Finite Group Databasebeta

← #14575482

Subgroups — #14575482

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#11927247C211yesmaximal, characteristic, complemented
2#11927189C211yesmaximal, characteristic, complemented
3#11926901C211yesmaximal, characteristic, complemented
4#11926881C211yesmaximal, characteristic, complemented
5#11926870C211yesmaximal, characteristic, complemented
6#11926781C211yesmaximal, characteristic, complemented
7#11926774C211yesmaximal, characteristic, complemented
8#11926760C211yesmaximal, characteristic, complemented
9#11926690C211yesmaximal, characteristic, complemented
10#11926679C211yesmaximal, characteristic, complemented
11C4×#64525C211yesmaximal, characteristic, complemented
12#11926609C211yesmaximal, characteristic, complemented
13#11926537C211yesmaximal, characteristic, complemented
14#102×D19C211yesmaximal, characteristic, complemented
15C19×#478C211yesmaximal, characteristic, complemented
16C2×#64543C2211yescharacteristic
17C2×D4×D19C2211yescharacteristic
18C19×#125C2211yescharacteristic, complemented
19C4×D4×C19C2211yescharacteristic
20C2×#64525C2211yescharacteristic
21#10597376—21no—
22C2×(C2×D19)⋊C4—21no—
23C2×D152C2211yescharacteristic
24C2×#64516C2211yescharacteristic, complemented
25C2×C8×D19C2211yescharacteristic
26C2×C8×D19C2211yescharacteristic, complemented
27#10597344—21no—
28#10597343C2211yescharacteristic
29#10597341—21no—
30#10597341C2211yescharacteristic
31#10597341C2211yescharacteristic
32#10597341C2211yescharacteristic, complemented
33#10597340—21no—
34#10597339—21no—
35#10597338C2211yescharacteristic, complemented
36C4⋊C4×D19C2211yescharacteristic
37#10597332—21no—
38#10597328—21no—
39#10597321C2211yescharacteristic
40C4×D76C2211yescharacteristic
41C4×D76C2211yescharacteristic, complemented
42C19×#107C2211yescharacteristic, complemented
43C19×#106C2211yescharacteristic, complemented
44C19×C4⋊C8C2211yescharacteristic, complemented
45C19×#102C2211yescharacteristic
46C19×#102C2211yescharacteristic
47#10597289C2211yescharacteristic
48#10597278C2211yescharacteristic
49(C2×D19)⋊C8C2211yescharacteristic
50(C2×D19)⋊C8C2211yescharacteristic, complemented
51#10597273C2211yescharacteristic, complemented
52#10597267C2211yescharacteristic, complemented
53#10597267C2211yescharacteristic, complemented
54#10597266C2211yescharacteristic
55#10597266C2211yescharacteristic
56#10597266C2211yescharacteristic, complemented
57#10597264C2211yescharacteristic, complemented
58C4×C19⋊C8C2211yescharacteristic, complemented
59C23×D19—21no—
60C2×D4×C19C2311yescharacteristic
61C22×C4×C19—21no—
62C2×C22⋊D19—21no—
63C2×C22⋊D19—21no—
64C22×Dic19—21no—
65#64543—22no—
66#64543—41no—
67D4×D19—22no—
68D4×D19—41no—
69C2×D76—21no—
70C2×D76—21no—
71C2×D76—21no—
72C2×D76D411yescharacteristic
73C2×D76C2311yescharacteristic
74C2×D76C2311yescharacteristic
75C2×C4×D19—21no—
76C2×C4×D19—21no—
77C2×C4×D19C2311yescharacteristic
78C2×C4×D19C2311yescharacteristic
79C2×Dic38C2311yescharacteristic
80C2×C8×C19C2311yescharacteristic
81C2×C8×C19C2311yescharacteristic
82C4⋊C4×C19—21no—
83C4⋊C4×C19—21no—
84C4⋊C4×C19C2311yescharacteristic
85C4⋊C4×C19C2311yescharacteristic
86C4⋊C4×C19C2311yescharacteristic
87C22⋊C4×C19—21no—
88C42×C19C2311yescharacteristic
89#64525—22no—
90(C2×D19)⋊C4—21no—
91(C2×D19)⋊C4—21no—
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)⋊C4—21no—
98(C2×D19)⋊C4D411yescharacteristic
99(C2×D19)⋊C4D411yescharacteristic
100C4⋊Dic19—21no—
101C4⋊Dic19D411yescharacteristic
102C4⋊Dic19C2311yescharacteristic
103Dic19⋊C4—21no—
104C4×Dic19—21no—
105C2×C19⋊C8C2311yescharacteristic
106C2×C19⋊C8C2311yescharacteristic
107D152—41no—
108#64516—41no—
109C8×D19—41no—
110C8×D19—41no—
111C23×C19—21no—
112C22×D19—21no—
113C22×D19—21no—
114C22×D19—42no—
115C22×D19—42no—
116C22×D19—81no—
117C22×D19C2×D411yescharacteristic
118C22×D19C2×D411yescharacteristic
119D4×C19—21no—
120D4×C19#4112yes—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—81no—
125C2×C4×C19C2×D411yescharacteristic
126C2×C4×C19C2×D411yescharacteristic
127C2×C4×C19C2411yescharacteristic
128C22⋊D19—42no—
129C22⋊D19—42no—
130C2×Dic19—21no—
131C2×Dic19—21no—
132C2×Dic19—42no—
133C2×Dic19C2×D411yescharacteristic
134C2×Dic19C2×D411yescharacteristic
135D76—22no—
136D76—21no—
137D76—21no—
138D76—21no—
139D76—21no—
140D76—42no—
141D76—81no—
142D76—81no—
143C4×D19—21no—
144C4×D19—21no—
145C4×D19—21no—
146C4×D19—21no—
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—22no—
157C22×C19—41no—
158C22×C19—41no—
159C22×C19C22×D411yescharacteristic
160C2×D19—21no—
161C2×D19—21no—
162C2×D19—21no—
163C2×D19—21no—
164C2×D19—21no—
165C2×D19—41no—
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—21no—
175C4×C19—41no—
176C4×C19—41no—
177C4×C19—41no—
178C4×C19C2×#4111yescharacteristic
179C4×C19H(5,𝔽2)11yescharacteristic
180Dic19—21no—
181Dic19—21no—
182Dic19—41no—
183Dic19—41no—
184#553—191no—
185#546—191no—
186#488—191no—
187#484—191no—
188#482—191no—
189#478D1911yescharacteristic, complemented
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—42no—
200C2×C19#54611yescharacteristic
201C2×C19C2×#13511yescharacteristic
202C2×C19#57611yescharacteristic
203D19—22no—
204D19—41no—
205D19—81no—
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#125C2×D1911yescharacteristic, complemented
216#124—191no—
217#123—381no—
218#123—381no—
219C22⋊Q8—191no—
220#121—191no—
221#121—191no—
222#121—191no—
223#121—381no—
224#121—381no—
225#120—381no—
226C4×D4—191no—
227C4×D4—191no—
228C4×D4—381no—
229C4×D4C2×D1911yescharacteristic
230#117—191no—
231C2×C4⋊C4—191no—
232C2×C22⋊C4—381no—
233#107—191no—
234#107C2×D1911yescharacteristic, complemented
235#106C2×D1911yescharacteristic, complemented
236C4⋊C8C2×D1911yescharacteristic, complemented
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⋊C8—191no—
249C4×C8—191no—
250C19#329711yescharacteristic, complemented, Sylow
251C24—381no—
252#41—382no—
253#41—761no—
254C2×Q8—191no—
255C2×D4—191no—
256C2×D4—191no—
257C2×D4—191no—
258C2×D4—381no—
259C2×D4—381no—
260C2×D4—381no—
261C2×D4—381no—
262C2×D4—382no—
263C2×D4—381no—
264C2×D4—761no—
265C2×D4C22×D1911yescharacteristic
266C22×C4—21no—
267C22×C4—191no—
268C22×C4—191no—
269C22×C4—381no—
270C22×C4—381no—
271C22×C4—381no—
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—21no—
282C4⋊C4—21no—
283C4⋊C4—191no—
284C4⋊C4—191no—
285C4⋊C4—381no—
286C4⋊C4—381no—
287C4⋊C4C22×D1911yescharacteristic
288C4⋊C4C22×D1911yescharacteristic
289C4⋊C4C22×D1911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—191no—
292C22⋊C4—191no—
293C22⋊C4—381no—
294C22⋊C4—381no—
295C22⋊C4—381no—
296C22⋊C4—381no—
297C22⋊C4—381no—
298C22⋊C4—381no—
299C22⋊C4—381no—
300C22⋊C4—381no—
301C42—381no—
302C42C22×D1911yescharacteristic
303C23—21no—
304C23—191no—
305C23—191no—
306C23—381no—
307C23—381no—
308C23—762no—
309C23—762no—
310C23—1521no—
311Q8—381no—
312Q8—381no—
313D4—21no—
314D4—382no—
315D4—381no—
316D4—381no—
317D4—381no—
318D4—381no—
319D4—762no—
320D4—762no—
321D4—762no—
322D4—1521no—
323D4—1521no—
324D4#6454512yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—81no—
329C2×C4—191no—
330C2×C4—191no—
331C2×C4—381no—
332C2×C4—381no—
333C2×C4—381no—
334C2×C4—381no—
335C2×C4—381no—
336C2×C4—381no—
337C2×C4—762no—
338C2×C4—1521no—
339C2×C4—1521no—
340C2×C4D4×D1911yescharacteristic
341C2×C4D4×D1911yescharacteristic
342C2×C4C23×D1911yescharacteristic
343C8—21no—
344C8—21no—
345C8—381no—
346C8—381no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—192no—
351C22—381no—
352C22—381no—
353C22—381no—
354C22—381no—
355C22—381no—
356C22—761no—
357C22—761no—
358C22—761no—
359C22—761no—
360C22—761no—
361C22—761no—
362C22—1524no—
363C22C2×D4×D1911yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—381no—
370C4—381no—
371C4—761no—
372C4—761no—
373C4C2×#6454511yescharacteristic
374C4#1059743511yescharacteristic
375C2—42no—
376C2—382no—
377C2—761no—
378C2—1521no—
379C2—1521no—
380C2#1192718511yescharacteristic
381C2#135×D1911yescharacteristic
382C2#1192734811yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#478C2
socleC22×C19C22×D4
hypercenter#478D19
hypocenterC19#3297
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #11927247C2semidirect
2. #11927189C2semidirect
3. #11926901C2semidirect
4. #11926881C2semidirect
5. #11926870C2semidirect
6. #11926781C2semidirect
7. #11926774C2semidirect
8. #11926760C2semidirect
9. #11926690C2semidirect
10. #11926679C2semidirect
11. C4×#64525C2semidirect
12. #11926609C2semidirect
13. #11926537C2semidirect
14. #102×D19C2semidirect
15. C19×#478C2semidirect
18. C19×#125C22semidirect
24. C2×#64516C22semidirect
26. C2×C8×D19C22semidirect
32. #10597341C22semidirect
35. #10597338C22semidirect
41. C4×D76C22semidirect
42. C19×#107C22semidirect
43. C19×#106C22semidirect
44. C19×C4⋊C8C22semidirect
50. (C2×D19)⋊C8C22semidirect
51. #10597273C22semidirect
52. #10597267C22semidirect
53. #10597267C22semidirect
56. #10597266C22semidirect
57. #10597264C22semidirect
58. C4×C19⋊C8C22semidirect
189. #478D19semidirect
215. #125C2×D19semidirect
234. #107C2×D19semidirect
235. #106C2×D19semidirect
236. C4⋊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
#119272472
#119271892
#119269012
#119268812
#119268702
#119267812
#119267742
#119267602
#119266902
#119266792
C4×#645252
#119266092
#119265372
#102×D192
C19×#4782
#329719