Finite Group Databasebeta

← #14574541

Subgroups — #14574541

Order 2432.

402 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#11927122C211yesmaximal, characteristic, complemented
2#11926874C211yesmaximal, characteristic, complemented
3#11926872C211yesmaximal, characteristic, complemented
4#11926862C211yesmaximal, characteristic, complemented
5#11926860C211yesmaximal, characteristic, complemented
6#11926800C211yesmaximal, characteristic, complemented
7#11926795C211yesmaximal, characteristic, complemented
8#11926775C211yesmaximal, characteristic, complemented
9#11926771C211yesmaximal, characteristic, complemented
10#11926706C211yesmaximal, characteristic, complemented
11#11926704C211yesmaximal, characteristic, complemented
12#11926689C211yesmaximal, characteristic, complemented
13#11926687C211yesmaximal, characteristic, complemented
14#11926511C211yesmaximal, characteristic, complemented
15C19×#537C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C2×#41×C19C2211yescharacteristic
18C2×#64541C2211yescharacteristic
19C19×C22⋊Q8—21no—
20C19×C22⋊Q8C2211yescharacteristic
21C19×C22⋊Q8C2211yescharacteristic
22C19×#121—21no—
23C19×#121—21no—
24C19×#121—21no—
25C19×#121C2211yescharacteristic
26C19×#121C2211yescharacteristic
27C2×C4⋊C4×C19C2211yescharacteristic
28#10597392—21no—
29C2×#64528C2211yescharacteristic
30C2×#64527C2211yescharacteristic
31#10597385—21no—
32#10597385—21no—
33#10597384—21no—
34C2×#64526C2211yescharacteristic
35C2×#64525C2211yescharacteristic
36#10597376C2211yescharacteristic
37#10597376C2211yescharacteristic
38C2×C4⋊Dic19C2211yescharacteristic
39#10597370C2211yescharacteristic
40#10597370C2211yescharacteristic
41C2×#64520C2211yescharacteristic
42C22×C19⋊C8C2211yescharacteristic
43#10597292C2211yescharacteristic
44#10597292C2211yescharacteristic
45#10597289C2211yescharacteristic
46#10597289C2211yescharacteristic
47C22⋊(C19⋊C8)C2211yescharacteristic
48C22⋊(C19⋊C8)C2211yescharacteristic
49C22⋊(C19⋊C8)C2211yescharacteristic
50C22⋊(C19⋊C8)C2211yescharacteristic
51#10597267C2211yescharacteristic
52#10597267C2211yescharacteristic
53#10597266C2211yescharacteristic
54#10597266C2211yescharacteristic
55#10597265C2211yescharacteristic
56#10597265C2211yescharacteristic
57#10597265C2211yescharacteristic
58#10597265C2211yescharacteristic
59#41×C19—41no—
60#41×C19—41no—
61#41×C19—41no—
62#41×C19—41no—
63C2×Q8×C19D411yescharacteristic
64C2×Q8×C19C2311yescharacteristic
65C2×D4×C19—21no—
66C2×D4×C19—21no—
67C2×D4×C19—21no—
68C2×D4×C19D411yescharacteristic
69C2×D4×C19D411yescharacteristic
70C2×D4×C19D411yescharacteristic
71C2×D4×C19C2311yescharacteristic
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19C2311yescharacteristic
75C22×C4×C19C2311yescharacteristic
76C22×C4×C19C2311yescharacteristic
77C2×C22⋊D19—21no—
78C2×C22⋊D19—21no—
79C2×C22⋊D19—21no—
80C22×Dic19—21no—
81#64541—41no—
82#64541—41no—
83C2×D76C2311yescharacteristic
84C2×C4×D19—21no—
85C2×Dic38C2311yescharacteristic
86C4⋊C4×C19—21no—
87C4⋊C4×C19—21no—
88C4⋊C4×C19—21no—
89C4⋊C4×C19C2311yescharacteristic
90C4⋊C4×C19C2311yescharacteristic
91C22⋊C4×C19—21no—
92C22⋊C4×C19—21no—
93C22⋊C4×C19—21no—
94C22⋊C4×C19—21no—
95C22⋊Dic19—21no—
96C22⋊Dic19—21no—
97#64528—41no—
98#64527—41no—
99#64526—41no—
100#64525—41no—
101(C2×D19)⋊C4—21no—
102(C2×D19)⋊C4—21no—
103C4⋊Dic19—21no—
104C4⋊Dic19C2311yescharacteristic
105C4⋊Dic19C2311yescharacteristic
106Dic19⋊C4—21no—
107Dic19⋊C4—21no—
108#64520—41no—
109C2×C19⋊C8—41no—
110C2×C19⋊C8C2311yescharacteristic
111C2×C19⋊C8C2311yescharacteristic
112C2×C19⋊C8C2311yescharacteristic
113C2×C19⋊C8C2311yescharacteristic
114C23×C19—21no—
115C23×C19C2×D411yescharacteristic
116C23×C19C2×D411yescharacteristic
117C23×C19C2×D411yescharacteristic
118C22×D19—21no—
119Q8×C19—21no—
120Q8×C19—21no—
121Q8×C19—41no—
122D4×C19—21no—
123D4×C19—21no—
124D4×C19—41no—
125D4×C19—41no—
126D4×C19—41no—
127D4×C19—42no—
128D4×C19—81no—
129D4×C19—81no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—42no—
140C2×C4×C19—81no—
141C2×C4×C19C2×D411yescharacteristic
142C2×C4×C19C2×D411yescharacteristic
143C2×C4×C19C2×D411yescharacteristic
144C2×C4×C19C2411yescharacteristic
145C22⋊D19—42no—
146C22⋊D19—81no—
147C22⋊D19—81no—
148C2×Dic19—21no—
149C2×Dic19—21no—
150C2×Dic19—21no—
151C2×Dic19—81no—
152D76—21no—
153D76—21no—
154C4×D19—42no—
155Dic38—21no—
156Dic38—21no—
157C19⋊C8—21no—
158C19⋊C8—21no—
159C19⋊C8—21no—
160C19⋊C8—21no—
161#3204—191nomaximal, Sylow
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—21no—
165C22×C19—21no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—41no—
172C22×C19—41no—
173C22×C19—41no—
174C22×C19C22×D411yescharacteristic
175C2×D19—41no—
176C2×D19—41no—
177C2×D19—41no—
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—21no—
181C4×C19—41no—
182C4×C19—41no—
183C4×C19—41no—
184C4×C19H(5,𝔽2)11yescharacteristic
185C4×C19H(5,𝔽2)11yescharacteristic
186Dic19—41no—
187Dic19—41no—
188Dic19—41no—
189#537—191no—
190#537D1911yescharacteristic, complemented
191#483—191no—
192#483—191no—
193#481—191no—
194#481—191no—
195#470—191no—
196#469—191no—
197#465—191no—
198#465—191no—
199#452—191no—
200#452—191no—
201#449—191no—
202#449—191no—
203#408—191no—
204C2×C19—41no—
205C2×C19—41no—
206C2×C19—41no—
207C2×C19—81no—
208C2×C19#53411yescharacteristic
209C2×C19#57711yescharacteristic
210C2×C19#57711yescharacteristic
211D19—81no—
212C2×#41—191no—
213C2×#41C2×D1911yescharacteristic
214C2×#41C2×D1911yescharacteristic
215C2×Q16—191no—
216C2×SD16—191no—
217C2×SD16—191no—
218C2×D8—191no—
219C2×M16—191no—
220C22×C8—191no—
221C22⋊Q8—21no—
222C22⋊Q8—191no—
223C22⋊Q8—191no—
224C22⋊Q8—381no—
225C22⋊Q8C2×D1911yescharacteristic
226C22⋊Q8C2×D1911yescharacteristic
227#121—21no—
228#121—21no—
229#121—21no—
230#121—191no—
231#121—191no—
232#121—381no—
233#121—381no—
234#121—381no—
235#121C2×D1911yescharacteristic
236#121C2×D1911yescharacteristic
237C2×C4⋊C4—191no—
238C2×C4⋊C4C2×D1911yescharacteristic
239#106—191no—
240#106—191no—
241#106—191no—
242#106—191no—
243#103—191no—
244#103—191no—
245#103—191no—
246#103—191no—
247#102—191no—
248#102—191no—
249#102—191no—
250#102—191no—
251C22⋊C8—191no—
252C22⋊C8—191no—
253C22⋊C8—191no—
254C22⋊C8—191no—
255C19#320411yescharacteristic, complemented, Sylow
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260#41—761no—
261#41—761no—
262C2×Q8—191no—
263C2×Q8C22⋊D1911yescharacteristic
264C2×Q8C22×D1911yescharacteristic
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—191no—
269C2×D4—381no—
270C2×D4—381no—
271C2×D4—381no—
272C2×D4C22⋊D1911yescharacteristic
273C2×D4C22⋊D1911yescharacteristic
274C2×D4C22⋊D1911yescharacteristic
275C2×D4C22×D1911yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—381no—
279C22×C4—381no—
280C22×C4C22×D1911yescharacteristic
281C22×C4C22×D1911yescharacteristic
282C22×C4C22×D1911yescharacteristic
283Q16—761no—
284SD16—761no—
285SD16—761no—
286D8—761no—
287M16—761no—
288C2×C8—191no—
289C2×C8—191no—
290C2×C8—191no—
291C2×C8—191no—
292C2×C8—761no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—191no—
297C4⋊C4—191no—
298C4⋊C4—381no—
299C4⋊C4—381no—
300C4⋊C4—381no—
301C4⋊C4C22×D1911yescharacteristic
302C4⋊C4C22×D1911yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—381no—
308C22⋊C4—381no—
309C22⋊C4—381no—
310C22⋊C4—381no—
311C23—21no—
312C23—381no—
313C23C2×C22⋊D1911yescharacteristic
314C23C2×C22⋊D1911yescharacteristic
315C23C2×C22⋊D1911yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—41no—
319Q8—381no—
320Q8—381no—
321D4—21no—
322D4—21no—
323D4—41no—
324D4—41no—
325D4—41no—
326D4—42no—
327D4—81no—
328D4—81no—
329D4—381no—
330D4—381no—
331D4—762no—
332D4—1521no—
333D4—1521no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—81no—
345C2×C4—381no—
346C2×C4—381no—
347C2×C4—381no—
348C2×C4—762no—
349C2×C4—1521no—
350C2×C4C2×C22⋊D1911yescharacteristic
351C2×C4C2×C22⋊D1911yescharacteristic
352C2×C4C2×C22⋊D1911yescharacteristic
353C2×C4C23×D1911yescharacteristic
354C8—381no—
355C8—381no—
356C8—381no—
357C8—381no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—761no—
371C22—761no—
372C22—761no—
373C22C22×C22⋊D1911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—761no—
381C4—761no—
382C4—761no—
383C4#1059743011yescharacteristic
384C4#1059743011yescharacteristic
385C2—41no—
386C2—41no—
387C2—41no—
388C2—81no—
389C2—1521no—
390C2#1192710311yescharacteristic
391C2#1192735211yescharacteristic
392C2#1192735511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#537C2
socleC22×C19C22×D4
hypercenter#537D19
hypocenterC19#3204
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #11927122C2semidirect
2. #11926874C2semidirect
3. #11926872C2semidirect
4. #11926862C2semidirect
5. #11926860C2semidirect
6. #11926800C2semidirect
7. #11926795C2semidirect
8. #11926775C2semidirect
9. #11926771C2semidirect
10. #11926706C2semidirect
11. #11926704C2semidirect
12. #11926689C2semidirect
13. #11926687C2semidirect
14. #11926511C2semidirect
15. C19×#537C2semidirect
190. #537D19semidirect
255. C19#3204semidirect

Maximal subgroups

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

subgroupindex
#119271222
#119268742
#119268722
#119268622
#119268602
#119268002
#119267952
#119267752
#119267712
#119267062
#119267042
#119266892
#119266872
#119265112
C19×#5372
#320419