Finite Group Databasebeta

← #14575488

Subgroups — #14575488

Order 2432.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927238C211yesmaximal, characteristic, complemented
2#11927191C211yesmaximal, characteristic, complemented
3#11926897C211yesmaximal, characteristic, complemented
4#11926881C211yesmaximal, characteristic, complemented
5#11926843C211yesmaximal, characteristic, complemented
6#11926778C211yesmaximal, characteristic, complemented
7#11926774C211yesmaximal, characteristic, complemented
8#11926758C211yesmaximal, characteristic, complemented
9#11926691C211yesmaximal, characteristic, complemented
10#11926679C211yesmaximal, characteristic, complemented
11#11926626C211yesmaximal, characteristic, complemented
12(C22⋊D19)⋊C8C211yesmaximal, characteristic, complemented
13#11926538C211yesmaximal, characteristic, complemented
14#102×D19C211yesmaximal, characteristic, complemented
15C19×#482C211yesmaximal, characteristic, complemented
16C2×D4×D19C2211yescharacteristic
17C2×#64541C2211yescharacteristic
18C19×#121C2211yescharacteristic
19C19×#117C2211yescharacteristic, complemented
20#10597384—21no—
21#10597383—21no—
22#10597382C2211yescharacteristic
23C2×#64525C2211yescharacteristic
24#10597376C2211yescharacteristic, complemented
25C4×C22⋊D19C2211yescharacteristic
26C22×C19⋊C8C2211yescharacteristic, complemented
27C2×D152C2211yescharacteristic
28C2×#64516C2211yescharacteristic, complemented
29C2×C8×D19C2211yescharacteristic
30#10597343C2211yescharacteristic
31#10597341C2211yescharacteristic
32#10597339C2211yescharacteristic
33#10597339C2211yescharacteristic, complemented
34C4⋊C4×D19C2211yescharacteristic
35#10597336C2211yescharacteristic, complemented
36#10597330—21no—
37#10597329—21no—
38#10597329—21no—
39C22⋊C4×D19—21no—
40#10597322—21no—
41C4×D76—21no—
42C19×#107C2211yescharacteristic, complemented
43C19×#106C2211yescharacteristic, complemented
44C19×#102C2211yescharacteristic
45C19×#102C2211yescharacteristic
46C19×C22⋊C8C2211yescharacteristic, complemented
47#10597289C2211yescharacteristic
48#10597278C2211yescharacteristic
49(C2×D19)⋊C8C2211yescharacteristic
50#10597273C2211yescharacteristic, complemented
51Dic19⋊C8C2211yescharacteristic, complemented
52C8×Dic19C2211yescharacteristic, complemented
53#10597267C2211yescharacteristic, complemented
54#10597267C2211yescharacteristic, complemented
55#10597266C2211yescharacteristic
56#10597266C2211yescharacteristic
57#10597266C2211yescharacteristic, complemented
58#10597264C2211yescharacteristic, complemented
59C23×D19—21no—
60C2×D4×C19—21no—
61C2×D4×C19C2311yescharacteristic
62C22×C4×C19C2311yescharacteristic
63C2×C22⋊D19—21no—
64C2×C22⋊D19—21no—
65C2×C22⋊D19—21no—
66C2×C22⋊D19D411yescharacteristic
67D4×D19—22no—
68D4×D19—41no—
69#64541—22no—
70#64541—41no—
71C2×D76—21no—
72C2×D76C2311yescharacteristic
73C2×D76C2311yescharacteristic
74C2×C4×D19—21no—
75C2×C4×D19—21no—
76C2×C4×D19—21no—
77C2×C4×D19—21no—
78C2×C4×D19C2311yescharacteristic
79C2×Dic38C2311yescharacteristic
80C2×C8×C19C2311yescharacteristic
81C2×C8×C19C2311yescharacteristic
82C4⋊C4×C19C2311yescharacteristic
83C4⋊C4×C19C2311yescharacteristic
84C4⋊C4×C19C2311yescharacteristic
85C22⋊C4×C19—21no—
86C22⋊C4×C19—21no—
87C42×C19—21no—
88C22⋊Dic19—21no—
89C22⋊Dic19—21no—
90C22⋊Dic19D411yescharacteristic
91#64525—41no—
92(C2×D19)⋊C4—21no—
93(C2×D19)⋊C4—21no—
94(C2×D19)⋊C4—21no—
95(C2×D19)⋊C4—21no—
96(C2×D19)⋊C4—21no—
97(C2×D19)⋊C4D411yescharacteristic
98C4⋊Dic19—21no—
99C4⋊Dic19—21no—
100C4⋊Dic19C2311yescharacteristic
101Dic19⋊C4—21no—
102Dic19⋊C4—21no—
103Dic19⋊C4D411yescharacteristic
104C4×Dic19C2311yescharacteristic
105C2×C19⋊C8—41no—
106C2×C19⋊C8C2311yescharacteristic
107C2×C19⋊C8C2311yescharacteristic
108D152—22no—
109#64516—41no—
110C8×D19—41no—
111C23×C19—21no—
112C23×C19C2×D411yescharacteristic
113C22×D19—21no—
114C22×D19—21no—
115C22×D19—42no—
116C22×D19—42no—
117C22×D19—81no—
118C22×D19C2×D411yescharacteristic
119D4×C19—21no—
120D4×C19—21no—
121D4×C19—81no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19C2×D411yescharacteristic
128C2×C4×C19C2411yescharacteristic
129C22⋊D19—22no—
130C22⋊D19—42no—
131C22⋊D19—42no—
132C22⋊D19—81no—
133C2×Dic19—21no—
134C2×Dic19—21no—
135C2×Dic19C2×D411yescharacteristic
136C2×Dic19C2×D411yescharacteristic
137C2×Dic19C2×D411yescharacteristic
138D76—21no—
139D76—21no—
140D76—21no—
141D76—42no—
142D76#4112yes—
143C4×D19—21no—
144C4×D19—21no—
145C4×D19—42no—
146C4×D19—81no—
147C4×D19—81no—
148C4×D19—81no—
149Dic38—21no—
150Dic38—21no—
151C8×C19—21no—
152C8×C19—21no—
153C19⋊C8—21no—
154C19⋊C8—21no—
155#3297—191nomaximal, Sylow
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—41no—
160C22×C19—41no—
161C22×C19—41no—
162C22×C19C22×D411yescharacteristic
163C2×D19—21no—
164C2×D19—21no—
165C2×D19—22no—
166C2×D19—41no—
167C2×D19—41no—
168C2×D19—41no—
169C2×D19—41no—
170C2×D19—41no—
171C2×D19—84no—
172C2×D19#13512yes—
173C4×C19—21no—
174C4×C19—41no—
175C4×C19—41no—
176C4×C19—41no—
177C4×C19C2×#4111yescharacteristic
178C4×C19H(5,𝔽2)11yescharacteristic
179Dic19—21no—
180Dic19—21no—
181Dic19—21no—
182Dic19—41no—
183Dic19—41no—
184#553—191no—
185#546—191no—
186#488—191no—
187#484—191no—
188#482D1911yescharacteristic, complemented
189#478—191no—
190#466—191no—
191#465—191no—
192#463—191no—
193#449—191no—
194#447—191no—
195C4×D8—191no—
196C8×D4—191no—
197#416—191no—
198C2×#102—191no—
199C2×C19—41no—
200C2×C19—81no—
201C2×C19#54611yescharacteristic
202C2×C19C2×#13511yescharacteristic
203C2×C19#57611yescharacteristic
204D19—22no—
205D19—42no—
206D19—81no—
207C2×#41—191no—
208C22×D4—191no—
209C2×SD16—191no—
210C2×D8—191no—
211C2×D8—191no—
212C22×C8—191no—
213C22×C8—191no—
214#126—381no—
215#125—191no—
216#124—191no—
217#123—381no—
218#123—381no—
219C22⋊Q8—191no—
220#121—191no—
221#121—191no—
222#121—381no—
223#121—381no—
224#121C2×D1911yescharacteristic
225#120—381no—
226C4×D4—191no—
227C4×D4—191no—
228C4×D4—191no—
229C4×D4—381no—
230#117C2×D1911yescharacteristic, complemented
231C2×C4⋊C4—191no—
232C2×C22⋊C4—381no—
233#107—191no—
234#107C2×D1911yescharacteristic, complemented
235#106C2×D1911yescharacteristic, complemented
236C4⋊C8—191no—
237#103—191no—
238#103—191no—
239#103—191no—
240#102—191no—
241#102—191no—
242#102—191no—
243#102—191no—
244#102—191no—
245#102C2×D1911yescharacteristic
246#102C2×D1911yescharacteristic
247C22⋊C8—191no—
248C22⋊C8C2×D1911yescharacteristic, complemented
249C4×C8—191no—
250C19#329711yescharacteristic, complemented, Sylow
251C24—381no—
252#41—382no—
253#41—761no—
254C2×Q8—191no—
255C2×D4—21no—
256C2×D4—191no—
257C2×D4—191no—
258C2×D4—191no—
259C2×D4—381no—
260C2×D4—381no—
261C2×D4—382no—
262C2×D4—381no—
263C2×D4—381no—
264C2×D4—761no—
265C2×D4C22×D1911yescharacteristic
266C22×C4—191no—
267C22×C4—381no—
268C22×C4—381no—
269C22×C4—381no—
270C22×C4—381no—
271C22×C4C22×D1911yescharacteristic
272SD16—761no—
273D8—382no—
274D8—761no—
275C2×C8—191no—
276C2×C8—191no—
277C2×C8—761no—
278C2×C8—761no—
279C2×C8C22×D1911yescharacteristic
280C2×C8C22×D1911yescharacteristic
281C4⋊C4—191no—
282C4⋊C4—191no—
283C4⋊C4—381no—
284C4⋊C4—381no—
285C4⋊C4—381no—
286C4⋊C4—381no—
287C4⋊C4C22×D1911yescharacteristic
288C4⋊C4C22×D1911yescharacteristic
289C4⋊C4C22×D1911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—191no—
293C22⋊C4—191no—
294C22⋊C4—381no—
295C22⋊C4—381no—
296C22⋊C4—381no—
297C22⋊C4—381no—
298C22⋊C4—381no—
299C22⋊C4—381no—
300C22⋊C4—381no—
301C42—21no—
302C42—191no—
303C23—21no—
304C23—191no—
305C23—381no—
306C23—381no—
307C23—762no—
308C23—762no—
309C23—1521no—
310C23D4×D1911yescharacteristic
311Q8—381no—
312Q8—381no—
313D4—21no—
314D4—21no—
315D4—81no—
316D4—192no—
317D4—382no—
318D4—381no—
319D4—381no—
320D4—381no—
321D4—762no—
322D4—762no—
323D4—762no—
324D4—1521no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—191no—
331C2×C4—191no—
332C2×C4—191no—
333C2×C4—381no—
334C2×C4—381no—
335C2×C4—381no—
336C2×C4—381no—
337C2×C4—762no—
338C2×C4—1521no—
339C2×C4—1521no—
340C2×C4—1521no—
341C2×C4D4×D1911yescharacteristic
342C2×C4C23×D1911yescharacteristic
343C8—21no—
344C8—21no—
345C8—381no—
346C8—381no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—192no—
354C22—381no—
355C22—381no—
356C22—382no—
357C22—761no—
358C22—761no—
359C22—761no—
360C22—761no—
361C22—761no—
362C22—1524no—
363C22C2×D4×D1911yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—381no—
369C4—381no—
370C4—381no—
371C4—761no—
372C4—761no—
373C4#41×D1911yescharacteristic
374C4#1059743511yescharacteristic
375C2—41no—
376C2—81no—
377C2—382no—
378C2—762no—
379C2—1521no—
380C2#1192718611yescharacteristic
381C2#135×D1911yescharacteristic
382C2#1192734811yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#482C2
socleC22×C19C22×D4
hypercenter#482D19
hypocenterC19#3297
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #11927238C2semidirect
2. #11927191C2semidirect
3. #11926897C2semidirect
4. #11926881C2semidirect
5. #11926843C2semidirect
6. #11926778C2semidirect
7. #11926774C2semidirect
8. #11926758C2semidirect
9. #11926691C2semidirect
10. #11926679C2semidirect
11. #11926626C2semidirect
12. (C22⋊D19)⋊C8C2semidirect
13. #11926538C2semidirect
14. #102×D19C2semidirect
15. C19×#482C2semidirect
19. C19×#117C22semidirect
24. #10597376C22semidirect
26. C22×C19⋊C8C22semidirect
28. C2×#64516C22semidirect
33. #10597339C22semidirect
35. #10597336C22semidirect
42. C19×#107C22semidirect
43. C19×#106C22semidirect
46. C19×C22⋊C8C22semidirect
50. #10597273C22semidirect
51. Dic19⋊C8C22semidirect
52. C8×Dic19C22semidirect
53. #10597267C22semidirect
54. #10597267C22semidirect
57. #10597266C22semidirect
58. #10597264C22semidirect
188. #482D19semidirect
230. #117C2×D19semidirect
234. #107C2×D19semidirect
235. #106C2×D19semidirect
248. C22⋊C8C2×D19semidirect
250. C19#3297semidirect

Maximal subgroups

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

subgroupindex
#119272382
#119271912
#119268972
#119268812
#119268432
#119267782
#119267742
#119267582
#119266912
#119266792
#119266262
(C22⋊D19)⋊C82
#119265382
#102×D192
C19×#4822
#329719