic, complemented
221C22×C8—191no—
222C4⋊Q8—381no—
223#127—381no—
224#124—381no—
225#124—381no—
226#123—381no—
227#123—381no—
228C22⋊Q8—191no—
229C22⋊Q8—191no—
230C22⋊Q8—191no—
231C22⋊Q8C2×D1911yescharacteristic, complemented
232#121—191no—
233#121—191no—
234#121—191no—
235#121C2×D1911yescharacteristic
236#120—381no—
237#120—381no—
238#117—191no—
239#117—191no—
240#107—191no—
241#107C2×D1911yescharacteristic, complemented
242#106—191no—
243#106—191no—
244#103—191no—
245#103—191no—
246#103—191no—
247#103C2×D1911yescharacteristic, complemented
248#102—191no—
249#102—191no—
250#102—191no—
251#102C2×D1911yescharacteristic
252C22⋊C8—191no—
253C22⋊C8—191no—
254C22⋊C8—191no—
255C22⋊C8—191no—
256C19#320011yescharacteristic, complemented, Sylow
257C24—381no—
258#41—761no—
259#41—761no—
260C2×Q8—191no—
261C2×Q8—191no—
262C2×Q8—381no—
263C2×Q8—761no—
264C2×Q8—761no—
265C2×Q8C22×D1911yescharacteristic
266C2×D4—21no—
267C2×D4—191no—
268C2×D4—191no—
269C2×D4—191no—
270C2×D4—191no—
271C2×D4—381no—
272C2×D4—381no—
273C2×D4—381no—
274C2×D4—381no—
275C2×D4—761no—
276C2×D4—761no—
277C2×D4C22×D1911yescharacteristic
278C22×C4—191no—
279C22×C4—191no—
280C22×C4—381no—
281C22×C4C22×D1911yescharacteristic
282SD16—41no—
283SD16—761no—
284SD16—761no—
285SD16—761no—
286M16—41no—
287C2×C8—191no—
288C2×C8—191no—
289C2×C8—761no—
290C2×C8C22×D1911yescharacteristic
291C2×C8C22×D1911yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—191no—
294C4⋊C4—191no—
295C4⋊C4—381no—
296C4⋊C4—381no—
297C4⋊C4—381no—
298C4⋊C4C22×D1911yescharacteristic
299C4⋊C4C22×D1911yescharacteristic
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—
310C42—381no—
311C42—381no—
312C23—21no—
313C23—191no—
314C23—191no—
315C23—381no—
316C23—762no—
317C23—1521no—
318C23—1521no—
319C23D4×D1911yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—381no—
323Q8—381no—
324Q8—761no—
325Q8—762no—
326D4—21no—
327D4—21no—
328D4—81no—
329D4—381no—
330D4—381no—
331D4—761no—
332D4—761no—
333D4—761no—
334D4—762no—
335D4—1521no—
336D4—1521no—
337D4—1521no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—191no—
344C2×C4—191no—
345C2×C4—381no—
346C2×C4—381no—
347C2×C4—381no—
348C2×C4—381no—
349C2×C4—381no—
350C2×C4—381no—
351C2×C4—381no—
352C2×C4—762no—
353C2×C4D4×D1911yescharacteristic
354C2×C4C23×D1911yescharacteristic
355C8—21no—
356C8—21no—
357C8—381no—
358C8—381no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—381no—
366C22—381no—
367C22—381no—
368C22—381no—
369C22—381no—
370C22—381no—
371C22—761no—
372C22—761no—
373C22—761no—
374C22—1524no—
375C22C2×D4×D1911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—381no—
381C4—381no—
382C4—761no—
383C4—761no—
384C4—761no—
385C4#1059743011yescharacteristic
386C4#1059743511yescharacteristic
387C2—41no—
388C2—81no—
389C2—761no—
390C2—761no—
391C2—1521no—
392C2#1192710211yescharacteristic
393C2#1192735311yescharacteristic
394C2#1192735411yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#468C2
socleC22×C19C22×D4
prime radical#11927110C2
hypercenter#468D19
hypocenterC19#3200
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #11927117C2semidirect
3. #11926887C2semidirect
4. #11926884C2semidirect
5. #11926871C2semidirect
6. #11926866C2semidirect
7. #11926790C2semidirect
8. #11926775C2semidirect
9. #11926771C2semidirect
10. #11926696C2semidirect
11. #11926693C2semidirect
12. #11926684C2semidirect
13. #11926681C2semidirect
14. #11926512C2semidirect
15. C19×#468C2semidirect
16. C2×Q8×D19C22semidirect
20. C2×M16×C19C22semidirect
21. C19×C22⋊Q8C22semidirect
30. #10597370C22semidirect
31. C22×C19⋊C8C22semidirect
37. #10597338C22semidirect
43. C19×#107C22semidirect
44. C19×#103C22semidirect
46. #10597292C22semidirect
51. (C2×D19)⋊C8C22semidirect
52. (C2×D19)⋊C8C22semidirect
53. #10597275C22semidirect
54. #10597273C22semidirect
55. #10597267C22semidirect
57. #10597265C22semidirect
58. #10597265C22semidirect
197. #468D19semidirect
220. C2×M16C2×D19semidirect
231. C22⋊Q8C2×D19semidirect
241. #107C2×D19semidirect
247. #103C2×D19semidirect
256. C19#3200semidirect

Maximal subgroups

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

subgroupindex
#119271172
#119271102
#119268872
#119268842
#119268712
#119268662
#119267902
#119267752
#119267712
#119266962
#119266932
#119266842
#119266812
#119265122
C19×#4682
#320019