Finite Group Databasebeta

← #14574705

Subgroups — #14574705

Order 2432.

396 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927154C211yesmaximal, characteristic, complemented
2#11927108C211yesmaximal, characteristic
3#11926937C211yesmaximal, characteristic, complemented
4#11926915C211yesmaximal, characteristic, complemented
5#11926907C211yesmaximal, characteristic, complemented
6#11926900C211yesmaximal, characteristic, complemented
7#11926769C211yesmaximal, characteristic, complemented
8#11926768C211yesmaximal, characteristic, complemented
9#11926743C211yesmaximal, characteristic, complemented
10#11926742C211yesmaximal, characteristic, complemented
11#11926706C211yesmaximal, characteristic, complemented
12#11926697C211yesmaximal, characteristic, complemented
13#11926694C211yesmaximal, 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
23Q8×Dic19C2211yescharacteristic, complemented
24#10597390C2211yescharacteristic, complemented
25C2×#64528C2211yescharacteristic, complemented
26C2×#64527C2211yescharacteristic
27C2×#64527C2211yescharacteristic
28#10597386C2211yescharacteristic
29#10597386C2211yescharacteristic
30#10597383—21no—
31#10597383—21no—
32C2×#64526C2211yescharacteristic, complemented
33#10597376—21no—
34#10597376—21no—
35#10597372C2211yescharacteristic
36#10597370C2211yescharacteristic
37C2×#64516C2211yescharacteristic
38C2×#64516C2211yescharacteristic
39#10597336—21no—
40#10597336C2211yescharacteristic, complemented
41#10597335—21no—
42#10597333C2211yescharacteristic, complemented
43#10597325—21no—
44#10597325—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×D76—21no—
73C2×D76—41no—
74C2×D76—41no—
75C2×D76C2311yescharacteristic
76C2×D76C2311yescharacteristic
77C2×Dic38C2311yescharacteristic
78Q16×C19—41no—
79SD16×C19—41no—
80C2×C8×C19C2311yescharacteristic
81C2×C8×C19C2311yescharacteristic
82C4⋊C4×C19—21no—
83C4⋊C4×C19C2311yescharacteristic
84C22⋊C4×C19—21no—
85C22⋊Dic19—21no—
86C22⋊Dic19D411yescharacteristic
87C22⋊Dic19D411yescharacteristic
88#64528—41no—
89#64527—41no—
90#64527—41no—
91#64526—41no—
92(C2×D19)⋊C4—21no—
93(C2×D19)⋊C4—21no—
94(C2×D19)⋊C4—21no—
95(C2×D19)⋊C4—21no—
96C4⋊Dic19—21no—
97C4⋊Dic19—21no—
98C4⋊Dic19D411yescharacteristic
99C4⋊Dic19D411yescharacteristic
100C4⋊Dic19C2311yescharacteristic
101Dic19⋊C4—21no—
102Dic19⋊C4—21no—
103Dic19⋊C4—21no—
104Dic19⋊C4—21no—
105Dic19⋊C4—21no—
106C4×Dic19—21no—
107C4×Dic19—21no—
108C4×Dic19C2311yescharacteristic
109C4×Dic19C2311yescharacteristic
110C2×C19⋊C8C2311yescharacteristic
111C2×C19⋊C8C2311yescharacteristic
112#64516—41no—
113#64516—41no—
114C23×C19—21no—
115C23×C19C2×D411yescharacteristic
116C22×D19—21no—
117C22×D19—21no—
118C22×D19—42no—
119C22×D19—81no—
120C22×D19—81no—
121Q8×C19—21no—
122Q8×C19—21no—
123Q8×C19—21no—
124Q8×C19—21no—
125D4×C19—21no—
126D4×C19—21no—
127D4×C19—42no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—42no—
134C2×C4×C19C2×D411yescharacteristic
135C2×C4×C19C2411yescharacteristic
136C22⋊D19—81no—
137C22⋊D19—81no—
138C22⋊D19—81no—
139C22⋊D19—81no—
140C2×Dic19—21no—
141C2×Dic19—21no—
142C2×Dic19C2×D411yescharacteristic
143C2×Dic19C2×D411yescharacteristic
144C2×Dic19C2×D411yescharacteristic
145C2×Dic19C2×D411yescharacteristic
146D76—21no—
147D76—21no—
148D76—21no—
149D76—21no—
150D76—42no—
151Dic38—21no—
152Dic38—21no—
153C8×C19—21no—
154C8×C19—21no—
155C19⋊C8—21no—
156C19⋊C8—21no—
157#3222—191nomaximal, Sylow
158C22×C19—21no—
159C22×C19—21no—
160C22×C19—21no—
161C22×C19—41no—
162C22×C19—41no—
163C22×C19—41no—
164C22×C19C22×D411yescharacteristic
165C2×D19—41no—
166C2×D19—41no—
167C2×D19—41no—
168C2×D19—41no—
169C2×D19—41no—
170C2×D19—41no—
171C2×D19—84no—
172C4×C19—21no—
173C4×C19—41no—
174C4×C19—41no—
175C4×C19—41no—
176C4×C19H(5,𝔽2)11yescharacteristic
177C4×C19H(5,𝔽2)11yescharacteristic
178Dic19—21no—
179Dic19—21no—
180Dic19—21no—
181Dic19—21no—
182Dic19—41no—
183Dic19—41no—
184#541—191no—
185#535—191no—
186#497—191no—
187#492—191no—
188#490—191no—
189#488—191no—
190#464—191no—
191#464—191no—
192#460—191no—
193#460—191no—
194#452—191no—
195#452D1911yescharacteristic, complemented
196#450—191no—
197#450—191no—
198#433—191no—
199C2×C19—41no—
200C2×C19—81no—
201C2×C19#53511yescharacteristic
202C2×C19#57711yescharacteristic
203C2×C19#57711yescharacteristic
204D19—81no—
205D19—81no—
206C2×#41C2×D1911yescharacteristic
207C22×D4—191no—
208C2×Q16—191no—
209C2×Q16C2×D1911yescharacteristic, complemented
210C2×SD16—191no—
211C2×SD16—191no—
212C2×SD16—191no—
213C2×SD16—191no—
214C2×SD16—191no—
215C2×SD16C2×D1911yescharacteristic, complemented
216C4⋊Q8—191no—
217#127—191no—
218#127—191no—
219#126—381no—
220#126—381no—
221#125—191no—
222#125—381no—
223#125—381no—
224#124—191no—
225#124—191no—
226C22⋊Q8—191no—
227C22⋊Q8C2×D1911yescharacteristic
228#121—381no—
229#121—381no—
230#120—381no—
231#120—381no—
232C4×Q8—191no—
233C4×Q8—191no—
234#117—191no—
235C4⋊C8—191no—
236C4⋊C8—191no—
237#103—191no—
238#103C2×D1911yescharacteristic, complemented
239#102—191no—
240#102—191no—
241#102—191no—
242#102—191no—
243#102—191no—
244#102C2×D1911yescharacteristic, complemented
245C22⋊C8—191no—
246C22⋊C8C2×D1911yescharacteristic
247#97—191no—
248C4×C8—191no—
249C19#322211yescharacteristic, complemented, Sylow
250C24—381no—
251#41—41no—
252#41—41no—
253C2×Q8—191no—
254C2×Q8C22×D1911yescharacteristic
255C2×Q8C22×D1911yescharacteristic
256C2×D4—21no—
257C2×D4—191no—
258C2×D4—191no—
259C2×D4—381no—
260C2×D4—381no—
261C2×D4—381no—
262C2×D4—381no—
263C2×D4—381no—
264C2×D4—761no—
265C2×D4—761no—
266C2×D4C22×D1911yescharacteristic
267C22×C4—21no—
268C22×C4C22×D1911yescharacteristic
269Q16—41no—
270Q16—761no—
271SD16—41no—
272SD16—761no—
273SD16—761no—
274SD16—761no—
275SD16—761no—
276SD16—761no—
277C2×C8—191no—
278C2×C8—191no—
279C2×C8C22×D1911yescharacteristic
280C2×C8C22×D1911yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—191no—
283C4⋊C4—191no—
284C4⋊C4—191no—
285C4⋊C4—381no—
286C4⋊C4—381no—
287C4⋊C4—381no—
288C4⋊C4—381no—
289C4⋊C4—381no—
290C4⋊C4—381no—
291C4⋊C4—381no—
292C4⋊C4C22×D1911yescharacteristic
293C22⋊C4—21no—
294C22⋊C4—191no—
295C22⋊C4—191no—
296C22⋊C4—381no—
297C22⋊C4—381no—
298C22⋊C4—381no—
299C22⋊C4—381no—
300C22⋊C4—381no—
301C42—191no—
302C42—191no—
303C42—381no—
304C42—381no—
305C23—21no—
306C23—381no—
307C23—381no—
308C23—762no—
309C23—1521no—
310C23—1521no—
311C23D4×D1911yescharacteristic
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—21no—
316Q8—381no—
317Q8—381no—
318D4—21no—
319D4—21no—
320D4—42no—
321D4—381no—
322D4—381no—
323D4—381no—
324D4—381no—
325D4—762no—
326D4—1521no—
327D4—1521no—
328D4—1521no—
329D4—1521no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—191no—
337C2×C4—191no—
338C2×C4—191no—
339C2×C4—191no—
340C2×C4—381no—
341C2×C4—381no—
342C2×C4D4×D1911yescharacteristic
343C2×C4C23×D1911yescharacteristic
344C8—21no—
345C8—21no—
346C8—381no—
347C8—381no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—761no—
355C22—761no—
356C22—761no—
357C22—761no—
358C22—761no—
359C22—761no—
360C22—1524no—
361C22C2×D4×D1911yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—381no—
367C4—381no—
368C4—381no—
369C4—381no—
370C4—761no—
371C4—761no—
372C4#1059743011yescharacteristic
373C4#1059743011yescharacteristic
374C2—41no—
375C2—81no—
376C2—1521no—
377C2—1521no—
378C2#1192710911yescharacteristic
379C2#1192735111yescharacteristic
380C2#1192735311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#452C2
socleC22×C19C22×D4
prime radical#11927108C2
hypercenter#452D19
hypocenterC19#3222
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. #11927154C2semidirect
3. #11926937C2semidirect
4. #11926915C2semidirect
5. #11926907C2semidirect
6. #11926900C2semidirect
7. #11926769C2semidirect
8. #11926768C2semidirect
9. #11926743C2semidirect
10. #11926742C2semidirect
11. #11926706C2semidirect
12. #11926697C2semidirect
13. #11926694C2semidirect
14. #11926602C2semidirect
15. C19×#452C2semidirect
18. C2×Q16×C19C22semidirect
19. C2×SD16×C19C22semidirect
23. Q8×Dic19C22semidirect
24. #10597390C22semidirect
25. C2×#64528C22semidirect
32. C2×#64526C22semidirect
40. #10597336C22semidirect
42. #10597333C22semidirect
45. C19×#103C22semidirect
46. C19×#102C22semidirect
48. #10597292C22semidirect
49. #10597289C22semidirect
53. #10597272C22semidirect
54. Dic19⋊C8C22semidirect
55. Dic19⋊C8C22semidirect
56. C8×Dic19C22semidirect
195. #452D19semidirect
209. C2×Q16C2×D19semidirect
215. C2×SD16C2×D19semidirect
238. #103C2×D19semidirect
244. #102C2×D19semidirect
249. C19#3222semidirect

Maximal subgroups

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

subgroupindex
#119271542
#119271082
#119269372
#119269152
#119269072
#119269002
#119267692
#119267682
#119267432
#119267422
#119267062
#119266972
#119266942
#119266022
C19×#4522
#322219