Finite Group Databasebeta

← #14574735

Subgroups — #14574735

Order 2432.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927167C211yesmaximal, characteristic, complemented
2#11927108C211yesmaximal, characteristic, complemented
3#11926930C211yesmaximal, characteristic, complemented
4#11926929C211yesmaximal, characteristic, complemented
5#11926905C211yesmaximal, characteristic, complemented
6#11926889C211yesmaximal, characteristic, complemented
7#11926768C211yesmaximal, characteristic, complemented
8#11926762C211yesmaximal, characteristic, complemented
9#11926742C211yesmaximal, characteristic, complemented
10#11926738C211yesmaximal, characteristic, complemented
11#11926694C211yesmaximal, characteristic, complemented
12#11926689C211yesmaximal, characteristic, complemented
13#11926680C211yesmaximal, characteristic, complemented
14#11926602C211yesmaximal, characteristic, complemented
15C19×#452C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C22×D76C2211yescharacteristic
18C2×Q16×C19C2211yescharacteristic, complemented
19C2×SD16×C19C2211yescharacteristic, complemented
20C19×C22⋊Q8C2211yescharacteristic
21#10597393C2211yescharacteristic
22#10597393C2211yescharacteristic
23#10597393C2211yescharacteristic, complemented
24Q8×Dic19C2211yescharacteristic, complemented
25C2×#64527C2211yescharacteristic
26C2×#64527C2211yescharacteristic
27C2×#64527C2211yescharacteristic, complemented
28#10597386C2211yescharacteristic
29#10597386C2211yescharacteristic
30#10597383—21no—
31#10597383—21no—
32C2×#64525C2211yescharacteristic, complemented
33#10597376—21no—
34#10597376—21no—
35#10597376C2211yescharacteristic
36#10597372C2211yescharacteristic
37C2×D152C2211yescharacteristic
38C2×D152C2211yescharacteristic
39#10597344—21no—
40#10597343—21no—
41#10597339C2211yescharacteristic, complemented
42#10597334C2211yescharacteristic, complemented
43#10597331—21no—
44#10597329—21no—
45C19×#103C2211yescharacteristic, complemented
46C19×#102C2211yescharacteristic, complemented
47C19×C22⋊C8C2211yescharacteristic
48#10597292C2211yescharacteristic, complemented
49#10597289C2211yescharacteristic, complemented
50C22⋊(C19⋊C8)C2211yescharacteristic
51#10597278C2211yescharacteristic
52#10597278C2211yescharacteristic
53#10597272C2211yescharacteristic, complemented
54Dic19⋊C8C2211yescharacteristic, complemented
55Dic19⋊C8C2211yescharacteristic, complemented
56C8×Dic19C2211yescharacteristic, complemented
57#10597266C2211yescharacteristic
58#10597266C2211yescharacteristic
59C23×D19—21no—
60#41×C19—41no—
61#41×C19—41no—
62C2×Q8×C19C2311yescharacteristic
63C2×Q8×C19C2311yescharacteristic
64C2×D4×C19—21no—
65C2×D4×C19C2311yescharacteristic
66C22×C4×C19—21no—
67C22×C4×C19C2311yescharacteristic
68C2×C22⋊D19—21no—
69C2×C22⋊D19—21no—
70C2×C22⋊D19—21no—
71C2×C22⋊D19—21no—
72C2×C22⋊D19—21no—
73C2×D76—21no—
74C2×D76—41no—
75C2×D76—41no—
76C2×D76C2311yescharacteristic
77C2×D76C2311yescharacteristic
78C2×D76C2311yescharacteristic
79C2×C4×D19—21no—
80C2×Dic38—21no—
81Q16×C19—41no—
82SD16×C19—41no—
83C2×C8×C19C2311yescharacteristic
84C2×C8×C19C2311yescharacteristic
85C4⋊C4×C19—21no—
86C4⋊C4×C19C2311yescharacteristic
87C22⋊C4×C19—21no—
88C22⋊Dic19D411yescharacteristic
89C22⋊Dic19D411yescharacteristic
90#64527—41no—
91#64527—41no—
92#64527—41no—
93#64525—41no—
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—
99(C2×D19)⋊C4—21no—
100(C2×D19)⋊C4—21no—
101(C2×D19)⋊C4—21no—
102C4⋊Dic19—21no—
103C4⋊Dic19D411yescharacteristic
104C4⋊Dic19D411yescharacteristic
105C4⋊Dic19C2311yescharacteristic
106Dic19⋊C4—21no—
107C4×Dic19—21no—
108C4×Dic19C2311yescharacteristic
109C4×Dic19C2311yescharacteristic
110C2×C19⋊C8C2311yescharacteristic
111C2×C19⋊C8C2311yescharacteristic
112D152—41no—
113D152—41no—
114C23×C19—21no—
115C23×C19C2×D411yescharacteristic
116C22×D19—21no—
117C22×D19—21no—
118C22×D19—21no—
119C22×D19—42no—
120C22×D19—81no—
121C22×D19—81no—
122Q8×C19—21no—
123Q8×C19—21no—
124Q8×C19—21no—
125Q8×C19—21no—
126D4×C19—21no—
127D4×C19—21no—
128D4×C19—42no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—42no—
135C2×C4×C19C2×D411yescharacteristic
136C2×C4×C19C2411yescharacteristic
137C22⋊D19—81no—
138C22⋊D19—81no—
139C22⋊D19—81no—
140C22⋊D19—81no—
141C22⋊D19—81no—
142C2×Dic19—21no—
143C2×Dic19C2×D411yescharacteristic
144C2×Dic19C2×D411yescharacteristic
145C2×Dic19C2×D411yescharacteristic
146C2×Dic19C2×D411yescharacteristic
147D76—21no—
148D76—21no—
149D76—21no—
150D76—21no—
151D76—21no—
152D76—21no—
153D76—42no—
154C4×D19—81no—
155Dic38—81no—
156C8×C19—21no—
157C8×C19—21no—
158C19⋊C8—21no—
159C19⋊C8—21no—
160#3224—191nomaximal, Sylow
161C22×C19—21no—
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—41no—
165C22×C19—41no—
166C22×C19—41no—
167C22×C19C22×D411yescharacteristic
168C2×D19—41no—
169C2×D19—41no—
170C2×D19—41no—
171C2×D19—41no—
172C2×D19—41no—
173C2×D19—41no—
174C2×D19—41no—
175C2×D19—41no—
176C2×D19—41no—
177C2×D19—84no—
178C4×C19—21no—
179C4×C19—41no—
180C4×C19—41no—
181C4×C19—41no—
182C4×C19H(5,𝔽2)11yescharacteristic
183C4×C19H(5,𝔽2)11yescharacteristic
184Dic19—21no—
185Dic19—21no—
186Dic19—21no—
187Dic19—21no—
188Dic19—41no—
189#542—191no—
190#535—191no—
191#496—191no—
192#495—191no—
193#489—191no—
194#486—191no—
195#464—191no—
196#463—191no—
197#460—191no—
198#459—191no—
199#452D1911yescharacteristic, complemented
200#450—191no—
201#449—191no—
202#447—191no—
203#433—191no—
204C2×C19—41no—
205C2×C19—81no—
206C2×C19#53511yescharacteristic
207C2×C19#57611yescharacteristic
208C2×C19#57711yescharacteristic
209D19—81no—
210D19—81no—
211D19—81no—
212C2×#41C2×D1911yescharacteristic
213C22×D4—191no—
214C2×Q16C2×D1911yescharacteristic, complemented
215C2×SD16—191no—
216C2×SD16—191no—
217C2×SD16—191no—
218C2×SD16C2×D1911yescharacteristic, complemented
219C2×D8—191no—
220C2×D8—191no—
221C2×D8—191no—
222C4⋊Q8—191no—
223#127—191no—
224#127—191no—
225#126—381no—
226#124—191no—
227#124—191no—
228#124—191no—
229#124—381no—
230#123—381no—
231C22⋊Q8—381no—
232C22⋊Q8C2×D1911yescharacteristic
233#121—191no—
234#121—381no—
235#121—381no—
236#120—381no—
237#120—381no—
238C4×Q8—191no—
239C4×D4—191no—
240#117—191no—
241C4⋊C8—191no—
242C4⋊C8—191no—
243#103—191no—
244#103C2×D1911yescharacteristic, complemented
245#102—191no—
246#102—191no—
247#102—191no—
248#102—191no—
249#102—191no—
250#102C2×D1911yescharacteristic, complemented
251C22⋊C8—191no—
252C22⋊C8C2×D1911yescharacteristic
253#97—191no—
254C4×C8—191no—
255C19#322411yescharacteristic, complemented, Sylow
256C24—381no—
257#41—41no—
258#41—41no—
259C2×Q8—381no—
260C2×Q8C22×D1911yescharacteristic
261C2×Q8C22×D1911yescharacteristic
262C2×D4—21no—
263C2×D4—191no—
264C2×D4—191no—
265C2×D4—191no—
266C2×D4—381no—
267C2×D4—381no—
268C2×D4—381no—
269C2×D4—381no—
270C2×D4—381no—
271C2×D4—381no—
272C2×D4—761no—
273C2×D4—761no—
274C2×D4C22×D1911yescharacteristic
275C22×C4—21no—
276C22×C4—381no—
277C22×C4C22×D1911yescharacteristic
278Q16—41no—
279SD16—41no—
280SD16—761no—
281SD16—761no—
282SD16—761no—
283D8—761no—
284D8—761no—
285D8—761no—
286C2×C8—191no—
287C2×C8—191no—
288C2×C8C22×D1911yescharacteristic
289C2×C8C22×D1911yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—191no—
292C4⋊C4—191no—
293C4⋊C4—191no—
294C4⋊C4—381no—
295C4⋊C4—381no—
296C4⋊C4C22×D1911yescharacteristic
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—
306C22⋊C4—381no—
307C22⋊C4—381no—
308C42—191no—
309C42—191no—
310C42—381no—
311C23—21no—
312C23—381no—
313C23—381no—
314C23—381no—
315C23—762no—
316C23—1521no—
317C23—1521no—
318C23D4×D1911yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—1521no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—381no—
328D4—381no—
329D4—381no—
330D4—381no—
331D4—381no—
332D4—381no—
333D4—762no—
334D4—1521no—
335D4—1521no—
336D4—1521no—
337D4—1521no—
338D4—1521no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—191no—
346C2×C4—191no—
347C2×C4—191no—
348C2×C4—191no—
349C2×C4—381no—
350C2×C4—1521no—
351C2×C4D4×D1911yescharacteristic
352C2×C4C23×D1911yescharacteristic
353C8—21no—
354C8—21no—
355C8—381no—
356C8—381no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—761no—
364C22—761no—
365C22—761no—
366C22—761no—
367C22—761no—
368C22—761no—
369C22—761no—
370C22—761no—
371C22—761no—
372C22—1524no—
373C22C2×D4×D1911yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—381no—
379C4—381no—
380C4—381no—
381C4—381no—
382C4—761no—
383C4#1059743011yescharacteristic
384C4#1059743011yescharacteristic
385C2—41no—
386C2—81no—
387C2—1521no—
388C2—1521no—
389C2—1521no—
390C2#1192710911yescharacteristic
391C2#1192734611yescharacteristic
392C2#1192735311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#452C2
socleC22×C19C22×D4
hypercenter#452D19
hypocenterC19#3224
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #11927167C2semidirect
2. #11927108C2semidirect
3. #11926930C2semidirect
4. #11926929C2semidirect
5. #11926905C2semidirect
6. #11926889C2semidirect
7. #11926768C2semidirect
8. #11926762C2semidirect
9. #11926742C2semidirect
10. #11926738C2semidirect
11. #11926694C2semidirect
12. #11926689C2semidirect
13. #11926680C2semidirect
14. #11926602C2semidirect
15. C19×#452C2semidirect
18. C2×Q16×C19C22semidirect
19. C2×SD16×C19C22semidirect
23. #10597393C22semidirect
24. Q8×Dic19C22semidirect
27. C2×#64527C22semidirect
32. C2×#64525C22semidirect
41. #10597339C22semidirect
42. #10597334C22semidirect
45. C19×#103C22semidirect
46. C19×#102C22semidirect
48. #10597292C22semidirect
49. #10597289C22semidirect
53. #10597272C22semidirect
54. Dic19⋊C8C22semidirect
55. Dic19⋊C8C22semidirect
56. C8×Dic19C22semidirect
199. #452D19semidirect
214. C2×Q16C2×D19semidirect
218. C2×SD16C2×D19semidirect
244. #103C2×D19semidirect
250. #102C2×D19semidirect
255. C19#3224semidirect

Maximal subgroups

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

subgroupindex
#119271672
#119271082
#119269302
#119269292
#119269052
#119268892
#119267682
#119267622
#119267422
#119267382
#119266942
#119266892
#119266802
#119266022
C19×#4522
#322419