Finite Group Databasebeta

← #14574398

Subgroups — #14574398

Order 2432.

472 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927051C211yesmaximal, characteristic, complemented
2#121×D19C211yesmaximal, characteristic, complemented
3#11926878C211yesmaximal, characteristic, complemented
4#11926869C211yesmaximal, characteristic, complemented
5#11926865C211yesmaximal, characteristic, complemented
6#11926861C211yesmaximal, characteristic, complemented
7#11926779C211yesmaximal, characteristic, complemented
8#11926777C211yesmaximal, characteristic, complemented
9#11926776C211yesmaximal, characteristic, complemented
10#11926770C211yesmaximal, characteristic, complemented
11#11926693C211yesmaximal, characteristic, complemented
12#11926689C211yesmaximal, characteristic, complemented
13#11926676C211yesmaximal, characteristic, complemented
14C22⋊C8×D19C211yesmaximal, characteristic, complemented
15C19×#449C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic, complemented
17C2×D4×D19—21no—
18C2×D4×D19C2211yescharacteristic
19C22×C4×D19C2211yescharacteristic
20C2×SD16×C19C2211yescharacteristic, complemented
21C2×D8×C19C2211yescharacteristic, complemented
22C19×#121C2211yescharacteristic
23#10597392C2211yescharacteristic
24#10597392C2211yescharacteristic, complemented
25C2×#64527C2211yescharacteristic, complemented
26#10597385—21no—
27#10597384C2211yescharacteristic
28#10597384C2211yescharacteristic
29#10597384C2211yescharacteristic, complemented
30#10597383—21no—
31#10597381—21no—
32C2×#64525C2211yescharacteristic, complemented
33#10597376C2211yescharacteristic
34C4×C22⋊D19—21no—
35C4×C22⋊D19—21no—
36#10597372C2211yescharacteristic, complemented
37C2×C8×D19C2211yescharacteristic, complemented
38C2×C8×D19C2211yescharacteristic, complemented
39#10597341C2211yescharacteristic
40C4⋊C4×D19C2211yescharacteristic
41#10597330—21no—
42C22⋊C4×D19—21no—
43C19×#103C2211yescharacteristic, complemented
44C19×#102C2211yescharacteristic, complemented
45C19×C22⋊C8C2211yescharacteristic, complemented
46#10597292C2211yescharacteristic, complemented
47#10597289C2211yescharacteristic, complemented
48#10597289C2211yescharacteristic, complemented
49#10597289C2211yescharacteristic, complemented
50C22⋊(C19⋊C8)C2211yescharacteristic, complemented
51#10597278C2211yescharacteristic, complemented
52#10597278C2211yescharacteristic, complemented
53(C2×D19)⋊C8C2211yescharacteristic
54(C2×D19)⋊C8C2211yescharacteristic
55#10597275C2211yescharacteristic, complemented
56#10597274C2211yescharacteristic, complemented
57#10597265C2211yescharacteristic, complemented
58#10597264C2211yescharacteristic, complemented
59C23×D19—21no—
60C23×D19D411yescharacteristic
61#41×C19—41no—
62#41×C19—41no—
63C2×Q8×C19C2311yescharacteristic
64C2×D4×C19—21no—
65C2×D4×C19—21no—
66C2×D4×C19C2311yescharacteristic
67C2×D4×C19C2311yescharacteristic
68C22×C4×C19—21no—
69C22×C4×C19C2311yescharacteristic
70C2×C22⋊D19—21no—
71C2×C22⋊D19—21no—
72C2×C22⋊D19—21no—
73C2×C22⋊D19—21no—
74C2×C22⋊D19—21no—
75C22×Dic19D411yescharacteristic
76D4×D19—41no—
77D4×D19—41no—
78D4×D19—44no—
79C2×D76—21no—
80C2×D76C2311yescharacteristic
81C2×C4×D19—21no—
82C2×C4×D19—41no—
83C2×C4×D19—41no—
84C2×C4×D19D411yescharacteristic
85C2×C4×D19D411yescharacteristic
86C2×C4×D19C2311yescharacteristic
87C2×C4×D19C2311yescharacteristic
88SD16×C19—41no—
89D8×C19—41no—
90C2×C8×C19C2311yescharacteristic
91C2×C8×C19C2311yescharacteristic
92C4⋊C4×C19C2311yescharacteristic
93C22⋊C4×C19—21no—
94C22⋊Dic19—21no—
95C22⋊Dic19—21no—
96C22⋊Dic19—21no—
97C22⋊Dic19—21no—
98#64527—41no—
99#64525—41no—
100(C2×D19)⋊C4—21no—
101(C2×D19)⋊C4—21no—
102(C2×D19)⋊C4—21no—
103(C2×D19)⋊C4—21no—
104C4⋊Dic19C2311yescharacteristic
105C4⋊Dic19C2311yescharacteristic
106C4⋊Dic19C2311yescharacteristic
107Dic19⋊C4—21no—
108Dic19⋊C4—21no—
109Dic19⋊C4—21no—
110C4×Dic19—21no—
111C2×C19⋊C8C2311yescharacteristic
112C2×C19⋊C8C2311yescharacteristic
113C8×D19—41no—
114C8×D19—41no—
115C23×C19—21no—
116C23×C19—21no—
117C23×C19C2×D411yescharacteristic
118C22×D19—22no—
119C22×D19—22no—
120C22×D19—21no—
121C22×D19—41no—
122C22×D19—42no—
123C22×D19—42no—
124C22×D19—42no—
125C22×D19C2×D411yescharacteristic
126C22×D19C2×D411yescharacteristic
127Q8×C19—21no—
128Q8×C19—21no—
129D4×C19—21no—
130D4×C19—21no—
131D4×C19—21no—
132D4×C19—21no—
133D4×C19—42no—
134D4×C19—42no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—42no—
140C2×C4×C19C2×D411yescharacteristic
141C2×C4×C19C2411yescharacteristic
142C22⋊D19—42no—
143C22⋊D19—42no—
144C22⋊D19—42no—
145C22⋊D19—42no—
146C22⋊D19—42no—
147C2×Dic19—21no—
148C2×Dic19—21no—
149C2×Dic19—21no—
150C2×Dic19—41no—
151C2×Dic19C2×D411yescharacteristic
152C2×Dic19C2×D411yescharacteristic
153D76—21no—
154D76—21no—
155D76—42no—
156C4×D19—21no—
157C4×D19—21no—
158C4×D19—21no—
159C4×D19—21no—
160C4×D19—41no—
161C4×D19—41no—
162C4×D19—42no—
163C8×C19—21no—
164C8×C19—21no—
165C19⋊C8—21no—
166C19⋊C8—21no—
167#3188—191nomaximal, Sylow
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—41no—
172C22×C19—41no—
173C22×C19—41no—
174C22×C19—41no—
175C22×C19—41no—
176C22×C19—41no—
177C22×C19C22×D411yescharacteristic
178C2×D19—21no—
179C2×D19—21no—
180C2×D19—21no—
181C2×D19—21no—
182C2×D19—44no—
183C2×D19—41no—
184C2×D19—41no—
185C2×D19—41no—
186C2×D19—84no—
187C2×D19#13512yes—
188C2×D19AGL(1,ℤ/8)12yes—
189C4×C19—21no—
190C4×C19—41no—
191C4×C19—41no—
192C4×C19H(5,𝔽2)11yescharacteristic
193C4×C19H(5,𝔽2)11yescharacteristic
194Dic19—21no—
195Dic19—21no—
196Dic19—41no—
197Dic19—41no—
198Dic19—41no—
199#525—191no—
200C2×#121—191no—
201#484—191no—
202#482—191no—
203#482—191no—
204#481—191no—
205#466—191no—
206#466—191no—
207#465—191no—
208#465—191no—
209#450—191no—
210#449—191no—
211#449D1911yescharacteristic, complemented
212#447—191no—
213C2×C22⋊C8—191no—
214C2×C19—41no—
215C2×C19—81no—
216C2×C19—81no—
217C2×C19#53411yescharacteristic
218C2×C19C2×#13511yescharacteristic
219C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
220D19—22no—
221D19—22no—
222D19—81no—
223C2×#41C2×D1911yescharacteristic, complemented
224C22×D4—191no—
225C22×D4—381no—
226C23×C4—191no—
227C2×SD16—191no—
228C2×SD16C2×D1911yescharacteristic, complemented
229C2×D8—191no—
230C2×D8C2×D1911yescharacteristic, complemented
231C22×C8—191no—
232C22×C8—191no—
233#123—381no—
234C22⋊Q8—191no—
235C22⋊Q8—191no—
236#121—191no—
237#121—191no—
238#121—191no—
239#121—191no—
240#121—191no—
241#121—381no—
242#121—381no—
243#121C2×D1911yescharacteristic
244#120—381no—
245C4×D4—381no—
246C4×D4—381no—
247#117—191no—
248C2×C4⋊C4—191no—
249C2×C22⋊C4—381no—
250#107—191no—
251#107—191no—
252#106—191no—
253#106—191no—
254#103—191no—
255#103C2×D1911yescharacteristic, complemented
256#102—191no—
257#102—191no—
258#102—191no—
259#102—191no—
260#102—191no—
261#102C2×D1911yescharacteristic, complemented
262C22⋊C8—191no—
263C22⋊C8—191no—
264C22⋊C8—191no—
265C22⋊C8C2×D1911yescharacteristic, complemented
266C19#318811yescharacteristic, complemented, Sylow
267C24—191no—
268C24—381no—
269#41—41no—
270#41—41no—
271C2×Q8C22×D1911yescharacteristic
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—191no—
275C2×D4—381no—
276C2×D4—381no—
277C2×D4—381no—
278C2×D4—381no—
279C2×D4—381no—
280C2×D4—381no—
281C2×D4—761no—
282C2×D4—761no—
283C2×D4—764no—
284C2×D4C22×D1911yescharacteristic
285C2×D4C22×D1911yescharacteristic
286C22×C4—21no—
287C22×C4—191no—
288C22×C4—191no—
289C22×C4—191no—
290C22×C4—191no—
291C22×C4—191no—
292C22×C4—381no—
293C22×C4—761no—
294C22×C4—761no—
295C22×C4C22×D1911yescharacteristic
296SD16—41no—
297SD16—761no—
298D8—41no—
299D8—761no—
300C2×C8—191no—
301C2×C8—191no—
302C2×C8—761no—
303C2×C8—761no—
304C2×C8C22×D1911yescharacteristic
305C2×C8C22×D1911yescharacteristic
306C4⋊C4—191no—
307C4⋊C4—191no—
308C4⋊C4—191no—
309C4⋊C4—381no—
310C4⋊C4—381no—
311C4⋊C4—381no—
312C4⋊C4C22×D1911yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—381no—
315C22⋊C4—381no—
316C22⋊C4—381no—
317C22⋊C4—381no—
318C22⋊C4—381no—
319C22⋊C4—381no—
320C22⋊C4—381no—
321C22⋊C4—381no—
322C42—381no—
323C23—21no—
324C23—21no—
325C23—191no—
326C23—191no—
327C23—382no—
328C23—382no—
329C23—381no—
330C23—761no—
331C23—762no—
332C23—762no—
333C23—762no—
334C23D4×D1911yescharacteristic
335Q8—21no—
336Q8—21no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—381no—
344D4—381no—
345D4—762no—
346D4—762no—
347D4—762no—
348D4—762no—
349D4—762no—
350D4—762no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—42no—
356C2×C4—191no—
357C2×C4—191no—
358C2×C4—381no—
359C2×C4—381no—
360C2×C4—381no—
361C2×C4—381no—
362C2×C4—381no—
363C2×C4—381no—
364C2×C4—381no—
365C2×C4—761no—
366C2×C4—761no—
367C2×C4—762no—
368C2×C4—761no—
369C2×C4D4×D1911yescharacteristic
370C2×C4C23×D1911yescharacteristic
371C8—21no—
372C8—21no—
373C8—381no—
374C8—381no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—192no—
385C22—192no—
386C22—381no—
387C22—381no—
388C22—381no—
389C22—381no—
390C22—764no—
391C22—761no—
392C22—761no—
393C22—761no—
394C22—1524no—
395C22C2×D4×D1911yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—381no—
400C4—381no—
401C4—761no—
402C4—761no—
403C4—761no—
404C4#1059743011yescharacteristic
405C4#1059743011yescharacteristic
406C2—41no—
407C2—81no—
408C2—81no—
409C2—382no—
410C2—382no—
411C2—1521no—
412C2#1192710411yescharacteristic
413C2#135×D1911yescharacteristic
414C2AGL(1,ℤ/8)×D1911yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#449C2
socleC22×C19C22×D4
hypercenter#449D19
hypocenterC19#3188
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #11927051C2semidirect
2. #121×D19C2semidirect
3. #11926878C2semidirect
4. #11926869C2semidirect
5. #11926865C2semidirect
6. #11926861C2semidirect
7. #11926779C2semidirect
8. #11926777C2semidirect
9. #11926776C2semidirect
10. #11926770C2semidirect
11. #11926693C2semidirect
12. #11926689C2semidirect
13. #11926676C2semidirect
14. C22⋊C8×D19C2semidirect
15. C19×#449C2semidirect
16. C2×#41×C19C22semidirect
20. C2×SD16×C19C22semidirect
21. C2×D8×C19C22semidirect
24. #10597392C22semidirect
25. C2×#64527C22semidirect
29. #10597384C22semidirect
32. C2×#64525C22semidirect
36. #10597372C22semidirect
37. C2×C8×D19C22semidirect
38. C2×C8×D19C22semidirect
43. C19×#103C22semidirect
44. C19×#102C22semidirect
45. C19×C22⋊C8C22semidirect
46. #10597292C22semidirect
47. #10597289C22semidirect
48. #10597289C22semidirect
49. #10597289C22semidirect
50. C22⋊(C19⋊C8)C22semidirect
51. #10597278C22semidirect
52. #10597278C22semidirect
55. #10597275C22semidirect
56. #10597274C22semidirect
57. #10597265C22semidirect
58. #10597264C22semidirect
211. #449D19semidirect
223. C2×#41C2×D19semidirect
228. C2×SD16C2×D19semidirect
230. C2×D8C2×D19semidirect
255. #103C2×D19semidirect
261. #102C2×D19semidirect
265. C22⋊C8C2×D19semidirect
266. C19#3188semidirect

Maximal subgroups

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

subgroupindex
#119270512
#121×D192
#119268782
#119268692
#119268652
#119268612
#119267792
#119267772
#119267762
#119267702
#119266932
#119266892
#119266762
C22⋊C8×D192
C19×#4492
#318819