Finite Group Databasebeta

← #14574466

Subgroups — #14574466

Order 2432.

414 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927057C211yesmaximal, characteristic
2C22⋊Q8×D19C211yesmaximal, characteristic, complemented
3#11926888C211yesmaximal, characteristic, complemented
4#11926884C211yesmaximal, characteristic, complemented
5#11926878C211yesmaximal, characteristic, complemented
6#11926864C211yesmaximal, characteristic, complemented
7#11926800C211yesmaximal, characteristic, complemented
8#11926792C211yesmaximal, characteristic, complemented
9#11926790C211yesmaximal, characteristic, complemented
10#11926709C211yesmaximal, characteristic, complemented
11#11926705C211yesmaximal, characteristic, complemented
12#11926698C211yesmaximal, characteristic, complemented
13#11926684C211yesmaximal, characteristic, complemented
14#11926507C211yesmaximal, characteristic, complemented
15C19×#470C211yesmaximal, characteristic, complemented
16C2×#64545C2211yescharacteristic
17C2×Q8×D19C2211yescharacteristic
18C22×C4×D19C2211yescharacteristic
19C2×Q16×C19C2211yescharacteristic, complemented
20C2×M16×C19C2211yescharacteristic
21C19×C22⋊Q8C2211yescharacteristic
22C19×C22⋊Q8C2211yescharacteristic
23#10597392C2211yescharacteristic
24#10597392C2211yescharacteristic
25C2×#64528C2211yescharacteristic, complemented
26C2×#64527C2211yescharacteristic, complemented
27#10597376C2211yescharacteristic
28#10597370C2211yescharacteristic
29C2×#64520C2211yescharacteristic
30C2×#64516C2211yescharacteristic, complemented
31#10597343C2211yescharacteristic
32#10597342—21no—
33#10597341C2211yescharacteristic
34#10597340—21no—
35#10597339—21no—
36#10597338C2211yescharacteristic
37C4⋊C4×D19—21no—
38C4⋊C4×D19C2211yescharacteristic
39#10597328—21no—
40(C22⋊D19)⋊C4—21no—
41C22⋊C4×D19—21no—
42#10597324—21no—
43C19×#106C2211yescharacteristic, complemented
44C19×#103C2211yescharacteristic, complemented
45C19×#103C2211yescharacteristic, complemented
46#10597292C2211yescharacteristic, complemented
47#10597292C2211yescharacteristic, complemented
48#10597278C2211yescharacteristic, complemented
49(C2×D19)⋊C8C2211yescharacteristic
50(C2×D19)⋊C8C2211yescharacteristic
51(C2×D19)⋊C8C2211yescharacteristic
52(C2×D19)⋊C8C2211yescharacteristic
53#10597275C2211yescharacteristic, complemented
54#10597273C2211yescharacteristic, complemented
55#10597267C2211yescharacteristic, complemented
56#10597266C2211yescharacteristic, complemented
57#10597265C2211yescharacteristic, complemented
58#10597264C2211yescharacteristic, complemented
59C23×D19D411yescharacteristic
60C2×Q8×C19C2311yescharacteristic
61C2×Q8×C19C2311yescharacteristic
62C22×C4×C19C2311yescharacteristic
63C2×C22⋊D19—21no—
64C22×Dic19D411yescharacteristic
65#64545—41no—
66#64545—41no—
67Q8×D19—41no—
68Q8×D19—41no—
69C2×D76—21no—
70C2×D76—21no—
71C2×D76C2311yescharacteristic
72C2×C4×D19—21no—
73C2×C4×D19—21no—
74C2×C4×D19—21no—
75C2×C4×D19—41no—
76C2×C4×D19—41no—
77C2×C4×D19D411yescharacteristic
78C2×C4×D19D411yescharacteristic
79C2×C4×D19C2311yescharacteristic
80C2×C4×D19C2311yescharacteristic
81C2×Dic38—21no—
82C2×Dic38C2311yescharacteristic
83Q16×C19—41no—
84M16×C19—41no—
85C2×C8×C19C2311yescharacteristic
86C2×C8×C19C2311yescharacteristic
87C4⋊C4×C19—21no—
88C4⋊C4×C19—21no—
89C4⋊C4×C19C2311yescharacteristic
90C4⋊C4×C19C2311yescharacteristic
91C22⋊C4×C19—21no—
92C22⋊C4×C19—21no—
93C22⋊Dic19—21no—
94#64528—41no—
95#64527—41no—
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⋊Dic19C2311yescharacteristic
104C4⋊Dic19C2311yescharacteristic
105Dic19⋊C4—21no—
106Dic19⋊C4—21no—
107Dic19⋊C4—21no—
108Dic19⋊C4—21no—
109C4×Dic19—21no—
110#64520—41no—
111C2×C19⋊C8C2311yescharacteristic
112C2×C19⋊C8C2311yescharacteristic
113#64516—41no—
114C23×C19C2×D411yescharacteristic
115C22×D19—22no—
116C22×D19—21no—
117C22×D19—41no—
118C22×D19—41no—
119C22×D19C2×D411yescharacteristic
120C22×D19C2×D411yescharacteristic
121Q8×C19—21no—
122Q8×C19—21no—
123Q8×C19—21no—
124Q8×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19C2×D411yescharacteristic
132C2×C4×C19C2411yescharacteristic
133C22⋊D19—42no—
134C2×Dic19—21no—
135C2×Dic19—21no—
136C2×Dic19—21no—
137C2×Dic19—41no—
138C2×Dic19C2×D411yescharacteristic
139C2×Dic19C2×D411yescharacteristic
140D76—21no—
141D76—21no—
142D76—42no—
143D76—42no—
144C4×D19—21no—
145C4×D19—21no—
146C4×D19—21no—
147C4×D19—21no—
148C4×D19—41no—
149C4×D19—41no—
150C4×D19—42no—
151C4×D19—42no—
152C4×D19—42no—
153Dic38—21no—
154Dic38—21no—
155Dic38—42no—
156C8×C19—21no—
157C8×C19—21no—
158C19⋊C8—21no—
159C19⋊C8—21no—
160#3196—191nomaximal, Sylow
161C22×C19—21no—
162C22×C19—21no—
163C22×C19—21no—
164C22×C19C22×D411yescharacteristic
165C2×D19—21no—
166C2×D19—21no—
167C2×D19—21no—
168C2×D19—21no—
169C2×D19—21no—
170C2×D19—44no—
171C2×D19—41no—
172C2×D19—41no—
173C2×D19—41no—
174C2×D19#13712yes—
175C4×C19—21no—
176C4×C19—41no—
177C4×C19—41no—
178C4×C19—41no—
179C4×C19—41no—
180C4×C19H(5,𝔽2)11yescharacteristic
181C4×C19H(5,𝔽2)11yescharacteristic
182Dic19—21no—
183Dic19—21no—
184Dic19—41no—
185Dic19—41no—
186Dic19—41no—
187#525—191no—
188C2×C22⋊Q8—191no—
189#485—191no—
190#485—191no—
191#484—191no—
192#481—191no—
193#470—191no—
194#470D1911yescharacteristic, complemented
195#468—191no—
196#468—191no—
197#452—191no—
198#452—191no—
199#451—191no—
200#448—191no—
201#407—191no—
202C2×C19—41no—
203C2×C19#53411yescharacteristic
204C2×C19C2×#13711yescharacteristic
205C2×C19#57511yescharacteristic
206D19—22no—
207D19—41no—
208D19—81no—
209C2×#41—191no—
210C22×Q8—191no—
211C23×C4—191no—
212C2×Q16—191no—
213C2×Q16C2×D1911yescharacteristic, complemented
214C2×SD16—191no—
215C2×SD16—191no—
216C2×M16—191no—
217C2×M16C2×D1911yescharacteristic
218#123—381no—
219C22⋊Q8—191no—
220C22⋊Q8—191no—
221C22⋊Q8—191no—
222C22⋊Q8—191no—
223C22⋊Q8—381no—
224C22⋊Q8—381no—
225C22⋊Q8C2×D1911yescharacteristic
226C22⋊Q8C2×D1911yescharacteristic
227#121—191no—
228#121—191no—
229#120—381no—
230C4×D4—381no—
231C4×D4—381no—
232#117—191no—
233C2×C4⋊C4—191no—
234C2×C4⋊C4—381no—
235C2×C22⋊C4—381no—
236#107—191no—
237#107—191no—
238#106—191no—
239#106C2×D1911yescharacteristic, complemented
240#103—191no—
241#103—191no—
242#103—191no—
243#103—191no—
244#103C2×D1911yescharacteristic, complemented
245#103C2×D1911yescharacteristic, complemented
246#102—191no—
247#102—191no—
248C22⋊C8—191no—
249C22⋊C8—191no—
250C22⋊C8—191no—
251C22⋊C8—191no—
252C19#319611yescharacteristic, complemented, Sylow
253C24—191no—
254#41—761no—
255#41—761no—
256C2×Q8—191no—
257C2×Q8—381no—
258C2×Q8—761no—
259C2×Q8—761no—
260C2×Q8C22×D1911yescharacteristic
261C2×Q8C22×D1911yescharacteristic
262C2×D4—191no—
263C2×D4—381no—
264C2×D4—381no—
265C2×D4—381no—
266C22×C4—191no—
267C22×C4—191no—
268C22×C4—191no—
269C22×C4—191no—
270C22×C4—191no—
271C22×C4—381no—
272C22×C4—381no—
273C22×C4—381no—
274C22×C4—761no—
275C22×C4—761no—
276C22×C4C22×D1911yescharacteristic
277Q16—41no—
278Q16—761no—
279SD16—761no—
280SD16—761no—
281M16—41no—
282M16—761no—
283C2×C8—191no—
284C2×C8—191no—
285C2×C8C22×D1911yescharacteristic
286C2×C8C22×D1911yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—191no—
290C4⋊C4—191no—
291C4⋊C4—381no—
292C4⋊C4—381no—
293C4⋊C4—381no—
294C4⋊C4—381no—
295C4⋊C4—381no—
296C4⋊C4C22×D1911yescharacteristic
297C4⋊C4C22×D1911yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—381no—
301C22⋊C4—381no—
302C22⋊C4—381no—
303C22⋊C4—381no—
304C22⋊C4—381no—
305C22⋊C4—381no—
306C22⋊C4—381no—
307C42—381no—
308C23—191no—
309C23—191no—
310C23—382no—
311C23—381no—
312C23—761no—
313C23—761no—
314C23D4×D1911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—21no—
318Q8—21no—
319Q8—381no—
320Q8—381no—
321Q8—762no—
322D4—381no—
323D4—381no—
324D4—762no—
325D4—762no—
326D4—762no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—191no—
334C2×C4—191no—
335C2×C4—381no—
336C2×C4—381no—
337C2×C4—381no—
338C2×C4—381no—
339C2×C4—381no—
340C2×C4—381no—
341C2×C4—381no—
342C2×C4—761no—
343C2×C4—761no—
344C2×C4—762no—
345C2×C4—762no—
346C2×C4—762no—
347C2×C4—761no—
348C2×C4D4×D1911yescharacteristic
349C2×C4C23×D1911yescharacteristic
350C8—21no—
351C8—21no—
352C8—381no—
353C8—381no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—192no—
358C22—381no—
359C22—381no—
360C22—381no—
361C22—381no—
362C22—381no—
363C22—764no—
364C22—761no—
365C22—761no—
366C22—761no—
367C22C2×D4×D1911yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—381no—
374C4—381no—
375C4—761no—
376C4—761no—
377C4—761no—
378C4#1059743011yescharacteristic
379C4#1059743511yescharacteristic
380C2—41no—
381C2—382no—
382C2—761no—
383C2—1521no—
384C2#1192710211yescharacteristic
385C2#137×D1911yescharacteristic
386C2#1192734311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#470C2
socleC22×C19C22×D4
prime radical#11927057C2
hypercenter#470D19
hypocenterC19#3196
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. C22⋊Q8×D19C2semidirect
3. #11926888C2semidirect
4. #11926884C2semidirect
5. #11926878C2semidirect
6. #11926864C2semidirect
7. #11926800C2semidirect
8. #11926792C2semidirect
9. #11926790C2semidirect
10. #11926709C2semidirect
11. #11926705C2semidirect
12. #11926698C2semidirect
13. #11926684C2semidirect
14. #11926507C2semidirect
15. C19×#470C2semidirect
19. C2×Q16×C19C22semidirect
25. C2×#64528C22semidirect
26. C2×#64527C22semidirect
30. C2×#64516C22semidirect
43. C19×#106C22semidirect
44. C19×#103C22semidirect
45. C19×#103C22semidirect
46. #10597292C22semidirect
47. #10597292C22semidirect
48. #10597278C22semidirect
53. #10597275C22semidirect
54. #10597273C22semidirect
55. #10597267C22semidirect
56. #10597266C22semidirect
57. #10597265C22semidirect
58. #10597264C22semidirect
194. #470D19semidirect
213. C2×Q16C2×D19semidirect
239. #106C2×D19semidirect
244. #103C2×D19semidirect
245. #103C2×D19semidirect
252. C19#3196semidirect

Maximal subgroups

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

subgroupindex
#119270572
C22⋊Q8×D192
#119268882
#119268842
#119268782
#119268642
#119268002
#119267922
#119267902
#119267092
#119267052
#119266982
#119266842
#119265072
C19×#4702
#319619