Finite Group Databasebeta

← #14574484

Subgroups — #14574484

Order 2432.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927122C211yesmaximal, characteristic, complemented
2#11927110C211yesmaximal, characteristic, complemented
3#11926884C211yesmaximal, characteristic, complemented
4#11926866C211yesmaximal, characteristic, complemented
5#11926860C211yesmaximal, characteristic, complemented
6#11926858C211yesmaximal, characteristic, complemented
7#11926796C211yesmaximal, characteristic, complemented
8#11926787C211yesmaximal, characteristic, complemented
9#11926777C211yesmaximal, characteristic, complemented
10#11926776C211yesmaximal, characteristic, complemented
11#11926693C211yesmaximal, characteristic, complemented
12#11926689C211yesmaximal, characteristic, complemented
13#11926676C211yesmaximal, characteristic, complemented
14#11926509C211yesmaximal, characteristic, complemented
15C19×#449C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic, complemented
17C2×D4×D19C2211yescharacteristic
18C2×#64541C2211yescharacteristic
19C2×SD16×C19C2211yescharacteristic
20C2×D8×C19C2211yescharacteristic
21C19×#121C2211yescharacteristic
22#10597392C2211yescharacteristic
23#10597392C2211yescharacteristic, complemented
24C2×#64527C2211yescharacteristic
25#10597386—21no—
26#10597385—21no—
27#10597385—21no—
28#10597384C2211yescharacteristic
29#10597384C2211yescharacteristic
30#10597384C2211yescharacteristic, complemented
31#10597383—21no—
32C2×#64525C2211yescharacteristic
33#10597376—21no—
34#10597376C2211yescharacteristic
35C2×C4⋊Dic19C2211yescharacteristic, complemented
36#10597370—21no—
37C2×#64515C2211yescharacteristic, complemented
38C2×C8×D19C2211yescharacteristic, complemented
39#10597341C2211yescharacteristic
40#10597338C2211yescharacteristic
41#10597331—21no—
42#10597328—21no—
43C19×#103C2211yescharacteristic, complemented
44C19×#102C2211yescharacteristic, complemented
45C19×C22⋊C8C2211yescharacteristic, complemented
46#10597292C2211yescharacteristic, complemented
47#10597289C2211yescharacteristic
48#10597289C2211yescharacteristic
49#10597289C2211yescharacteristic, complemented
50C22⋊(C19⋊C8)C2211yescharacteristic, complemented
51#10597278C2211yescharacteristic
52#10597278C2211yescharacteristic
53(C2×D19)⋊C8C2211yescharacteristic
54(C2×D19)⋊C8C2211yescharacteristic
55#10597275C2211yescharacteristic, complemented
56#10597275C2211yescharacteristic, complemented
57#10597265C2211yescharacteristic, complemented
58#10597265C2211yescharacteristic, complemented
59C23×D19—21no—
60#41×C19—41no—
61#41×C19—41no—
62C2×Q8×C19C2311yescharacteristic
63C2×D4×C19—21no—
64C2×D4×C19—21no—
65C2×D4×C19C2311yescharacteristic
66C2×D4×C19C2311yescharacteristic
67C22×C4×C19—21no—
68C22×C4×C19C2311yescharacteristic
69C2×C22⋊D19—21no—
70C2×C22⋊D19—21no—
71C2×C22⋊D19—21no—
72C2×C22⋊D19—21no—
73C2×C22⋊D19—21no—
74C2×C22⋊D19D411yescharacteristic
75C2×C22⋊D19D411yescharacteristic
76C22×Dic19—21no—
77D4×D19—41no—
78D4×D19—41no—
79#64541—41no—
80#64541—41no—
81C2×D76—21no—
82C2×D76D411yescharacteristic
83C2×D76C2311yescharacteristic
84C2×C4×D19C2311yescharacteristic
85C2×C4×D19C2311yescharacteristic
86C2×Dic38D411yescharacteristic
87SD16×C19—41no—
88D8×C19—41no—
89C2×C8×C19C2311yescharacteristic
90C2×C8×C19C2311yescharacteristic
91C4⋊C4×C19C2311yescharacteristic
92C22⋊C4×C19—21no—
93C22⋊Dic19—21no—
94C22⋊Dic19—21no—
95C22⋊Dic19—21no—
96#64527—41no—
97#64525—41no—
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
106C4⋊Dic19C2311yescharacteristic
107Dic19⋊C4—21no—
108Dic19⋊C4—21no—
109C4×Dic19—21no—
110C2×C19⋊C8C2311yescharacteristic
111C2×C19⋊C8C2311yescharacteristic
112#64515—41no—
113C8×D19—41no—
114C23×C19—21no—
115C23×C19—21no—
116C23×C19C2×D411yescharacteristic
117C22×D19—21no—
118C22×D19—42no—
119C22×D19—81no—
120C22×D19—81no—
121C22×D19C2×D411yescharacteristic
122C22×D19C2×D411yescharacteristic
123Q8×C19—21no—
124Q8×C19—21no—
125D4×C19—21no—
126D4×C19—21no—
127D4×C19—21no—
128D4×C19—21no—
129D4×C19—42no—
130D4×C19—81no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—42no—
136C2×C4×C19C2×D411yescharacteristic
137C2×C4×C19C2411yescharacteristic
138C22⋊D19—41no—
139C22⋊D19—41no—
140C22⋊D19—42no—
141C22⋊D19—81no—
142C22⋊D19—81no—
143C22⋊D19—81no—
144C22⋊D19—81no—
145C2×Dic19—21no—
146C2×Dic19—21no—
147C2×Dic19—21no—
148C2×Dic19—81no—
149C2×Dic19C2×D411yescharacteristic
150C2×Dic19C2×D411yescharacteristic
151D76—21no—
152D76—21no—
153D76—41no—
154D76—81no—
155C4×D19—21no—
156C4×D19—21no—
157C4×D19—21no—
158C4×D19—21no—
159Dic38—41no—
160C8×C19—21no—
161C8×C19—21no—
162C19⋊C8—21no—
163C19⋊C8—21no—
164#3198—191nomaximal, Sylow
165C22×C19—21no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—41no—
169C22×C19—41no—
170C22×C19—41no—
171C22×C19—41no—
172C22×C19—41no—
173C22×C19—41no—
174C22×C19C22×D411yescharacteristic
175C2×D19—21no—
176C2×D19—21no—
177C2×D19—21no—
178C2×D19—21no—
179C2×D19—21no—
180C2×D19—21no—
181C2×D19—41no—
182C2×D19—41no—
183C2×D19—41no—
184C2×D19—84no—
185C4×C19—21no—
186C4×C19—41no—
187C4×C19—41no—
188C4×C19H(5,𝔽2)11yescharacteristic
189C4×C19H(5,𝔽2)11yescharacteristic
190Dic19—21no—
191Dic19—21no—
192Dic19—41no—
193Dic19—41no—
194Dic19—41no—
195#537—191no—
196#535—191no—
197#485—191no—
198#482—191no—
199#481—191no—
200#480—191no—
201#469—191no—
202#468—191no—
203#466—191no—
204#465—191no—
205#450—191no—
206#449—191no—
207#449D1911yescharacteristic, complemented
208#447—191no—
209#408—191no—
210C2×C19—41no—
211C2×C19—81no—
212C2×C19—81no—
213C2×C19#53411yescharacteristic
214C2×C19#57611yescharacteristic
215C2×C19#57711yescharacteristic
216D19—41no—
217D19—41no—
218D19—81no—
219C2×#41—191no—
220C2×#41C2×D1911yescharacteristic, complemented
221C22×D4—191no—
222C2×SD16—191no—
223C2×SD16C2×D1911yescharacteristic
224C2×D8—191no—
225C2×D8C2×D1911yescharacteristic
226C2×M16—191no—
227C22×C8—191no—
228#127—381no—
229#124—381no—
230C22⋊Q8—191no—
231C22⋊Q8—191no—
232C22⋊Q8—381no—
233#121—191no—
234#121—191no—
235#121—191no—
236#121—191no—
237#121—191no—
238#121—381no—
239#121—381no—
240#121—381no—
241#121C2×D1911yescharacteristic
242#120—381no—
243#120—381no—
244#117—191no—
245C2×C4⋊C4—191no—
246#107—191no—
247#107—191no—
248#106—191no—
249#106—191no—
250#103—191no—
251#103C2×D1911yescharacteristic, complemented
252#102—191no—
253#102—191no—
254#102—191no—
255#102—191no—
256#102—191no—
257#102C2×D1911yescharacteristic, complemented
258C22⋊C8—191no—
259C22⋊C8—191no—
260C22⋊C8—191no—
261C22⋊C8C2×D1911yescharacteristic, complemented
262C19#319811yescharacteristic, complemented, Sylow
263C24—381no—
264#41—41no—
265#41—41no—
266#41—761no—
267#41—761no—
268C2×Q8—191no—
269C2×Q8C22×D1911yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—191no—
273C2×D4—191no—
274C2×D4—191no—
275C2×D4—191no—
276C2×D4—381no—
277C2×D4—381no—
278C2×D4—381no—
279C2×D4—381no—
280C2×D4—381no—
281C2×D4—381no—
282C2×D4—761no—
283C2×D4—761no—
284C2×D4C22×D1911yescharacteristic
285C2×D4C22×D1911yescharacteristic
286C22×C4—21no—
287C22×C4—191no—
288C22×C4—191no—
289C22×C4—381no—
290C22×C4C22×D1911yescharacteristic
291SD16—41no—
292SD16—761no—
293D8—41no—
294D8—761no—
295M16—761no—
296C2×C8—191no—
297C2×C8—191no—
298C2×C8—761no—
299C2×C8C22×D1911yescharacteristic
300C2×C8C22×D1911yescharacteristic
301C4⋊C4—191no—
302C4⋊C4—191no—
303C4⋊C4—191no—
304C4⋊C4—381no—
305C4⋊C4—381no—
306C4⋊C4—381no—
307C4⋊C4C22×D1911yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—381no—
310C22⋊C4—381no—
311C22⋊C4—381no—
312C22⋊C4—381no—
313C22⋊C4—381no—
314C22⋊C4—381no—
315C22⋊C4—381no—
316C22⋊C4—381no—
317C42—381no—
318C23—21no—
319C23—21no—
320C23—191no—
321C23—191no—
322C23—381no—
323C23—762no—
324C23—1521no—
325C23—1521no—
326C23D4×D1911yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—761no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—81no—
336D4—381no—
337D4—381no—
338D4—761no—
339D4—761no—
340D4—761no—
341D4—762no—
342D4—1521no—
343D4—1521no—
344D4—1521no—
345D4—1521no—
346D4—1521no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—191no—
353C2×C4—191no—
354C2×C4—381no—
355C2×C4—381no—
356C2×C4—381no—
357C2×C4—381no—
358C2×C4—381no—
359C2×C4—381no—
360C2×C4—381no—
361C2×C4—1521no—
362C2×C4D4×D1911yescharacteristic
363C2×C4C23×D1911yescharacteristic
364C8—21no—
365C8—21no—
366C8—381no—
367C8—381no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—381no—
378C22—381no—
379C22—381no—
380C22—381no—
381C22—381no—
382C22—381no—
383C22—761no—
384C22—761no—
385C22—761no—
386C22—1524no—
387C22C2×D4×D1911yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—381no—
392C4—381no—
393C4—761no—
394C4—761no—
395C4—761no—
396C4#1059743011yescharacteristic
397C4#1059743011yescharacteristic
398C2—41no—
399C2—81no—
400C2—81no—
401C2—761no—
402C2—761no—
403C2—1521no—
404C2#1192710411yescharacteristic
405C2#1192734611yescharacteristic
406C2#1192735411yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#449C2
socleC22×C19C22×D4
hypercenter#449D19
hypocenterC19#3198
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #11927122C2semidirect
2. #11927110C2semidirect
3. #11926884C2semidirect
4. #11926866C2semidirect
5. #11926860C2semidirect
6. #11926858C2semidirect
7. #11926796C2semidirect
8. #11926787C2semidirect
9. #11926777C2semidirect
10. #11926776C2semidirect
11. #11926693C2semidirect
12. #11926689C2semidirect
13. #11926676C2semidirect
14. #11926509C2semidirect
15. C19×#449C2semidirect
16. C2×#41×C19C22semidirect
23. #10597392C22semidirect
30. #10597384C22semidirect
35. C2×C4⋊Dic19C22semidirect
37. C2×#64515C22semidirect
38. C2×C8×D19C22semidirect
43. C19×#103C22semidirect
44. C19×#102C22semidirect
45. C19×C22⋊C8C22semidirect
46. #10597292C22semidirect
49. #10597289C22semidirect
50. C22⋊(C19⋊C8)C22semidirect
55. #10597275C22semidirect
56. #10597275C22semidirect
57. #10597265C22semidirect
58. #10597265C22semidirect
207. #449D19semidirect
220. C2×#41C2×D19semidirect
251. #103C2×D19semidirect
257. #102C2×D19semidirect
261. C22⋊C8C2×D19semidirect
262. C19#3198semidirect

Maximal subgroups

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

subgroupindex
#119271222
#119271102
#119268842
#119268662
#119268602
#119268582
#119267962
#119267872
#119267772
#119267762
#119266932
#119266892
#119266762
#119265092
C19×#4492
#319819